man complex_lin (3): complex

Functions

program cchkaa
CCHKAA
subroutine cchkeq (THRESH, NOUT)
CCHKEQ
subroutine cchkgb (DOTYPE, NM, MVAL, NN, NVAL, NNB, NBVAL, NNS, NSVAL, THRESH, TSTERR, A, LA, AFAC, LAFAC, B, X, XACT, WORK, RWORK, IWORK, NOUT)
CCHKGB
subroutine cchkge (DOTYPE, NM, MVAL, NN, NVAL, NNB, NBVAL, NNS, NSVAL, THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK, NOUT)
CCHKGE
subroutine cchkgt (DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR, A, AF, B, X, XACT, WORK, RWORK, IWORK, NOUT)
CCHKGT
subroutine cchkhe (DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL, THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK, NOUT)
CCHKHE
subroutine cchkhe_rook (DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL, THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK, NOUT)
CCHKHE_ROOK
subroutine cchkhp (DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK, NOUT)
CCHKHP
subroutine cchklq (DOTYPE, NM, MVAL, NN, NVAL, NNB, NBVAL, NXVAL, NRHS, THRESH, TSTERR, NMAX, A, AF, AQ, AL, AC, B, X, XACT, TAU, WORK, RWORK, NOUT)
CCHKLQ
subroutine cchkpb (DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL, THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK, NOUT)
CCHKPB
subroutine cchkpo (DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL, THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK, NOUT)
CCHKPO
subroutine cchkpp (DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK, NOUT)
CCHKPP
subroutine cchkps (DOTYPE, NN, NVAL, NNB, NBVAL, NRANK, RANKVAL, THRESH, TSTERR, NMAX, A, AFAC, PERM, PIV, WORK, RWORK, NOUT)
CCHKPS
subroutine cchkpt (DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR, A, D, E, B, X, XACT, WORK, RWORK, NOUT)
CCHKPT
subroutine cchkq3 (DOTYPE, NM, MVAL, NN, NVAL, NNB, NBVAL, NXVAL, THRESH, A, COPYA, S, TAU, WORK, RWORK, IWORK, NOUT)
CCHKQ3
subroutine cchkql (DOTYPE, NM, MVAL, NN, NVAL, NNB, NBVAL, NXVAL, NRHS, THRESH, TSTERR, NMAX, A, AF, AQ, AL, AC, B, X, XACT, TAU, WORK, RWORK, NOUT)
CCHKQL
subroutine cchkqr (DOTYPE, NM, MVAL, NN, NVAL, NNB, NBVAL, NXVAL, NRHS, THRESH, TSTERR, NMAX, A, AF, AQ, AR, AC, B, X, XACT, TAU, WORK, RWORK, IWORK, NOUT)
CCHKQR
subroutine cchkqrt (THRESH, TSTERR, NM, MVAL, NN, NVAL, NNB, NBVAL, NOUT)
CCHKQRT
subroutine cchkqrtp (THRESH, TSTERR, NM, MVAL, NN, NVAL, NNB, NBVAL, NOUT)
CCHKQRTP
program cchkrfp
CCHKRFP
subroutine cchkrq (DOTYPE, NM, MVAL, NN, NVAL, NNB, NBVAL, NXVAL, NRHS, THRESH, TSTERR, NMAX, A, AF, AQ, AR, AC, B, X, XACT, TAU, WORK, RWORK, IWORK, NOUT)
CCHKRQ
subroutine cchksp (DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK, NOUT)
CCHKSP
subroutine cchksy (DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL, THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK, NOUT)
CCHKSY
subroutine cchksy_rook (DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL, THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK, NOUT)
CCHKSY_ROOK
subroutine cchktb (DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR, NMAX, AB, AINV, B, X, XACT, WORK, RWORK, NOUT)
CCHKTB
subroutine cchktp (DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR, NMAX, AP, AINVP, B, X, XACT, WORK, RWORK, NOUT)
CCHKTP
subroutine cchktr (DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL, THRESH, TSTERR, NMAX, A, AINV, B, X, XACT, WORK, RWORK, NOUT)
CCHKTR
subroutine cchktz (DOTYPE, NM, MVAL, NN, NVAL, THRESH, TSTERR, A, COPYA, S, TAU, WORK, RWORK, NOUT)
CCHKTZ
subroutine cdrvgb (DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, A, LA, AFB, LAFB, ASAV, B, BSAV, X, XACT, S, WORK, RWORK, IWORK, NOUT)
CDRVGB
subroutine cdrvge (DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX, A, AFAC, ASAV, B, BSAV, X, XACT, S, WORK, RWORK, IWORK, NOUT)
CDRVGE
subroutine cdrvgt (DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, A, AF, B, X, XACT, WORK, RWORK, IWORK, NOUT)
CDRVGT
subroutine cdrvhe (DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK, NOUT)
CDRVHE
subroutine cdrvhe_rook (DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK, NOUT)
CDRVHE_ROOK
subroutine cdrvhp (DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK, NOUT)
CDRVHP
subroutine cdrvls (DOTYPE, NM, MVAL, NN, NVAL, NNS, NSVAL, NNB, NBVAL, NXVAL, THRESH, TSTERR, A, COPYA, B, COPYB, C, S, COPYS, WORK, RWORK, IWORK, NOUT)
CDRVLS
subroutine cdrvpb (DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX, A, AFAC, ASAV, B, BSAV, X, XACT, S, WORK, RWORK, NOUT)
CDRVPB
subroutine cdrvpo (DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX, A, AFAC, ASAV, B, BSAV, X, XACT, S, WORK, RWORK, NOUT)
CDRVPO
subroutine cdrvpp (DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX, A, AFAC, ASAV, B, BSAV, X, XACT, S, WORK, RWORK, NOUT)
CDRVPP
subroutine cdrvpt (DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, A, D, E, B, X, XACT, WORK, RWORK, NOUT)
CDRVPT
subroutine cdrvrf1 (NOUT, NN, NVAL, THRESH, A, LDA, ARF, WORK)
CDRVRF1
subroutine cdrvrf2 (NOUT, NN, NVAL, A, LDA, ARF, AP, ASAV)
CDRVRF2
subroutine cdrvrf3 (NOUT, NN, NVAL, THRESH, A, LDA, ARF, B1, B2, S_WORK_CLANGE, C_WORK_CGEQRF, TAU)
CDRVRF3
subroutine cdrvrf4 (NOUT, NN, NVAL, THRESH, C1, C2, LDC, CRF, A, LDA, S_WORK_CLANGE)
CDRVRF4
subroutine cdrvrfp (NOUT, NN, NVAL, NNS, NSVAL, NNT, NTVAL, THRESH, A, ASAV, AFAC, AINV, B, BSAV, XACT, X, ARF, ARFINV, C_WORK_CLATMS, C_WORK_CPOT02, C_WORK_CPOT03, S_WORK_CLATMS, S_WORK_CLANHE, S_WORK_CPOT01, S_WORK_CPOT02, S_WORK_CPOT03)
CDRVRFP
subroutine cdrvsp (DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK, NOUT)
CDRVSP
subroutine cdrvsy (DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK, NOUT)
CDRVSY
subroutine cdrvsy_rook (DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK, NOUT)
CDRVSY_ROOK
subroutine cebchvxx (THRESH, PATH)
CEBCHVXX
subroutine cerrge (PATH, NUNIT)
CERRGE
subroutine cerrgt (PATH, NUNIT)
CERRGT
subroutine cerrhe (PATH, NUNIT)
CERRHE
subroutine cerrlq (PATH, NUNIT)
CERRLQ
subroutine cerrls (PATH, NUNIT)
CERRLS
subroutine cerrpo (PATH, NUNIT)
CERRPO
subroutine cerrps (PATH, NUNIT)
CERRPS
subroutine cerrql (PATH, NUNIT)
CERRQL
subroutine cerrqp (PATH, NUNIT)
CERRQP
subroutine cerrqr (PATH, NUNIT)
CERRQR
subroutine cerrqrt (PATH, NUNIT)
CERRQRT
subroutine cerrqrtp (PATH, NUNIT)
CERRQRTP
subroutine cerrrfp (NUNIT)
CERRRFP
subroutine cerrrq (PATH, NUNIT)
CERRRQ
subroutine cerrsy (PATH, NUNIT)
CERRSY
subroutine cerrtr (PATH, NUNIT)
CERRTR
subroutine cerrtz (PATH, NUNIT)
CERRTZ
subroutine cerrvx (PATH, NUNIT)
CERRVX
subroutine cgbt01 (M, N, KL, KU, A, LDA, AFAC, LDAFAC, IPIV, WORK, RESID)
CGBT01
subroutine cgbt02 (TRANS, M, N, KL, KU, NRHS, A, LDA, X, LDX, B, LDB, RESID)
CGBT02
subroutine cgbt05 (TRANS, N, KL, KU, NRHS, AB, LDAB, B, LDB, X, LDX, XACT, LDXACT, FERR, BERR, RESLTS)
CGBT05
subroutine cgelqs (M, N, NRHS, A, LDA, TAU, B, LDB, WORK, LWORK, INFO)
CGELQS
logical function cgennd (M, N, A, LDA)
CGENND
subroutine cgeqls (M, N, NRHS, A, LDA, TAU, B, LDB, WORK, LWORK, INFO)
CGEQLS
subroutine cgeqrs (M, N, NRHS, A, LDA, TAU, B, LDB, WORK, LWORK, INFO)
CGEQRS
subroutine cgerqs (M, N, NRHS, A, LDA, TAU, B, LDB, WORK, LWORK, INFO)
CGERQS
subroutine cget01 (M, N, A, LDA, AFAC, LDAFAC, IPIV, RWORK, RESID)
CGET01
subroutine cget02 (TRANS, M, N, NRHS, A, LDA, X, LDX, B, LDB, RWORK, RESID)
CGET02
subroutine cget03 (N, A, LDA, AINV, LDAINV, WORK, LDWORK, RWORK, RCOND, RESID)
CGET03
subroutine cget04 (N, NRHS, X, LDX, XACT, LDXACT, RCOND, RESID)
CGET04
subroutine cget07 (TRANS, N, NRHS, A, LDA, B, LDB, X, LDX, XACT, LDXACT, FERR, CHKFERR, BERR, RESLTS)
CGET07
subroutine cgtt01 (N, DL, D, DU, DLF, DF, DUF, DU2, IPIV, WORK, LDWORK, RWORK, RESID)
CGTT01
subroutine cgtt02 (TRANS, N, NRHS, DL, D, DU, X, LDX, B, LDB, RESID)
CGTT02
subroutine cgtt05 (TRANS, N, NRHS, DL, D, DU, B, LDB, X, LDX, XACT, LDXACT, FERR, BERR, RESLTS)
CGTT05
subroutine chet01 (UPLO, N, A, LDA, AFAC, LDAFAC, IPIV, C, LDC, RWORK, RESID)
CHET01
subroutine chet01_rook (UPLO, N, A, LDA, AFAC, LDAFAC, IPIV, C, LDC, RWORK, RESID)
CHET01_ROOK
subroutine chkxer (SRNAMT, INFOT, NOUT, LERR, OK)
CHKXER
subroutine chpt01 (UPLO, N, A, AFAC, IPIV, C, LDC, RWORK, RESID)
CHPT01
subroutine clahilb (N, NRHS, A, LDA, X, LDX, B, LDB, WORK, INFO, PATH)
CLAHILB
subroutine claipd (N, A, INDA, VINDA)
CLAIPD
subroutine claptm (UPLO, N, NRHS, ALPHA, D, E, X, LDX, BETA, B, LDB)
CLAPTM
subroutine clarhs (PATH, XTYPE, UPLO, TRANS, M, N, KL, KU, NRHS, A, LDA, X, LDX, B, LDB, ISEED, INFO)
CLARHS
subroutine clatb4 (PATH, IMAT, M, N, TYPE, KL, KU, ANORM, MODE, CNDNUM, DIST)
CLATB4
subroutine clatb5 (PATH, IMAT, N, TYPE, KL, KU, ANORM, MODE, CNDNUM, DIST)
CLATB5
subroutine clatsp (UPLO, N, X, ISEED)
CLATSP
subroutine clatsy (UPLO, N, X, LDX, ISEED)
CLATSY
subroutine clattb (IMAT, UPLO, TRANS, DIAG, ISEED, N, KD, AB, LDAB, B, WORK, RWORK, INFO)
CLATTB
subroutine clattp (IMAT, UPLO, TRANS, DIAG, ISEED, N, AP, B, WORK, RWORK, INFO)
CLATTP
subroutine clattr (IMAT, UPLO, TRANS, DIAG, ISEED, N, A, LDA, B, WORK, RWORK, INFO)
CLATTR
subroutine clavhe (UPLO, TRANS, DIAG, N, NRHS, A, LDA, IPIV, B, LDB, INFO)
CLAVHE
subroutine clavhe_rook (UPLO, TRANS, DIAG, N, NRHS, A, LDA, IPIV, B, LDB, INFO)
CLAVHE_ROOK
subroutine clavhp (UPLO, TRANS, DIAG, N, NRHS, A, IPIV, B, LDB, INFO)
CLAVHP
subroutine clavsp (UPLO, TRANS, DIAG, N, NRHS, A, IPIV, B, LDB, INFO)
CLAVSP
subroutine clavsy (UPLO, TRANS, DIAG, N, NRHS, A, LDA, IPIV, B, LDB, INFO)
CLAVSY
subroutine clavsy_rook (UPLO, TRANS, DIAG, N, NRHS, A, LDA, IPIV, B, LDB, INFO)
CLAVSY_ROOK
subroutine clqt01 (M, N, A, AF, Q, L, LDA, TAU, WORK, LWORK, RWORK, RESULT)
CLQT01
subroutine clqt02 (M, N, K, A, AF, Q, L, LDA, TAU, WORK, LWORK, RWORK, RESULT)
CLQT02
subroutine clqt03 (M, N, K, AF, C, CC, Q, LDA, TAU, WORK, LWORK, RWORK, RESULT)
CLQT03
subroutine cpbt01 (UPLO, N, KD, A, LDA, AFAC, LDAFAC, RWORK, RESID)
CPBT01
subroutine cpbt02 (UPLO, N, KD, NRHS, A, LDA, X, LDX, B, LDB, RWORK, RESID)
CPBT02
subroutine cpbt05 (UPLO, N, KD, NRHS, AB, LDAB, B, LDB, X, LDX, XACT, LDXACT, FERR, BERR, RESLTS)
CPBT05
subroutine cpot01 (UPLO, N, A, LDA, AFAC, LDAFAC, RWORK, RESID)
CPOT01
subroutine cpot02 (UPLO, N, NRHS, A, LDA, X, LDX, B, LDB, RWORK, RESID)
CPOT02
subroutine cpot03 (UPLO, N, A, LDA, AINV, LDAINV, WORK, LDWORK, RWORK, RCOND, RESID)
CPOT03
subroutine cpot05 (UPLO, N, NRHS, A, LDA, B, LDB, X, LDX, XACT, LDXACT, FERR, BERR, RESLTS)
CPOT05
subroutine cppt01 (UPLO, N, A, AFAC, RWORK, RESID)
CPPT01
subroutine cppt02 (UPLO, N, NRHS, A, X, LDX, B, LDB, RWORK, RESID)
CPPT02
subroutine cppt03 (UPLO, N, A, AINV, WORK, LDWORK, RWORK, RCOND, RESID)
CPPT03
subroutine cppt05 (UPLO, N, NRHS, AP, B, LDB, X, LDX, XACT, LDXACT, FERR, BERR, RESLTS)
CPPT05
subroutine cpst01 (UPLO, N, A, LDA, AFAC, LDAFAC, PERM, LDPERM, PIV, RWORK, RESID, RANK)
CPST01
subroutine cptt01 (N, D, E, DF, EF, WORK, RESID)
CPTT01
subroutine cptt02 (UPLO, N, NRHS, D, E, X, LDX, B, LDB, RESID)
CPTT02
subroutine cptt05 (N, NRHS, D, E, B, LDB, X, LDX, XACT, LDXACT, FERR, BERR, RESLTS)
CPTT05
subroutine cqlt01 (M, N, A, AF, Q, L, LDA, TAU, WORK, LWORK, RWORK, RESULT)
CQLT01
subroutine cqlt02 (M, N, K, A, AF, Q, L, LDA, TAU, WORK, LWORK, RWORK, RESULT)
CQLT02
subroutine cqlt03 (M, N, K, AF, C, CC, Q, LDA, TAU, WORK, LWORK, RWORK, RESULT)
CQLT03
real function cqpt01 (M, N, K, A, AF, LDA, TAU, JPVT, WORK, LWORK)
CQPT01
subroutine cqrt01 (M, N, A, AF, Q, R, LDA, TAU, WORK, LWORK, RWORK, RESULT)
CQRT01
subroutine cqrt01p (M, N, A, AF, Q, R, LDA, TAU, WORK, LWORK, RWORK, RESULT)
CQRT01P
subroutine cqrt02 (M, N, K, A, AF, Q, R, LDA, TAU, WORK, LWORK, RWORK, RESULT)
CQRT02
subroutine cqrt03 (M, N, K, AF, C, CC, Q, LDA, TAU, WORK, LWORK, RWORK, RESULT)
CQRT03
subroutine cqrt04 (M, N, NB, RESULT)
CQRT04
subroutine cqrt05 (M, N, L, NB, RESULT)
CQRT05
real function cqrt11 (M, K, A, LDA, TAU, WORK, LWORK)
CQRT11
real function cqrt12 (M, N, A, LDA, S, WORK, LWORK, RWORK)
CQRT12
subroutine cqrt13 (SCALE, M, N, A, LDA, NORMA, ISEED)
CQRT13
real function cqrt14 (TRANS, M, N, NRHS, A, LDA, X, LDX, WORK, LWORK)
CQRT14
subroutine cqrt15 (SCALE, RKSEL, M, N, NRHS, A, LDA, B, LDB, S, RANK, NORMA, NORMB, ISEED, WORK, LWORK)
CQRT15
subroutine cqrt16 (TRANS, M, N, NRHS, A, LDA, X, LDX, B, LDB, RWORK, RESID)
CQRT16
real function cqrt17 (TRANS, IRESID, M, N, NRHS, A, LDA, X, LDX, B, LDB, C, WORK, LWORK)
CQRT17
subroutine crqt01 (M, N, A, AF, Q, R, LDA, TAU, WORK, LWORK, RWORK, RESULT)
CRQT01
subroutine crqt02 (M, N, K, A, AF, Q, R, LDA, TAU, WORK, LWORK, RWORK, RESULT)
CRQT02
subroutine crqt03 (M, N, K, AF, C, CC, Q, LDA, TAU, WORK, LWORK, RWORK, RESULT)
CRQT03
real function crzt01 (M, N, A, AF, LDA, TAU, WORK, LWORK)
CRZT01
real function crzt02 (M, N, AF, LDA, TAU, WORK, LWORK)
CRZT02
subroutine csbmv (UPLO, N, K, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
CSBMV
subroutine cspt01 (UPLO, N, A, AFAC, IPIV, C, LDC, RWORK, RESID)
CSPT01
subroutine cspt02 (UPLO, N, NRHS, A, X, LDX, B, LDB, RWORK, RESID)
CSPT02
subroutine cspt03 (UPLO, N, A, AINV, WORK, LDW, RWORK, RCOND, RESID)
CSPT03
subroutine csyt01 (UPLO, N, A, LDA, AFAC, LDAFAC, IPIV, C, LDC, RWORK, RESID)
CSYT01
subroutine csyt01_rook (UPLO, N, A, LDA, AFAC, LDAFAC, IPIV, C, LDC, RWORK, RESID)
CSYT01_ROOK
subroutine csyt02 (UPLO, N, NRHS, A, LDA, X, LDX, B, LDB, RWORK, RESID)
CSYT02
subroutine csyt03 (UPLO, N, A, LDA, AINV, LDAINV, WORK, LDWORK, RWORK, RCOND, RESID)
CSYT03
subroutine ctbt02 (UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, X, LDX, B, LDB, WORK, RWORK, RESID)
CTBT02
subroutine ctbt03 (UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, SCALE, CNORM, TSCAL, X, LDX, B, LDB, WORK, RESID)
CTBT03
subroutine ctbt05 (UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, B, LDB, X, LDX, XACT, LDXACT, FERR, BERR, RESLTS)
CTBT05
subroutine ctbt06 (RCOND, RCONDC, UPLO, DIAG, N, KD, AB, LDAB, RWORK, RAT)
CTBT06
subroutine ctpt01 (UPLO, DIAG, N, AP, AINVP, RCOND, RWORK, RESID)
CTPT01
subroutine ctpt02 (UPLO, TRANS, DIAG, N, NRHS, AP, X, LDX, B, LDB, WORK, RWORK, RESID)
CTPT02
subroutine ctpt03 (UPLO, TRANS, DIAG, N, NRHS, AP, SCALE, CNORM, TSCAL, X, LDX, B, LDB, WORK, RESID)
CTPT03
subroutine ctpt05 (UPLO, TRANS, DIAG, N, NRHS, AP, B, LDB, X, LDX, XACT, LDXACT, FERR, BERR, RESLTS)
CTPT05
subroutine ctpt06 (RCOND, RCONDC, UPLO, DIAG, N, AP, RWORK, RAT)
CTPT06
subroutine ctrt01 (UPLO, DIAG, N, A, LDA, AINV, LDAINV, RCOND, RWORK, RESID)
CTRT01
subroutine ctrt02 (UPLO, TRANS, DIAG, N, NRHS, A, LDA, X, LDX, B, LDB, WORK, RWORK, RESID)
CTRT02
subroutine ctrt03 (UPLO, TRANS, DIAG, N, NRHS, A, LDA, SCALE, CNORM, TSCAL, X, LDX, B, LDB, WORK, RESID)
CTRT03
subroutine ctrt05 (UPLO, TRANS, DIAG, N, NRHS, A, LDA, B, LDB, X, LDX, XACT, LDXACT, FERR, BERR, RESLTS)
CTRT05
subroutine ctrt06 (RCOND, RCONDC, UPLO, DIAG, N, A, LDA, RWORK, RAT)
CTRT06

Detailed Description

This is the group of complex LAPACK TESTING LIN routines.

Function Documentation

program cchkaa ()

CCHKAA

Purpose:

 CCHKAA is the main test program for the COMPLEX linear equation
 routines.
 The program must be driven by a short data file. The first 15 records
 (not including the first comment  line) specify problem dimensions
 and program options using list-directed input. The remaining lines
 specify the LAPACK test paths and the number of matrix types to use
 in testing.  An annotated example of a data file can be obtained by
 deleting the first 3 characters from the following 42 lines:
 Data file for testing COMPLEX LAPACK linear equation routines
 7                      Number of values of M
 0 1 2 3 5 10 16        Values of M (row dimension)
 7                      Number of values of N
 0 1 2 3 5 10 16        Values of N (column dimension)
 1                      Number of values of NRHS
 2                      Values of NRHS (number of right hand sides)
 5                      Number of values of NB
 1 3 3 3 20             Values of NB (the blocksize)
 1 0 5 9 1              Values of NX (crossover point)
 3                      Number of values of RANK
 30 50 90               Values of rank (as a % of N)
 30.0                   Threshold value of test ratio
 T                      Put T to test the LAPACK routines
 T                      Put T to test the driver routines
 T                      Put T to test the error exits
 CGE   11               List types on next line if 0 < NTYPES < 11
 CGB    8               List types on next line if 0 < NTYPES <  8
 CGT   12               List types on next line if 0 < NTYPES < 12
 CPO    9               List types on next line if 0 < NTYPES <  9
 CPO    9               List types on next line if 0 < NTYPES <  9
 CPP    9               List types on next line if 0 < NTYPES <  9
 CPB    8               List types on next line if 0 < NTYPES <  8
 CPT   12               List types on next line if 0 < NTYPES < 12
 CHE   10               List types on next line if 0 < NTYPES < 10
 CHR   10               List types on next line if 0 < NTYPES < 10
 CHP   10               List types on next line if 0 < NTYPES < 10
 CSY   11               List types on next line if 0 < NTYPES < 11
 CSR   11               List types on next line if 0 < NTYPES < 11
 CSP   11               List types on next line if 0 < NTYPES < 11
 CTR   18               List types on next line if 0 < NTYPES < 18
 CTP   18               List types on next line if 0 < NTYPES < 18
 CTB   17               List types on next line if 0 < NTYPES < 17
 CQR    8               List types on next line if 0 < NTYPES <  8
 CRQ    8               List types on next line if 0 < NTYPES <  8
 CLQ    8               List types on next line if 0 < NTYPES <  8
 CQL    8               List types on next line if 0 < NTYPES <  8
 CQP    6               List types on next line if 0 < NTYPES <  6
 CTZ    3               List types on next line if 0 < NTYPES <  3
 CLS    6               List types on next line if 0 < NTYPES <  6
 CEQ
 CQT
 CQX

  NMAX    INTEGER
          The maximum allowable value for M and N.
  MAXIN   INTEGER
          The number of different values that can be used for each of
          M, N, NRHS, NB, NX and RANK
  MAXRHS  INTEGER
          The maximum number of right hand sides
  MATMAX  INTEGER
          The maximum number of matrix types to use for testing
  NIN     INTEGER
          The unit number for input
  NOUT    INTEGER
          The unit number for output

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2015

subroutine cchkeq (real THRESH, integer NOUT)

CCHKEQ

Purpose:

 CCHKEQ tests CGEEQU, CGBEQU, CPOEQU, CPPEQU and CPBEQU

Parameters:

THRESH

          THRESH is REAL
          Threshold for testing routines. Should be between 2 and 10.

NOUT

          NOUT is INTEGER
          The unit number for output.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine cchkgb (logical, dimension( * ) DOTYPE, integer NM, integer, dimension( * ) MVAL, integer NN, integer, dimension( * ) NVAL, integer NNB, integer, dimension( * ) NBVAL, integer NNS, integer, dimension( * ) NSVAL, real THRESH, logical TSTERR, complex, dimension( * ) A, integer LA, complex, dimension( * ) AFAC, integer LAFAC, complex, dimension( * ) B, complex, dimension( * ) X, complex, dimension( * ) XACT, complex, dimension( * ) WORK, real, dimension( * ) RWORK, integer, dimension( * ) IWORK, integer NOUT)

CCHKGB

Purpose:

 CCHKGB tests CGBTRF, -TRS, -RFS, and -CON

Parameters:

DOTYPE

          DOTYPE is LOGICAL array, dimension (NTYPES)
          The matrix types to be used for testing.  Matrices of type j
          (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
          .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.

          NM is INTEGER
          The number of values of M contained in the vector MVAL.

MVAL

          MVAL is INTEGER array, dimension (NM)
          The values of the matrix row dimension M.

          NN is INTEGER
          The number of values of N contained in the vector NVAL.

NVAL

          NVAL is INTEGER array, dimension (NN)
          The values of the matrix column dimension N.

NNB

          NNB is INTEGER
          The number of values of NB contained in the vector NBVAL.

NBVAL

          NBVAL is INTEGER array, dimension (NNB)
          The values of the blocksize NB.

NNS

          NNS is INTEGER
          The number of values of NRHS contained in the vector NSVAL.

NSVAL

          NSVAL is INTEGER array, dimension (NNS)
          The values of the number of right hand sides NRHS.

THRESH

          THRESH is REAL
          The threshold value for the test ratios.  A result is
          included in the output file if RESULT >= THRESH.  To have
          every test ratio printed, use THRESH = 0.

TSTERR

          TSTERR is LOGICAL
          Flag that indicates whether error exits are to be tested.

          A is COMPLEX array, dimension (LA)

          LA is INTEGER
          The length of the array A.  LA >= (KLMAX+KUMAX+1)*NMAX
          where KLMAX is the largest entry in the local array KLVAL,
                KUMAX is the largest entry in the local array KUVAL and
                NMAX is the largest entry in the input array NVAL.

AFAC

          AFAC is COMPLEX array, dimension (LAFAC)

LAFAC

          LAFAC is INTEGER
          The length of the array AFAC. LAFAC >= (2*KLMAX+KUMAX+1)*NMAX
          where KLMAX is the largest entry in the local array KLVAL,
                KUMAX is the largest entry in the local array KUVAL and
                NMAX is the largest entry in the input array NVAL.

          B is COMPLEX array, dimension (NMAX*NSMAX)

          X is COMPLEX array, dimension (NMAX*NSMAX)

XACT

          XACT is COMPLEX array, dimension (NMAX*NSMAX)

WORK

          WORK is COMPLEX array, dimension
                      (NMAX*max(3,NSMAX,NMAX))

RWORK

          RWORK is REAL array, dimension
                      (max(NMAX,2*NSMAX))

IWORK

          IWORK is INTEGER array, dimension (NMAX)

NOUT

          NOUT is INTEGER
          The unit number for output.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine cchkge (logical, dimension( * ) DOTYPE, integer NM, integer, dimension( * ) MVAL, integer NN, integer, dimension( * ) NVAL, integer NNB, integer, dimension( * ) NBVAL, integer NNS, integer, dimension( * ) NSVAL, real THRESH, logical TSTERR, integer NMAX, complex, dimension( * ) A, complex, dimension( * ) AFAC, complex, dimension( * ) AINV, complex, dimension( * ) B, complex, dimension( * ) X, complex, dimension( * ) XACT, complex, dimension( * ) WORK, real, dimension( * ) RWORK, integer, dimension( * ) IWORK, integer NOUT)

CCHKGE

Purpose:

 CCHKGE tests CGETRF, -TRI, -TRS, -RFS, and -CON.

Parameters:

DOTYPE

          DOTYPE is LOGICAL array, dimension (NTYPES)
          The matrix types to be used for testing.  Matrices of type j
          (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
          .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.

          NM is INTEGER
          The number of values of M contained in the vector MVAL.

MVAL

          MVAL is INTEGER array, dimension (NM)
          The values of the matrix row dimension M.

          NN is INTEGER
          The number of values of N contained in the vector NVAL.

NVAL

          NVAL is INTEGER array, dimension (NN)
          The values of the matrix column dimension N.

NNB

          NNB is INTEGER
          The number of values of NB contained in the vector NBVAL.

NBVAL

          NBVAL is INTEGER array, dimension (NBVAL)
          The values of the blocksize NB.

NNS

          NNS is INTEGER
          The number of values of NRHS contained in the vector NSVAL.

NSVAL

          NSVAL is INTEGER array, dimension (NNS)
          The values of the number of right hand sides NRHS.

THRESH

          THRESH is REAL
          The threshold value for the test ratios.  A result is
          included in the output file if RESULT >= THRESH.  To have
          every test ratio printed, use THRESH = 0.

TSTERR

          TSTERR is LOGICAL
          Flag that indicates whether error exits are to be tested.

NMAX

          NMAX is INTEGER
          The maximum value permitted for M or N, used in dimensioning
          the work arrays.

          A is COMPLEX array, dimension (NMAX*NMAX)

AFAC

          AFAC is COMPLEX array, dimension (NMAX*NMAX)

AINV

          AINV is COMPLEX array, dimension (NMAX*NMAX)

          B is COMPLEX array, dimension (NMAX*NSMAX)
          where NSMAX is the largest entry in NSVAL.

          X is COMPLEX array, dimension (NMAX*NSMAX)

XACT

          XACT is COMPLEX array, dimension (NMAX*NSMAX)

WORK

          WORK is COMPLEX array, dimension
                      (NMAX*max(3,NSMAX))

RWORK

          RWORK is REAL array, dimension
                      (max(2*NMAX,2*NSMAX+NWORK))

IWORK

          IWORK is INTEGER array, dimension (NMAX)

NOUT

          NOUT is INTEGER
          The unit number for output.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine cchkgt (logical, dimension( * ) DOTYPE, integer NN, integer, dimension( * ) NVAL, integer NNS, integer, dimension( * ) NSVAL, real THRESH, logical TSTERR, complex, dimension( * ) A, complex, dimension( * ) AF, complex, dimension( * ) B, complex, dimension( * ) X, complex, dimension( * ) XACT, complex, dimension( * ) WORK, real, dimension( * ) RWORK, integer, dimension( * ) IWORK, integer NOUT)

CCHKGT

Purpose:

 CCHKGT tests CGTTRF, -TRS, -RFS, and -CON

Parameters:

DOTYPE

          DOTYPE is LOGICAL array, dimension (NTYPES)
          The matrix types to be used for testing.  Matrices of type j
          (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
          .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.

          NN is INTEGER
          The number of values of N contained in the vector NVAL.

NVAL

          NVAL is INTEGER array, dimension (NN)
          The values of the matrix dimension N.

NNS

          NNS is INTEGER
          The number of values of NRHS contained in the vector NSVAL.

NSVAL

          NSVAL is INTEGER array, dimension (NNS)
          The values of the number of right hand sides NRHS.

THRESH

          THRESH is REAL
          The threshold value for the test ratios.  A result is
          included in the output file if RESULT >= THRESH.  To have
          every test ratio printed, use THRESH = 0.

TSTERR

          TSTERR is LOGICAL
          Flag that indicates whether error exits are to be tested.

          A is COMPLEX array, dimension (NMAX*4)

          AF is COMPLEX array, dimension (NMAX*4)

          B is COMPLEX array, dimension (NMAX*NSMAX)
          where NSMAX is the largest entry in NSVAL.

          X is COMPLEX array, dimension (NMAX*NSMAX)

XACT

          XACT is COMPLEX array, dimension (NMAX*NSMAX)

WORK

          WORK is COMPLEX array, dimension
                      (NMAX*max(3,NSMAX))

RWORK

          RWORK is REAL array, dimension
                      (max(NMAX)+2*NSMAX)

IWORK

          IWORK is INTEGER array, dimension (NMAX)

NOUT

          NOUT is INTEGER
          The unit number for output.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine cchkhe (logical, dimension( * ) DOTYPE, integer NN, integer, dimension( * ) NVAL, integer NNB, integer, dimension( * ) NBVAL, integer NNS, integer, dimension( * ) NSVAL, real THRESH, logical TSTERR, integer NMAX, complex, dimension( * ) A, complex, dimension( * ) AFAC, complex, dimension( * ) AINV, complex, dimension( * ) B, complex, dimension( * ) X, complex, dimension( * ) XACT, complex, dimension( * ) WORK, real, dimension( * ) RWORK, integer, dimension( * ) IWORK, integer NOUT)

CCHKHE

Purpose:

 CCHKHE tests CHETRF, -TRI2, -TRS, -TRS2, -RFS, and -CON.

Parameters:

DOTYPE

          DOTYPE is LOGICAL array, dimension (NTYPES)
          The matrix types to be used for testing.  Matrices of type j
          (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
          .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.

          NN is INTEGER
          The number of values of N contained in the vector NVAL.

NVAL

          NVAL is INTEGER array, dimension (NN)
          The values of the matrix dimension N.

NNB

          NNB is INTEGER
          The number of values of NB contained in the vector NBVAL.

NBVAL

          NBVAL is INTEGER array, dimension (NBVAL)
          The values of the blocksize NB.

NNS

          NNS is INTEGER
          The number of values of NRHS contained in the vector NSVAL.

NSVAL

          NSVAL is INTEGER array, dimension (NNS)
          The values of the number of right hand sides NRHS.

THRESH

          THRESH is REAL
          The threshold value for the test ratios.  A result is
          included in the output file if RESULT >= THRESH.  To have
          every test ratio printed, use THRESH = 0.

TSTERR

          TSTERR is LOGICAL
          Flag that indicates whether error exits are to be tested.

NMAX

          NMAX is INTEGER
          The maximum value permitted for N, used in dimensioning the
          work arrays.

          A is COMPLEX array, dimension (NMAX*NMAX)

AFAC

          AFAC is COMPLEX array, dimension (NMAX*NMAX)

AINV

          AINV is COMPLEX array, dimension (NMAX*NMAX)

          B is COMPLEX array, dimension (NMAX*NSMAX)
          where NSMAX is the largest entry in NSVAL.

          X is COMPLEX array, dimension (NMAX*NSMAX)

XACT

          XACT is COMPLEX array, dimension (NMAX*NSMAX)

WORK

          WORK is COMPLEX array, dimension (NMAX*max(3,NSMAX))

RWORK

          RWORK is REAL array, dimension (max(NMAX,2*NSMAX))

IWORK

          IWORK is INTEGER array, dimension (NMAX)

NOUT

          NOUT is INTEGER
          The unit number for output.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2013

subroutine cchkhe_rook (logical, dimension( * ) DOTYPE, integer NN, integer, dimension( * ) NVAL, integer NNB, integer, dimension( * ) NBVAL, integer NNS, integer, dimension( * ) NSVAL, real THRESH, logical TSTERR, integer NMAX, complex, dimension( * ) A, complex, dimension( * ) AFAC, complex, dimension( * ) AINV, complex, dimension( * ) B, complex, dimension( * ) X, complex, dimension( * ) XACT, complex, dimension( * ) WORK, real, dimension( * ) RWORK, integer, dimension( * ) IWORK, integer NOUT)

CCHKHE_ROOK

Purpose:

 CCHKHE_ROOK tests CHETRF_ROOK, -TRI_ROOK, -TRS_ROOK,
 and -CON_ROOK.

Parameters:

DOTYPE

          DOTYPE is LOGICAL array, dimension (NTYPES)
          The matrix types to be used for testing.  Matrices of type j
          (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
          .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.

          NN is INTEGER
          The number of values of N contained in the vector NVAL.

NVAL

          NVAL is INTEGER array, dimension (NN)
          The values of the matrix dimension N.

NNB

          NNB is INTEGER
          The number of values of NB contained in the vector NBVAL.

NBVAL

          NBVAL is INTEGER array, dimension (NBVAL)
          The values of the blocksize NB.

NNS

          NNS is INTEGER
          The number of values of NRHS contained in the vector NSVAL.

NSVAL

          NSVAL is INTEGER array, dimension (NNS)
          The values of the number of right hand sides NRHS.

THRESH

          THRESH is REAL
          The threshold value for the test ratios.  A result is
          included in the output file if RESULT >= THRESH.  To have
          every test ratio printed, use THRESH = 0.

TSTERR

          TSTERR is LOGICAL
          Flag that indicates whether error exits are to be tested.

NMAX

          NMAX is INTEGER
          The maximum value permitted for N, used in dimensioning the
          work arrays.

          A is COMPLEX array, dimension (NMAX*NMAX)

AFAC

          AFAC is COMPLEX array, dimension (NMAX*NMAX)

AINV

          AINV is COMPLEX array, dimension (NMAX*NMAX)

          B is COMPLEX array, dimension (NMAX*NSMAX)
          where NSMAX is the largest entry in NSVAL.

          X is COMPLEX array, dimension (NMAX*NSMAX)

XACT

          XACT is COMPLEX array, dimension (NMAX*NSMAX)

WORK

          WORK is COMPLEX array, dimension (NMAX*max(3,NSMAX))

RWORK

          RWORK is REAL array, dimension (max(NMAX,2*NSMAX)

IWORK

          IWORK is INTEGER array, dimension (2*NMAX)

NOUT

          NOUT is INTEGER
          The unit number for output.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2015

subroutine cchkhp (logical, dimension( * ) DOTYPE, integer NN, integer, dimension( * ) NVAL, integer NNS, integer, dimension( * ) NSVAL, real THRESH, logical TSTERR, integer NMAX, complex, dimension( * ) A, complex, dimension( * ) AFAC, complex, dimension( * ) AINV, complex, dimension( * ) B, complex, dimension( * ) X, complex, dimension( * ) XACT, complex, dimension( * ) WORK, real, dimension( * ) RWORK, integer, dimension( * ) IWORK, integer NOUT)

CCHKHP

Purpose:

 CCHKHP tests CHPTRF, -TRI, -TRS, -RFS, and -CON

Parameters:

DOTYPE

          DOTYPE is LOGICAL array, dimension (NTYPES)
          The matrix types to be used for testing.  Matrices of type j
          (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
          .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.

          NN is INTEGER
          The number of values of N contained in the vector NVAL.

NVAL

          NVAL is INTEGER array, dimension (NN)
          The values of the matrix dimension N.

NNS

          NNS is INTEGER
          The number of values of NRHS contained in the vector NSVAL.

NSVAL

          NSVAL is INTEGER array, dimension (NNS)
          The values of the number of right hand sides NRHS.

THRESH

          THRESH is REAL
          The threshold value for the test ratios.  A result is
          included in the output file if RESULT >= THRESH.  To have
          every test ratio printed, use THRESH = 0.

TSTERR

          TSTERR is LOGICAL
          Flag that indicates whether error exits are to be tested.

NMAX

          NMAX is INTEGER
          The maximum value permitted for N, used in dimensioning the
          work arrays.

          A is COMPLEX array, dimension
                      (NMAX*(NMAX+1)/2)

AFAC

          AFAC is COMPLEX array, dimension
                      (NMAX*(NMAX+1)/2)

AINV

          AINV is COMPLEX array, dimension
                      (NMAX*(NMAX+1)/2)

          B is COMPLEX array, dimension (NMAX*NSMAX)
          where NSMAX is the largest entry in NSVAL.

          X is COMPLEX array, dimension (NMAX*NSMAX)

XACT

          XACT is COMPLEX array, dimension (NMAX*NSMAX)

WORK

          WORK is COMPLEX array, dimension
                      (NMAX*max(2,NSMAX))

RWORK

          RWORK is REAL array,
                                 dimension (NMAX+2*NSMAX)

IWORK

          IWORK is INTEGER array, dimension (NMAX)

NOUT

          NOUT is INTEGER
          The unit number for output.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine cchklq (logical, dimension( * ) DOTYPE, integer NM, integer, dimension( * ) MVAL, integer NN, integer, dimension( * ) NVAL, integer NNB, integer, dimension( * ) NBVAL, integer, dimension( * ) NXVAL, integer NRHS, real THRESH, logical TSTERR, integer NMAX, complex, dimension( * ) A, complex, dimension( * ) AF, complex, dimension( * ) AQ, complex, dimension( * ) AL, complex, dimension( * ) AC, complex, dimension( * ) B, complex, dimension( * ) X, complex, dimension( * ) XACT, complex, dimension( * ) TAU, complex, dimension( * ) WORK, real, dimension( * ) RWORK, integer NOUT)

CCHKLQ

Purpose:

 CCHKLQ tests CGELQF, CUNGLQ and CUNMLQ.

Parameters:

DOTYPE

          DOTYPE is LOGICAL array, dimension (NTYPES)
          The matrix types to be used for testing.  Matrices of type j
          (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
          .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.

          NM is INTEGER
          The number of values of M contained in the vector MVAL.

MVAL

          MVAL is INTEGER array, dimension (NM)
          The values of the matrix row dimension M.

          NN is INTEGER
          The number of values of N contained in the vector NVAL.

NVAL

          NVAL is INTEGER array, dimension (NN)
          The values of the matrix column dimension N.

NNB

          NNB is INTEGER
          The number of values of NB and NX contained in the
          vectors NBVAL and NXVAL.  The blocking parameters are used
          in pairs (NB,NX).

NBVAL

          NBVAL is INTEGER array, dimension (NNB)
          The values of the blocksize NB.

NXVAL

          NXVAL is INTEGER array, dimension (NNB)
          The values of the crossover point NX.

NRHS

          NRHS is INTEGER
          The number of right hand side vectors to be generated for
          each linear system.

THRESH

          THRESH is REAL
          The threshold value for the test ratios.  A result is
          included in the output file if RESULT >= THRESH.  To have
          every test ratio printed, use THRESH = 0.

TSTERR

          TSTERR is LOGICAL
          Flag that indicates whether error exits are to be tested.

NMAX

          NMAX is INTEGER
          The maximum value permitted for M or N, used in dimensioning
          the work arrays.

          A is COMPLEX array, dimension (NMAX*NMAX)

          AF is COMPLEX array, dimension (NMAX*NMAX)

          AQ is COMPLEX array, dimension (NMAX*NMAX)

          AL is COMPLEX array, dimension (NMAX*NMAX)

          AC is COMPLEX array, dimension (NMAX*NMAX)

          B is COMPLEX array, dimension (NMAX*NRHS)

          X is COMPLEX array, dimension (NMAX*NRHS)

XACT

          XACT is COMPLEX array, dimension (NMAX*NRHS)

TAU

          TAU is COMPLEX array, dimension (NMAX)

WORK

          WORK is COMPLEX array, dimension (NMAX*NMAX)

RWORK

          RWORK is REAL array, dimension (NMAX)

NOUT

          NOUT is INTEGER
          The unit number for output.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine cchkpb (logical, dimension( * ) DOTYPE, integer NN, integer, dimension( * ) NVAL, integer NNB, integer, dimension( * ) NBVAL, integer NNS, integer, dimension( * ) NSVAL, real THRESH, logical TSTERR, integer NMAX, complex, dimension( * ) A, complex, dimension( * ) AFAC, complex, dimension( * ) AINV, complex, dimension( * ) B, complex, dimension( * ) X, complex, dimension( * ) XACT, complex, dimension( * ) WORK, real, dimension( * ) RWORK, integer NOUT)

CCHKPB

Purpose:

 CCHKPB tests CPBTRF, -TRS, -RFS, and -CON.

Parameters:

DOTYPE

          DOTYPE is LOGICAL array, dimension (NTYPES)
          The matrix types to be used for testing.  Matrices of type j
          (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
          .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.

          NN is INTEGER
          The number of values of N contained in the vector NVAL.

NVAL

          NVAL is INTEGER array, dimension (NN)
          The values of the matrix dimension N.

NNB

          NNB is INTEGER
          The number of values of NB contained in the vector NBVAL.

NBVAL

          NBVAL is INTEGER array, dimension (NBVAL)
          The values of the blocksize NB.

NNS

          NNS is INTEGER
          The number of values of NRHS contained in the vector NSVAL.

NSVAL

          NSVAL is INTEGER array, dimension (NNS)
          The values of the number of right hand sides NRHS.

THRESH

          THRESH is REAL
          The threshold value for the test ratios.  A result is
          included in the output file if RESULT >= THRESH.  To have
          every test ratio printed, use THRESH = 0.

TSTERR

          TSTERR is LOGICAL
          Flag that indicates whether error exits are to be tested.

NMAX

          NMAX is INTEGER
          The maximum value permitted for N, used in dimensioning the
          work arrays.

          A is REAL array, dimension (NMAX*NMAX)

AFAC

          AFAC is REAL array, dimension (NMAX*NMAX)

AINV

          AINV is REAL array, dimension (NMAX*NMAX)

          B is REAL array, dimension (NMAX*NSMAX)
          where NSMAX is the largest entry in NSVAL.

          X is REAL array, dimension (NMAX*NSMAX)

XACT

          XACT is REAL array, dimension (NMAX*NSMAX)

WORK

          WORK is REAL array, dimension
                      (NMAX*max(3,NSMAX))

RWORK

          RWORK is REAL array, dimension
                      (max(NMAX,2*NSMAX))

NOUT

          NOUT is INTEGER
          The unit number for output.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine cchkpo (logical, dimension( * ) DOTYPE, integer NN, integer, dimension( * ) NVAL, integer NNB, integer, dimension( * ) NBVAL, integer NNS, integer, dimension( * ) NSVAL, real THRESH, logical TSTERR, integer NMAX, complex, dimension( * ) A, complex, dimension( * ) AFAC, complex, dimension( * ) AINV, complex, dimension( * ) B, complex, dimension( * ) X, complex, dimension( * ) XACT, complex, dimension( * ) WORK, real, dimension( * ) RWORK, integer NOUT)

CCHKPO

Purpose:

 CCHKPO tests CPOTRF, -TRI, -TRS, -RFS, and -CON

Parameters:

DOTYPE

          DOTYPE is LOGICAL array, dimension (NTYPES)
          The matrix types to be used for testing.  Matrices of type j
          (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
          .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.

          NN is INTEGER
          The number of values of N contained in the vector NVAL.

NVAL

          NVAL is INTEGER array, dimension (NN)
          The values of the matrix dimension N.

NNB

          NNB is INTEGER
          The number of values of NB contained in the vector NBVAL.

NBVAL

          NBVAL is INTEGER array, dimension (NBVAL)
          The values of the blocksize NB.

NNS

          NNS is INTEGER
          The number of values of NRHS contained in the vector NSVAL.

NSVAL

          NSVAL is INTEGER array, dimension (NNS)
          The values of the number of right hand sides NRHS.

THRESH

          THRESH is REAL
          The threshold value for the test ratios.  A result is
          included in the output file if RESULT >= THRESH.  To have
          every test ratio printed, use THRESH = 0.

TSTERR

          TSTERR is LOGICAL
          Flag that indicates whether error exits are to be tested.

NMAX

          NMAX is INTEGER
          The maximum value permitted for N, used in dimensioning the
          work arrays.

          A is COMPLEX array, dimension (NMAX*NMAX)

AFAC

          AFAC is COMPLEX array, dimension (NMAX*NMAX)

AINV

          AINV is COMPLEX array, dimension (NMAX*NMAX)

          B is COMPLEX array, dimension (NMAX*NSMAX)
          where NSMAX is the largest entry in NSVAL.

          X is COMPLEX array, dimension (NMAX*NSMAX)

XACT

          XACT is COMPLEX array, dimension (NMAX*NSMAX)

WORK

          WORK is COMPLEX array, dimension
                      (NMAX*max(3,NSMAX))

RWORK

          RWORK is REAL array, dimension
                      (NMAX+2*NSMAX)

NOUT

          NOUT is INTEGER
          The unit number for output.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine cchkpp (logical, dimension( * ) DOTYPE, integer NN, integer, dimension( * ) NVAL, integer NNS, integer, dimension( * ) NSVAL, real THRESH, logical TSTERR, integer NMAX, complex, dimension( * ) A, complex, dimension( * ) AFAC, complex, dimension( * ) AINV, complex, dimension( * ) B, complex, dimension( * ) X, complex, dimension( * ) XACT, complex, dimension( * ) WORK, real, dimension( * ) RWORK, integer NOUT)

CCHKPP

Purpose:

 CCHKPP tests CPPTRF, -TRI, -TRS, -RFS, and -CON

Parameters:

DOTYPE

          DOTYPE is LOGICAL array, dimension (NTYPES)
          The matrix types to be used for testing.  Matrices of type j
          (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
          .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.

          NN is INTEGER
          The number of values of N contained in the vector NVAL.

NVAL

          NVAL is INTEGER array, dimension (NN)
          The values of the matrix dimension N.

NNS

          NNS is INTEGER
          The number of values of NRHS contained in the vector NSVAL.

NSVAL

          NSVAL is INTEGER array, dimension (NNS)
          The values of the number of right hand sides NRHS.

THRESH

          THRESH is REAL
          The threshold value for the test ratios.  A result is
          included in the output file if RESULT >= THRESH.  To have
          every test ratio printed, use THRESH = 0.

TSTERR

          TSTERR is LOGICAL
          Flag that indicates whether error exits are to be tested.

NMAX

          NMAX is INTEGER
          The maximum value permitted for N, used in dimensioning the
          work arrays.

          A is COMPLEX array, dimension
                      (NMAX*(NMAX+1)/2)

AFAC

          AFAC is COMPLEX array, dimension
                      (NMAX*(NMAX+1)/2)

AINV

          AINV is COMPLEX array, dimension
                      (NMAX*(NMAX+1)/2)

          B is COMPLEX array, dimension (NMAX*NSMAX)
          where NSMAX is the largest entry in NSVAL.

          X is COMPLEX array, dimension (NMAX*NSMAX)

XACT

          XACT is COMPLEX array, dimension (NMAX*NSMAX)

WORK

          WORK is COMPLEX array, dimension
                      (NMAX*max(3,NSMAX))

RWORK

          RWORK is REAL array, dimension
                      (max(NMAX,2*NSMAX))

NOUT

          NOUT is INTEGER
          The unit number for output.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine cchkps (logical, dimension( * ) DOTYPE, integer NN, integer, dimension( * ) NVAL, integer NNB, integer, dimension( * ) NBVAL, integer NRANK, integer, dimension( * ) RANKVAL, real THRESH, logical TSTERR, integer NMAX, complex, dimension( * ) A, complex, dimension( * ) AFAC, complex, dimension( * ) PERM, integer, dimension( * ) PIV, complex, dimension( * ) WORK, real, dimension( * ) RWORK, integer NOUT)

CCHKPS

Purpose:

 CCHKPS tests CPSTRF.

Parameters:

DOTYPE

          DOTYPE is LOGICAL array, dimension (NTYPES)
          The matrix types to be used for testing.  Matrices of type j
          (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
          .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.

          NN is INTEGER
          The number of values of N contained in the vector NVAL.

NVAL

          NVAL is INTEGER array, dimension (NN)
          The values of the matrix dimension N.

NNB

          NNB is INTEGER
          The number of values of NB contained in the vector NBVAL.

NBVAL

          NBVAL is INTEGER array, dimension (NBVAL)
          The values of the block size NB.

NRANK

          NRANK is INTEGER
          The number of values of RANK contained in the vector RANKVAL.

RANKVAL

          RANKVAL is INTEGER array, dimension (NBVAL)
          The values of the block size NB.

THRESH

          THRESH is REAL
          The threshold value for the test ratios.  A result is
          included in the output file if RESULT >= THRESH.  To have
          every test ratio printed, use THRESH = 0.

TSTERR

          TSTERR is LOGICAL
          Flag that indicates whether error exits are to be tested.

NMAX

          NMAX is INTEGER
          The maximum value permitted for N, used in dimensioning the
          work arrays.

          A is COMPLEX array, dimension (NMAX*NMAX)

AFAC

          AFAC is COMPLEX array, dimension (NMAX*NMAX)

PERM

          PERM is COMPLEX array, dimension (NMAX*NMAX)

PIV

          PIV is INTEGER array, dimension (NMAX)

WORK

          WORK is COMPLEX array, dimension (NMAX*3)

RWORK

          RWORK is REAL array, dimension (NMAX)

NOUT

          NOUT is INTEGER
          The unit number for output.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine cchkpt (logical, dimension( * ) DOTYPE, integer NN, integer, dimension( * ) NVAL, integer NNS, integer, dimension( * ) NSVAL, real THRESH, logical TSTERR, complex, dimension( * ) A, real, dimension( * ) D, complex, dimension( * ) E, complex, dimension( * ) B, complex, dimension( * ) X, complex, dimension( * ) XACT, complex, dimension( * ) WORK, real, dimension( * ) RWORK, integer NOUT)

CCHKPT

Purpose:

 CCHKPT tests CPTTRF, -TRS, -RFS, and -CON

Parameters:

DOTYPE

          DOTYPE is LOGICAL array, dimension (NTYPES)
          The matrix types to be used for testing.  Matrices of type j
          (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
          .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.

          NN is INTEGER
          The number of values of N contained in the vector NVAL.

NVAL

          NVAL is INTEGER array, dimension (NN)
          The values of the matrix dimension N.

NNS

          NNS is INTEGER
          The number of values of NRHS contained in the vector NSVAL.

NSVAL

          NSVAL is INTEGER array, dimension (NNS)
          The values of the number of right hand sides NRHS.

THRESH

          THRESH is REAL
          The threshold value for the test ratios.  A result is
          included in the output file if RESULT >= THRESH.  To have
          every test ratio printed, use THRESH = 0.

TSTERR

          TSTERR is LOGICAL
          Flag that indicates whether error exits are to be tested.

          A is COMPLEX array, dimension (NMAX*2)

          D is REAL array, dimension (NMAX*2)

          E is COMPLEX array, dimension (NMAX*2)

          B is COMPLEX array, dimension (NMAX*NSMAX)
          where NSMAX is the largest entry in NSVAL.

          X is COMPLEX array, dimension (NMAX*NSMAX)

XACT

          XACT is COMPLEX array, dimension (NMAX*NSMAX)

WORK

          WORK is COMPLEX array, dimension
                      (NMAX*max(3,NSMAX))

RWORK

          RWORK is REAL array, dimension
                      (max(NMAX,2*NSMAX))

NOUT

          NOUT is INTEGER
          The unit number for output.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine cchkq3 (logical, dimension( * ) DOTYPE, integer NM, integer, dimension( * ) MVAL, integer NN, integer, dimension( * ) NVAL, integer NNB, integer, dimension( * ) NBVAL, integer, dimension( * ) NXVAL, real THRESH, complex, dimension( * ) A, complex, dimension( * ) COPYA, real, dimension( * ) S, complex, dimension( * ) TAU, complex, dimension( * ) WORK, real, dimension( * ) RWORK, integer, dimension( * ) IWORK, integer NOUT)

CCHKQ3

Purpose:

 CCHKQ3 tests CGEQP3.

Parameters:

DOTYPE

          DOTYPE is LOGICAL array, dimension (NTYPES)
          The matrix types to be used for testing.  Matrices of type j
          (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
          .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.

          NM is INTEGER
          The number of values of M contained in the vector MVAL.

MVAL

          MVAL is INTEGER array, dimension (NM)
          The values of the matrix row dimension M.

          NN is INTEGER
          The number of values of N contained in the vector NVAL.

NVAL

          NVAL is INTEGER array, dimension (NN)
          The values of the matrix column dimension N.

NNB

          NNB is INTEGER
          The number of values of NB and NX contained in the
          vectors NBVAL and NXVAL.  The blocking parameters are used
          in pairs (NB,NX).

NBVAL

          NBVAL is INTEGER array, dimension (NNB)
          The values of the blocksize NB.

NXVAL

          NXVAL is INTEGER array, dimension (NNB)
          The values of the crossover point NX.

THRESH

          THRESH is REAL
          The threshold value for the test ratios.  A result is
          included in the output file if RESULT >= THRESH.  To have
          every test ratio printed, use THRESH = 0.

          A is COMPLEX array, dimension (MMAX*NMAX)
          where MMAX is the maximum value of M in MVAL and NMAX is the
          maximum value of N in NVAL.

COPYA

          COPYA is COMPLEX array, dimension (MMAX*NMAX)

          S is REAL array, dimension
                      (min(MMAX,NMAX))

TAU

          TAU is COMPLEX array, dimension (MMAX)

WORK

          WORK is COMPLEX array, dimension
                      (max(M*max(M,N) + 4*min(M,N) + max(M,N)))

RWORK

          RWORK is REAL array, dimension (4*NMAX)

IWORK

          IWORK is INTEGER array, dimension (2*NMAX)

NOUT

          NOUT is INTEGER
          The unit number for output.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine cchkql (logical, dimension( * ) DOTYPE, integer NM, integer, dimension( * ) MVAL, integer NN, integer, dimension( * ) NVAL, integer NNB, integer, dimension( * ) NBVAL, integer, dimension( * ) NXVAL, integer NRHS, real THRESH, logical TSTERR, integer NMAX, complex, dimension( * ) A, complex, dimension( * ) AF, complex, dimension( * ) AQ, complex, dimension( * ) AL, complex, dimension( * ) AC, complex, dimension( * ) B, complex, dimension( * ) X, complex, dimension( * ) XACT, complex, dimension( * ) TAU, complex, dimension( * ) WORK, real, dimension( * ) RWORK, integer NOUT)

CCHKQL

Purpose:

 CCHKQL tests CGEQLF, CUNGQL and CUNMQL.

Parameters:

DOTYPE

          DOTYPE is LOGICAL array, dimension (NTYPES)
          The matrix types to be used for testing.  Matrices of type j
          (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
          .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.

          NM is INTEGER
          The number of values of M contained in the vector MVAL.

MVAL

          MVAL is INTEGER array, dimension (NM)
          The values of the matrix row dimension M.

          NN is INTEGER
          The number of values of N contained in the vector NVAL.

NVAL

          NVAL is INTEGER array, dimension (NN)
          The values of the matrix column dimension N.

NNB

          NNB is INTEGER
          The number of values of NB and NX contained in the
          vectors NBVAL and NXVAL.  The blocking parameters are used
          in pairs (NB,NX).

NBVAL

          NBVAL is INTEGER array, dimension (NNB)
          The values of the blocksize NB.

NXVAL

          NXVAL is INTEGER array, dimension (NNB)
          The values of the crossover point NX.

NRHS

          NRHS is INTEGER
          The number of right hand side vectors to be generated for
          each linear system.

THRESH

          THRESH is REAL
          The threshold value for the test ratios.  A result is
          included in the output file if RESULT >= THRESH.  To have
          every test ratio printed, use THRESH = 0.

TSTERR

          TSTERR is LOGICAL
          Flag that indicates whether error exits are to be tested.

NMAX

          NMAX is INTEGER
          The maximum value permitted for M or N, used in dimensioning
          the work arrays.

          A is COMPLEX array, dimension (NMAX*NMAX)

          AF is COMPLEX array, dimension (NMAX*NMAX)

          AQ is COMPLEX array, dimension (NMAX*NMAX)

          AL is COMPLEX array, dimension (NMAX*NMAX)

          AC is COMPLEX array, dimension (NMAX*NMAX)

          B is COMPLEX array, dimension (NMAX*NRHS)

          X is COMPLEX array, dimension (NMAX*NRHS)

XACT

          XACT is COMPLEX array, dimension (NMAX*NRHS)

TAU

          TAU is COMPLEX array, dimension (NMAX)

WORK

          WORK is COMPLEX array, dimension (NMAX*NMAX)

RWORK

          RWORK is REAL array, dimension (NMAX)

NOUT

          NOUT is INTEGER
          The unit number for output.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine cchkqr (logical, dimension( * ) DOTYPE, integer NM, integer, dimension( * ) MVAL, integer NN, integer, dimension( * ) NVAL, integer NNB, integer, dimension( * ) NBVAL, integer, dimension( * ) NXVAL, integer NRHS, real THRESH, logical TSTERR, integer NMAX, complex, dimension( * ) A, complex, dimension( * ) AF, complex, dimension( * ) AQ, complex, dimension( * ) AR, complex, dimension( * ) AC, complex, dimension( * ) B, complex, dimension( * ) X, complex, dimension( * ) XACT, complex, dimension( * ) TAU, complex, dimension( * ) WORK, real, dimension( * ) RWORK, integer, dimension( * ) IWORK, integer NOUT)

CCHKQR

Purpose:

 CCHKQR tests CGEQRF, CUNGQR and CUNMQR.

Parameters:

DOTYPE

          DOTYPE is LOGICAL array, dimension (NTYPES)
          The matrix types to be used for testing.  Matrices of type j
          (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
          .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.

          NM is INTEGER
          The number of values of M contained in the vector MVAL.

MVAL

          MVAL is INTEGER array, dimension (NM)
          The values of the matrix row dimension M.

          NN is INTEGER
          The number of values of N contained in the vector NVAL.

NVAL

          NVAL is INTEGER array, dimension (NN)
          The values of the matrix column dimension N.

NNB

          NNB is INTEGER
          The number of values of NB and NX contained in the
          vectors NBVAL and NXVAL.  The blocking parameters are used
          in pairs (NB,NX).

NBVAL

          NBVAL is INTEGER array, dimension (NNB)
          The values of the blocksize NB.

NXVAL

          NXVAL is INTEGER array, dimension (NNB)
          The values of the crossover point NX.

NRHS

          NRHS is INTEGER
          The number of right hand side vectors to be generated for
          each linear system.

THRESH

          THRESH is REAL
          The threshold value for the test ratios.  A result is
          included in the output file if RESULT >= THRESH.  To have
          every test ratio printed, use THRESH = 0.

TSTERR

          TSTERR is LOGICAL
          Flag that indicates whether error exits are to be tested.

NMAX

          NMAX is INTEGER
          The maximum value permitted for M or N, used in dimensioning
          the work arrays.

          A is COMPLEX array, dimension (NMAX*NMAX)

          AF is COMPLEX array, dimension (NMAX*NMAX)

          AQ is COMPLEX array, dimension (NMAX*NMAX)

          AR is COMPLEX array, dimension (NMAX*NMAX)

          AC is COMPLEX array, dimension (NMAX*NMAX)

          B is COMPLEX array, dimension (NMAX*NRHS)

          X is COMPLEX array, dimension (NMAX*NRHS)

XACT

          XACT is COMPLEX array, dimension (NMAX*NRHS)

TAU

          TAU is COMPLEX array, dimension (NMAX)

WORK

          WORK is COMPLEX array, dimension (NMAX*NMAX)

RWORK

          RWORK is REAL array, dimension (NMAX)

IWORK

          IWORK is INTEGER array, dimension (NMAX)

NOUT

          NOUT is INTEGER
          The unit number for output.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2015

subroutine cchkqrt (real THRESH, logical TSTERR, integer NM, integer, dimension( * ) MVAL, integer NN, integer, dimension( * ) NVAL, integer NNB, integer, dimension( * ) NBVAL, integer NOUT)

CCHKQRT

Purpose:

 CCHKQRT tests CGEQRT and CGEMQRT.

Parameters:

THRESH

          THRESH is REAL
          The threshold value for the test ratios.  A result is
          included in the output file if RESULT >= THRESH.  To have
          every test ratio printed, use THRESH = 0.

TSTERR

          TSTERR is LOGICAL
          Flag that indicates whether error exits are to be tested.

          NM is INTEGER
          The number of values of M contained in the vector MVAL.

MVAL

          MVAL is INTEGER array, dimension (NM)
          The values of the matrix row dimension M.

          NN is INTEGER
          The number of values of N contained in the vector NVAL.

NVAL

          NVAL is INTEGER array, dimension (NN)
          The values of the matrix column dimension N.

NNB

          NNB is INTEGER
          The number of values of NB contained in the vector NBVAL.

NBVAL

          NBVAL is INTEGER array, dimension (NBVAL)
          The values of the blocksize NB.

NOUT

          NOUT is INTEGER
          The unit number for output.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine cchkqrtp (real THRESH, logical TSTERR, integer NM, integer, dimension( * ) MVAL, integer NN, integer, dimension( * ) NVAL, integer NNB, integer, dimension( * ) NBVAL, integer NOUT)

CCHKQRTP

Purpose:

 CCHKQRTP tests CTPQRT and CTPMQRT.

Parameters:

THRESH

          THRESH is REAL
          The threshold value for the test ratios.  A result is
          included in the output file if RESULT >= THRESH.  To have
          every test ratio printed, use THRESH = 0.

TSTERR

          TSTERR is LOGICAL
          Flag that indicates whether error exits are to be tested.

          NM is INTEGER
          The number of values of M contained in the vector MVAL.

MVAL

          MVAL is INTEGER array, dimension (NM)
          The values of the matrix row dimension M.

          NN is INTEGER
          The number of values of N contained in the vector NVAL.

NVAL

          NVAL is INTEGER array, dimension (NN)
          The values of the matrix column dimension N.

NNB

          NNB is INTEGER
          The number of values of NB contained in the vector NBVAL.

NBVAL

          NBVAL is INTEGER array, dimension (NBVAL)
          The values of the blocksize NB.

NOUT

          NOUT is INTEGER
          The unit number for output.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

program cchkrfp ()

CCHKRFP

Purpose:

 CCHKRFP is the main test program for the COMPLEX linear equation
 routines with RFP storage format

  MAXIN   INTEGER
          The number of different values that can be used for each of
          M, N, or NB
  MAXRHS  INTEGER
          The maximum number of right hand sides
  NTYPES  INTEGER
  NMAX    INTEGER
          The maximum allowable value for N.
  NIN     INTEGER
          The unit number for input
  NOUT    INTEGER
          The unit number for output

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: April 2012

subroutine cchkrq (logical, dimension( * ) DOTYPE, integer NM, integer, dimension( * ) MVAL, integer NN, integer, dimension( * ) NVAL, integer NNB, integer, dimension( * ) NBVAL, integer, dimension( * ) NXVAL, integer NRHS, real THRESH, logical TSTERR, integer NMAX, complex, dimension( * ) A, complex, dimension( * ) AF, complex, dimension( * ) AQ, complex, dimension( * ) AR, complex, dimension( * ) AC, complex, dimension( * ) B, complex, dimension( * ) X, complex, dimension( * ) XACT, complex, dimension( * ) TAU, complex, dimension( * ) WORK, real, dimension( * ) RWORK, integer, dimension( * ) IWORK, integer NOUT)

CCHKRQ

Purpose:

 CCHKRQ tests CGERQF, CUNGRQ and CUNMRQ.

Parameters:

DOTYPE

          DOTYPE is LOGICAL array, dimension (NTYPES)
          The matrix types to be used for testing.  Matrices of type j
          (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
          .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.

          NM is INTEGER
          The number of values of M contained in the vector MVAL.

MVAL

          MVAL is INTEGER array, dimension (NM)
          The values of the matrix row dimension M.

          NN is INTEGER
          The number of values of N contained in the vector NVAL.

NVAL

          NVAL is INTEGER array, dimension (NN)
          The values of the matrix column dimension N.

NNB

          NNB is INTEGER
          The number of values of NB and NX contained in the
          vectors NBVAL and NXVAL.  The blocking parameters are used
          in pairs (NB,NX).

NBVAL

          NBVAL is INTEGER array, dimension (NNB)
          The values of the blocksize NB.

NXVAL

          NXVAL is INTEGER array, dimension (NNB)
          The values of the crossover point NX.

NRHS

          NRHS is INTEGER
          The number of right hand side vectors to be generated for
          each linear system.

THRESH

          THRESH is REAL
          The threshold value for the test ratios.  A result is
          included in the output file if RESULT >= THRESH.  To have
          every test ratio printed, use THRESH = 0.

TSTERR

          TSTERR is LOGICAL
          Flag that indicates whether error exits are to be tested.

NMAX

          NMAX is INTEGER
          The maximum value permitted for M or N, used in dimensioning
          the work arrays.

          A is COMPLEX array, dimension (NMAX*NMAX)

          AF is COMPLEX array, dimension (NMAX*NMAX)

          AQ is COMPLEX array, dimension (NMAX*NMAX)

          AR is COMPLEX array, dimension (NMAX*NMAX)

          AC is COMPLEX array, dimension (NMAX*NMAX)

          B is COMPLEX array, dimension (NMAX*NRHS)

          X is COMPLEX array, dimension (NMAX*NRHS)

XACT

          XACT is COMPLEX array, dimension (NMAX*NRHS)

TAU

          TAU is COMPLEX array, dimension (NMAX)

WORK

          WORK is COMPLEX array, dimension (NMAX*NMAX)

RWORK

          RWORK is REAL array, dimension (NMAX)

IWORK

          IWORK is INTEGER array, dimension (NMAX)

NOUT

          NOUT is INTEGER
          The unit number for output.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine cchksp (logical, dimension( * ) DOTYPE, integer NN, integer, dimension( * ) NVAL, integer NNS, integer, dimension( * ) NSVAL, real THRESH, logical TSTERR, integer NMAX, complex, dimension( * ) A, complex, dimension( * ) AFAC, complex, dimension( * ) AINV, complex, dimension( * ) B, complex, dimension( * ) X, complex, dimension( * ) XACT, complex, dimension( * ) WORK, real, dimension( * ) RWORK, integer, dimension( * ) IWORK, integer NOUT)

CCHKSP

Purpose:

 CCHKSP tests CSPTRF, -TRI, -TRS, -RFS, and -CON

Parameters:

DOTYPE

          DOTYPE is LOGICAL array, dimension (NTYPES)
          The matrix types to be used for testing.  Matrices of type j
          (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
          .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.

          NN is INTEGER
          The number of values of N contained in the vector NVAL.

NVAL

          NVAL is INTEGER array, dimension (NN)
          The values of the matrix dimension N.

NNS

          NNS is INTEGER
          The number of values of NRHS contained in the vector NSVAL.

NSVAL

          NSVAL is INTEGER array, dimension (NNS)
          The values of the number of right hand sides NRHS.

THRESH

          THRESH is REAL
          The threshold value for the test ratios.  A result is
          included in the output file if RESULT >= THRESH.  To have
          every test ratio printed, use THRESH = 0.

TSTERR

          TSTERR is LOGICAL
          Flag that indicates whether error exits are to be tested.

NMAX

          NMAX is INTEGER
          The maximum value permitted for N, used in dimensioning the
          work arrays.

          A is COMPLEX array, dimension
                      (NMAX*(NMAX+1)/2)

AFAC

          AFAC is COMPLEX array, dimension
                      (NMAX*(NMAX+1)/2)

AINV

          AINV is COMPLEX array, dimension
                      (NMAX*(NMAX+1)/2)

          B is COMPLEX array, dimension (NMAX*NSMAX)
          where NSMAX is the largest entry in NSVAL.

          X is COMPLEX array, dimension (NMAX*NSMAX)

XACT

          XACT is COMPLEX array, dimension (NMAX*NSMAX)

WORK

          WORK is COMPLEX array, dimension
                      (NMAX*max(2,NSMAX))

RWORK

          RWORK is REAL array,
                                 dimension (NMAX+2*NSMAX)

IWORK

          IWORK is INTEGER array, dimension (NMAX)

NOUT

          NOUT is INTEGER
          The unit number for output.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine cchksy (logical, dimension( * ) DOTYPE, integer NN, integer, dimension( * ) NVAL, integer NNB, integer, dimension( * ) NBVAL, integer NNS, integer, dimension( * ) NSVAL, real THRESH, logical TSTERR, integer NMAX, complex, dimension( * ) A, complex, dimension( * ) AFAC, complex, dimension( * ) AINV, complex, dimension( * ) B, complex, dimension( * ) X, complex, dimension( * ) XACT, complex, dimension( * ) WORK, real, dimension( * ) RWORK, integer, dimension( * ) IWORK, integer NOUT)

CCHKSY

Purpose:

 CCHKSY tests CSYTRF, -TRI2, -TRS, -TRS2, -RFS, and -CON.

Parameters:

DOTYPE

          DOTYPE is LOGICAL array, dimension (NTYPES)
          The matrix types to be used for testing.  Matrices of type j
          (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
          .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.

          NN is INTEGER
          The number of values of N contained in the vector NVAL.

NVAL

          NVAL is INTEGER array, dimension (NN)
          The values of the matrix dimension N.

NNB

          NNB is INTEGER
          The number of values of NB contained in the vector NBVAL.

NBVAL

          NBVAL is INTEGER array, dimension (NBVAL)
          The values of the blocksize NB.

NNS

          NNS is INTEGER
          The number of values of NRHS contained in the vector NSVAL.

NSVAL

          NSVAL is INTEGER array, dimension (NNS)
          The values of the number of right hand sides NRHS.

THRESH

          THRESH is REAL
          The threshold value for the test ratios.  A result is
          included in the output file if RESULT >= THRESH.  To have
          every test ratio printed, use THRESH = 0.

TSTERR

          TSTERR is LOGICAL
          Flag that indicates whether error exits are to be tested.

NMAX

          NMAX is INTEGER
          The maximum value permitted for N, used in dimensioning the
          work arrays.

          A is COMPLEX array, dimension (NMAX*NMAX)

AFAC

          AFAC is COMPLEX array, dimension (NMAX*NMAX)

AINV

          AINV is COMPLEX array, dimension (NMAX*NMAX)

          B is COMPLEX array, dimension (NMAX*NSMAX)
          where NSMAX is the largest entry in NSVAL.

          X is COMPLEX array, dimension (NMAX*NSMAX)

XACT

          XACT is COMPLEX array, dimension (NMAX*NSMAX)

WORK

          WORK is COMPLEX array, dimension (NMAX*max(2,NSMAX))

RWORK

          RWORK is REAL array, dimension (NMAX+2*NSMAX)

IWORK

          IWORK is INTEGER array, dimension (NMAX)

NOUT

          NOUT is INTEGER
          The unit number for output.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2013

subroutine cchksy_rook (logical, dimension( * ) DOTYPE, integer NN, integer, dimension( * ) NVAL, integer NNB, integer, dimension( * ) NBVAL, integer NNS, integer, dimension( * ) NSVAL, real THRESH, logical TSTERR, integer NMAX, complex, dimension( * ) A, complex, dimension( * ) AFAC, complex, dimension( * ) AINV, complex, dimension( * ) B, complex, dimension( * ) X, complex, dimension( * ) XACT, complex, dimension( * ) WORK, real, dimension( * ) RWORK, integer, dimension( * ) IWORK, integer NOUT)

CCHKSY_ROOK

Purpose:

 CCHKSY_ROOK tests CSYTRF_ROOK, -TRI_ROOK, -TRS_ROOK,
 and -CON_ROOK.

Parameters:

DOTYPE

          DOTYPE is LOGICAL array, dimension (NTYPES)
          The matrix types to be used for testing.  Matrices of type j
          (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
          .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.

          NN is INTEGER
          The number of values of N contained in the vector NVAL.

NVAL

          NVAL is INTEGER array, dimension (NN)
          The values of the matrix dimension N.

NNB

          NNB is INTEGER
          The number of values of NB contained in the vector NBVAL.

NBVAL

          NBVAL is INTEGER array, dimension (NBVAL)
          The values of the blocksize NB.

NNS

          NNS is INTEGER
          The number of values of NRHS contained in the vector NSVAL.

NSVAL

          NSVAL is INTEGER array, dimension (NNS)
          The values of the number of right hand sides NRHS.

THRESH

          THRESH is REAL
          The threshold value for the test ratios.  A result is
          included in the output file if RESULT >= THRESH.  To have
          every test ratio printed, use THRESH = 0.

TSTERR

          TSTERR is LOGICAL
          Flag that indicates whether error exits are to be tested.

NMAX

          NMAX is INTEGER
          The maximum value permitted for N, used in dimensioning the
          work arrays.

          A is COMPLEX array, dimension (NMAX*NMAX)

AFAC

          AFAC is COMPLEX array, dimension (NMAX*NMAX)

AINV

          AINV is COMPLEX array, dimension (NMAX*NMAX)

          B is COMPLEX array, dimension (NMAX*NSMAX)
          where NSMAX is the largest entry in NSVAL.

          X is COMPLEX array, dimension (NMAX*NSMAX)

XACT

          XACT is COMPLEX array, dimension (NMAX*NSMAX)

WORK

          WORK is COMPLEX array, dimension (NMAX*max(3,NSMAX))

RWORK

          RWORK is REAL array, dimension (max(NMAX,2*NSMAX))

IWORK

          IWORK is INTEGER array, dimension (2*NMAX)

NOUT

          NOUT is INTEGER
          The unit number for output.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2015

subroutine cchktb (logical, dimension( * ) DOTYPE, integer NN, integer, dimension( * ) NVAL, integer NNS, integer, dimension( * ) NSVAL, real THRESH, logical TSTERR, integer NMAX, complex, dimension( * ) AB, complex, dimension( * ) AINV, complex, dimension( * ) B, complex, dimension( * ) X, complex, dimension( * ) XACT, complex, dimension( * ) WORK, real, dimension( * ) RWORK, integer NOUT)

CCHKTB

Purpose:

 CCHKTB tests CTBTRS, -RFS, and -CON, and CLATBS.

Parameters:

DOTYPE

          DOTYPE is LOGICAL array, dimension (NTYPES)
          The matrix types to be used for testing.  Matrices of type j
          (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
          .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.

          NN is INTEGER
          The number of values of N contained in the vector NVAL.

NVAL

          NVAL is INTEGER array, dimension (NN)
          The values of the matrix column dimension N.

NNS

          NNS is INTEGER
          The number of values of NRHS contained in the vector NSVAL.

NSVAL

          NSVAL is INTEGER array, dimension (NNS)
          The values of the number of right hand sides NRHS.

THRESH

          THRESH is REAL
          The threshold value for the test ratios.  A result is
          included in the output file if RESULT >= THRESH.  To have
          every test ratio printed, use THRESH = 0.

TSTERR

          TSTERR is LOGICAL
          Flag that indicates whether error exits are to be tested.

NMAX

          NMAX is INTEGER
          The leading dimension of the work arrays.
          NMAX >= the maximum value of N in NVAL.

          AB is COMPLEX array, dimension (NMAX*NMAX)

AINV

          AINV is COMPLEX array, dimension (NMAX*NMAX)

          B is COMPLEX array, dimension (NMAX*NSMAX)
          where NSMAX is the largest entry in NSVAL.

          X is COMPLEX array, dimension (NMAX*NSMAX)

XACT

          XACT is COMPLEX array, dimension (NMAX*NSMAX)

WORK

          WORK is COMPLEX array, dimension
                      (NMAX*max(3,NSMAX))

RWORK

          RWORK is REAL array, dimension
                      (max(NMAX,2*NSMAX))

NOUT

          NOUT is INTEGER
          The unit number for output.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine cchktp (logical, dimension( * ) DOTYPE, integer NN, integer, dimension( * ) NVAL, integer NNS, integer, dimension( * ) NSVAL, real THRESH, logical TSTERR, integer NMAX, complex, dimension( * ) AP, complex, dimension( * ) AINVP, complex, dimension( * ) B, complex, dimension( * ) X, complex, dimension( * ) XACT, complex, dimension( * ) WORK, real, dimension( * ) RWORK, integer NOUT)

CCHKTP

Purpose:

 CCHKTP tests CTPTRI, -TRS, -RFS, and -CON, and CLATPS

Parameters:

DOTYPE

          DOTYPE is LOGICAL array, dimension (NTYPES)
          The matrix types to be used for testing.  Matrices of type j
          (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
          .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.

          NN is INTEGER
          The number of values of N contained in the vector NVAL.

NVAL

          NVAL is INTEGER array, dimension (NN)
          The values of the matrix column dimension N.

NNS

          NNS is INTEGER
          The number of values of NRHS contained in the vector NSVAL.

NSVAL

          NSVAL is INTEGER array, dimension (NNS)
          The values of the number of right hand sides NRHS.

THRESH

          THRESH is REAL
          The threshold value for the test ratios.  A result is
          included in the output file if RESULT >= THRESH.  To have
          every test ratio printed, use THRESH = 0.

TSTERR

          TSTERR is LOGICAL
          Flag that indicates whether error exits are to be tested.

NMAX

          NMAX is INTEGER
          The leading dimension of the work arrays.  NMAX >= the
          maximumm value of N in NVAL.

          AP is COMPLEX array, dimension (NMAX*(NMAX+1)/2)

AINVP

          AINVP is COMPLEX array, dimension (NMAX*(NMAX+1)/2)

          B is COMPLEX array, dimension (NMAX*NSMAX)
          where NSMAX is the largest entry in NSVAL.

          X is COMPLEX array, dimension (NMAX*NSMAX)

XACT

          XACT is COMPLEX array, dimension (NMAX*NSMAX)

WORK

          WORK is COMPLEX array, dimension
                      (NMAX*max(3,NSMAX))

RWORK

          RWORK is REAL array, dimension
                      (max(NMAX,2*NSMAX))

NOUT

          NOUT is INTEGER
          The unit number for output.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine cchktr (logical, dimension( * ) DOTYPE, integer NN, integer, dimension( * ) NVAL, integer NNB, integer, dimension( * ) NBVAL, integer NNS, integer, dimension( * ) NSVAL, real THRESH, logical TSTERR, integer NMAX, complex, dimension( * ) A, complex, dimension( * ) AINV, complex, dimension( * ) B, complex, dimension( * ) X, complex, dimension( * ) XACT, complex, dimension( * ) WORK, real, dimension( * ) RWORK, integer NOUT)

CCHKTR

Purpose:

 CCHKTR tests CTRTRI, -TRS, -RFS, and -CON, and CLATRS

Parameters:

DOTYPE

          DOTYPE is LOGICAL array, dimension (NTYPES)
          The matrix types to be used for testing.  Matrices of type j
          (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
          .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.

          NN is INTEGER
          The number of values of N contained in the vector NVAL.

NVAL

          NVAL is INTEGER array, dimension (NN)
          The values of the matrix column dimension N.

NNB

          NNB is INTEGER
          The number of values of NB contained in the vector NBVAL.

NBVAL

          NBVAL is INTEGER array, dimension (NNB)
          The values of the blocksize NB.

NNS

          NNS is INTEGER
          The number of values of NRHS contained in the vector NSVAL.

NSVAL

          NSVAL is INTEGER array, dimension (NNS)
          The values of the number of right hand sides NRHS.

THRESH

          THRESH is REAL
          The threshold value for the test ratios.  A result is
          included in the output file if RESULT >= THRESH.  To have
          every test ratio printed, use THRESH = 0.

TSTERR

          TSTERR is LOGICAL
          Flag that indicates whether error exits are to be tested.

NMAX

          NMAX is INTEGER
          The leading dimension of the work arrays.
          NMAX >= the maximum value of N in NVAL.

          A is COMPLEX array, dimension (NMAX*NMAX)

AINV

          AINV is COMPLEX array, dimension (NMAX*NMAX)

          B is COMPLEX array, dimension (NMAX*NSMAX)
          where NSMAX is the largest entry in NSVAL.

          X is COMPLEX array, dimension (NMAX*NSMAX)

XACT

          XACT is COMPLEX array, dimension (NMAX*NSMAX)

WORK

          WORK is COMPLEX array, dimension
                      (NMAX*max(3,NSMAX))

RWORK

          RWORK is REAL array, dimension
                      (max(NMAX,2*NSMAX))

NOUT

          NOUT is INTEGER
          The unit number for output.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine cchktz (logical, dimension( * ) DOTYPE, integer NM, integer, dimension( * ) MVAL, integer NN, integer, dimension( * ) NVAL, real THRESH, logical TSTERR, complex, dimension( * ) A, complex, dimension( * ) COPYA, real, dimension( * ) S, complex, dimension( * ) TAU, complex, dimension( * ) WORK, real, dimension( * ) RWORK, integer NOUT)

CCHKTZ

Purpose:

 CCHKTZ tests CTZRZF.

Parameters:

DOTYPE

          DOTYPE is LOGICAL array, dimension (NTYPES)
          The matrix types to be used for testing.  Matrices of type j
          (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
          .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.

          NM is INTEGER
          The number of values of M contained in the vector MVAL.

MVAL

          MVAL is INTEGER array, dimension (NM)
          The values of the matrix row dimension M.

          NN is INTEGER
          The number of values of N contained in the vector NVAL.

NVAL

          NVAL is INTEGER array, dimension (NN)
          The values of the matrix column dimension N.

THRESH

          THRESH is REAL
          The threshold value for the test ratios.  A result is
          included in the output file if RESULT >= THRESH.  To have
          every test ratio printed, use THRESH = 0.

TSTERR

          TSTERR is LOGICAL
          Flag that indicates whether error exits are to be tested.

          A is COMPLEX array, dimension (MMAX*NMAX)
          where MMAX is the maximum value of M in MVAL and NMAX is the
          maximum value of N in NVAL.

COPYA

          COPYA is COMPLEX array, dimension (MMAX*NMAX)

          S is REAL array, dimension
                      (min(MMAX,NMAX))

TAU

          TAU is COMPLEX array, dimension (MMAX)

WORK

          WORK is COMPLEX array, dimension
                      (MMAX*NMAX + 4*NMAX + MMAX)

RWORK

          RWORK is REAL array, dimension (2*NMAX)

NOUT

          NOUT is INTEGER
          The unit number for output.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2015

subroutine cdrvgb (logical, dimension( * ) DOTYPE, integer NN, integer, dimension( * ) NVAL, integer NRHS, real THRESH, logical TSTERR, complex, dimension( * ) A, integer LA, complex, dimension( * ) AFB, integer LAFB, complex, dimension( * ) ASAV, complex, dimension( * ) B, complex, dimension( * ) BSAV, complex, dimension( * ) X, complex, dimension( * ) XACT, real, dimension( * ) S, complex, dimension( * ) WORK, real, dimension( * ) RWORK, integer, dimension( * ) IWORK, integer NOUT)

CDRVGB CDRVGBX

Purpose:

 CDRVGB tests the driver routines CGBSV and -SVX.

Parameters:

DOTYPE

          DOTYPE is LOGICAL array, dimension (NTYPES)
          The matrix types to be used for testing.  Matrices of type j
          (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
          .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.

          NN is INTEGER
          The number of values of N contained in the vector NVAL.

NVAL

          NVAL is INTEGER array, dimension (NN)
          The values of the matrix column dimension N.

NRHS

          NRHS is INTEGER
          The number of right hand side vectors to be generated for
          each linear system.

THRESH

          THRESH is REAL
          The threshold value for the test ratios.  A result is
          included in the output file if RESULT >= THRESH.  To have
          every test ratio printed, use THRESH = 0.

TSTERR

          TSTERR is LOGICAL
          Flag that indicates whether error exits are to be tested.

          A is COMPLEX array, dimension (LA)

          LA is INTEGER
          The length of the array A.  LA >= (2*NMAX-1)*NMAX
          where NMAX is the largest entry in NVAL.

AFB

          AFB is COMPLEX array, dimension (LAFB)

LAFB

          LAFB is INTEGER
          The length of the array AFB.  LAFB >= (3*NMAX-2)*NMAX
          where NMAX is the largest entry in NVAL.

ASAV

          ASAV is COMPLEX array, dimension (LA)

          B is COMPLEX array, dimension (NMAX*NRHS)

BSAV

          BSAV is COMPLEX array, dimension (NMAX*NRHS)

          X is COMPLEX array, dimension (NMAX*NRHS)

XACT

          XACT is COMPLEX array, dimension (NMAX*NRHS)

          S is REAL array, dimension (2*NMAX)

WORK

          WORK is COMPLEX array, dimension
                      (NMAX*max(3,NRHS,NMAX))

RWORK

          RWORK is REAL array, dimension
                      (max(NMAX,2*NRHS))

IWORK

          IWORK is INTEGER array, dimension (NMAX)

NOUT

          NOUT is INTEGER
          The unit number for output.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2015

Purpose:

 CDRVGB tests the driver routines CGBSV, -SVX, and -SVXX.
 Note that this file is used only when the XBLAS are available,
 otherwise cdrvgb.f defines this subroutine.

Parameters:

DOTYPE

          DOTYPE is LOGICAL array, dimension (NTYPES)
          The matrix types to be used for testing.  Matrices of type j
          (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
          .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.

          NN is INTEGER
          The number of values of N contained in the vector NVAL.

NVAL

          NVAL is INTEGER array, dimension (NN)
          The values of the matrix column dimension N.

NRHS

          NRHS is INTEGER
          The number of right hand side vectors to be generated for
          each linear system.

THRESH

          THRESH is REAL
          The threshold value for the test ratios.  A result is
          included in the output file if RESULT >= THRESH.  To have
          every test ratio printed, use THRESH = 0.

TSTERR

          TSTERR is LOGICAL
          Flag that indicates whether error exits are to be tested.

          A is COMPLEX array, dimension (LA)

          LA is INTEGER
          The length of the array A.  LA >= (2*NMAX-1)*NMAX
          where NMAX is the largest entry in NVAL.

AFB

          AFB is COMPLEX array, dimension (LAFB)

LAFB

          LAFB is INTEGER
          The length of the array AFB.  LAFB >= (3*NMAX-2)*NMAX
          where NMAX is the largest entry in NVAL.

ASAV

          ASAV is COMPLEX array, dimension (LA)

          B is COMPLEX array, dimension (NMAX*NRHS)

BSAV

          BSAV is COMPLEX array, dimension (NMAX*NRHS)

          X is COMPLEX array, dimension (NMAX*NRHS)

XACT

          XACT is COMPLEX array, dimension (NMAX*NRHS)

          S is REAL array, dimension (2*NMAX)

WORK

          WORK is COMPLEX array, dimension
                      (NMAX*max(3,NRHS,NMAX))

RWORK

          RWORK is REAL array, dimension
                      (max(NMAX,2*NRHS))

IWORK

          IWORK is INTEGER array, dimension (NMAX)

NOUT

          NOUT is INTEGER
          The unit number for output.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine cdrvge (logical, dimension( * ) DOTYPE, integer NN, integer, dimension( * ) NVAL, integer NRHS, real THRESH, logical TSTERR, integer NMAX, complex, dimension( * ) A, complex, dimension( * ) AFAC, complex, dimension( * ) ASAV, complex, dimension( * ) B, complex, dimension( * ) BSAV, complex, dimension( * ) X, complex, dimension( * ) XACT, real, dimension( * ) S, complex, dimension( * ) WORK, real, dimension( * ) RWORK, integer, dimension( * ) IWORK, integer NOUT)

CDRVGE CDRVGEX

Purpose:

 CDRVGE tests the driver routines CGESV and -SVX.

Parameters:

DOTYPE

          DOTYPE is LOGICAL array, dimension (NTYPES)
          The matrix types to be used for testing.  Matrices of type j
          (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
          .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.

          NN is INTEGER
          The number of values of N contained in the vector NVAL.

NVAL

          NVAL is INTEGER array, dimension (NN)
          The values of the matrix column dimension N.

NRHS

          NRHS is INTEGER
          The number of right hand side vectors to be generated for
          each linear system.

THRESH

          THRESH is REAL
          The threshold value for the test ratios.  A result is
          included in the output file if RESULT >= THRESH.  To have
          every test ratio printed, use THRESH = 0.

TSTERR

          TSTERR is LOGICAL
          Flag that indicates whether error exits are to be tested.

NMAX

          NMAX is INTEGER
          The maximum value permitted for N, used in dimensioning the
          work arrays.

          A is COMPLEX array, dimension (NMAX*NMAX)

AFAC

          AFAC is COMPLEX array, dimension (NMAX*NMAX)

ASAV

          ASAV is COMPLEX array, dimension (NMAX*NMAX)

          B is COMPLEX array, dimension (NMAX*NRHS)

BSAV

          BSAV is COMPLEX array, dimension (NMAX*NRHS)

          X is COMPLEX array, dimension (NMAX*NRHS)

XACT

          XACT is COMPLEX array, dimension (NMAX*NRHS)

          S is REAL array, dimension (2*NMAX)

WORK

          WORK is COMPLEX array, dimension
                      (NMAX*max(3,NRHS))

RWORK

          RWORK is REAL array, dimension (2*NRHS+NMAX)

IWORK

          IWORK is INTEGER array, dimension (NMAX)

NOUT

          NOUT is INTEGER
          The unit number for output.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2015

Purpose:

 CDRVGE tests the driver routines CGESV, -SVX, and -SVXX.
 Note that this file is used only when the XBLAS are available,
 otherwise cdrvge.f defines this subroutine.

Parameters:

DOTYPE

          DOTYPE is LOGICAL array, dimension (NTYPES)
          The matrix types to be used for testing.  Matrices of type j
          (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
          .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.

          NN is INTEGER
          The number of values of N contained in the vector NVAL.

NVAL

          NVAL is INTEGER array, dimension (NN)
          The values of the matrix column dimension N.

NRHS

          NRHS is INTEGER
          The number of right hand side vectors to be generated for
          each linear system.

THRESH

          THRESH is REAL
          The threshold value for the test ratios.  A result is
          included in the output file if RESULT >= THRESH.  To have
          every test ratio printed, use THRESH = 0.

TSTERR

          TSTERR is LOGICAL
          Flag that indicates whether error exits are to be tested.

NMAX

          NMAX is INTEGER
          The maximum value permitted for N, used in dimensioning the
          work arrays.

          A is COMPLEX array, dimension (NMAX*NMAX)

AFAC

          AFAC is COMPLEX array, dimension (NMAX*NMAX)

ASAV

          ASAV is COMPLEX array, dimension (NMAX*NMAX)

          B is COMPLEX array, dimension (NMAX*NRHS)

BSAV

          BSAV is COMPLEX array, dimension (NMAX*NRHS)

          X is COMPLEX array, dimension (NMAX*NRHS)

XACT

          XACT is COMPLEX array, dimension (NMAX*NRHS)

          S is REAL array, dimension (2*NMAX)

WORK

          WORK is COMPLEX array, dimension
                      (NMAX*max(3,NRHS))

RWORK

          RWORK is REAL array, dimension (2*NRHS+NMAX)

IWORK

          IWORK is INTEGER array, dimension (NMAX)

NOUT

          NOUT is INTEGER
          The unit number for output.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: April 2012

subroutine cdrvgt (logical, dimension( * ) DOTYPE, integer NN, integer, dimension( * ) NVAL, integer NRHS, real THRESH, logical TSTERR, complex, dimension( * ) A, complex, dimension( * ) AF, complex, dimension( * ) B, complex, dimension( * ) X, complex, dimension( * ) XACT, complex, dimension( * ) WORK, real, dimension( * ) RWORK, integer, dimension( * ) IWORK, integer NOUT)

CDRVGT

Purpose:

 CDRVGT tests CGTSV and -SVX.

Parameters:

DOTYPE

          DOTYPE is LOGICAL array, dimension (NTYPES)
          The matrix types to be used for testing.  Matrices of type j
          (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
          .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.

          NN is INTEGER
          The number of values of N contained in the vector NVAL.

NVAL

          NVAL is INTEGER array, dimension (NN)
          The values of the matrix dimension N.

NRHS

          NRHS is INTEGER
          The number of right hand sides, NRHS >= 0.

THRESH

          THRESH is REAL
          The threshold value for the test ratios.  A result is
          included in the output file if RESULT >= THRESH.  To have
          every test ratio printed, use THRESH = 0.

TSTERR

          TSTERR is LOGICAL
          Flag that indicates whether error exits are to be tested.

          A is COMPLEX array, dimension (NMAX*4)

          AF is COMPLEX array, dimension (NMAX*4)

          B is COMPLEX array, dimension (NMAX*NRHS)

          X is COMPLEX array, dimension (NMAX*NRHS)

XACT

          XACT is COMPLEX array, dimension (NMAX*NRHS)

WORK

          WORK is COMPLEX array, dimension
                      (NMAX*max(3,NRHS))

RWORK

          RWORK is REAL array, dimension (NMAX+2*NRHS)

IWORK

          IWORK is INTEGER array, dimension (2*NMAX)

NOUT

          NOUT is INTEGER
          The unit number for output.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine cdrvhe (logical, dimension( * ) DOTYPE, integer NN, integer, dimension( * ) NVAL, integer NRHS, real THRESH, logical TSTERR, integer NMAX, complex, dimension( * ) A, complex, dimension( * ) AFAC, complex, dimension( * ) AINV, complex, dimension( * ) B, complex, dimension( * ) X, complex, dimension( * ) XACT, complex, dimension( * ) WORK, real, dimension( * ) RWORK, integer, dimension( * ) IWORK, integer NOUT)

CDRVHE CDRVHEX

Purpose:

 CDRVHE tests the driver routines CHESV and -SVX.

Parameters:

DOTYPE

          DOTYPE is LOGICAL array, dimension (NTYPES)
          The matrix types to be used for testing.  Matrices of type j
          (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
          .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.

          NN is INTEGER
          The number of values of N contained in the vector NVAL.

NVAL

          NVAL is INTEGER array, dimension (NN)
          The values of the matrix dimension N.

NRHS

          NRHS is INTEGER
          The number of right hand side vectors to be generated for
          each linear system.

THRESH

          THRESH is REAL
          The threshold value for the test ratios.  A result is
          included in the output file if RESULT >= THRESH.  To have
          every test ratio printed, use THRESH = 0.

TSTERR

          TSTERR is LOGICAL
          Flag that indicates whether error exits are to be tested.

NMAX

          NMAX is INTEGER
          The maximum value permitted for N, used in dimensioning the
          work arrays.

          A is COMPLEX array, dimension (NMAX*NMAX)

AFAC

          AFAC is COMPLEX array, dimension (NMAX*NMAX)

AINV

          AINV is COMPLEX array, dimension (NMAX*NMAX)

          B is COMPLEX array, dimension (NMAX*NRHS)

          X is COMPLEX array, dimension (NMAX*NRHS)

XACT

          XACT is COMPLEX array, dimension (NMAX*NRHS)

WORK

          WORK is COMPLEX array, dimension (NMAX*max(2,NRHS))

RWORK

          RWORK is REAL array, dimension (NMAX+2*NRHS)

IWORK

          IWORK is INTEGER array, dimension (NMAX)

NOUT

          NOUT is INTEGER
          The unit number for output.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2013

Purpose:

 CDRVHE tests the driver routines CHESV, -SVX, and -SVXX.
 Note that this file is used only when the XBLAS are available,
 otherwise cdrvhe.f defines this subroutine.

Parameters:

DOTYPE

          DOTYPE is LOGICAL array, dimension (NTYPES)
          The matrix types to be used for testing.  Matrices of type j
          (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
          .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.

          NN is INTEGER
          The number of values of N contained in the vector NVAL.

NVAL

          NVAL is INTEGER array, dimension (NN)
          The values of the matrix dimension N.

NRHS

          NRHS is INTEGER
          The number of right hand side vectors to be generated for
          each linear system.

THRESH

          THRESH is REAL
          The threshold value for the test ratios.  A result is
          included in the output file if RESULT >= THRESH.  To have
          every test ratio printed, use THRESH = 0.

TSTERR

          TSTERR is LOGICAL
          Flag that indicates whether error exits are to be tested.

NMAX

          NMAX is INTEGER
          The maximum value permitted for N, used in dimensioning the
          work arrays.

          A is COMPLEX array, dimension (NMAX*NMAX)

AFAC

          AFAC is COMPLEX array, dimension (NMAX*NMAX)

AINV

          AINV is COMPLEX array, dimension (NMAX*NMAX)

          B is COMPLEX array, dimension (NMAX*NRHS)

          X is COMPLEX array, dimension (NMAX*NRHS)

XACT

          XACT is COMPLEX array, dimension (NMAX*NRHS)

WORK

          WORK is COMPLEX array, dimension
                      (NMAX*max(2,NRHS))

RWORK

          RWORK is REAL array, dimension (2*NMAX+2*NRHS)

IWORK

          IWORK is INTEGER array, dimension (NMAX)

NOUT

          NOUT is INTEGER
          The unit number for output.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: April 2012

subroutine cdrvhe_rook (logical, dimension( * ) DOTYPE, integer NN, integer, dimension( * ) NVAL, integer NRHS, real THRESH, logical TSTERR, integer NMAX, complex, dimension( * ) A, complex, dimension( * ) AFAC, complex, dimension( * ) AINV, complex, dimension( * ) B, complex, dimension( * ) X, complex, dimension( * ) XACT, complex, dimension( * ) WORK, real, dimension( * ) RWORK, integer, dimension( * ) IWORK, integer NOUT)

CDRVHE_ROOK

Purpose:

 CDRVHE_ROOK tests the driver routines CHESV_ROOK.

Parameters:

DOTYPE

          DOTYPE is LOGICAL array, dimension (NTYPES)
          The matrix types to be used for testing.  Matrices of type j
          (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
          .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.

          NN is INTEGER
          The number of values of N contained in the vector NVAL.

NVAL

          NVAL is INTEGER array, dimension (NN)
          The values of the matrix dimension N.

NRHS

          NRHS is INTEGER
          The number of right hand side vectors to be generated for
          each linear system.

THRESH

          THRESH is REAL
          The threshold value for the test ratios.  A result is
          included in the output file if RESULT >= THRESH.  To have
          every test ratio printed, use THRESH = 0.

TSTERR

          TSTERR is LOGICAL
          Flag that indicates whether error exits are to be tested.

NMAX

          NMAX is INTEGER
          The maximum value permitted for N, used in dimensioning the
          work arrays.

          A is COMPLEX array, dimension (NMAX*NMAX)

AFAC

          AFAC is COMPLEX array, dimension (NMAX*NMAX)

AINV

          AINV is COMPLEX array, dimension (NMAX*NMAX)

          B is COMPLEX array, dimension (NMAX*NRHS)

          X is COMPLEX array, dimension (NMAX*NRHS)

XACT

          XACT is COMPLEX array, dimension (NMAX*NRHS)

WORK

          WORK is COMPLEX array, dimension (NMAX*max(2,NRHS))

RWORK

          RWORK is REAL array, dimension (NMAX+2*NRHS)

IWORK

          IWORK is INTEGER array, dimension (NMAX)

NOUT

          NOUT is INTEGER
          The unit number for output.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2013

subroutine cdrvhp (logical, dimension( * ) DOTYPE, integer NN, integer, dimension( * ) NVAL, integer NRHS, real THRESH, logical TSTERR, integer NMAX, complex, dimension( * ) A, complex, dimension( * ) AFAC, complex, dimension( * ) AINV, complex, dimension( * ) B, complex, dimension( * ) X, complex, dimension( * ) XACT, complex, dimension( * ) WORK, real, dimension( * ) RWORK, integer, dimension( * ) IWORK, integer NOUT)

CDRVHP

Purpose:

 CDRVHP tests the driver routines CHPSV and -SVX.

Parameters:

DOTYPE

          DOTYPE is LOGICAL array, dimension (NTYPES)
          The matrix types to be used for testing.  Matrices of type j
          (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
          .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.

          NN is INTEGER
          The number of values of N contained in the vector NVAL.

NVAL

          NVAL is INTEGER array, dimension (NN)
          The values of the matrix dimension N.

NRHS

          NRHS is INTEGER
          The number of right hand side vectors to be generated for
          each linear system.

THRESH

          THRESH is REAL
          The threshold value for the test ratios.  A result is
          included in the output file if RESULT >= THRESH.  To have
          every test ratio printed, use THRESH = 0.

TSTERR

          TSTERR is LOGICAL
          Flag that indicates whether error exits are to be tested.

NMAX

          NMAX is INTEGER
          The maximum value permitted for N, used in dimensioning the
          work arrays.

          A is COMPLEX array, dimension
                      (NMAX*(NMAX+1)/2)

AFAC

          AFAC is COMPLEX array, dimension
                      (NMAX*(NMAX+1)/2)

AINV

          AINV is COMPLEX array, dimension
                      (NMAX*(NMAX+1)/2)

          B is COMPLEX array, dimension (NMAX*NRHS)

          X is COMPLEX array, dimension (NMAX*NRHS)

XACT

          XACT is COMPLEX array, dimension (NMAX*NRHS)

WORK

          WORK is COMPLEX array, dimension
                      (NMAX*max(2,NRHS))

RWORK

          RWORK is REAL array, dimension (NMAX+2*NRHS)

IWORK

          IWORK is INTEGER array, dimension (NMAX)

NOUT

          NOUT is INTEGER
          The unit number for output.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine cdrvls (logical, dimension( * ) DOTYPE, integer NM, integer, dimension( * ) MVAL, integer NN, integer, dimension( * ) NVAL, integer NNS, integer, dimension( * ) NSVAL, integer NNB, integer, dimension( * ) NBVAL, integer, dimension( * ) NXVAL, real THRESH, logical TSTERR, complex, dimension( * ) A, complex, dimension( * ) COPYA, complex, dimension( * ) B, complex, dimension( * ) COPYB, complex, dimension( * ) C, real, dimension( * ) S, real, dimension( * ) COPYS, complex, dimension( * ) WORK, real, dimension( * ) RWORK, integer, dimension( * ) IWORK, integer NOUT)

CDRVLS

Purpose:

 CDRVLS tests the least squares driver routines CGELS, CGELSS, CGELSY
 and CGELSD.

Parameters:

DOTYPE

          DOTYPE is LOGICAL array, dimension (NTYPES)
          The matrix types to be used for testing.  Matrices of type j
          (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
          .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
          The matrix of type j is generated as follows:
          j=1: A = U*D*V where U and V are random unitary matrices
               and D has random entries (> 0.1) taken from a uniform
               distribution (0,1). A is full rank.
          j=2: The same of 1, but A is scaled up.
          j=3: The same of 1, but A is scaled down.
          j=4: A = U*D*V where U and V are random unitary matrices
               and D has 3*min(M,N)/4 random entries (> 0.1) taken
               from a uniform distribution (0,1) and the remaining
               entries set to 0. A is rank-deficient.
          j=5: The same of 4, but A is scaled up.
          j=6: The same of 5, but A is scaled down.

          NM is INTEGER
          The number of values of M contained in the vector MVAL.

MVAL

          MVAL is INTEGER array, dimension (NM)
          The values of the matrix row dimension M.

          NN is INTEGER
          The number of values of N contained in the vector NVAL.

NVAL

          NVAL is INTEGER array, dimension (NN)
          The values of the matrix column dimension N.

NNB

          NNB is INTEGER
          The number of values of NB and NX contained in the
          vectors NBVAL and NXVAL.  The blocking parameters are used
          in pairs (NB,NX).

NBVAL

          NBVAL is INTEGER array, dimension (NNB)
          The values of the blocksize NB.

NXVAL

          NXVAL is INTEGER array, dimension (NNB)
          The values of the crossover point NX.

NNS

          NNS is INTEGER
          The number of values of NRHS contained in the vector NSVAL.

NSVAL

          NSVAL is INTEGER array, dimension (NNS)
          The values of the number of right hand sides NRHS.

THRESH

          THRESH is REAL
          The threshold value for the test ratios.  A result is
          included in the output file if RESULT >= THRESH.  To have
          every test ratio printed, use THRESH = 0.

TSTERR

          TSTERR is LOGICAL
          Flag that indicates whether error exits are to be tested.

          A is COMPLEX array, dimension (MMAX*NMAX)
          where MMAX is the maximum value of M in MVAL and NMAX is the
          maximum value of N in NVAL.

COPYA

          COPYA is COMPLEX array, dimension (MMAX*NMAX)

          B is COMPLEX array, dimension (MMAX*NSMAX)
          where MMAX is the maximum value of M in MVAL and NSMAX is the
          maximum value of NRHS in NSVAL.

COPYB

          COPYB is COMPLEX array, dimension (MMAX*NSMAX)

          C is COMPLEX array, dimension (MMAX*NSMAX)

          S is REAL array, dimension
                      (min(MMAX,NMAX))

COPYS

          COPYS is REAL array, dimension
                      (min(MMAX,NMAX))

WORK

          WORK is COMPLEX array, dimension
                      (MMAX*NMAX + 4*NMAX + MMAX).

RWORK

          RWORK is REAL array, dimension (5*NMAX-1)

IWORK

          IWORK is INTEGER array, dimension (15*NMAX)

NOUT

          NOUT is INTEGER
          The unit number for output.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2015

subroutine cdrvpb (logical, dimension( * ) DOTYPE, integer NN, integer, dimension( * ) NVAL, integer NRHS, real THRESH, logical TSTERR, integer NMAX, complex, dimension( * ) A, complex, dimension( * ) AFAC, complex, dimension( * ) ASAV, complex, dimension( * ) B, complex, dimension( * ) BSAV, complex, dimension( * ) X, complex, dimension( * ) XACT, real, dimension( * ) S, complex, dimension( * ) WORK, real, dimension( * ) RWORK, integer NOUT)

CDRVPB

Purpose:

 CDRVPB tests the driver routines CPBSV and -SVX.

Parameters:

DOTYPE

          DOTYPE is LOGICAL array, dimension (NTYPES)
          The matrix types to be used for testing.  Matrices of type j
          (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
          .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.

          NN is INTEGER
          The number of values of N contained in the vector NVAL.

NVAL

          NVAL is INTEGER array, dimension (NN)
          The values of the matrix dimension N.

NRHS

          NRHS is INTEGER
          The number of right hand side vectors to be generated for
          each linear system.

THRESH

          THRESH is REAL
          The threshold value for the test ratios.  A result is
          included in the output file if RESULT >= THRESH.  To have
          every test ratio printed, use THRESH = 0.

TSTERR

          TSTERR is LOGICAL
          Flag that indicates whether error exits are to be tested.

NMAX

          NMAX is INTEGER
          The maximum value permitted for N, used in dimensioning the
          work arrays.

          A is COMPLEX array, dimension (NMAX*NMAX)

AFAC

          AFAC is COMPLEX array, dimension (NMAX*NMAX)

ASAV

          ASAV is COMPLEX array, dimension (NMAX*NMAX)

          B is COMPLEX array, dimension (NMAX*NRHS)

BSAV

          BSAV is COMPLEX array, dimension (NMAX*NRHS)

          X is COMPLEX array, dimension (NMAX*NRHS)

XACT

          XACT is COMPLEX array, dimension (NMAX*NRHS)

          S is REAL array, dimension (NMAX)

WORK

          WORK is COMPLEX array, dimension
                      (NMAX*max(3,NRHS))

RWORK

          RWORK is REAL array, dimension (NMAX+2*NRHS)

NOUT

          NOUT is INTEGER
          The unit number for output.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine cdrvpo (logical, dimension( * ) DOTYPE, integer NN, integer, dimension( * ) NVAL, integer NRHS, real THRESH, logical TSTERR, integer NMAX, complex, dimension( * ) A, complex, dimension( * ) AFAC, complex, dimension( * ) ASAV, complex, dimension( * ) B, complex, dimension( * ) BSAV, complex, dimension( * ) X, complex, dimension( * ) XACT, real, dimension( * ) S, complex, dimension( * ) WORK, real, dimension( * ) RWORK, integer NOUT)

CDRVPO CDRVPOX

Purpose:

 CDRVPO tests the driver routines CPOSV and -SVX.

Parameters:

DOTYPE

          DOTYPE is LOGICAL array, dimension (NTYPES)
          The matrix types to be used for testing.  Matrices of type j
          (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
          .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.

          NN is INTEGER
          The number of values of N contained in the vector NVAL.

NVAL

          NVAL is INTEGER array, dimension (NN)
          The values of the matrix dimension N.

NRHS

          NRHS is INTEGER
          The number of right hand side vectors to be generated for
          each linear system.

THRESH

          THRESH is REAL
          The threshold value for the test ratios.  A result is
          included in the output file if RESULT >= THRESH.  To have
          every test ratio printed, use THRESH = 0.

TSTERR

          TSTERR is LOGICAL
          Flag that indicates whether error exits are to be tested.

NMAX

          NMAX is INTEGER
          The maximum value permitted for N, used in dimensioning the
          work arrays.

          A is COMPLEX array, dimension (NMAX*NMAX)

AFAC

          AFAC is COMPLEX array, dimension (NMAX*NMAX)

ASAV

          ASAV is COMPLEX array, dimension (NMAX*NMAX)

          B is COMPLEX array, dimension (NMAX*NRHS)

BSAV

          BSAV is COMPLEX array, dimension (NMAX*NRHS)

          X is COMPLEX array, dimension (NMAX*NRHS)

XACT

          XACT is COMPLEX array, dimension (NMAX*NRHS)

          S is REAL array, dimension (NMAX)

WORK

          WORK is COMPLEX array, dimension
                      (NMAX*max(3,NRHS))

RWORK

          RWORK is REAL array, dimension (NMAX+2*NRHS)

NOUT

          NOUT is INTEGER
          The unit number for output.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

Purpose:

 CDRVPO tests the driver routines CPOSV, -SVX, and -SVXX.
 Note that this file is used only when the XBLAS are available,
 otherwise cdrvpo.f defines this subroutine.

Parameters:

DOTYPE

          DOTYPE is LOGICAL array, dimension (NTYPES)
          The matrix types to be used for testing.  Matrices of type j
          (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
          .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.

          NN is INTEGER
          The number of values of N contained in the vector NVAL.

NVAL

          NVAL is INTEGER array, dimension (NN)
          The values of the matrix dimension N.

NRHS

          NRHS is INTEGER
          The number of right hand side vectors to be generated for
          each linear system.

THRESH

          THRESH is REAL
          The threshold value for the test ratios.  A result is
          included in the output file if RESULT >= THRESH.  To have
          every test ratio printed, use THRESH = 0.

TSTERR

          TSTERR is LOGICAL
          Flag that indicates whether error exits are to be tested.

NMAX

          NMAX is INTEGER
          The maximum value permitted for N, used in dimensioning the
          work arrays.

          A is COMPLEX array, dimension (NMAX*NMAX)

AFAC

          AFAC is COMPLEX array, dimension (NMAX*NMAX)

ASAV

          ASAV is COMPLEX array, dimension (NMAX*NMAX)

          B is COMPLEX array, dimension (NMAX*NRHS)

BSAV

          BSAV is COMPLEX array, dimension (NMAX*NRHS)

          X is COMPLEX array, dimension (NMAX*NRHS)

XACT

          XACT is COMPLEX array, dimension (NMAX*NRHS)

          S is REAL array, dimension (NMAX)

WORK

          WORK is COMPLEX array, dimension
                      (NMAX*max(3,NRHS))

RWORK

          RWORK is REAL array, dimension (NMAX+2*NRHS)

NOUT

          NOUT is INTEGER
          The unit number for output.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2013

subroutine cdrvpp (logical, dimension( * ) DOTYPE, integer NN, integer, dimension( * ) NVAL, integer NRHS, real THRESH, logical TSTERR, integer NMAX, complex, dimension( * ) A, complex, dimension( * ) AFAC, complex, dimension( * ) ASAV, complex, dimension( * ) B, complex, dimension( * ) BSAV, complex, dimension( * ) X, complex, dimension( * ) XACT, real, dimension( * ) S, complex, dimension( * ) WORK, real, dimension( * ) RWORK, integer NOUT)

CDRVPP

Purpose:

 CDRVPP tests the driver routines CPPSV and -SVX.

Parameters:

DOTYPE

          DOTYPE is LOGICAL array, dimension (NTYPES)
          The matrix types to be used for testing.  Matrices of type j
          (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
          .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.

          NN is INTEGER
          The number of values of N contained in the vector NVAL.

NVAL

          NVAL is INTEGER array, dimension (NN)
          The values of the matrix dimension N.

NRHS

          NRHS is INTEGER
          The number of right hand side vectors to be generated for
          each linear system.

THRESH

          THRESH is REAL
          The threshold value for the test ratios.  A result is
          included in the output file if RESULT >= THRESH.  To have
          every test ratio printed, use THRESH = 0.

TSTERR

          TSTERR is LOGICAL
          Flag that indicates whether error exits are to be tested.

NMAX

          NMAX is INTEGER
          The maximum value permitted for N, used in dimensioning the
          work arrays.

          A is COMPLEX array, dimension (NMAX*(NMAX+1)/2)

AFAC

          AFAC is COMPLEX array, dimension (NMAX*(NMAX+1)/2)

ASAV

          ASAV is COMPLEX array, dimension (NMAX*(NMAX+1)/2)

          B is COMPLEX array, dimension (NMAX*NRHS)

BSAV

          BSAV is COMPLEX array, dimension (NMAX*NRHS)

          X is COMPLEX array, dimension (NMAX*NRHS)

XACT

          XACT is COMPLEX array, dimension (NMAX*NRHS)

          S is REAL array, dimension (NMAX)

WORK

          WORK is COMPLEX array, dimension
                      (NMAX*max(3,NRHS))

RWORK

          RWORK is REAL array, dimension (NMAX+2*NRHS)

NOUT

          NOUT is INTEGER
          The unit number for output.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine cdrvpt (logical, dimension( * ) DOTYPE, integer NN, integer, dimension( * ) NVAL, integer NRHS, real THRESH, logical TSTERR, complex, dimension( * ) A, real, dimension( * ) D, complex, dimension( * ) E, complex, dimension( * ) B, complex, dimension( * ) X, complex, dimension( * ) XACT, complex, dimension( * ) WORK, real, dimension( * ) RWORK, integer NOUT)

CDRVPT

Purpose:

 CDRVPT tests CPTSV and -SVX.

Parameters:

DOTYPE

          DOTYPE is LOGICAL array, dimension (NTYPES)
          The matrix types to be used for testing.  Matrices of type j
          (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
          .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.

          NN is INTEGER
          The number of values of N contained in the vector NVAL.

NVAL

          NVAL is INTEGER array, dimension (NN)
          The values of the matrix dimension N.

NRHS

          NRHS is INTEGER
          The number of right hand side vectors to be generated for
          each linear system.

THRESH

          THRESH is REAL
          The threshold value for the test ratios.  A result is
          included in the output file if RESULT >= THRESH.  To have
          every test ratio printed, use THRESH = 0.

TSTERR

          TSTERR is LOGICAL
          Flag that indicates whether error exits are to be tested.

          A is COMPLEX array, dimension (NMAX*2)

          D is REAL array, dimension (NMAX*2)

          E is COMPLEX array, dimension (NMAX*2)

          B is COMPLEX array, dimension (NMAX*NRHS)

          X is COMPLEX array, dimension (NMAX*NRHS)

XACT

          XACT is COMPLEX array, dimension (NMAX*NRHS)

WORK

          WORK is COMPLEX array, dimension
                      (NMAX*max(3,NRHS))

RWORK

          RWORK is REAL array, dimension (NMAX+2*NRHS)

NOUT

          NOUT is INTEGER
          The unit number for output.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine cdrvrf1 (integer NOUT, integer NN, integer, dimension( nn ) NVAL, real THRESH, complex, dimension( lda, * ) A, integer LDA, complex, dimension( * ) ARF, real, dimension( * ) WORK)

CDRVRF1

Purpose:

 CDRVRF1 tests the LAPACK RFP routines:
     CLANHF.F

Parameters:

NOUT

          NOUT is INTEGER
                The unit number for output.

          NN is INTEGER
                The number of values of N contained in the vector NVAL.

NVAL

          NVAL is INTEGER array, dimension (NN)
                The values of the matrix dimension N.

THRESH

          THRESH is REAL
                The threshold value for the test ratios.  A result is
                included in the output file if RESULT >= THRESH.  To have
                every test ratio printed, use THRESH = 0.

          A is COMPLEX array, dimension (LDA,NMAX)

LDA

          LDA is INTEGER
                The leading dimension of the array A.  LDA >= max(1,NMAX).

ARF

          ARF is COMPLEX array, dimension ((NMAX*(NMAX+1))/2).

WORK

          WORK is COMPLEX array, dimension ( NMAX )

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine cdrvrf2 (integer NOUT, integer NN, integer, dimension( nn ) NVAL, complex, dimension( lda, * ) A, integer LDA, complex, dimension( * ) ARF, complex, dimension() AP, complex, dimension( lda, ) ASAV)

CDRVRF2

Purpose:

 CDRVRF2 tests the LAPACK RFP conversion routines.

Parameters:

NOUT

          NOUT is INTEGER
                The unit number for output.

          NN is INTEGER
                The number of values of N contained in the vector NVAL.

NVAL

          NVAL is INTEGER array, dimension (NN)
                The values of the matrix dimension N.

          A is COMPLEX array, dimension (LDA,NMAX)

LDA

          LDA is INTEGER
                The leading dimension of the array A.  LDA >= max(1,NMAX).

ARF

          ARF is COMPLEX array, dimension ((NMAX*(NMAX+1))/2).

          AP is COMPLEX array, dimension ((NMAX*(NMAX+1))/2).

ASAV

          ASAV is COMPLEX6 array, dimension (LDA,NMAX)

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine cdrvrf3 (integer NOUT, integer NN, integer, dimension( nn ) NVAL, real THRESH, complex, dimension( lda, * ) A, integer LDA, complex, dimension( * ) ARF, complex, dimension( lda, * ) B1, complex, dimension( lda, * ) B2, real, dimension( * ) S_WORK_CLANGE, complex, dimension( * ) C_WORK_CGEQRF, complex, dimension( * ) TAU)

CDRVRF3

Purpose:

 CDRVRF3 tests the LAPACK RFP routines:
     CTFSM

Parameters:

NOUT

          NOUT is INTEGER
                The unit number for output.

          NN is INTEGER
                The number of values of N contained in the vector NVAL.

NVAL

          NVAL is INTEGER array, dimension (NN)
                The values of the matrix dimension N.

THRESH

          THRESH is DOUBLE PRECISION
                The threshold value for the test ratios.  A result is
                included in the output file if RESULT >= THRESH.  To have
                every test ratio printed, use THRESH = 0.

          A is COMPLEX*16 array, dimension (LDA,NMAX)

LDA

          LDA is INTEGER
                The leading dimension of the array A.  LDA >= max(1,NMAX).

ARF

          ARF is COMPLEX array, dimension ((NMAX*(NMAX+1))/2).

          B1 is COMPLEX array, dimension (LDA,NMAX)

          B2 is COMPLEX array, dimension (LDA,NMAX)

S_WORK_CLANGE

          S_WORK_CLANGE is REAL array, dimension (NMAX)

C_WORK_CGEQRF

          C_WORK_CGEQRF is COMPLEX array, dimension (NMAX)

TAU

          TAU is COMPLEX array, dimension (NMAX)

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine cdrvrf4 (integer NOUT, integer NN, integer, dimension( nn ) NVAL, real THRESH, complex, dimension( ldc, * ) C1, complex, dimension( ldc, ) C2, integer LDC, complex, dimension( ) CRF, complex, dimension( lda, * ) A, integer LDA, real, dimension( * ) S_WORK_CLANGE)

CDRVRF4

Purpose:

 CDRVRF4 tests the LAPACK RFP routines:
     CHFRK

Parameters:

NOUT

          NOUT is INTEGER
                The unit number for output.

          NN is INTEGER
                The number of values of N contained in the vector NVAL.

NVAL

          NVAL is INTEGER array, dimension (NN)
                The values of the matrix dimension N.

THRESH

          THRESH is REAL
                The threshold value for the test ratios.  A result is
                included in the output file if RESULT >= THRESH.  To have
                every test ratio printed, use THRESH = 0.

          C1 is COMPLEX array, dimension (LDC,NMAX)

          C2 is COMPLEX array, dimension (LDC,NMAX)

LDC

          LDC is INTEGER
                The leading dimension of the array A.  LDA >= max(1,NMAX).

CRF

          CRF is COMPLEX array, dimension ((NMAX*(NMAX+1))/2).

          A is COMPLEX array, dimension (LDA,NMAX)

LDA

          LDA is INTEGER
                The leading dimension of the array A.  LDA >= max(1,NMAX).

S_WORK_CLANGE

          S_WORK_CLANGE is REAL array, dimension (NMAX)

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine cdrvrfp (integer NOUT, integer NN, integer, dimension( nn ) NVAL, integer NNS, integer, dimension( nns ) NSVAL, integer NNT, integer, dimension( nnt ) NTVAL, real THRESH, complex, dimension( * ) A, complex, dimension( * ) ASAV, complex, dimension( * ) AFAC, complex, dimension( * ) AINV, complex, dimension( * ) B, complex, dimension( * ) BSAV, complex, dimension( * ) XACT, complex, dimension( * ) X, complex, dimension( * ) ARF, complex, dimension( * ) ARFINV, complex, dimension( * ) C_WORK_CLATMS, complex, dimension( * ) C_WORK_CPOT02, complex, dimension( * ) C_WORK_CPOT03, real, dimension( * ) S_WORK_CLATMS, real, dimension( * ) S_WORK_CLANHE, real, dimension( * ) S_WORK_CPOT01, real, dimension( * ) S_WORK_CPOT02, real, dimension( * ) S_WORK_CPOT03)

CDRVRFP

Purpose:

 CDRVRFP tests the LAPACK RFP routines:
     CPFTRF, CPFTRS, and CPFTRI.
 This testing routine follow the same tests as CDRVPO (test for the full
 format Symmetric Positive Definite solver).
 The tests are performed in Full Format, conversion back and forth from
 full format to RFP format are performed using the routines CTRTTF and
 CTFTTR.
 First, a specific matrix A of size N is created. There is nine types of 
 different matrixes possible.
  1. Diagonal                        6. Random, CNDNUM = sqrt(0.1/EPS)
  2. Random, CNDNUM = 2              7. Random, CNDNUM = 0.1/EPS
 *3. First row and column zero       8. Scaled near underflow
 *4. Last row and column zero        9. Scaled near overflow
 *5. Middle row and column zero
 (* - tests error exits from CPFTRF, no test ratios are computed)
 A solution XACT of size N-by-NRHS is created and the associated right
 hand side B as well. Then CPFTRF is called to compute L (or U), the
 Cholesky factor of A. Then L (or U) is used to solve the linear system
 of equations AX = B. This gives X. Then L (or U) is used to compute the
 inverse of A, AINV. The following four tests are then performed:
 (1) norm( L*L' - A ) / ( N * norm(A) * EPS ) or
     norm( U'*U - A ) / ( N * norm(A) * EPS ),
 (2) norm(B - A*X) / ( norm(A) * norm(X) * EPS ),
 (3) norm( I - A*AINV ) / ( N * norm(A) * norm(AINV) * EPS ),
 (4) ( norm(X-XACT) * RCOND ) / ( norm(XACT) * EPS ),
 where EPS is the machine precision, RCOND the condition number of A, and
 norm( . ) the 1-norm for (1,2,3) and the inf-norm for (4).
 Errors occur when INFO parameter is not as expected. Failures occur when
 a test ratios is greater than THRES.

Parameters:

NOUT

          NOUT is INTEGER
                The unit number for output.

          NN is INTEGER
                The number of values of N contained in the vector NVAL.

NVAL

          NVAL is INTEGER array, dimension (NN)
                The values of the matrix dimension N.

NNS

          NNS is INTEGER
                The number of values of NRHS contained in the vector NSVAL.

NSVAL

          NSVAL is INTEGER array, dimension (NNS)
                The values of the number of right-hand sides NRHS.

NNT

          NNT is INTEGER
                The number of values of MATRIX TYPE contained in the vector NTVAL.

NTVAL

          NTVAL is INTEGER array, dimension (NNT)
                The values of matrix type (between 0 and 9 for PO/PP/PF matrices).

THRESH

          THRESH is REAL
                The threshold value for the test ratios.  A result is
                included in the output file if RESULT >= THRESH.  To have
                every test ratio printed, use THRESH = 0.

          A is COMPLEX array, dimension (NMAX*NMAX)

ASAV

          ASAV is COMPLEX array, dimension (NMAX*NMAX)

AFAC

          AFAC is COMPLEX array, dimension (NMAX*NMAX)

AINV

          AINV is COMPLEX array, dimension (NMAX*NMAX)

          B is COMPLEX array, dimension (NMAX*MAXRHS)

BSAV

          BSAV is COMPLEX array, dimension (NMAX*MAXRHS)

XACT

          XACT is COMPLEX array, dimension (NMAX*MAXRHS)

          X is COMPLEX array, dimension (NMAX*MAXRHS)

ARF

          ARF is COMPLEX array, dimension ((NMAX*(NMAX+1))/2)

ARFINV

          ARFINV is COMPLEX array, dimension ((NMAX*(NMAX+1))/2)

C_WORK_CLATMS

          C_WORK_CLATMS is COMPLEX array, dimension ( 3*NMAX )

C_WORK_CPOT02

          C_WORK_CPOT02 is COMPLEX array, dimension ( NMAX*MAXRHS )

C_WORK_CPOT03

          C_WORK_CPOT03 is COMPLEX array, dimension ( NMAX*NMAX )

S_WORK_CLATMS

          S_WORK_CLATMS is REAL array, dimension ( NMAX )

S_WORK_CLANHE

          S_WORK_CLANHE is REAL array, dimension ( NMAX )

S_WORK_CPOT01

          S_WORK_CPOT01 is REAL array, dimension ( NMAX )

S_WORK_CPOT02

          S_WORK_CPOT02 is REAL array, dimension ( NMAX )

S_WORK_CPOT03

          S_WORK_CPOT03 is REAL array, dimension ( NMAX )

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2013

subroutine cdrvsp (logical, dimension( * ) DOTYPE, integer NN, integer, dimension( * ) NVAL, integer NRHS, real THRESH, logical TSTERR, integer NMAX, complex, dimension( * ) A, complex, dimension( * ) AFAC, complex, dimension( * ) AINV, complex, dimension( * ) B, complex, dimension( * ) X, complex, dimension( * ) XACT, complex, dimension( * ) WORK, real, dimension( * ) RWORK, integer, dimension( * ) IWORK, integer NOUT)

CDRVSP

Purpose:

 CDRVSP tests the driver routines CSPSV and -SVX.

Parameters:

DOTYPE

          DOTYPE is LOGICAL array, dimension (NTYPES)
          The matrix types to be used for testing.  Matrices of type j
          (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
          .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.

          NN is INTEGER
          The number of values of N contained in the vector NVAL.

NVAL

          NVAL is INTEGER array, dimension (NN)
          The values of the matrix dimension N.

NRHS

          NRHS is INTEGER
          The number of right hand side vectors to be generated for
          each linear system.

THRESH

          THRESH is REAL
          The threshold value for the test ratios.  A result is
          included in the output file if RESULT >= THRESH.  To have
          every test ratio printed, use THRESH = 0.

TSTERR

          TSTERR is LOGICAL
          Flag that indicates whether error exits are to be tested.

NMAX

          NMAX is INTEGER
          The maximum value permitted for N, used in dimensioning the
          work arrays.

          A is COMPLEX array, dimension
                      (NMAX*(NMAX+1)/2)

AFAC

          AFAC is COMPLEX array, dimension
                      (NMAX*(NMAX+1)/2)

AINV

          AINV is COMPLEX array, dimension
                      (NMAX*(NMAX+1)/2)

          B is COMPLEX array, dimension (NMAX*NRHS)

          X is COMPLEX array, dimension (NMAX*NRHS)

XACT

          XACT is COMPLEX array, dimension (NMAX*NRHS)

WORK

          WORK is COMPLEX array, dimension
                      (NMAX*max(2,NRHS))

RWORK

          RWORK is REAL array, dimension (NMAX+2*NRHS)

IWORK

          IWORK is INTEGER array, dimension (NMAX)

NOUT

          NOUT is INTEGER
          The unit number for output.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine cdrvsy (logical, dimension( * ) DOTYPE, integer NN, integer, dimension( * ) NVAL, integer NRHS, real THRESH, logical TSTERR, integer NMAX, complex, dimension( * ) A, complex, dimension( * ) AFAC, complex, dimension( * ) AINV, complex, dimension( * ) B, complex, dimension( * ) X, complex, dimension( * ) XACT, complex, dimension( * ) WORK, real, dimension( * ) RWORK, integer, dimension( * ) IWORK, integer NOUT)

CDRVSY CDRVSYX

Purpose:

 CDRVSY tests the driver routines CSYSV and -SVX.

Parameters:

DOTYPE

          DOTYPE is LOGICAL array, dimension (NTYPES)
          The matrix types to be used for testing.  Matrices of type j
          (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
          .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.

          NN is INTEGER
          The number of values of N contained in the vector NVAL.

NVAL

          NVAL is INTEGER array, dimension (NN)
          The values of the matrix dimension N.

NRHS

          NRHS is INTEGER
          The number of right hand side vectors to be generated for
          each linear system.

THRESH

          THRESH is REAL
          The threshold value for the test ratios.  A result is
          included in the output file if RESULT >= THRESH.  To have
          every test ratio printed, use THRESH = 0.

TSTERR

          TSTERR is LOGICAL
          Flag that indicates whether error exits are to be tested.

NMAX

          NMAX is INTEGER
          The maximum value permitted for N, used in dimensioning the
          work arrays.

          A is COMPLEX array, dimension (NMAX*NMAX)

AFAC

          AFAC is COMPLEX array, dimension (NMAX*NMAX)

AINV

          AINV is COMPLEX array, dimension (NMAX*NMAX)

          B is COMPLEX array, dimension (NMAX*NRHS)

          X is COMPLEX array, dimension (NMAX*NRHS)

XACT

          XACT is COMPLEX array, dimension (NMAX*NRHS)

WORK

          WORK is COMPLEX array, dimension (NMAX*max(2,NRHS))

RWORK

          RWORK is REAL array, dimension (NMAX+2*NRHS)

IWORK

          IWORK is INTEGER array, dimension (NMAX)

NOUT

          NOUT is INTEGER
          The unit number for output.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2013

Purpose:

 CDRVSY tests the driver routines CSYSV, -SVX, and -SVXX.
 Note that this file is used only when the XBLAS are available,
 otherwise cdrvsy.f defines this subroutine.

Parameters:

DOTYPE

          DOTYPE is LOGICAL array, dimension (NTYPES)
          The matrix types to be used for testing.  Matrices of type j
          (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
          .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.

          NN is INTEGER
          The number of values of N contained in the vector NVAL.

NVAL

          NVAL is INTEGER array, dimension (NN)
          The values of the matrix dimension N.

NRHS

          NRHS is INTEGER
          The number of right hand side vectors to be generated for
          each linear system.

THRESH

          THRESH is REAL
          The threshold value for the test ratios.  A result is
          included in the output file if RESULT >= THRESH.  To have
          every test ratio printed, use THRESH = 0.

TSTERR

          TSTERR is LOGICAL
          Flag that indicates whether error exits are to be tested.

NMAX

          NMAX is INTEGER
          The maximum value permitted for N, used in dimensioning the
          work arrays.

          A is COMPLEX array, dimension (NMAX*NMAX)

AFAC

          AFAC is COMPLEX array, dimension (NMAX*NMAX)

AINV

          AINV is COMPLEX array, dimension (NMAX*NMAX)

          B is COMPLEX array, dimension (NMAX*NRHS)

          X is COMPLEX array, dimension (NMAX*NRHS)

XACT

          XACT is COMPLEX array, dimension (NMAX*NRHS)

WORK

          WORK is COMPLEX array, dimension
                      (NMAX*max(2,NRHS))

RWORK

          RWORK is REAL array, dimension (2*NMAX+2*NRHS)

IWORK

          IWORK is INTEGER array, dimension (NMAX)

NOUT

          NOUT is INTEGER
          The unit number for output.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: April 2012

subroutine cdrvsy_rook (logical, dimension( * ) DOTYPE, integer NN, integer, dimension( * ) NVAL, integer NRHS, real THRESH, logical TSTERR, integer NMAX, complex, dimension( * ) A, complex, dimension( * ) AFAC, complex, dimension( * ) AINV, complex, dimension( * ) B, complex, dimension( * ) X, complex, dimension( * ) XACT, complex, dimension( * ) WORK, real, dimension( * ) RWORK, integer, dimension( * ) IWORK, integer NOUT)

CDRVSY_ROOK

Purpose:

 CDRVSY_ROOK tests the driver routines CSYSV_ROOK.

Parameters:

DOTYPE

          DOTYPE is LOGICAL array, dimension (NTYPES)
          The matrix types to be used for testing.  Matrices of type j
          (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
          .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.

          NN is INTEGER
          The number of values of N contained in the vector NVAL.

NVAL

          NVAL is INTEGER array, dimension (NN)
          The values of the matrix dimension N.

NRHS

          NRHS is INTEGER
          The number of right hand side vectors to be generated for
          each linear system.

THRESH

          THRESH is REAL
          The threshold value for the test ratios.  A result is
          included in the output file if RESULT >= THRESH.  To have
          every test ratio printed, use THRESH = 0.

TSTERR

          TSTERR is LOGICAL
          Flag that indicates whether error exits are to be tested.

NMAX

          NMAX is INTEGER
          The maximum value permitted for N, used in dimensioning the
          work arrays.

          A is COMPLEX array, dimension (NMAX*NMAX)

AFAC

          AFAC is COMPLEX array, dimension (NMAX*NMAX)

AINV

          AINV is COMPLEX array, dimension (NMAX*NMAX)

          B is COMPLEX array, dimension (NMAX*NRHS)

          X is COMPLEX array, dimension (NMAX*NRHS)

XACT

          XACT is COMPLEX array, dimension (NMAX*NRHS)

WORK

RWORK

          RWORK is REAL array, dimension (NMAX+2*NRHS)

IWORK

          IWORK is INTEGER array, dimension (NMAX)

NOUT

          NOUT is INTEGER
          The unit number for output.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2013

subroutine cebchvxx (real THRESH, character*3 PATH)

CEBCHVXX Purpose:

  CEBCHVXX will run CGESVXX on a series of Hilbert matrices and then
  compare the error bounds returned by CGESVXX to see if the returned
  answer indeed falls within those bounds.
  Eight test ratios will be computed.  The tests will pass if they are .LT.
  THRESH.  There are two cases that are determined by 1 / (SQRT( N ) * EPS).
  If that value is .LE. to the component wise reciprocal condition number,
  it uses the guaranteed case, other wise it uses the unguaranteed case.
  Test ratios:
     Let Xc be X_computed and Xt be X_truth.
     The norm used is the infinity norm.
     Let A be the guaranteed case and B be the unguaranteed case.
       1. Normwise guaranteed forward error bound.
       A: norm ( abs( Xc - Xt ) / norm ( Xt ) .LE. ERRBND( *, nwise_i, bnd_i ) and
          ERRBND( *, nwise_i, bnd_i ) .LE. MAX(SQRT(N),10) * EPS.
          If these conditions are met, the test ratio is set to be
          ERRBND( *, nwise_i, bnd_i ) / MAX(SQRT(N), 10).  Otherwise it is 1/EPS.
       B: For this case, CGESVXX should just return 1.  If it is less than
          one, treat it the same as in 1A.  Otherwise it fails. (Set test
          ratio to ERRBND( *, nwise_i, bnd_i ) * THRESH?)
       2. Componentwise guaranteed forward error bound.
       A: norm ( abs( Xc(j) - Xt(j) ) ) / norm (Xt(j)) .LE. ERRBND( *, cwise_i, bnd_i )
          for all j .AND. ERRBND( *, cwise_i, bnd_i ) .LE. MAX(SQRT(N), 10) * EPS.
          If these conditions are met, the test ratio is set to be
          ERRBND( *, cwise_i, bnd_i ) / MAX(SQRT(N), 10).  Otherwise it is 1/EPS.
       B: Same as normwise test ratio.
       3. Backwards error.
       A: The test ratio is set to BERR/EPS.
       B: Same test ratio.
       4. Reciprocal condition number.
       A: A condition number is computed with Xt and compared with the one
          returned from CGESVXX.  Let RCONDc be the RCOND returned by CGESVXX
          and RCONDt be the RCOND from the truth value.  Test ratio is set to
          MAX(RCONDc/RCONDt, RCONDt/RCONDc).
       B: Test ratio is set to 1 / (EPS * RCONDc).
       5. Reciprocal normwise condition number.
       A: The test ratio is set to
          MAX(ERRBND( *, nwise_i, cond_i ) / NCOND, NCOND / ERRBND( *, nwise_i, cond_i )).
       B: Test ratio is set to 1 / (EPS * ERRBND( *, nwise_i, cond_i )).
       6. Reciprocal componentwise condition number.
       A: Test ratio is set to
          MAX(ERRBND( *, cwise_i, cond_i ) / CCOND, CCOND / ERRBND( *, cwise_i, cond_i )).
       B: Test ratio is set to 1 / (EPS * ERRBND( *, cwise_i, cond_i )).
     .. Parameters ..
     NMAX is determined by the largest number in the inverse of the hilbert
     matrix.  Precision is exhausted when the largest entry in it is greater
     than 2 to the power of the number of bits in the fraction of the data
     type used plus one, which is 24 for single precision.
     NMAX should be 6 for single and 11 for double.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine cerrge (character*3 PATH, integer NUNIT)

CERRGE CERRGEX

Purpose:

 CERRGE tests the error exits for the COMPLEX routines
 for general matrices.

Parameters:

PATH

          PATH is CHARACTER*3
          The LAPACK path name for the routines to be tested.

NUNIT

          NUNIT is INTEGER
          The unit number for output.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

Purpose:

 CERRGE tests the error exits for the COMPLEX routines
 for general matrices.
 Note that this file is used only when the XBLAS are available,
 otherwise cerrge.f defines this subroutine.

Parameters:

PATH

          PATH is CHARACTER*3
          The LAPACK path name for the routines to be tested.

NUNIT

          NUNIT is INTEGER
          The unit number for output.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine cerrgt (character*3 PATH, integer NUNIT)

CERRGT

Purpose:

 CERRGT tests the error exits for the COMPLEX tridiagonal
 routines.

Parameters:

PATH

          PATH is CHARACTER*3
          The LAPACK path name for the routines to be tested.

NUNIT

          NUNIT is INTEGER
          The unit number for output.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine cerrhe (character*3 PATH, integer NUNIT)

CERRHE CERRHEX

Purpose:

 CERRHE tests the error exits for the COMPLEX routines
 for Hermitian indefinite matrices.

Parameters:

PATH

          PATH is CHARACTER*3
          The LAPACK path name for the routines to be tested.

NUNIT

          NUNIT is INTEGER
          The unit number for output.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2013

Purpose:

 CERRHE tests the error exits for the COMPLEX routines
 for Hermitian indefinite matrices.
 Note that this file is used only when the XBLAS are available,
 otherwise cerrhe.f defines this subroutine.

Parameters:

PATH

          PATH is CHARACTER*3
          The LAPACK path name for the routines to be tested.

NUNIT

          NUNIT is INTEGER
          The unit number for output.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2015

subroutine cerrlq (character*3 PATH, integer NUNIT)

CERRLQ

Purpose:

 CERRLQ tests the error exits for the COMPLEX routines
 that use the LQ decomposition of a general matrix.

Parameters:

PATH

          PATH is CHARACTER*3
          The LAPACK path name for the routines to be tested.

NUNIT

          NUNIT is INTEGER
          The unit number for output.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine cerrls (character*3 PATH, integer NUNIT)

CERRLS

Purpose:

 CERRLS tests the error exits for the COMPLEX least squares
 driver routines (CGELS, CGELSS, CGELSY, CGELSD).

Parameters:

PATH

          PATH is CHARACTER*3
          The LAPACK path name for the routines to be tested.

NUNIT

          NUNIT is INTEGER
          The unit number for output.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2015

subroutine cerrpo (character*3 PATH, integer NUNIT)

CERRPO CERRPOX

Purpose:

 CERRPO tests the error exits for the COMPLEX routines
 for Hermitian positive definite matrices.

Parameters:

PATH

          PATH is CHARACTER*3
          The LAPACK path name for the routines to be tested.

NUNIT

          NUNIT is INTEGER
          The unit number for output.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

Purpose:

 CERRPO tests the error exits for the COMPLEX routines
 for Hermitian positive definite matrices.
 Note that this file is used only when the XBLAS are available,
 otherwise cerrpo.f defines this subroutine.

Parameters:

PATH

          PATH is CHARACTER*3
          The LAPACK path name for the routines to be tested.

NUNIT

          NUNIT is INTEGER
          The unit number for output.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2015

subroutine cerrps (character*3 PATH, integer NUNIT)

CERRPS

Purpose:

 CERRPS tests the error exits for the COMPLEX routines
 for CPSTRF..

Parameters:

PATH

          PATH is CHARACTER*3
          The LAPACK path name for the routines to be tested.

NUNIT

          NUNIT is INTEGER
          The unit number for output.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine cerrql (character*3 PATH, integer NUNIT)

CERRQL

Purpose:

 CERRQL tests the error exits for the COMPLEX routines
 that use the QL decomposition of a general matrix.

Parameters:

PATH

          PATH is CHARACTER*3
          The LAPACK path name for the routines to be tested.

NUNIT

          NUNIT is INTEGER
          The unit number for output.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine cerrqp (character*3 PATH, integer NUNIT)

CERRQP

Purpose:

 CERRQP tests the error exits for CGEQP3.

Parameters:

PATH

          PATH is CHARACTER*3
          The LAPACK path name for the routines to be tested.

NUNIT

          NUNIT is INTEGER
          The unit number for output.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2015

subroutine cerrqr (character*3 PATH, integer NUNIT)

CERRQR

Purpose:

 CERRQR tests the error exits for the COMPLEX routines
 that use the QR decomposition of a general matrix.

Parameters:

PATH

          PATH is CHARACTER*3
          The LAPACK path name for the routines to be tested.

NUNIT

          NUNIT is INTEGER
          The unit number for output.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine cerrqrt (character*3 PATH, integer NUNIT)

CERRQRT

Purpose:

 CERRQRT tests the error exits for the COMPLEX routines
 that use the QRT decomposition of a general matrix.

Parameters:

PATH

          PATH is CHARACTER*3
          The LAPACK path name for the routines to be tested.

NUNIT

          NUNIT is INTEGER
          The unit number for output.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine cerrqrtp (character*3 PATH, integer NUNIT)

CERRQRTP

Purpose:

 CERRQRTP tests the error exits for the REAL routines
 that use the QRT decomposition of a triangular-pentagonal matrix.

Parameters:

PATH

          PATH is CHARACTER*3
          The LAPACK path name for the routines to be tested.

NUNIT

          NUNIT is INTEGER
          The unit number for output.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine cerrrfp (integer NUNIT)

CERRRFP

Purpose:

 CERRRFP tests the error exits for the COMPLEX driver routines
 for solving linear systems of equations.
 CDRVRFP tests the COMPLEX LAPACK RFP routines:
     CTFSM, CTFTRI, CHFRK, CTFTTP, CTFTTR, CPFTRF, CPFTRS, CTPTTF,
     CTPTTR, CTRTTF, and CTRTTP

Parameters:

NUNIT

          NUNIT is INTEGER
          The unit number for output.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine cerrrq (character*3 PATH, integer NUNIT)

CERRRQ

Purpose:

 CERRRQ tests the error exits for the COMPLEX routines
 that use the RQ decomposition of a general matrix.

Parameters:

PATH

          PATH is CHARACTER*3
          The LAPACK path name for the routines to be tested.

NUNIT

          NUNIT is INTEGER
          The unit number for output.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine cerrsy (character*3 PATH, integer NUNIT)

CERRSY CERRSYX

Purpose:

 CERRSY tests the error exits for the COMPLEX routines
 for symmetric indefinite matrices.

Parameters:

PATH

          PATH is CHARACTER*3
          The LAPACK path name for the routines to be tested.

NUNIT

          NUNIT is INTEGER
          The unit number for output.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2013

Purpose:

 CERRSY tests the error exits for the COMPLEX routines
 for symmetric indefinite matrices.
 Note that this file is used only when the XBLAS are available,
 otherwise cerrsy.f defines this subroutine.

Parameters:

PATH

          PATH is CHARACTER*3
          The LAPACK path name for the routines to be tested.

NUNIT

          NUNIT is INTEGER
          The unit number for output.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2015

subroutine cerrtr (character*3 PATH, integer NUNIT)

CERRTR

Purpose:

 CERRTR tests the error exits for the COMPLEX triangular routines.

Parameters:

PATH

          PATH is CHARACTER*3
          The LAPACK path name for the routines to be tested.

NUNIT

          NUNIT is INTEGER
          The unit number for output.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine cerrtz (character*3 PATH, integer NUNIT)

CERRTZ

Purpose:

 CERRTZ tests the error exits for CTZRZF.

Parameters:

PATH

          PATH is CHARACTER*3
          The LAPACK path name for the routines to be tested.

NUNIT

          NUNIT is INTEGER
          The unit number for output.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2015

subroutine cerrvx (character*3 PATH, integer NUNIT)

CERRVX CERRVXX

Purpose:

 CERRVX tests the error exits for the COMPLEX driver routines
 for solving linear systems of equations.

Parameters:

PATH

          PATH is CHARACTER*3
          The LAPACK path name for the routines to be tested.

NUNIT

          NUNIT is INTEGER
          The unit number for output.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2013

Purpose:

 CERRVX tests the error exits for the COMPLEX driver routines
 for solving linear systems of equations.

Parameters:

PATH

          PATH is CHARACTER*3
          The LAPACK path name for the routines to be tested.

NUNIT

          NUNIT is INTEGER
          The unit number for output.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2015

subroutine cgbt01 (integer M, integer N, integer KL, integer KU, complex, dimension( lda, * ) A, integer LDA, complex, dimension( ldafac, * ) AFAC, integer LDAFAC, integer, dimension( * ) IPIV, complex, dimension( * ) WORK, real RESID)

CGBT01

Purpose:

 CGBT01 reconstructs a band matrix  A  from its L*U factorization and
 computes the residual:
    norm(L*U - A) / ( N * norm(A) * EPS ),
 where EPS is the machine epsilon.
 The expression L*U - A is computed one column at a time, so A and
 AFAC are not modified.

Parameters:

          M is INTEGER
          The number of rows of the matrix A.  M >= 0.

          N is INTEGER
          The number of columns of the matrix A.  N >= 0.

          KL is INTEGER
          The number of subdiagonals within the band of A.  KL >= 0.

          KU is INTEGER
          The number of superdiagonals within the band of A.  KU >= 0.

          A is COMPLEX array, dimension (LDA,N)
          The original matrix A in band storage, stored in rows 1 to
          KL+KU+1.

LDA

          LDA is INTEGER.
          The leading dimension of the array A.  LDA >= max(1,KL+KU+1).

AFAC

          AFAC is COMPLEX array, dimension (LDAFAC,N)
          The factored form of the matrix A.  AFAC contains the banded
          factors L and U from the L*U factorization, as computed by
          CGBTRF.  U is stored as an upper triangular band matrix with
          KL+KU superdiagonals in rows 1 to KL+KU+1, and the
          multipliers used during the factorization are stored in rows
          KL+KU+2 to 2*KL+KU+1.  See CGBTRF for further details.

LDAFAC

          LDAFAC is INTEGER
          The leading dimension of the array AFAC.
          LDAFAC >= max(1,2*KL*KU+1).

IPIV

          IPIV is INTEGER array, dimension (min(M,N))
          The pivot indices from CGBTRF.

WORK

          WORK is COMPLEX array, dimension (2*KL+KU+1)

RESID

          RESID is REAL
          norm(L*U - A) / ( N * norm(A) * EPS )

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine cgbt02 (character TRANS, integer M, integer N, integer KL, integer KU, integer NRHS, complex, dimension( lda, * ) A, integer LDA, complex, dimension( ldx, * ) X, integer LDX, complex, dimension( ldb, * ) B, integer LDB, real RESID)

CGBT02

Purpose:

 CGBT02 computes the residual for a solution of a banded system of
 equations  A*x = b  or  A'*x = b:
    RESID = norm( B - A*X ) / ( norm(A) * norm(X) * EPS).
 where EPS is the machine precision.

Parameters:

TRANS

          TRANS is CHARACTER*1
          Specifies the form of the system of equations:
          = 'N':  A *x = b
          = 'T':  A'*x = b, where A' is the transpose of A
          = 'C':  A'*x = b, where A' is the transpose of A

          M is INTEGER
          The number of rows of the matrix A.  M >= 0.

          N is INTEGER
          The number of columns of the matrix A.  N >= 0.

          KL is INTEGER
          The number of subdiagonals within the band of A.  KL >= 0.

          KU is INTEGER
          The number of superdiagonals within the band of A.  KU >= 0.

NRHS

          NRHS is INTEGER
          The number of columns of B.  NRHS >= 0.

          A is COMPLEX array, dimension (LDA,N)
          The original matrix A in band storage, stored in rows 1 to
          KL+KU+1.

LDA

          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,KL+KU+1).

          X is COMPLEX array, dimension (LDX,NRHS)
          The computed solution vectors for the system of linear
          equations.

LDX

          LDX is INTEGER
          The leading dimension of the array X.  If TRANS = 'N',
          LDX >= max(1,N); if TRANS = 'T' or 'C', LDX >= max(1,M).

          B is COMPLEX array, dimension (LDB,NRHS)
          On entry, the right hand side vectors for the system of
          linear equations.
          On exit, B is overwritten with the difference B - A*X.

LDB

          LDB is INTEGER
          The leading dimension of the array B.  IF TRANS = 'N',
          LDB >= max(1,M); if TRANS = 'T' or 'C', LDB >= max(1,N).

RESID

          RESID is REAL
          The maximum over the number of right hand sides of
          norm(B - A*X) / ( norm(A) * norm(X) * EPS ).

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine cgbt05 (character TRANS, integer N, integer KL, integer KU, integer NRHS, complex, dimension( ldab, * ) AB, integer LDAB, complex, dimension( ldb, * ) B, integer LDB, complex, dimension( ldx, * ) X, integer LDX, complex, dimension( ldxact, * ) XACT, integer LDXACT, real, dimension( * ) FERR, real, dimension( * ) BERR, real, dimension( * ) RESLTS)

CGBT05

Purpose:

 CGBT05 tests the error bounds from iterative refinement for the
 computed solution to a system of equations op(A)*X = B, where A is a
 general band matrix of order n with kl subdiagonals and ku
 superdiagonals and op(A) = A or A**T, depending on TRANS.
 RESLTS(1) = test of the error bound
           = norm(X - XACT) / ( norm(X) * FERR )
 A large value is returned if this ratio is not less than one.
 RESLTS(2) = residual from the iterative refinement routine
           = the maximum of BERR / ( NZ*EPS + (*) ), where
             (*) = NZ*UNFL / (min_i (abs(op(A))*abs(X) +abs(b))_i )
             and NZ = max. number of nonzeros in any row of A, plus 1

Parameters:

TRANS

          TRANS is CHARACTER*1
          Specifies the form of the system of equations.
          = 'N':  A * X = B     (No transpose)
          = 'T':  A**T * X = B  (Transpose)
          = 'C':  A**H * X = B  (Conjugate transpose = Transpose)

          N is INTEGER
          The number of rows of the matrices X, B, and XACT, and the
          order of the matrix A.  N >= 0.

          KL is INTEGER
          The number of subdiagonals within the band of A.  KL >= 0.

          KU is INTEGER
          The number of superdiagonals within the band of A.  KU >= 0.

NRHS

          NRHS is INTEGER
          The number of columns of the matrices X, B, and XACT.
          NRHS >= 0.

          AB is COMPLEX array, dimension (LDAB,N)
          The original band matrix A, stored in rows 1 to KL+KU+1.
          The j-th column of A is stored in the j-th column of the
          array AB as follows:
          AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(n,j+kl).

LDAB

          LDAB is INTEGER
          The leading dimension of the array AB.  LDAB >= KL+KU+1.

          B is COMPLEX array, dimension (LDB,NRHS)
          The right hand side vectors for the system of linear
          equations.

LDB

          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,N).

          X is COMPLEX array, dimension (LDX,NRHS)
          The computed solution vectors.  Each vector is stored as a
          column of the matrix X.

LDX

          LDX is INTEGER
          The leading dimension of the array X.  LDX >= max(1,N).

XACT

          XACT is COMPLEX array, dimension (LDX,NRHS)
          The exact solution vectors.  Each vector is stored as a
          column of the matrix XACT.

LDXACT

          LDXACT is INTEGER
          The leading dimension of the array XACT.  LDXACT >= max(1,N).

FERR

          FERR is REAL array, dimension (NRHS)
          The estimated forward error bounds for each solution vector
          X.  If XTRUE is the true solution, FERR bounds the magnitude
          of the largest entry in (X - XTRUE) divided by the magnitude
          of the largest entry in X.

BERR

          BERR is REAL array, dimension (NRHS)
          The componentwise relative backward error of each solution
          vector (i.e., the smallest relative change in any entry of A
          or B that makes X an exact solution).

RESLTS

          RESLTS is REAL array, dimension (2)
          The maximum over the NRHS solution vectors of the ratios:
          RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR )
          RESLTS(2) = BERR / ( NZ*EPS + (*) )

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine cgelqs (integer M, integer N, integer NRHS, complex, dimension( lda, * ) A, integer LDA, complex, dimension( * ) TAU, complex, dimension( ldb, * ) B, integer LDB, complex, dimension( lwork ) WORK, integer LWORK, integer INFO)

CGELQS

Purpose:

 Compute a minimum-norm solution
     min || A*X - B ||
 using the LQ factorization
     A = L*Q
 computed by CGELQF.

Parameters:

          M is INTEGER
          The number of rows of the matrix A.  M >= 0.

          N is INTEGER
          The number of columns of the matrix A.  N >= M >= 0.

NRHS

          NRHS is INTEGER
          The number of columns of B.  NRHS >= 0.

          A is COMPLEX array, dimension (LDA,N)
          Details of the LQ factorization of the original matrix A as
          returned by CGELQF.

LDA

          LDA is INTEGER
          The leading dimension of the array A.  LDA >= M.

TAU

          TAU is COMPLEX array, dimension (M)
          Details of the orthogonal matrix Q.

          B is COMPLEX array, dimension (LDB,NRHS)
          On entry, the m-by-nrhs right hand side matrix B.
          On exit, the n-by-nrhs solution matrix X.

LDB

          LDB is INTEGER
          The leading dimension of the array B. LDB >= N.

WORK

          WORK is COMPLEX array, dimension (LWORK)

LWORK

          LWORK is INTEGER
          The length of the array WORK.  LWORK must be at least NRHS,
          and should be at least NRHS*NB, where NB is the block size
          for this environment.

INFO

          INFO is INTEGER
          = 0: successful exit
          < 0: if INFO = -i, the i-th argument had an illegal value

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

logical function cgennd (integer M, integer N, complex, dimension( lda, * ) A, integer LDA)

CGENND

Purpose:

    CGENND tests that its argument has a real, non-negative diagonal.

Parameters:

          M is INTEGER
          The number of rows in A.

          N is INTEGER
          The number of columns in A.

          A is COMPLEX array, dimension (LDA, N)
          The matrix.

LDA

          LDA is INTEGER
          Leading dimension of A.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine cgeqls (integer M, integer N, integer NRHS, complex, dimension( lda, * ) A, integer LDA, complex, dimension( * ) TAU, complex, dimension( ldb, * ) B, integer LDB, complex, dimension( lwork ) WORK, integer LWORK, integer INFO)

CGEQLS

Purpose:

 Solve the least squares problem
     min || A*X - B ||
 using the QL factorization
     A = Q*L
 computed by CGEQLF.

Parameters:

          M is INTEGER
          The number of rows of the matrix A.  M >= 0.

          N is INTEGER
          The number of columns of the matrix A.  M >= N >= 0.

NRHS

          NRHS is INTEGER
          The number of columns of B.  NRHS >= 0.

          A is COMPLEX array, dimension (LDA,N)
          Details of the QL factorization of the original matrix A as
          returned by CGEQLF.

LDA

          LDA is INTEGER
          The leading dimension of the array A.  LDA >= M.

TAU

          TAU is COMPLEX array, dimension (N)
          Details of the orthogonal matrix Q.

          B is COMPLEX array, dimension (LDB,NRHS)
          On entry, the m-by-nrhs right hand side matrix B.
          On exit, the n-by-nrhs solution matrix X, stored in rows
          m-n+1:m.

LDB

          LDB is INTEGER
          The leading dimension of the array B. LDB >= M.

WORK

          WORK is COMPLEX array, dimension (LWORK)

LWORK

          LWORK is INTEGER
          The length of the array WORK.  LWORK must be at least NRHS,
          and should be at least NRHS*NB, where NB is the block size
          for this environment.

INFO

          INFO is INTEGER
          = 0: successful exit
          < 0: if INFO = -i, the i-th argument had an illegal value

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine cgeqrs (integer M, integer N, integer NRHS, complex, dimension( lda, * ) A, integer LDA, complex, dimension( * ) TAU, complex, dimension( ldb, * ) B, integer LDB, complex, dimension( lwork ) WORK, integer LWORK, integer INFO)

CGEQRS

Purpose:

 Solve the least squares problem
     min || A*X - B ||
 using the QR factorization
     A = Q*R
 computed by CGEQRF.

Parameters:

          M is INTEGER
          The number of rows of the matrix A.  M >= 0.

          N is INTEGER
          The number of columns of the matrix A.  M >= N >= 0.

NRHS

          NRHS is INTEGER
          The number of columns of B.  NRHS >= 0.

          A is COMPLEX array, dimension (LDA,N)
          Details of the QR factorization of the original matrix A as
          returned by CGEQRF.

LDA

          LDA is INTEGER
          The leading dimension of the array A.  LDA >= M.

TAU

          TAU is COMPLEX array, dimension (N)
          Details of the orthogonal matrix Q.

          B is COMPLEX array, dimension (LDB,NRHS)
          On entry, the m-by-nrhs right hand side matrix B.
          On exit, the n-by-nrhs solution matrix X.

LDB

          LDB is INTEGER
          The leading dimension of the array B. LDB >= M.

WORK

          WORK is COMPLEX array, dimension (LWORK)

LWORK

          LWORK is INTEGER
          The length of the array WORK.  LWORK must be at least NRHS,
          and should be at least NRHS*NB, where NB is the block size
          for this environment.

INFO

          INFO is INTEGER
          = 0: successful exit
          < 0: if INFO = -i, the i-th argument had an illegal value

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine cgerqs (integer M, integer N, integer NRHS, complex, dimension( lda, * ) A, integer LDA, complex, dimension( * ) TAU, complex, dimension( ldb, * ) B, integer LDB, complex, dimension( lwork ) WORK, integer LWORK, integer INFO)

CGERQS

Purpose:

 Compute a minimum-norm solution
     min || A*X - B ||
 using the RQ factorization
     A = R*Q
 computed by CGERQF.

Parameters:

          M is INTEGER
          The number of rows of the matrix A.  M >= 0.

          N is INTEGER
          The number of columns of the matrix A.  N >= M >= 0.

NRHS

          NRHS is INTEGER
          The number of columns of B.  NRHS >= 0.

          A is COMPLEX array, dimension (LDA,N)
          Details of the RQ factorization of the original matrix A as
          returned by CGERQF.

LDA

          LDA is INTEGER
          The leading dimension of the array A.  LDA >= M.

TAU

          TAU is COMPLEX array, dimension (M)
          Details of the orthogonal matrix Q.

          B is COMPLEX array, dimension (LDB,NRHS)
          On entry, the right hand side vectors for the linear system.
          On exit, the solution vectors X.  Each solution vector
          is contained in rows 1:N of a column of B.

LDB

          LDB is INTEGER
          The leading dimension of the array B. LDB >= max(1,N).

WORK

          WORK is COMPLEX array, dimension (LWORK)

LWORK

          LWORK is INTEGER
          The length of the array WORK.  LWORK must be at least NRHS,
          and should be at least NRHS*NB, where NB is the block size
          for this environment.

INFO

          INFO is INTEGER
          = 0: successful exit
          < 0: if INFO = -i, the i-th argument had an illegal value

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine cget01 (integer M, integer N, complex, dimension( lda, * ) A, integer LDA, complex, dimension( ldafac, * ) AFAC, integer LDAFAC, integer, dimension( * ) IPIV, real, dimension( * ) RWORK, real RESID)

CGET01

Purpose:

 CGET01 reconstructs a matrix A from its L*U factorization and
 computes the residual
    norm(L*U - A) / ( N * norm(A) * EPS ),
 where EPS is the machine epsilon.

Parameters:

          M is INTEGER
          The number of rows of the matrix A.  M >= 0.

          N is INTEGER
          The number of columns of the matrix A.  N >= 0.

          A is COMPLEX array, dimension (LDA,N)
          The original M x N matrix A.

LDA

          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,M).

AFAC

          AFAC is COMPLEX array, dimension (LDAFAC,N)
          The factored form of the matrix A.  AFAC contains the factors
          L and U from the L*U factorization as computed by CGETRF.
          Overwritten with the reconstructed matrix, and then with the
          difference L*U - A.

LDAFAC

          LDAFAC is INTEGER
          The leading dimension of the array AFAC.  LDAFAC >= max(1,M).

IPIV

          IPIV is INTEGER array, dimension (N)
          The pivot indices from CGETRF.

RWORK

          RWORK is REAL array, dimension (M)

RESID

          RESID is REAL
          norm(L*U - A) / ( N * norm(A) * EPS )

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine cget02 (character TRANS, integer M, integer N, integer NRHS, complex, dimension( lda, * ) A, integer LDA, complex, dimension( ldx, * ) X, integer LDX, complex, dimension( ldb, * ) B, integer LDB, real, dimension( * ) RWORK, real RESID)

CGET02

Purpose:

 CGET02 computes the residual for a solution of a system of linear
 equations  A*x = b  or  A'*x = b:
    RESID = norm(B - A*X) / ( norm(A) * norm(X) * EPS ),
 where EPS is the machine epsilon.

Parameters:

TRANS

          TRANS is CHARACTER*1
          Specifies the form of the system of equations:
          = 'N':  A *x = b
          = 'T':  A^T*x = b, where A^T is the transpose of A
          = 'C':  A^H*x = b, where A^H is the conjugate transpose of A

          M is INTEGER
          The number of rows of the matrix A.  M >= 0.

          N is INTEGER
          The number of columns of the matrix A.  N >= 0.

NRHS

          NRHS is INTEGER
          The number of columns of B, the matrix of right hand sides.
          NRHS >= 0.

          A is COMPLEX array, dimension (LDA,N)
          The original M x N matrix A.

LDA

          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,M).

          X is COMPLEX array, dimension (LDX,NRHS)
          The computed solution vectors for the system of linear
          equations.

LDX

          LDX is INTEGER
          The leading dimension of the array X.  If TRANS = 'N',
          LDX >= max(1,N); if TRANS = 'T' or 'C', LDX >= max(1,M).

          B is COMPLEX array, dimension (LDB,NRHS)
          On entry, the right hand side vectors for the system of
          linear equations.
          On exit, B is overwritten with the difference B - A*X.

LDB

          LDB is INTEGER
          The leading dimension of the array B.  IF TRANS = 'N',
          LDB >= max(1,M); if TRANS = 'T' or 'C', LDB >= max(1,N).

RWORK

          RWORK is REAL array, dimension (M)

RESID

          RESID is REAL
          The maximum over the number of right hand sides of
          norm(B - A*X) / ( norm(A) * norm(X) * EPS ).

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2015

subroutine cget03 (integer N, complex, dimension( lda, * ) A, integer LDA, complex, dimension( ldainv, * ) AINV, integer LDAINV, complex, dimension( ldwork, * ) WORK, integer LDWORK, real, dimension( * ) RWORK, real RCOND, real RESID)

CGET03

Purpose:

 CGET03 computes the residual for a general matrix times its inverse:
    norm( I - AINV*A ) / ( N * norm(A) * norm(AINV) * EPS ),
 where EPS is the machine epsilon.

Parameters:

          N is INTEGER
          The number of rows and columns of the matrix A.  N >= 0.

          A is COMPLEX array, dimension (LDA,N)
          The original N x N matrix A.

LDA

          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N).

AINV

          AINV is COMPLEX array, dimension (LDAINV,N)
          The inverse of the matrix A.

LDAINV

          LDAINV is INTEGER
          The leading dimension of the array AINV.  LDAINV >= max(1,N).

WORK

          WORK is COMPLEX array, dimension (LDWORK,N)

LDWORK

          LDWORK is INTEGER
          The leading dimension of the array WORK.  LDWORK >= max(1,N).

RWORK

          RWORK is REAL array, dimension (N)

RCOND

          RCOND is REAL
          The reciprocal of the condition number of A, computed as
          ( 1/norm(A) ) / norm(AINV).

RESID

          RESID is REAL
          norm(I - AINV*A) / ( N * norm(A) * norm(AINV) * EPS )

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine cget04 (integer N, integer NRHS, complex, dimension( ldx, * ) X, integer LDX, complex, dimension( ldxact, * ) XACT, integer LDXACT, real RCOND, real RESID)

CGET04

Purpose:

 CGET04 computes the difference between a computed solution and the
 true solution to a system of linear equations.
 RESID =  ( norm(X-XACT) * RCOND ) / ( norm(XACT) * EPS ),
 where RCOND is the reciprocal of the condition number and EPS is the
 machine epsilon.

Parameters:

          N is INTEGER
          The number of rows of the matrices X and XACT.  N >= 0.

NRHS

          NRHS is INTEGER
          The number of columns of the matrices X and XACT.  NRHS >= 0.

          X is COMPLEX array, dimension (LDX,NRHS)
          The computed solution vectors.  Each vector is stored as a
          column of the matrix X.

LDX

          LDX is INTEGER
          The leading dimension of the array X.  LDX >= max(1,N).

XACT

          XACT is COMPLEX array, dimension (LDX,NRHS)
          The exact solution vectors.  Each vector is stored as a
          column of the matrix XACT.

LDXACT

          LDXACT is INTEGER
          The leading dimension of the array XACT.  LDXACT >= max(1,N).

RCOND

          RCOND is REAL
          The reciprocal of the condition number of the coefficient
          matrix in the system of equations.

RESID

          RESID is REAL
          The maximum over the NRHS solution vectors of
          ( norm(X-XACT) * RCOND ) / ( norm(XACT) * EPS )

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine cget07 (character TRANS, integer N, integer NRHS, complex, dimension( lda, * ) A, integer LDA, complex, dimension( ldb, * ) B, integer LDB, complex, dimension( ldx, * ) X, integer LDX, complex, dimension( ldxact, * ) XACT, integer LDXACT, real, dimension( * ) FERR, logical CHKFERR, real, dimension( * ) BERR, real, dimension( * ) RESLTS)

CGET07

Purpose:

 CGET07 tests the error bounds from iterative refinement for the
 computed solution to a system of equations op(A)*X = B, where A is a
 general n by n matrix and op(A) = A or A**T, depending on TRANS.
 RESLTS(1) = test of the error bound
           = norm(X - XACT) / ( norm(X) * FERR )
 A large value is returned if this ratio is not less than one.
 RESLTS(2) = residual from the iterative refinement routine
           = the maximum of BERR / ( (n+1)*EPS + (*) ), where
             (*) = (n+1)*UNFL / (min_i (abs(op(A))*abs(X) +abs(b))_i )

Parameters:

TRANS

          TRANS is CHARACTER*1
          Specifies the form of the system of equations.
          = 'N':  A * X = B     (No transpose)
          = 'T':  A**T * X = B  (Transpose)
          = 'C':  A**H * X = B  (Conjugate transpose = Transpose)

          N is INTEGER
          The number of rows of the matrices X and XACT.  N >= 0.

NRHS

          NRHS is INTEGER
          The number of columns of the matrices X and XACT.  NRHS >= 0.

          A is COMPLEX array, dimension (LDA,N)
          The original n by n matrix A.

LDA

          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N).

          B is COMPLEX array, dimension (LDB,NRHS)
          The right hand side vectors for the system of linear
          equations.

LDB

          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,N).

          X is COMPLEX array, dimension (LDX,NRHS)
          The computed solution vectors.  Each vector is stored as a
          column of the matrix X.

LDX

          LDX is INTEGER
          The leading dimension of the array X.  LDX >= max(1,N).

XACT

          XACT is COMPLEX array, dimension (LDX,NRHS)
          The exact solution vectors.  Each vector is stored as a
          column of the matrix XACT.

LDXACT

          LDXACT is INTEGER
          The leading dimension of the array XACT.  LDXACT >= max(1,N).

FERR

          FERR is REAL array, dimension (NRHS)
          The estimated forward error bounds for each solution vector
          X.  If XTRUE is the true solution, FERR bounds the magnitude
          of the largest entry in (X - XTRUE) divided by the magnitude
          of the largest entry in X.

CHKFERR

          CHKFERR is LOGICAL
          Set to .TRUE. to check FERR, .FALSE. not to check FERR.
          When the test system is ill-conditioned, the "true"
          solution in XACT may be incorrect.

BERR

          BERR is REAL array, dimension (NRHS)
          The componentwise relative backward error of each solution
          vector (i.e., the smallest relative change in any entry of A
          or B that makes X an exact solution).

RESLTS

          RESLTS is REAL array, dimension (2)
          The maximum over the NRHS solution vectors of the ratios:
          RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR )
          RESLTS(2) = BERR / ( (n+1)*EPS + (*) )

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine cgtt01 (integer N, complex, dimension( * ) DL, complex, dimension( * ) D, complex, dimension( * ) DU, complex, dimension( * ) DLF, complex, dimension( * ) DF, complex, dimension( * ) DUF, complex, dimension( * ) DU2, integer, dimension( * ) IPIV, complex, dimension( ldwork, * ) WORK, integer LDWORK, real, dimension( * ) RWORK, real RESID)

CGTT01

Purpose:

 CGTT01 reconstructs a tridiagonal matrix A from its LU factorization
 and computes the residual
    norm(L*U - A) / ( norm(A) * EPS ),
 where EPS is the machine epsilon.

Parameters:

          N is INTEGTER
          The order of the matrix A.  N >= 0.

          DL is COMPLEX array, dimension (N-1)
          The (n-1) sub-diagonal elements of A.

          D is COMPLEX array, dimension (N)
          The diagonal elements of A.

          DU is COMPLEX array, dimension (N-1)
          The (n-1) super-diagonal elements of A.

DLF

          DLF is COMPLEX array, dimension (N-1)
          The (n-1) multipliers that define the matrix L from the
          LU factorization of A.

          DF is COMPLEX array, dimension (N)
          The n diagonal elements of the upper triangular matrix U from
          the LU factorization of A.

DUF

          DUF is COMPLEX array, dimension (N-1)
          The (n-1) elements of the first super-diagonal of U.

DU2

          DU2 is COMPLEX array, dimension (N-2)
          The (n-2) elements of the second super-diagonal of U.

IPIV

          IPIV is INTEGER array, dimension (N)
          The pivot indices; for 1 <= i <= n, row i of the matrix was
          interchanged with row IPIV(i).  IPIV(i) will always be either
          i or i+1; IPIV(i) = i indicates a row interchange was not
          required.

WORK

          WORK is COMPLEX array, dimension (LDWORK,N)

LDWORK

          LDWORK is INTEGER
          The leading dimension of the array WORK.  LDWORK >= max(1,N).

RWORK

          RWORK is REAL array, dimension (N)

RESID

          RESID is REAL
          The scaled residual:  norm(L*U - A) / (norm(A) * EPS)

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine cgtt02 (character TRANS, integer N, integer NRHS, complex, dimension( * ) DL, complex, dimension( * ) D, complex, dimension( * ) DU, complex, dimension( ldx, * ) X, integer LDX, complex, dimension( ldb, * ) B, integer LDB, real RESID)

CGTT02

Purpose:

 CGTT02 computes the residual for the solution to a tridiagonal
 system of equations:
    RESID = norm(B - op(A)*X) / (norm(A) * norm(X) * EPS),
 where EPS is the machine epsilon.

Parameters:

TRANS

          TRANS is CHARACTER
          Specifies the form of the residual.
          = 'N':  B - A * X     (No transpose)
          = 'T':  B - A**T * X  (Transpose)
          = 'C':  B - A**H * X  (Conjugate transpose)

          N is INTEGTER
          The order of the matrix A.  N >= 0.

NRHS

          NRHS is INTEGER
          The number of right hand sides, i.e., the number of columns
          of the matrices B and X.  NRHS >= 0.

          DL is COMPLEX array, dimension (N-1)
          The (n-1) sub-diagonal elements of A.

          D is COMPLEX array, dimension (N)
          The diagonal elements of A.

          DU is COMPLEX array, dimension (N-1)
          The (n-1) super-diagonal elements of A.

          X is COMPLEX array, dimension (LDX,NRHS)
          The computed solution vectors X.

LDX

          LDX is INTEGER
          The leading dimension of the array X.  LDX >= max(1,N).

          B is COMPLEX array, dimension (LDB,NRHS)
          On entry, the right hand side vectors for the system of
          linear equations.
          On exit, B is overwritten with the difference B - op(A)*X.

LDB

          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,N).

RESID

          RESID is REAL
          norm(B - op(A)*X) / (norm(A) * norm(X) * EPS)

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine cgtt05 (character TRANS, integer N, integer NRHS, complex, dimension( * ) DL, complex, dimension( * ) D, complex, dimension( * ) DU, complex, dimension( ldb, * ) B, integer LDB, complex, dimension( ldx, * ) X, integer LDX, complex, dimension( ldxact, * ) XACT, integer LDXACT, real, dimension( * ) FERR, real, dimension( * ) BERR, real, dimension( * ) RESLTS)

CGTT05

Purpose:

 CGTT05 tests the error bounds from iterative refinement for the
 computed solution to a system of equations A*X = B, where A is a
 general tridiagonal matrix of order n and op(A) = A or A**T,
 depending on TRANS.
 RESLTS(1) = test of the error bound
           = norm(X - XACT) / ( norm(X) * FERR )
 A large value is returned if this ratio is not less than one.
 RESLTS(2) = residual from the iterative refinement routine
           = the maximum of BERR / ( NZ*EPS + (*) ), where
             (*) = NZ*UNFL / (min_i (abs(op(A))*abs(X) +abs(b))_i )
             and NZ = max. number of nonzeros in any row of A, plus 1

Parameters:

TRANS

          TRANS is CHARACTER*1
          Specifies the form of the system of equations.
          = 'N':  A * X = B     (No transpose)
          = 'T':  A**T * X = B  (Transpose)
          = 'C':  A**H * X = B  (Conjugate transpose = Transpose)

          N is INTEGER
          The number of rows of the matrices X and XACT.  N >= 0.

NRHS

          NRHS is INTEGER
          The number of columns of the matrices X and XACT.  NRHS >= 0.

          DL is COMPLEX array, dimension (N-1)
          The (n-1) sub-diagonal elements of A.

          D is COMPLEX array, dimension (N)
          The diagonal elements of A.

          DU is COMPLEX array, dimension (N-1)
          The (n-1) super-diagonal elements of A.

          B is COMPLEX array, dimension (LDB,NRHS)
          The right hand side vectors for the system of linear
          equations.

LDB

          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,N).

          X is COMPLEX array, dimension (LDX,NRHS)
          The computed solution vectors.  Each vector is stored as a
          column of the matrix X.

LDX

          LDX is INTEGER
          The leading dimension of the array X.  LDX >= max(1,N).

XACT

          XACT is COMPLEX array, dimension (LDX,NRHS)
          The exact solution vectors.  Each vector is stored as a
          column of the matrix XACT.

LDXACT

          LDXACT is INTEGER
          The leading dimension of the array XACT.  LDXACT >= max(1,N).

FERR

          FERR is REAL array, dimension (NRHS)
          The estimated forward error bounds for each solution vector
          X.  If XTRUE is the true solution, FERR bounds the magnitude
          of the largest entry in (X - XTRUE) divided by the magnitude
          of the largest entry in X.

BERR

          BERR is REAL array, dimension (NRHS)
          The componentwise relative backward error of each solution
          vector (i.e., the smallest relative change in any entry of A
          or B that makes X an exact solution).

RESLTS

          RESLTS is REAL array, dimension (2)
          The maximum over the NRHS solution vectors of the ratios:
          RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR )
          RESLTS(2) = BERR / ( NZ*EPS + (*) )

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine chet01 (character UPLO, integer N, complex, dimension( lda, * ) A, integer LDA, complex, dimension( ldafac, * ) AFAC, integer LDAFAC, integer, dimension( * ) IPIV, complex, dimension( ldc, * ) C, integer LDC, real, dimension( * ) RWORK, real RESID)

CHET01

Purpose:

 CHET01 reconstructs a Hermitian indefinite matrix A from its
 block L*D*L' or U*D*U' factorization and computes the residual
    norm( C - A ) / ( N * norm(A) * EPS ),
 where C is the reconstructed matrix, EPS is the machine epsilon,
 L' is the conjugate transpose of L, and U' is the conjugate transpose
 of U.

Parameters:

UPLO

          UPLO is CHARACTER*1
          Specifies whether the upper or lower triangular part of the
          Hermitian matrix A is stored:
          = 'U':  Upper triangular
          = 'L':  Lower triangular

          N is INTEGER
          The number of rows and columns of the matrix A.  N >= 0.

          A is COMPLEX array, dimension (LDA,N)
          The original Hermitian matrix A.

LDA

          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N)

AFAC

          AFAC is COMPLEX array, dimension (LDAFAC,N)
          The factored form of the matrix A.  AFAC contains the block
          diagonal matrix D and the multipliers used to obtain the
          factor L or U from the block L*D*L' or U*D*U' factorization
          as computed by CHETRF.

LDAFAC

          LDAFAC is INTEGER
          The leading dimension of the array AFAC.  LDAFAC >= max(1,N).

IPIV

          IPIV is INTEGER array, dimension (N)
          The pivot indices from CHETRF.

          C is COMPLEX array, dimension (LDC,N)

LDC

          LDC is INTEGER
          The leading dimension of the array C.  LDC >= max(1,N).

RWORK

          RWORK is REAL array, dimension (N)

RESID

          RESID is REAL
          If UPLO = 'L', norm(L*D*L' - A) / ( N * norm(A) * EPS )
          If UPLO = 'U', norm(U*D*U' - A) / ( N * norm(A) * EPS )

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2013

subroutine chet01_rook (character UPLO, integer N, complex, dimension( lda, * ) A, integer LDA, complex, dimension( ldafac, * ) AFAC, integer LDAFAC, integer, dimension( * ) IPIV, complex, dimension( ldc, * ) C, integer LDC, real, dimension( * ) RWORK, real RESID)

CHET01_ROOK

Purpose:

 CHET01_ROOK reconstructs a complex Hermitian indefinite matrix A from its
 block L*D*L' or U*D*U' factorization and computes the residual
    norm( C - A ) / ( N * norm(A) * EPS ),
 where C is the reconstructed matrix, EPS is the machine epsilon,
 L' is the transpose of L, and U' is the transpose of U.

Parameters:

UPLO

          UPLO is CHARACTER*1
          Specifies whether the upper or lower triangular part of the
          complex Hermitian matrix A is stored:
          = 'U':  Upper triangular
          = 'L':  Lower triangular

          N is INTEGER
          The number of rows and columns of the matrix A.  N >= 0.

          A is COMPLEX array, dimension (LDA,N)
          The original complex Hermitian matrix A.

LDA

          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N)

AFAC

          AFAC is COMPLEX array, dimension (LDAFAC,N)
          The factored form of the matrix A.  AFAC contains the block
          diagonal matrix D and the multipliers used to obtain the
          factor L or U from the block L*D*L' or U*D*U' factorization
          as computed by CSYTRF_ROOK.

LDAFAC

          LDAFAC is INTEGER
          The leading dimension of the array AFAC.  LDAFAC >= max(1,N).

IPIV

          IPIV is INTEGER array, dimension (N)
          The pivot indices from CSYTRF_ROOK.

          C is COMPLEX array, dimension (LDC,N)

LDC

          LDC is INTEGER
          The leading dimension of the array C.  LDC >= max(1,N).

RWORK

          RWORK is REAL array, dimension (N)

RESID

          RESID is REAL
          If UPLO = 'L', norm(L*D*L' - A) / ( N * norm(A) * EPS )
          If UPLO = 'U', norm(U*D*U' - A) / ( N * norm(A) * EPS )

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2013

subroutine chkxer (character() SRNAMT, integer INFOT, integer NOUT, logical LERR, logical OK)

CHKXER

Purpose:

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine chpt01 (character UPLO, integer N, complex, dimension( * ) A, complex, dimension( * ) AFAC, integer, dimension( * ) IPIV, complex, dimension( ldc, * ) C, integer LDC, real, dimension( * ) RWORK, real RESID)

CHPT01

Purpose:

 CHPT01 reconstructs a Hermitian indefinite packed matrix A from its
 block L*D*L' or U*D*U' factorization and computes the residual
    norm( C - A ) / ( N * norm(A) * EPS ),
 where C is the reconstructed matrix, EPS is the machine epsilon,
 L' is the conjugate transpose of L, and U' is the conjugate transpose
 of U.

Parameters:

UPLO

          UPLO is CHARACTER*1
          Specifies whether the upper or lower triangular part of the
          Hermitian matrix A is stored:
          = 'U':  Upper triangular
          = 'L':  Lower triangular

          N is INTEGER
          The number of rows and columns of the matrix A.  N >= 0.

          A is COMPLEX array, dimension (N*(N+1)/2)
          The original Hermitian matrix A, stored as a packed
          triangular matrix.

AFAC

          AFAC is COMPLEX array, dimension (N*(N+1)/2)
          The factored form of the matrix A, stored as a packed
          triangular matrix.  AFAC contains the block diagonal matrix D
          and the multipliers used to obtain the factor L or U from the
          block L*D*L' or U*D*U' factorization as computed by CHPTRF.

IPIV

          IPIV is INTEGER array, dimension (N)
          The pivot indices from CHPTRF.

          C is COMPLEX array, dimension (LDC,N)

LDC

          LDC is INTEGER
          The leading dimension of the array C.  LDC >= max(1,N).

RWORK

          RWORK is REAL array, dimension (N)

RESID

          RESID is REAL
          If UPLO = 'L', norm(L*D*L' - A) / ( N * norm(A) * EPS )
          If UPLO = 'U', norm(U*D*U' - A) / ( N * norm(A) * EPS )

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine clahilb (integer N, integer NRHS, complex, dimension(lda,n) A, integer LDA, complex, dimension(ldx, nrhs) X, integer LDX, complex, dimension(ldb, nrhs) B, integer LDB, real, dimension(n) WORK, integer INFO, character*3 PATH)

CLAHILB

Purpose:

 CLAHILB generates an N by N scaled Hilbert matrix in A along with
 NRHS right-hand sides in B and solutions in X such that A*X=B.
 The Hilbert matrix is scaled by M = LCM(1, 2, ..., 2*N-1) so that all
 entries are integers.  The right-hand sides are the first NRHS
 columns of M * the identity matrix, and the solutions are the
 first NRHS columns of the inverse Hilbert matrix.
 The condition number of the Hilbert matrix grows exponentially with
 its size, roughly as O(e ** (3.5*N)).  Additionally, the inverse
 Hilbert matrices beyond a relatively small dimension cannot be
 generated exactly without extra precision.  Precision is exhausted
 when the largest entry in the inverse Hilbert matrix is greater than
 2 to the power of the number of bits in the fraction of the data type
 used plus one, which is 24 for single precision.
 In single, the generated solution is exact for N <= 6 and has
 small componentwise error for 7 <= N <= 11.

Parameters:

          N is INTEGER
          The dimension of the matrix A.

NRHS

          NRHS is NRHS
          The requested number of right-hand sides.

          A is COMPLEX array, dimension (LDA, N)
          The generated scaled Hilbert matrix.

LDA

          LDA is INTEGER
          The leading dimension of the array A.  LDA >= N.

          X is COMPLEX array, dimension (LDX, NRHS)
          The generated exact solutions.  Currently, the first NRHS
          columns of the inverse Hilbert matrix.

LDX

          LDX is INTEGER
          The leading dimension of the array X.  LDX >= N.

          B is REAL array, dimension (LDB, NRHS)
          The generated right-hand sides.  Currently, the first NRHS
          columns of LCM(1, 2, ..., 2*N-1) * the identity matrix.

LDB

          LDB is INTEGER
          The leading dimension of the array B.  LDB >= N.

WORK

          WORK is REAL array, dimension (N)

INFO

          INFO is INTEGER
          = 0: successful exit
          = 1: N is too large; the data is still generated but may not
               be not exact.
          < 0: if INFO = -i, the i-th argument had an illegal value

PATH

          PATH is CHARACTER*3
          The LAPACK path name.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine claipd (integer N, complex, dimension( * ) A, integer INDA, integer VINDA)

CLAIPD

Purpose:

 CLAIPD sets the imaginary part of the diagonal elements of a complex
 matrix A to a large value.  This is used to test LAPACK routines for
 complex Hermitian matrices, which are not supposed to access or use
 the imaginary parts of the diagonals.

Parameters:

          N is INTEGER
         The number of diagonal elements of A.

          A is COMPLEX array, dimension
                        (1+(N-1)*INDA+(N-2)*VINDA)
         On entry, the complex (Hermitian) matrix A.
         On exit, the imaginary parts of the diagonal elements are set
         to BIGNUM = EPS / SAFMIN, where EPS is the machine epsilon and
         SAFMIN is the safe minimum.

INDA

          INDA is INTEGER
         The increment between A(1) and the next diagonal element of A.
         Typical values are
         = LDA+1:  square matrices with leading dimension LDA
         = 2:  packed upper triangular matrix, starting at A(1,1)
         = N:  packed lower triangular matrix, starting at A(1,1)

VINDA

          VINDA is INTEGER
         The change in the diagonal increment between columns of A.
         Typical values are
         = 0:  no change, the row and column increments in A are fixed
         = 1:  packed upper triangular matrix
         = -1:  packed lower triangular matrix

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine claptm (character UPLO, integer N, integer NRHS, real ALPHA, real, dimension( * ) D, complex, dimension( * ) E, complex, dimension( ldx, * ) X, integer LDX, real BETA, complex, dimension( ldb, * ) B, integer LDB)

CLAPTM

Purpose:

 CLAPTM multiplies an N by NRHS matrix X by a Hermitian tridiagonal
 matrix A and stores the result in a matrix B.  The operation has the
 form
    B := alpha * A * X + beta * B
 where alpha may be either 1. or -1. and beta may be 0., 1., or -1.

Parameters:

UPLO

          UPLO is CHARACTER
          Specifies whether the superdiagonal or the subdiagonal of the
          tridiagonal matrix A is stored.
          = 'U':  Upper, E is the superdiagonal of A.
          = 'L':  Lower, E is the subdiagonal of A.

          N is INTEGER
          The order of the matrix A.  N >= 0.

NRHS

          NRHS is INTEGER
          The number of right hand sides, i.e., the number of columns
          of the matrices X and B.

ALPHA

          ALPHA is REAL
          The scalar alpha.  ALPHA must be 1. or -1.; otherwise,
          it is assumed to be 0.

          D is REAL array, dimension (N)
          The n diagonal elements of the tridiagonal matrix A.

          E is COMPLEX array, dimension (N-1)
          The (n-1) subdiagonal or superdiagonal elements of A.

          X is COMPLEX array, dimension (LDX,NRHS)
          The N by NRHS matrix X.

LDX

          LDX is INTEGER
          The leading dimension of the array X.  LDX >= max(N,1).

BETA

          BETA is REAL
          The scalar beta.  BETA must be 0., 1., or -1.; otherwise,
          it is assumed to be 1.

          B is COMPLEX array, dimension (LDB,NRHS)
          On entry, the N by NRHS matrix B.
          On exit, B is overwritten by the matrix expression
          B := alpha * A * X + beta * B.

LDB

          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(N,1).

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine clarhs (character3 PATH, character XTYPE, character UPLO, character TRANS, integer M, integer N, integer KL, integer KU, integer NRHS, complex, dimension( lda, ) A, integer LDA, complex, dimension( ldx, * ) X, integer LDX, complex, dimension( ldb, * ) B, integer LDB, integer, dimension( 4 ) ISEED, integer INFO)

CLARHS

Purpose:

 CLARHS chooses a set of NRHS random solution vectors and sets
 up the right hand sides for the linear system
    op( A ) * X = B,
 where op( A ) may be A, A**T (transpose of A), or A**H (conjugate
 transpose of A).

Parameters:

PATH

          PATH is CHARACTER*3
          The type of the complex matrix A.  PATH may be given in any
          combination of upper and lower case.  Valid paths include
             xGE:  General m x n matrix
             xGB:  General banded matrix
             xPO:  Hermitian positive definite, 2-D storage
             xPP:  Hermitian positive definite packed
             xPB:  Hermitian positive definite banded
             xHE:  Hermitian indefinite, 2-D storage
             xHP:  Hermitian indefinite packed
             xHB:  Hermitian indefinite banded
             xSY:  Symmetric indefinite, 2-D storage
             xSP:  Symmetric indefinite packed
             xSB:  Symmetric indefinite banded
             xTR:  Triangular
             xTP:  Triangular packed
             xTB:  Triangular banded
             xQR:  General m x n matrix
             xLQ:  General m x n matrix
             xQL:  General m x n matrix
             xRQ:  General m x n matrix
          where the leading character indicates the precision.

XTYPE

          XTYPE is CHARACTER*1
          Specifies how the exact solution X will be determined:
          = 'N':  New solution; generate a random X.
          = 'C':  Computed; use value of X on entry.

UPLO

          UPLO is CHARACTER*1
          Used only if A is symmetric or triangular; specifies whether
          the upper or lower triangular part of the matrix A is stored.
          = 'U':  Upper triangular
          = 'L':  Lower triangular

TRANS

          TRANS is CHARACTER*1
          Used only if A is nonsymmetric; specifies the operation
          applied to the matrix A.
          = 'N':  B := A    * X
          = 'T':  B := A**T * X
          = 'C':  B := A**H * X

          M is INTEGER
          The number of rows of the matrix A.  M >= 0.

          N is INTEGER
          The number of columns of the matrix A.  N >= 0.

          KL is INTEGER
          Used only if A is a band matrix; specifies the number of
          subdiagonals of A if A is a general band matrix or if A is
          symmetric or triangular and UPLO = 'L'; specifies the number
          of superdiagonals of A if A is symmetric or triangular and
          UPLO = 'U'.  0 <= KL <= M-1.

          KU is INTEGER
          Used only if A is a general band matrix or if A is
          triangular.
          If PATH = xGB, specifies the number of superdiagonals of A,
          and 0 <= KU <= N-1.
          If PATH = xTR, xTP, or xTB, specifies whether or not the
          matrix has unit diagonal:
          = 1:  matrix has non-unit diagonal (default)
          = 2:  matrix has unit diagonal

NRHS

          NRHS is INTEGER
          The number of right hand side vectors in the system A*X = B.

          A is COMPLEX array, dimension (LDA,N)
          The test matrix whose type is given by PATH.

LDA

          LDA is INTEGER
          The leading dimension of the array A.
          If PATH = xGB, LDA >= KL+KU+1.
          If PATH = xPB, xSB, xHB, or xTB, LDA >= KL+1.
          Otherwise, LDA >= max(1,M).

          X is or output) COMPLEX array, dimension (LDX,NRHS)
          On entry, if XTYPE = 'C' (for 'Computed'), then X contains
          the exact solution to the system of linear equations.
          On exit, if XTYPE = 'N' (for 'New'), then X is initialized
          with random values.

LDX

          LDX is INTEGER
          The leading dimension of the array X.  If TRANS = 'N',
          LDX >= max(1,N); if TRANS = 'T', LDX >= max(1,M).

          B is COMPLEX array, dimension (LDB,NRHS)
          The right hand side vector(s) for the system of equations,
          computed from B = op(A) * X, where op(A) is determined by
          TRANS.

LDB

          LDB is INTEGER
          The leading dimension of the array B.  If TRANS = 'N',
          LDB >= max(1,M); if TRANS = 'T', LDB >= max(1,N).

ISEED

          ISEED is INTEGER array, dimension (4)
          The seed vector for the random number generator (used in
          CLATMS).  Modified on exit.

INFO

          INFO is INTEGER
          = 0: successful exit
          < 0: if INFO = -k, the k-th argument had an illegal value

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine clatb4 (character*3 PATH, integer IMAT, integer M, integer N, character TYPE, integer KL, integer KU, real ANORM, integer MODE, real CNDNUM, character DIST)

CLATB4

Purpose:

 CLATB4 sets parameters for the matrix generator based on the type of
 matrix to be generated.

Parameters:

PATH

          PATH is CHARACTER*3
          The LAPACK path name.

IMAT

          IMAT is INTEGER
          An integer key describing which matrix to generate for this
          path.

          M is INTEGER
          The number of rows in the matrix to be generated.

          N is INTEGER
          The number of columns in the matrix to be generated.

TYPE

          TYPE is CHARACTER*1
          The type of the matrix to be generated:
          = 'S':  symmetric matrix
          = 'H':  Hermitian matrix
          = 'P':  Hermitian positive (semi)definite matrix
          = 'N':  nonsymmetric matrix

          KL is INTEGER
          The lower band width of the matrix to be generated.

          KU is INTEGER
          The upper band width of the matrix to be generated.

ANORM

          ANORM is REAL
          The desired norm of the matrix to be generated.  The diagonal
          matrix of singular values or eigenvalues is scaled by this
          value.

MODE

          MODE is INTEGER
          A key indicating how to choose the vector of eigenvalues.

CNDNUM

          CNDNUM is REAL
          The desired condition number.

DIST

          DIST is CHARACTER*1
          The type of distribution to be used by the random number
          generator.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2013

subroutine clatb5 (character*3 PATH, integer IMAT, integer N, character TYPE, integer KL, integer KU, real ANORM, integer MODE, real CNDNUM, character DIST)

CLATB5

Purpose:

 CLATB5 sets parameters for the matrix generator based on the type
 of matrix to be generated.

Parameters:

PATH

          PATH is CHARACTER*3
          The LAPACK path name.

IMAT

          IMAT is INTEGER
          An integer key describing which matrix to generate for this
          path.

          N is INTEGER
          The number of rows and columns in the matrix to be generated.

TYPE

          TYPE is CHARACTER*1
          The type of the matrix to be generated:
          = 'S':  symmetric matrix
          = 'P':  symmetric positive (semi)definite matrix
          = 'N':  nonsymmetric matrix

          KL is INTEGER
          The lower band width of the matrix to be generated.

          KU is INTEGER
          The upper band width of the matrix to be generated.

ANORM

          ANORM is REAL
          The desired norm of the matrix to be generated.  The diagonal
          matrix of singular values or eigenvalues is scaled by this
          value.

MODE

          MODE is INTEGER
          A key indicating how to choose the vector of eigenvalues.

CNDNUM

          CNDNUM is REAL
          The desired condition number.

DIST

          DIST is CHARACTER*1
          The type of distribution to be used by the random number
          generator.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine clatsp (character UPLO, integer N, complex, dimension( * ) X, integer, dimension( * ) ISEED)

CLATSP

Purpose:

 CLATSP generates a special test matrix for the complex symmetric
 (indefinite) factorization for packed matrices.  The pivot blocks of
 the generated matrix will be in the following order:
    2x2 pivot block, non diagonalizable
    1x1 pivot block
    2x2 pivot block, diagonalizable
    (cycle repeats)
 A row interchange is required for each non-diagonalizable 2x2 block.

Parameters:

UPLO

          UPLO is CHARACTER
          Specifies whether the generated matrix is to be upper or
          lower triangular.
          = 'U':  Upper triangular
          = 'L':  Lower triangular

          N is INTEGER
          The dimension of the matrix to be generated.

          X is COMPLEX array, dimension (N*(N+1)/2)
          The generated matrix in packed storage format.  The matrix
          consists of 3x3 and 2x2 diagonal blocks which result in the
          pivot sequence given above.  The matrix outside these
          diagonal blocks is zero.

ISEED

          ISEED is INTEGER array, dimension (4)
          On entry, the seed for the random number generator.  The last
          of the four integers must be odd.  (modified on exit)

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine clatsy (character UPLO, integer N, complex, dimension( ldx, * ) X, integer LDX, integer, dimension( * ) ISEED)

CLATSY

Purpose:

 CLATSY generates a special test matrix for the complex symmetric
 (indefinite) factorization.  The pivot blocks of the generated matrix
 will be in the following order:
    2x2 pivot block, non diagonalizable
    1x1 pivot block
    2x2 pivot block, diagonalizable
    (cycle repeats)
 A row interchange is required for each non-diagonalizable 2x2 block.

Parameters:

UPLO

          UPLO is CHARACTER
          Specifies whether the generated matrix is to be upper or
          lower triangular.
          = 'U':  Upper triangular
          = 'L':  Lower triangular

          N is INTEGER
          The dimension of the matrix to be generated.

          X is COMPLEX array, dimension (LDX,N)
          The generated matrix, consisting of 3x3 and 2x2 diagonal
          blocks which result in the pivot sequence given above.
          The matrix outside of these diagonal blocks is zero.

LDX

          LDX is INTEGER
          The leading dimension of the array X.

ISEED

          ISEED is INTEGER array, dimension (4)
          On entry, the seed for the random number generator.  The last
          of the four integers must be odd.  (modified on exit)

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine clattb (integer IMAT, character UPLO, character TRANS, character DIAG, integer, dimension( 4 ) ISEED, integer N, integer KD, complex, dimension( ldab, * ) AB, integer LDAB, complex, dimension( * ) B, complex, dimension( * ) WORK, real, dimension( * ) RWORK, integer INFO)

CLATTB

Purpose:

 CLATTB generates a triangular test matrix in 2-dimensional storage.
 IMAT and UPLO uniquely specify the properties of the test matrix,
 which is returned in the array A.

Parameters:

IMAT

          IMAT is INTEGER
          An integer key describing which matrix to generate for this
          path.

UPLO

          UPLO is CHARACTER*1
          Specifies whether the matrix A will be upper or lower
          triangular.
          = 'U':  Upper triangular
          = 'L':  Lower triangular

TRANS

          TRANS is CHARACTER*1
          Specifies whether the matrix or its transpose will be used.
          = 'N':  No transpose
          = 'T':  Transpose
          = 'C':  Conjugate transpose (= transpose)

DIAG

          DIAG is CHARACTER*1
          Specifies whether or not the matrix A is unit triangular.
          = 'N':  Non-unit triangular
          = 'U':  Unit triangular

ISEED

          ISEED is INTEGER array, dimension (4)
          The seed vector for the random number generator (used in
          CLATMS).  Modified on exit.

          N is INTEGER
          The order of the matrix to be generated.

          KD is INTEGER
          The number of superdiagonals or subdiagonals of the banded
          triangular matrix A.  KD >= 0.

          AB is COMPLEX array, dimension (LDAB,N)
          The upper or lower triangular banded matrix A, stored in the
          first KD+1 rows of AB.  Let j be a column of A, 1<=j<=n.
          If UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j.
          If UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).

LDAB

          LDAB is INTEGER
          The leading dimension of the array AB.  LDAB >= KD+1.

          B is COMPLEX array, dimension (N)

WORK

          WORK is COMPLEX array, dimension (2*N)

RWORK

          RWORK is REAL array, dimension (N)

INFO

          INFO is INTEGER
          = 0:  successful exit
          < 0:  if INFO = -i, the i-th argument had an illegal value

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine clattp (integer IMAT, character UPLO, character TRANS, character DIAG, integer, dimension( 4 ) ISEED, integer N, complex, dimension( * ) AP, complex, dimension( * ) B, complex, dimension( * ) WORK, real, dimension( * ) RWORK, integer INFO)

CLATTP

Purpose:

 CLATTP generates a triangular test matrix in packed storage.
 IMAT and UPLO uniquely specify the properties of the test matrix,
 which is returned in the array AP.

Parameters:

IMAT

          IMAT is INTEGER
          An integer key describing which matrix to generate for this
          path.

UPLO

          UPLO is CHARACTER*1
          Specifies whether the matrix A will be upper or lower
          triangular.
          = 'U':  Upper triangular
          = 'L':  Lower triangular

TRANS

          TRANS is CHARACTER*1
          Specifies whether the matrix or its transpose will be used.
          = 'N':  No transpose
          = 'T':  Transpose
          = 'C':  Conjugate transpose

DIAG

          DIAG is CHARACTER*1
          Specifies whether or not the matrix A is unit triangular.
          = 'N':  Non-unit triangular
          = 'U':  Unit triangular

ISEED

          ISEED is INTEGER array, dimension (4)
          The seed vector for the random number generator (used in
          CLATMS).  Modified on exit.

          N is INTEGER
          The order of the matrix to be generated.

          AP is COMPLEX array, dimension (N*(N+1)/2)
          The upper or lower triangular matrix A, packed columnwise in
          a linear array.  The j-th column of A is stored in the array
          AP as follows:
          if UPLO = 'U', AP((j-1)*j/2 + i) = A(i,j) for 1<=i<=j;
          if UPLO = 'L',
             AP((j-1)*(n-j) + j*(j+1)/2 + i-j) = A(i,j) for j<=i<=n.

          B is COMPLEX array, dimension (N)
          The right hand side vector, if IMAT > 10.

WORK

          WORK is COMPLEX array, dimension (2*N)

RWORK

          RWORK is REAL array, dimension (N)

INFO

          INFO is INTEGER
          = 0:  successful exit
          < 0:  if INFO = -i, the i-th argument had an illegal value

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine clattr (integer IMAT, character UPLO, character TRANS, character DIAG, integer, dimension( 4 ) ISEED, integer N, complex, dimension( lda, * ) A, integer LDA, complex, dimension( * ) B, complex, dimension( * ) WORK, real, dimension( * ) RWORK, integer INFO)

CLATTR

Purpose:

 CLATTR generates a triangular test matrix in 2-dimensional storage.
 IMAT and UPLO uniquely specify the properties of the test matrix,
 which is returned in the array A.

Parameters:

IMAT

          IMAT is INTEGER
          An integer key describing which matrix to generate for this
          path.

UPLO

          UPLO is CHARACTER*1
          Specifies whether the matrix A will be upper or lower
          triangular.
          = 'U':  Upper triangular
          = 'L':  Lower triangular

TRANS

          TRANS is CHARACTER*1
          Specifies whether the matrix or its transpose will be used.
          = 'N':  No transpose
          = 'T':  Transpose
          = 'C':  Conjugate transpose

DIAG

          DIAG is CHARACTER*1
          Specifies whether or not the matrix A is unit triangular.
          = 'N':  Non-unit triangular
          = 'U':  Unit triangular

ISEED

          ISEED is INTEGER array, dimension (4)
          The seed vector for the random number generator (used in
          CLATMS).  Modified on exit.

          N is INTEGER
          The order of the matrix to be generated.

          A is COMPLEX array, dimension (LDA,N)
          The triangular matrix A.  If UPLO = 'U', the leading N x N
          upper triangular part of the array A contains the upper
          triangular matrix, and the strictly lower triangular part of
          A is not referenced.  If UPLO = 'L', the leading N x N lower
          triangular part of the array A contains the lower triangular
          matrix and the strictly upper triangular part of A is not
          referenced.

LDA

          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N).

          B is COMPLEX array, dimension (N)
          The right hand side vector, if IMAT > 10.

WORK

          WORK is COMPLEX array, dimension (2*N)

RWORK

          RWORK is REAL array, dimension (N)

INFO

          INFO is INTEGER
          = 0:  successful exit
          < 0:  if INFO = -i, the i-th argument had an illegal value

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine clavhe (character UPLO, character TRANS, character DIAG, integer N, integer NRHS, complex, dimension( lda, * ) A, integer LDA, integer, dimension( * ) IPIV, complex, dimension( ldb, * ) B, integer LDB, integer INFO)

CLAVHE

Purpose:

 CLAVHE performs one of the matrix-vector operations
    x := A*x  or  x := A^H*x,
 where x is an N element vector and  A is one of the factors
 from the block U*D*U' or L*D*L' factorization computed by CHETRF.
 If TRANS = 'N', multiplies by U  or U * D  (or L  or L * D)
 If TRANS = 'C', multiplies by U' or D * U' (or L' or D * L')

Parameters:

UPLO

          UPLO is CHARACTER*1
          Specifies whether the factor stored in A is upper or lower
          triangular.
          = 'U':  Upper triangular
          = 'L':  Lower triangular

TRANS

          TRANS is CHARACTER*1
          Specifies the operation to be performed:
          = 'N':  x := A*x
          = 'C':   x := A^H*x

DIAG

          DIAG is CHARACTER*1
          Specifies whether or not the diagonal blocks are unit
          matrices.  If the diagonal blocks are assumed to be unit,
          then A = U or A = L, otherwise A = U*D or A = L*D.
          = 'U':  Diagonal blocks are assumed to be unit matrices.
          = 'N':  Diagonal blocks are assumed to be non-unit matrices.

          N is INTEGER
          The number of rows and columns of the matrix A.  N >= 0.

NRHS

          NRHS is INTEGER
          The number of right hand sides, i.e., the number of vectors
          x to be multiplied by A.  NRHS >= 0.

          A is COMPLEX array, dimension (LDA,N)
          The block diagonal matrix D and the multipliers used to
          obtain the factor U or L as computed by CHETRF_ROOK.
          Stored as a 2-D triangular matrix.

LDA

          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N).

IPIV

          IPIV is INTEGER array, dimension (N)
          Details of the interchanges and the block structure of D,
          as determined by CHETRF.
          If UPLO = 'U':
               If IPIV(k) > 0, then rows and columns k and IPIV(k)
               were interchanged and D(k,k) is a 1-by-1 diagonal block.
               (If IPIV( k ) = k, no interchange was done).
               If IPIV(k) = IPIV(k-1) < 0, then rows and
               columns k-1 and -IPIV(k) were interchanged,
               D(k-1:k,k-1:k) is a 2-by-2 diagonal block.
          If UPLO = 'L':
               If IPIV(k) > 0, then rows and columns k and IPIV(k)
               were interchanged and D(k,k) is a 1-by-1 diagonal block.
               (If IPIV( k ) = k, no interchange was done).
               If IPIV(k) = IPIV(k+1) < 0, then rows and
               columns k+1 and -IPIV(k) were interchanged,
               D(k:k+1,k:k+1) is a 2-by-2 diagonal block.

          B is COMPLEX array, dimension (LDB,NRHS)
          On entry, B contains NRHS vectors of length N.
          On exit, B is overwritten with the product A * B.

LDB

          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,N).

INFO

          INFO is INTEGER
          = 0: successful exit
          < 0: if INFO = -k, the k-th argument had an illegal value

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2013

subroutine clavhe_rook (character UPLO, character TRANS, character DIAG, integer N, integer NRHS, complex, dimension( lda, * ) A, integer LDA, integer, dimension( * ) IPIV, complex, dimension( ldb, * ) B, integer LDB, integer INFO)

CLAVHE_ROOK

Purpose:

 CLAVHE_ROOK performs one of the matrix-vector operations
    x := A*x  or  x := A^H*x,
 where x is an N element vector and  A is one of the factors
 from the block U*D*U' or L*D*L' factorization computed by CHETRF_ROOK.
 If TRANS = 'N', multiplies by U  or U * D  (or L  or L * D)
 If TRANS = 'C', multiplies by U' or D * U' (or L' or D * L')

Parameters:

UPLO

          UPLO is CHARACTER*1
          Specifies whether the factor stored in A is upper or lower
          triangular.
          = 'U':  Upper triangular
          = 'L':  Lower triangular

TRANS

          TRANS is CHARACTER*1
          Specifies the operation to be performed:
          = 'N':  x := A*x
          = 'C':   x := A^H*x

DIAG

          DIAG is CHARACTER*1
          Specifies whether or not the diagonal blocks are unit
          matrices.  If the diagonal blocks are assumed to be unit,
          then A = U or A = L, otherwise A = U*D or A = L*D.
          = 'U':  Diagonal blocks are assumed to be unit matrices.
          = 'N':  Diagonal blocks are assumed to be non-unit matrices.

          N is INTEGER
          The number of rows and columns of the matrix A.  N >= 0.

NRHS

          NRHS is INTEGER
          The number of right hand sides, i.e., the number of vectors
          x to be multiplied by A.  NRHS >= 0.

          A is COMPLEX array, dimension (LDA,N)
          The block diagonal matrix D and the multipliers used to
          obtain the factor U or L as computed by CHETRF_ROOK.
          Stored as a 2-D triangular matrix.

LDA

          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N).

IPIV

          IPIV is INTEGER array, dimension (N)
          Details of the interchanges and the block structure of D,
          as determined by CHETRF_ROOK.
          If UPLO = 'U':
             Only the last KB elements of IPIV are set.
             If IPIV(k) > 0, then rows and columns k and IPIV(k) were
             interchanged and D(k,k) is a 1-by-1 diagonal block.
             If IPIV(k) < 0 and IPIV(k-1) < 0, then rows and
             columns k and -IPIV(k) were interchanged and rows and
             columns k-1 and -IPIV(k-1) were inerchaged,
             D(k-1:k,k-1:k) is a 2-by-2 diagonal block.
          If UPLO = 'L':
             Only the first KB elements of IPIV are set.
             If IPIV(k) > 0, then rows and columns k and IPIV(k)
             were interchanged and D(k,k) is a 1-by-1 diagonal block.
             If IPIV(k) < 0 and IPIV(k+1) < 0, then rows and
             columns k and -IPIV(k) were interchanged and rows and
             columns k+1 and -IPIV(k+1) were inerchaged,
             D(k:k+1,k:k+1) is a 2-by-2 diagonal block.

          B is COMPLEX array, dimension (LDB,NRHS)
          On entry, B contains NRHS vectors of length N.
          On exit, B is overwritten with the product A * B.

LDB

          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,N).

INFO

          INFO is INTEGER
          = 0: successful exit
          < 0: if INFO = -k, the k-th argument had an illegal value

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2013

subroutine clavhp (character UPLO, character TRANS, character DIAG, integer N, integer NRHS, complex, dimension( * ) A, integer, dimension( * ) IPIV, complex, dimension( ldb, * ) B, integer LDB, integer INFO)

CLAVHP

Purpose:

    CLAVHP  performs one of the matrix-vector operations
       x := A*x  or  x := A^H*x,
    where x is an N element vector and  A is one of the factors
    from the symmetric factorization computed by CHPTRF.
    CHPTRF produces a factorization of the form
         U * D * U^H     or     L * D * L^H,
    where U (or L) is a product of permutation and unit upper (lower)
    triangular matrices, U^H (or L^H) is the conjugate transpose of
    U (or L), and D is Hermitian and block diagonal with 1 x 1 and
    2 x 2 diagonal blocks.  The multipliers for the transformations
    and the upper or lower triangular parts of the diagonal blocks
    are stored columnwise in packed format in the linear array A.
    If TRANS = 'N' or 'n', CLAVHP multiplies either by U or U * D
    (or L or L * D).
    If TRANS = 'C' or 'c', CLAVHP multiplies either by U^H or D * U^H
    (or L^H or D * L^H ).

  UPLO   - CHARACTER*1
           On entry, UPLO specifies whether the triangular matrix
           stored in A is upper or lower triangular.
              UPLO = 'U' or 'u'   The matrix is upper triangular.
              UPLO = 'L' or 'l'   The matrix is lower triangular.
           Unchanged on exit.
  TRANS  - CHARACTER*1
           On entry, TRANS specifies the operation to be performed as
           follows:
              TRANS = 'N' or 'n'   x := A*x.
              TRANS = 'C' or 'c'   x := A^H*x.
           Unchanged on exit.
  DIAG   - CHARACTER*1
           On entry, DIAG specifies whether the diagonal blocks are
           assumed to be unit matrices, as follows:
              DIAG = 'U' or 'u'   Diagonal blocks are unit matrices.
              DIAG = 'N' or 'n'   Diagonal blocks are non-unit.
           Unchanged on exit.
  N      - INTEGER
           On entry, N specifies the order of the matrix A.
           N must be at least zero.
           Unchanged on exit.
  NRHS   - INTEGER
           On entry, NRHS specifies the number of right hand sides,
           i.e., the number of vectors x to be multiplied by A.
           NRHS must be at least zero.
           Unchanged on exit.
  A      - COMPLEX array, dimension( N*(N+1)/2 )
           On entry, A contains a block diagonal matrix and the
           multipliers of the transformations used to obtain it,
           stored as a packed triangular matrix.
           Unchanged on exit.
  IPIV   - INTEGER array, dimension( N )
           On entry, IPIV contains the vector of pivot indices as
           determined by CSPTRF or CHPTRF.
           If IPIV( K ) = K, no interchange was done.
           If IPIV( K ) <> K but IPIV( K ) > 0, then row K was inter-
           changed with row IPIV( K ) and a 1 x 1 pivot block was used.
           If IPIV( K ) < 0 and UPLO = 'U', then row K-1 was exchanged
           with row | IPIV( K ) | and a 2 x 2 pivot block was used.
           If IPIV( K ) < 0 and UPLO = 'L', then row K+1 was exchanged
           with row | IPIV( K ) | and a 2 x 2 pivot block was used.
  B      - COMPLEX array, dimension( LDB, NRHS )
           On entry, B contains NRHS vectors of length N.
           On exit, B is overwritten with the product A * B.
  LDB    - INTEGER
           On entry, LDB contains the leading dimension of B as
           declared in the calling program.  LDB must be at least
           max( 1, N ).
           Unchanged on exit.
  INFO   - INTEGER
           INFO is the error flag.
           On exit, a value of 0 indicates a successful exit.
           A negative value, say -K, indicates that the K-th argument
           has an illegal value.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine clavsp (character UPLO, character TRANS, character DIAG, integer N, integer NRHS, complex, dimension( * ) A, integer, dimension( * ) IPIV, complex, dimension( ldb, * ) B, integer LDB, integer INFO)

CLAVSP

Purpose:

    CLAVSP  performs one of the matrix-vector operations
       x := A*x  or  x := A^T*x,
    where x is an N element vector and  A is one of the factors
    from the symmetric factorization computed by CSPTRF.
    CSPTRF produces a factorization of the form
         U * D * U^T     or     L * D * L^T,
    where U (or L) is a product of permutation and unit upper (lower)
    triangular matrices, U^T (or L^T) is the transpose of
    U (or L), and D is symmetric and block diagonal with 1 x 1 and
    2 x 2 diagonal blocks.  The multipliers for the transformations
    and the upper or lower triangular parts of the diagonal blocks
    are stored columnwise in packed format in the linear array A.
    If TRANS = 'N' or 'n', CLAVSP multiplies either by U or U * D
    (or L or L * D).
    If TRANS = 'C' or 'c', CLAVSP multiplies either by U^T or D * U^T
    (or L^T or D * L^T ).

  UPLO   - CHARACTER*1
           On entry, UPLO specifies whether the triangular matrix
           stored in A is upper or lower triangular.
              UPLO = 'U' or 'u'   The matrix is upper triangular.
              UPLO = 'L' or 'l'   The matrix is lower triangular.
           Unchanged on exit.
  TRANS  - CHARACTER*1
           On entry, TRANS specifies the operation to be performed as
           follows:
              TRANS = 'N' or 'n'   x := A*x.
              TRANS = 'T' or 't'   x := A^T*x.
           Unchanged on exit.
  DIAG   - CHARACTER*1
           On entry, DIAG specifies whether the diagonal blocks are
           assumed to be unit matrices, as follows:
              DIAG = 'U' or 'u'   Diagonal blocks are unit matrices.
              DIAG = 'N' or 'n'   Diagonal blocks are non-unit.
           Unchanged on exit.
  N      - INTEGER
           On entry, N specifies the order of the matrix A.
           N must be at least zero.
           Unchanged on exit.
  NRHS   - INTEGER
           On entry, NRHS specifies the number of right hand sides,
           i.e., the number of vectors x to be multiplied by A.
           NRHS must be at least zero.
           Unchanged on exit.
  A      - COMPLEX array, dimension( N*(N+1)/2 )
           On entry, A contains a block diagonal matrix and the
           multipliers of the transformations used to obtain it,
           stored as a packed triangular matrix.
           Unchanged on exit.
  IPIV   - INTEGER array, dimension( N )
           On entry, IPIV contains the vector of pivot indices as
           determined by CSPTRF.
           If IPIV( K ) = K, no interchange was done.
           If IPIV( K ) <> K but IPIV( K ) > 0, then row K was inter-
           changed with row IPIV( K ) and a 1 x 1 pivot block was used.
           If IPIV( K ) < 0 and UPLO = 'U', then row K-1 was exchanged
           with row | IPIV( K ) | and a 2 x 2 pivot block was used.
           If IPIV( K ) < 0 and UPLO = 'L', then row K+1 was exchanged
           with row | IPIV( K ) | and a 2 x 2 pivot block was used.
  B      - COMPLEX array, dimension( LDB, NRHS )
           On entry, B contains NRHS vectors of length N.
           On exit, B is overwritten with the product A * B.
  LDB    - INTEGER
           On entry, LDB contains the leading dimension of B as
           declared in the calling program.  LDB must be at least
           max( 1, N ).
           Unchanged on exit.
  INFO   - INTEGER
           INFO is the error flag.
           On exit, a value of 0 indicates a successful exit.
           A negative value, say -K, indicates that the K-th argument
           has an illegal value.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine clavsy (character UPLO, character TRANS, character DIAG, integer N, integer NRHS, complex, dimension( lda, * ) A, integer LDA, integer, dimension( * ) IPIV, complex, dimension( ldb, * ) B, integer LDB, integer INFO)

CLAVSY

Purpose:

 CLAVSY performs one of the matrix-vector operations
    x := A*x  or  x := A'*x,
 where x is an N element vector and  A is one of the factors
 from the block U*D*U' or L*D*L' factorization computed by CSYTRF.
 If TRANS = 'N', multiplies by U  or U * D  (or L  or L * D)
 If TRANS = 'T', multiplies by U' or D * U' (or L' or D * L')

Parameters:

UPLO

          UPLO is CHARACTER*1
          Specifies whether the factor stored in A is upper or lower
          triangular.
          = 'U':  Upper triangular
          = 'L':  Lower triangular

TRANS

          TRANS is CHARACTER*1
          Specifies the operation to be performed:
          = 'N':  x := A*x
          = 'T':  x := A'*x

DIAG

          DIAG is CHARACTER*1
          Specifies whether or not the diagonal blocks are unit
          matrices.  If the diagonal blocks are assumed to be unit,
          then A = U or A = L, otherwise A = U*D or A = L*D.
          = 'U':  Diagonal blocks are assumed to be unit matrices.
          = 'N':  Diagonal blocks are assumed to be non-unit matrices.

          N is INTEGER
          The number of rows and columns of the matrix A.  N >= 0.

NRHS

          NRHS is INTEGER
          The number of right hand sides, i.e., the number of vectors
          x to be multiplied by A.  NRHS >= 0.

          A is COMPLEX array, dimension (LDA,N)
          The block diagonal matrix D and the multipliers used to
          obtain the factor U or L as computed by CSYTRF.
          Stored as a 2-D triangular matrix.

LDA

          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N).

IPIV

          IPIV is INTEGER array, dimension (N)
          Details of the interchanges and the block structure of D,
          as determined by CSYTRF.
          If UPLO = 'U':
               If IPIV(k) > 0, then rows and columns k and IPIV(k)
               were interchanged and D(k,k) is a 1-by-1 diagonal block.
               (If IPIV( k ) = k, no interchange was done).
               If IPIV(k) = IPIV(k-1) < 0, then rows and
               columns k-1 and -IPIV(k) were interchanged,
               D(k-1:k,k-1:k) is a 2-by-2 diagonal block.
          If UPLO = 'L':
               If IPIV(k) > 0, then rows and columns k and IPIV(k)
               were interchanged and D(k,k) is a 1-by-1 diagonal block.
               (If IPIV( k ) = k, no interchange was done).
               If IPIV(k) = IPIV(k+1) < 0, then rows and
               columns k+1 and -IPIV(k) were interchanged,
               D(k:k+1,k:k+1) is a 2-by-2 diagonal block.

          B is COMPLEX array, dimension (LDB,NRHS)
          On entry, B contains NRHS vectors of length N.
          On exit, B is overwritten with the product A * B.

LDB

          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,N).

INFO

          INFO is INTEGER
          = 0: successful exit
          < 0: if INFO = -k, the k-th argument had an illegal value

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2013

subroutine clavsy_rook (character UPLO, character TRANS, character DIAG, integer N, integer NRHS, complex, dimension( lda, * ) A, integer LDA, integer, dimension( * ) IPIV, complex, dimension( ldb, * ) B, integer LDB, integer INFO)

CLAVSY_ROOK

Purpose:

 CLAVSY_ROOK performs one of the matrix-vector operations
    x := A*x  or  x := A'*x,
 where x is an N element vector and  A is one of the factors
 from the block U*D*U' or L*D*L' factorization computed by CSYTRF_ROOK.
 If TRANS = 'N', multiplies by U  or U * D  (or L  or L * D)
 If TRANS = 'T', multiplies by U' or D * U' (or L' or D * L')

Parameters:

UPLO

          UPLO is CHARACTER*1
          Specifies whether the factor stored in A is upper or lower
          triangular.
          = 'U':  Upper triangular
          = 'L':  Lower triangular

TRANS

          TRANS is CHARACTER*1
          Specifies the operation to be performed:
          = 'N':  x := A*x
          = 'T':  x := A'*x

DIAG

          DIAG is CHARACTER*1
          Specifies whether or not the diagonal blocks are unit
          matrices.  If the diagonal blocks are assumed to be unit,
          then A = U or A = L, otherwise A = U*D or A = L*D.
          = 'U':  Diagonal blocks are assumed to be unit matrices.
          = 'N':  Diagonal blocks are assumed to be non-unit matrices.

          N is INTEGER
          The number of rows and columns of the matrix A.  N >= 0.

NRHS

          NRHS is INTEGER
          The number of right hand sides, i.e., the number of vectors
          x to be multiplied by A.  NRHS >= 0.

          A is COMPLEX array, dimension (LDA,N)
          The block diagonal matrix D and the multipliers used to
          obtain the factor U or L as computed by CSYTRF_ROOK.
          Stored as a 2-D triangular matrix.

LDA

          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N).

IPIV

          IPIV is INTEGER array, dimension (N)
          Details of the interchanges and the block structure of D,
          as determined by CSYTRF_ROOK.
          If UPLO = 'U':
               If IPIV(k) > 0, then rows and columns k and IPIV(k)
               were interchanged and D(k,k) is a 1-by-1 diagonal block.
               (If IPIV( k ) = k, no interchange was done).
               If IPIV(k) < 0 and IPIV(k-1) < 0, then rows and
               columns k and -IPIV(k) were interchanged and rows and
               columns k-1 and -IPIV(k-1) were inerchaged,
               D(k-1:k,k-1:k) is a 2-by-2 diagonal block.
          If UPLO = 'L':
               If IPIV(k) > 0, then rows and columns k and IPIV(k)
               were interchanged and D(k,k) is a 1-by-1 diagonal block.
               (If IPIV( k ) = k, no interchange was done).
               If IPIV(k) < 0 and IPIV(k+1) < 0, then rows and
               columns k and -IPIV(k) were interchanged and rows and
               columns k+1 and -IPIV(k+1) were inerchaged,
               D(k:k+1,k:k+1) is a 2-by-2 diagonal block.

          B is COMPLEX array, dimension (LDB,NRHS)
          On entry, B contains NRHS vectors of length N.
          On exit, B is overwritten with the product A * B.

LDB

          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,N).

INFO

          INFO is INTEGER
          = 0: successful exit
          < 0: if INFO = -k, the k-th argument had an illegal value

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2013

subroutine clqt01 (integer M, integer N, complex, dimension( lda, * ) A, complex, dimension( lda, * ) AF, complex, dimension( lda, * ) Q, complex, dimension( lda, * ) L, integer LDA, complex, dimension( * ) TAU, complex, dimension( lwork ) WORK, integer LWORK, real, dimension( * ) RWORK, real, dimension( * ) RESULT)

CLQT01

Purpose:

 CLQT01 tests CGELQF, which computes the LQ factorization of an m-by-n
 matrix A, and partially tests CUNGLQ which forms the n-by-n
 orthogonal matrix Q.
 CLQT01 compares L with A*Q', and checks that Q is orthogonal.

Parameters:

          M is INTEGER
          The number of rows of the matrix A.  M >= 0.

          N is INTEGER
          The number of columns of the matrix A.  N >= 0.

          A is COMPLEX array, dimension (LDA,N)
          The m-by-n matrix A.

          AF is COMPLEX array, dimension (LDA,N)
          Details of the LQ factorization of A, as returned by CGELQF.
          See CGELQF for further details.

          Q is COMPLEX array, dimension (LDA,N)
          The n-by-n orthogonal matrix Q.

          L is COMPLEX array, dimension (LDA,max(M,N))

LDA

          LDA is INTEGER
          The leading dimension of the arrays A, AF, Q and L.
          LDA >= max(M,N).

TAU

          TAU is COMPLEX array, dimension (min(M,N))
          The scalar factors of the elementary reflectors, as returned
          by CGELQF.

WORK

          WORK is COMPLEX array, dimension (LWORK)

LWORK

          LWORK is INTEGER
          The dimension of the array WORK.

RWORK

          RWORK is REAL array, dimension (max(M,N))

RESULT

          RESULT is REAL array, dimension (2)
          The test ratios:
          RESULT(1) = norm( L - A*Q' ) / ( N * norm(A) * EPS )
          RESULT(2) = norm( I - Q*Q' ) / ( N * EPS )

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine clqt02 (integer M, integer N, integer K, complex, dimension( lda, * ) A, complex, dimension( lda, * ) AF, complex, dimension( lda, * ) Q, complex, dimension( lda, * ) L, integer LDA, complex, dimension( * ) TAU, complex, dimension( lwork ) WORK, integer LWORK, real, dimension( * ) RWORK, real, dimension( * ) RESULT)

CLQT02

Purpose:

 CLQT02 tests CUNGLQ, which generates an m-by-n matrix Q with
 orthonornmal rows that is defined as the product of k elementary
 reflectors.
 Given the LQ factorization of an m-by-n matrix A, CLQT02 generates
 the orthogonal matrix Q defined by the factorization of the first k
 rows of A; it compares L(1:k,1:m) with A(1:k,1:n)*Q(1:m,1:n)', and
 checks that the rows of Q are orthonormal.

Parameters:

          M is INTEGER
          The number of rows of the matrix Q to be generated.  M >= 0.

          N is INTEGER
          The number of columns of the matrix Q to be generated.
          N >= M >= 0.

          K is INTEGER
          The number of elementary reflectors whose product defines the
          matrix Q. M >= K >= 0.

          A is COMPLEX array, dimension (LDA,N)
          The m-by-n matrix A which was factorized by CLQT01.

          AF is COMPLEX array, dimension (LDA,N)
          Details of the LQ factorization of A, as returned by CGELQF.
          See CGELQF for further details.

          Q is COMPLEX array, dimension (LDA,N)

          L is COMPLEX array, dimension (LDA,M)

LDA

          LDA is INTEGER
          The leading dimension of the arrays A, AF, Q and L. LDA >= N.

TAU

          TAU is COMPLEX array, dimension (M)
          The scalar factors of the elementary reflectors corresponding
          to the LQ factorization in AF.

WORK

          WORK is COMPLEX array, dimension (LWORK)

LWORK

          LWORK is INTEGER
          The dimension of the array WORK.

RWORK

          RWORK is REAL array, dimension (M)

RESULT

          RESULT is REAL array, dimension (2)
          The test ratios:
          RESULT(1) = norm( L - A*Q' ) / ( N * norm(A) * EPS )
          RESULT(2) = norm( I - Q*Q' ) / ( N * EPS )

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine clqt03 (integer M, integer N, integer K, complex, dimension( lda, * ) AF, complex, dimension( lda, * ) C, complex, dimension( lda, * ) CC, complex, dimension( lda, * ) Q, integer LDA, complex, dimension( * ) TAU, complex, dimension( lwork ) WORK, integer LWORK, real, dimension( * ) RWORK, real, dimension( * ) RESULT)

CLQT03

Purpose:

 CLQT03 tests CUNMLQ, which computes Q*C, Q'*C, C*Q or C*Q'.
 CLQT03 compares the results of a call to CUNMLQ with the results of
 forming Q explicitly by a call to CUNGLQ and then performing matrix
 multiplication by a call to CGEMM.

Parameters:

          M is INTEGER
          The number of rows or columns of the matrix C; C is n-by-m if
          Q is applied from the left, or m-by-n if Q is applied from
          the right.  M >= 0.

          N is INTEGER
          The order of the orthogonal matrix Q.  N >= 0.

          K is INTEGER
          The number of elementary reflectors whose product defines the
          orthogonal matrix Q.  N >= K >= 0.

          AF is COMPLEX array, dimension (LDA,N)
          Details of the LQ factorization of an m-by-n matrix, as
          returned by CGELQF. See CGELQF for further details.

          C is COMPLEX array, dimension (LDA,N)

          CC is COMPLEX array, dimension (LDA,N)

          Q is COMPLEX array, dimension (LDA,N)

LDA

          LDA is INTEGER
          The leading dimension of the arrays AF, C, CC, and Q.

TAU

          TAU is COMPLEX array, dimension (min(M,N))
          The scalar factors of the elementary reflectors corresponding
          to the LQ factorization in AF.

WORK

          WORK is COMPLEX array, dimension (LWORK)

LWORK

          LWORK is INTEGER
          The length of WORK.  LWORK must be at least M, and should be
          M*NB, where NB is the blocksize for this environment.

RWORK

          RWORK is REAL array, dimension (M)

RESULT

          RESULT is REAL array, dimension (4)
          The test ratios compare two techniques for multiplying a
          random matrix C by an n-by-n orthogonal matrix Q.
          RESULT(1) = norm( Q*C - Q*C )  / ( N * norm(C) * EPS )
          RESULT(2) = norm( C*Q - C*Q )  / ( N * norm(C) * EPS )
          RESULT(3) = norm( Q'*C - Q'*C )/ ( N * norm(C) * EPS )
          RESULT(4) = norm( C*Q' - C*Q' )/ ( N * norm(C) * EPS )

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine cpbt01 (character UPLO, integer N, integer KD, complex, dimension( lda, * ) A, integer LDA, complex, dimension( ldafac, * ) AFAC, integer LDAFAC, real, dimension( * ) RWORK, real RESID)

CPBT01

Purpose:

 CPBT01 reconstructs a Hermitian positive definite band matrix A from
 its L*L' or U'*U factorization and computes the residual
    norm( L*L' - A ) / ( N * norm(A) * EPS ) or
    norm( U'*U - A ) / ( N * norm(A) * EPS ),
 where EPS is the machine epsilon, L' is the conjugate transpose of
 L, and U' is the conjugate transpose of U.

Parameters:

UPLO

          UPLO is CHARACTER*1
          Specifies whether the upper or lower triangular part of the
          Hermitian matrix A is stored:
          = 'U':  Upper triangular
          = 'L':  Lower triangular

          N is INTEGER
          The number of rows and columns of the matrix A.  N >= 0.

          KD is INTEGER
          The number of super-diagonals of the matrix A if UPLO = 'U',
          or the number of sub-diagonals if UPLO = 'L'.  KD >= 0.

          A is COMPLEX array, dimension (LDA,N)
          The original Hermitian band matrix A.  If UPLO = 'U', the
          upper triangular part of A is stored as a band matrix; if
          UPLO = 'L', the lower triangular part of A is stored.  The
          columns of the appropriate triangle are stored in the columns
          of A and the diagonals of the triangle are stored in the rows
          of A.  See CPBTRF for further details.

LDA

          LDA is INTEGER.
          The leading dimension of the array A.  LDA >= max(1,KD+1).

AFAC

          AFAC is COMPLEX array, dimension (LDAFAC,N)
          The factored form of the matrix A.  AFAC contains the factor
          L or U from the L*L' or U'*U factorization in band storage
          format, as computed by CPBTRF.

LDAFAC

          LDAFAC is INTEGER
          The leading dimension of the array AFAC.
          LDAFAC >= max(1,KD+1).

RWORK

          RWORK is REAL array, dimension (N)

RESID

          RESID is REAL
          If UPLO = 'L', norm(L*L' - A) / ( N * norm(A) * EPS )
          If UPLO = 'U', norm(U'*U - A) / ( N * norm(A) * EPS )

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine cpbt02 (character UPLO, integer N, integer KD, integer NRHS, complex, dimension( lda, * ) A, integer LDA, complex, dimension( ldx, * ) X, integer LDX, complex, dimension( ldb, * ) B, integer LDB, real, dimension( * ) RWORK, real RESID)

CPBT02

Purpose:

 CPBT02 computes the residual for a solution of a Hermitian banded
 system of equations  A*x = b:
    RESID = norm( B - A*X ) / ( norm(A) * norm(X) * EPS)
 where EPS is the machine precision.

Parameters:

UPLO

          UPLO is CHARACTER*1
          Specifies whether the upper or lower triangular part of the
          Hermitian matrix A is stored:
          = 'U':  Upper triangular
          = 'L':  Lower triangular

          N is INTEGER
          The number of rows and columns of the matrix A.  N >= 0.

          KD is INTEGER
          The number of super-diagonals of the matrix A if UPLO = 'U',
          or the number of sub-diagonals if UPLO = 'L'.  KD >= 0.

NRHS

          NRHS is INTEGER
          The number of right hand sides. NRHS >= 0.

          A is COMPLEX array, dimension (LDA,N)
          The original Hermitian band matrix A.  If UPLO = 'U', the
          upper triangular part of A is stored as a band matrix; if
          UPLO = 'L', the lower triangular part of A is stored.  The
          columns of the appropriate triangle are stored in the columns
          of A and the diagonals of the triangle are stored in the rows
          of A.  See CPBTRF for further details.

LDA

          LDA is INTEGER.
          The leading dimension of the array A.  LDA >= max(1,KD+1).

          X is COMPLEX array, dimension (LDX,NRHS)
          The computed solution vectors for the system of linear
          equations.

LDX

          LDX is INTEGER
          The leading dimension of the array X.   LDX >= max(1,N).

          B is COMPLEX array, dimension (LDB,NRHS)
          On entry, the right hand side vectors for the system of
          linear equations.
          On exit, B is overwritten with the difference B - A*X.

LDB

          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,N).

RWORK

          RWORK is REAL array, dimension (N)

RESID

          RESID is REAL
          The maximum over the number of right hand sides of
          norm(B - A*X) / ( norm(A) * norm(X) * EPS ).

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine cpbt05 (character UPLO, integer N, integer KD, integer NRHS, complex, dimension( ldab, * ) AB, integer LDAB, complex, dimension( ldb, * ) B, integer LDB, complex, dimension( ldx, * ) X, integer LDX, complex, dimension( ldxact, * ) XACT, integer LDXACT, real, dimension( * ) FERR, real, dimension( * ) BERR, real, dimension( * ) RESLTS)

CPBT05

Purpose:

 CPBT05 tests the error bounds from iterative refinement for the
 computed solution to a system of equations A*X = B, where A is a
 Hermitian band matrix.
 RESLTS(1) = test of the error bound
           = norm(X - XACT) / ( norm(X) * FERR )
 A large value is returned if this ratio is not less than one.
 RESLTS(2) = residual from the iterative refinement routine
           = the maximum of BERR / ( NZ*EPS + (*) ), where
             (*) = NZ*UNFL / (min_i (abs(A)*abs(X) +abs(b))_i )
             and NZ = max. number of nonzeros in any row of A, plus 1

Parameters:

UPLO

          UPLO is CHARACTER*1
          Specifies whether the upper or lower triangular part of the
          Hermitian matrix A is stored.
          = 'U':  Upper triangular
          = 'L':  Lower triangular

          N is INTEGER
          The number of rows of the matrices X, B, and XACT, and the
          order of the matrix A.  N >= 0.

          KD is INTEGER
          The number of super-diagonals of the matrix A if UPLO = 'U',
          or the number of sub-diagonals if UPLO = 'L'.  KD >= 0.

NRHS

          NRHS is INTEGER
          The number of columns of the matrices X, B, and XACT.
          NRHS >= 0.

          AB is COMPLEX array, dimension (LDAB,N)
          The upper or lower triangle of the Hermitian band matrix A,
          stored in the first KD+1 rows of the array.  The j-th column
          of A is stored in the j-th column of the array AB as follows:
          if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).

LDAB

          LDAB is INTEGER
          The leading dimension of the array AB.  LDAB >= KD+1.

          B is COMPLEX array, dimension (LDB,NRHS)
          The right hand side vectors for the system of linear
          equations.

LDB

          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,N).

          X is COMPLEX array, dimension (LDX,NRHS)
          The computed solution vectors.  Each vector is stored as a
          column of the matrix X.

LDX

          LDX is INTEGER
          The leading dimension of the array X.  LDX >= max(1,N).

XACT

          XACT is COMPLEX array, dimension (LDX,NRHS)
          The exact solution vectors.  Each vector is stored as a
          column of the matrix XACT.

LDXACT

          LDXACT is INTEGER
          The leading dimension of the array XACT.  LDXACT >= max(1,N).

FERR

          FERR is REAL array, dimension (NRHS)
          The estimated forward error bounds for each solution vector
          X.  If XTRUE is the true solution, FERR bounds the magnitude
          of the largest entry in (X - XTRUE) divided by the magnitude
          of the largest entry in X.

BERR

          BERR is REAL array, dimension (NRHS)
          The componentwise relative backward error of each solution
          vector (i.e., the smallest relative change in any entry of A
          or B that makes X an exact solution).

RESLTS

          RESLTS is REAL array, dimension (2)
          The maximum over the NRHS solution vectors of the ratios:
          RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR )
          RESLTS(2) = BERR / ( NZ*EPS + (*) )

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine cpot01 (character UPLO, integer N, complex, dimension( lda, * ) A, integer LDA, complex, dimension( ldafac, * ) AFAC, integer LDAFAC, real, dimension( * ) RWORK, real RESID)

CPOT01

Purpose:

 CPOT01 reconstructs a Hermitian positive definite matrix  A  from
 its L*L' or U'*U factorization and computes the residual
    norm( L*L' - A ) / ( N * norm(A) * EPS ) or
    norm( U'*U - A ) / ( N * norm(A) * EPS ),
 where EPS is the machine epsilon, L' is the conjugate transpose of L,
 and U' is the conjugate transpose of U.

Parameters:

UPLO

          UPLO is CHARACTER*1
          Specifies whether the upper or lower triangular part of the
          Hermitian matrix A is stored:
          = 'U':  Upper triangular
          = 'L':  Lower triangular

          N is INTEGER
          The number of rows and columns of the matrix A.  N >= 0.

          A is COMPLEX array, dimension (LDA,N)
          The original Hermitian matrix A.

LDA

          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N)

AFAC

          AFAC is COMPLEX array, dimension (LDAFAC,N)
          On entry, the factor L or U from the L*L' or U'*U
          factorization of A.
          Overwritten with the reconstructed matrix, and then with the
          difference L*L' - A (or U'*U - A).

LDAFAC

          LDAFAC is INTEGER
          The leading dimension of the array AFAC.  LDAFAC >= max(1,N).

RWORK

          RWORK is REAL array, dimension (N)

RESID

          RESID is REAL
          If UPLO = 'L', norm(L*L' - A) / ( N * norm(A) * EPS )
          If UPLO = 'U', norm(U'*U - A) / ( N * norm(A) * EPS )

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine cpot02 (character UPLO, integer N, integer NRHS, complex, dimension( lda, * ) A, integer LDA, complex, dimension( ldx, * ) X, integer LDX, complex, dimension( ldb, * ) B, integer LDB, real, dimension( * ) RWORK, real RESID)

CPOT02

Purpose:

 CPOT02 computes the residual for the solution of a Hermitian system
 of linear equations  A*x = b:
    RESID = norm(B - A*X) / ( norm(A) * norm(X) * EPS ),
 where EPS is the machine epsilon.

Parameters:

UPLO

          UPLO is CHARACTER*1
          Specifies whether the upper or lower triangular part of the
          Hermitian matrix A is stored:
          = 'U':  Upper triangular
          = 'L':  Lower triangular

          N is INTEGER
          The number of rows and columns of the matrix A.  N >= 0.

NRHS

          NRHS is INTEGER
          The number of columns of B, the matrix of right hand sides.
          NRHS >= 0.

          A is COMPLEX array, dimension (LDA,N)
          The original Hermitian matrix A.

LDA

          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N)

          X is COMPLEX array, dimension (LDX,NRHS)
          The computed solution vectors for the system of linear
          equations.

LDX

          LDX is INTEGER
          The leading dimension of the array X.   LDX >= max(1,N).

          B is COMPLEX array, dimension (LDB,NRHS)
          On entry, the right hand side vectors for the system of
          linear equations.
          On exit, B is overwritten with the difference B - A*X.

LDB

          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,N).

RWORK

          RWORK is REAL array, dimension (N)

RESID

          RESID is REAL
          The maximum over the number of right hand sides of
          norm(B - A*X) / ( norm(A) * norm(X) * EPS ).

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine cpot03 (character UPLO, integer N, complex, dimension( lda, * ) A, integer LDA, complex, dimension( ldainv, * ) AINV, integer LDAINV, complex, dimension( ldwork, * ) WORK, integer LDWORK, real, dimension( * ) RWORK, real RCOND, real RESID)

CPOT03

Purpose:

 CPOT03 computes the residual for a Hermitian matrix times its
 inverse:
    norm( I - A*AINV ) / ( N * norm(A) * norm(AINV) * EPS ),
 where EPS is the machine epsilon.

Parameters:

UPLO

          UPLO is CHARACTER*1
          Specifies whether the upper or lower triangular part of the
          Hermitian matrix A is stored:
          = 'U':  Upper triangular
          = 'L':  Lower triangular

          N is INTEGER
          The number of rows and columns of the matrix A.  N >= 0.

          A is COMPLEX array, dimension (LDA,N)
          The original Hermitian matrix A.

LDA

          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N)

AINV

          AINV is COMPLEX array, dimension (LDAINV,N)
          On entry, the inverse of the matrix A, stored as a Hermitian
          matrix in the same format as A.
          In this version, AINV is expanded into a full matrix and
          multiplied by A, so the opposing triangle of AINV will be
          changed; i.e., if the upper triangular part of AINV is
          stored, the lower triangular part will be used as work space.

LDAINV

          LDAINV is INTEGER
          The leading dimension of the array AINV.  LDAINV >= max(1,N).

WORK

          WORK is COMPLEX array, dimension (LDWORK,N)

LDWORK

          LDWORK is INTEGER
          The leading dimension of the array WORK.  LDWORK >= max(1,N).

RWORK

          RWORK is REAL array, dimension (N)

RCOND

          RCOND is REAL
          The reciprocal of the condition number of A, computed as
          ( 1/norm(A) ) / norm(AINV).

RESID

          RESID is REAL
          norm(I - A*AINV) / ( N * norm(A) * norm(AINV) * EPS )

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine cpot05 (character UPLO, integer N, integer NRHS, complex, dimension( lda, * ) A, integer LDA, complex, dimension( ldb, * ) B, integer LDB, complex, dimension( ldx, * ) X, integer LDX, complex, dimension( ldxact, * ) XACT, integer LDXACT, real, dimension( * ) FERR, real, dimension( * ) BERR, real, dimension( * ) RESLTS)

CPOT05

Purpose:

 CPOT05 tests the error bounds from iterative refinement for the
 computed solution to a system of equations A*X = B, where A is a
 Hermitian n by n matrix.
 RESLTS(1) = test of the error bound
           = norm(X - XACT) / ( norm(X) * FERR )
 A large value is returned if this ratio is not less than one.
 RESLTS(2) = residual from the iterative refinement routine
           = the maximum of BERR / ( (n+1)*EPS + (*) ), where
             (*) = (n+1)*UNFL / (min_i (abs(A)*abs(X) +abs(b))_i )

Parameters:

UPLO

          UPLO is CHARACTER*1
          Specifies whether the upper or lower triangular part of the
          Hermitian matrix A is stored.
          = 'U':  Upper triangular
          = 'L':  Lower triangular

          N is INTEGER
          The number of rows of the matrices X, B, and XACT, and the
          order of the matrix A.  N >= 0.

NRHS

          NRHS is INTEGER
          The number of columns of the matrices X, B, and XACT.
          NRHS >= 0.

          A is COMPLEX array, dimension (LDA,N)
          The Hermitian matrix A.  If UPLO = 'U', the leading n by n
          upper triangular part of A contains the upper triangular part
          of the matrix A, and the strictly lower triangular part of A
          is not referenced.  If UPLO = 'L', the leading n by n lower
          triangular part of A contains the lower triangular part of
          the matrix A, and the strictly upper triangular part of A is
          not referenced.

LDA

          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N).

          B is COMPLEX array, dimension (LDB,NRHS)
          The right hand side vectors for the system of linear
          equations.

LDB

          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,N).

          X is COMPLEX array, dimension (LDX,NRHS)
          The computed solution vectors.  Each vector is stored as a
          column of the matrix X.

LDX

          LDX is INTEGER
          The leading dimension of the array X.  LDX >= max(1,N).

XACT

          XACT is COMPLEX array, dimension (LDX,NRHS)
          The exact solution vectors.  Each vector is stored as a
          column of the matrix XACT.

LDXACT

          LDXACT is INTEGER
          The leading dimension of the array XACT.  LDXACT >= max(1,N).

FERR

          FERR is REAL array, dimension (NRHS)
          The estimated forward error bounds for each solution vector
          X.  If XTRUE is the true solution, FERR bounds the magnitude
          of the largest entry in (X - XTRUE) divided by the magnitude
          of the largest entry in X.

BERR

          BERR is REAL array, dimension (NRHS)
          The componentwise relative backward error of each solution
          vector (i.e., the smallest relative change in any entry of A
          or B that makes X an exact solution).

RESLTS

          RESLTS is REAL array, dimension (2)
          The maximum over the NRHS solution vectors of the ratios:
          RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR )
          RESLTS(2) = BERR / ( (n+1)*EPS + (*) )

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine cppt01 (character UPLO, integer N, complex, dimension( * ) A, complex, dimension( * ) AFAC, real, dimension( * ) RWORK, real RESID)

CPPT01

Purpose:

 CPPT01 reconstructs a Hermitian positive definite packed matrix A
 from its L*L' or U'*U factorization and computes the residual
    norm( L*L' - A ) / ( N * norm(A) * EPS ) or
    norm( U'*U - A ) / ( N * norm(A) * EPS ),
 where EPS is the machine epsilon, L' is the conjugate transpose of
 L, and U' is the conjugate transpose of U.

Parameters:

UPLO

          UPLO is CHARACTER*1
          Specifies whether the upper or lower triangular part of the
          Hermitian matrix A is stored:
          = 'U':  Upper triangular
          = 'L':  Lower triangular

          N is INTEGER
          The number of rows and columns of the matrix A.  N >= 0.

          A is COMPLEX array, dimension (N*(N+1)/2)
          The original Hermitian matrix A, stored as a packed
          triangular matrix.

AFAC

          AFAC is COMPLEX array, dimension (N*(N+1)/2)
          On entry, the factor L or U from the L*L' or U'*U
          factorization of A, stored as a packed triangular matrix.
          Overwritten with the reconstructed matrix, and then with the
          difference L*L' - A (or U'*U - A).

RWORK

          RWORK is REAL array, dimension (N)

RESID

          RESID is REAL
          If UPLO = 'L', norm(L*L' - A) / ( N * norm(A) * EPS )
          If UPLO = 'U', norm(U'*U - A) / ( N * norm(A) * EPS )

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine cppt02 (character UPLO, integer N, integer NRHS, complex, dimension( * ) A, complex, dimension( ldx, * ) X, integer LDX, complex, dimension( ldb, * ) B, integer LDB, real, dimension( * ) RWORK, real RESID)

CPPT02

Purpose:

 CPPT02 computes the residual in the solution of a Hermitian system
 of linear equations  A*x = b  when packed storage is used for the
 coefficient matrix.  The ratio computed is
    RESID = norm(B - A*X) / ( norm(A) * norm(X) * EPS),
 where EPS is the machine precision.

Parameters:

UPLO

          UPLO is CHARACTER*1
          Specifies whether the upper or lower triangular part of the
          Hermitian matrix A is stored:
          = 'U':  Upper triangular
          = 'L':  Lower triangular

          N is INTEGER
          The number of rows and columns of the matrix A.  N >= 0.

NRHS

          NRHS is INTEGER
          The number of columns of B, the matrix of right hand sides.
          NRHS >= 0.

          A is COMPLEX array, dimension (N*(N+1)/2)
          The original Hermitian matrix A, stored as a packed
          triangular matrix.

          X is COMPLEX array, dimension (LDX,NRHS)
          The computed solution vectors for the system of linear
          equations.

LDX

          LDX is INTEGER
          The leading dimension of the array X.   LDX >= max(1,N).

          B is COMPLEX array, dimension (LDB,NRHS)
          On entry, the right hand side vectors for the system of
          linear equations.
          On exit, B is overwritten with the difference B - A*X.

LDB

          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,N).

RWORK

          RWORK is REAL array, dimension (N)

RESID

          RESID is REAL
          The maximum over the number of right hand sides of
          norm(B - A*X) / ( norm(A) * norm(X) * EPS ).

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine cppt03 (character UPLO, integer N, complex, dimension( * ) A, complex, dimension( * ) AINV, complex, dimension( ldwork, * ) WORK, integer LDWORK, real, dimension( * ) RWORK, real RCOND, real RESID)

CPPT03

Purpose:

 CPPT03 computes the residual for a Hermitian packed matrix times its
 inverse:
    norm( I - A*AINV ) / ( N * norm(A) * norm(AINV) * EPS ),
 where EPS is the machine epsilon.

Parameters:

UPLO

          UPLO is CHARACTER*1
          Specifies whether the upper or lower triangular part of the
          Hermitian matrix A is stored:
          = 'U':  Upper triangular
          = 'L':  Lower triangular

          N is INTEGER
          The number of rows and columns of the matrix A.  N >= 0.

          A is COMPLEX array, dimension (N*(N+1)/2)
          The original Hermitian matrix A, stored as a packed
          triangular matrix.

AINV

          AINV is COMPLEX array, dimension (N*(N+1)/2)
          The (Hermitian) inverse of the matrix A, stored as a packed
          triangular matrix.

WORK

          WORK is COMPLEX array, dimension (LDWORK,N)

LDWORK

          LDWORK is INTEGER
          The leading dimension of the array WORK.  LDWORK >= max(1,N).

RWORK

          RWORK is REAL array, dimension (N)

RCOND

          RCOND is REAL
          The reciprocal of the condition number of A, computed as
          ( 1/norm(A) ) / norm(AINV).

RESID

          RESID is REAL
          norm(I - A*AINV) / ( N * norm(A) * norm(AINV) * EPS )

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine cppt05 (character UPLO, integer N, integer NRHS, complex, dimension( * ) AP, complex, dimension( ldb, * ) B, integer LDB, complex, dimension( ldx, * ) X, integer LDX, complex, dimension( ldxact, * ) XACT, integer LDXACT, real, dimension( * ) FERR, real, dimension( * ) BERR, real, dimension( * ) RESLTS)

CPPT05

Purpose:

 CPPT05 tests the error bounds from iterative refinement for the
 computed solution to a system of equations A*X = B, where A is a
 Hermitian matrix in packed storage format.
 RESLTS(1) = test of the error bound
           = norm(X - XACT) / ( norm(X) * FERR )
 A large value is returned if this ratio is not less than one.
 RESLTS(2) = residual from the iterative refinement routine
           = the maximum of BERR / ( (n+1)*EPS + (*) ), where
             (*) = (n+1)*UNFL / (min_i (abs(A)*abs(X) +abs(b))_i )

Parameters:

UPLO

          UPLO is CHARACTER*1
          Specifies whether the upper or lower triangular part of the
          Hermitian matrix A is stored.
          = 'U':  Upper triangular
          = 'L':  Lower triangular

          N is INTEGER
          The number of rows of the matrices X, B, and XACT, and the
          order of the matrix A.  N >= 0.

NRHS

          NRHS is INTEGER
          The number of columns of the matrices X, B, and XACT.
          NRHS >= 0.

          AP is COMPLEX array, dimension (N*(N+1)/2)
          The upper or lower triangle of the Hermitian matrix A, packed
          columnwise in a linear array.  The j-th column of A is stored
          in the array AP as follows:
          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.

          B is COMPLEX array, dimension (LDB,NRHS)
          The right hand side vectors for the system of linear
          equations.

LDB

          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,N).

          X is COMPLEX array, dimension (LDX,NRHS)
          The computed solution vectors.  Each vector is stored as a
          column of the matrix X.

LDX

          LDX is INTEGER
          The leading dimension of the array X.  LDX >= max(1,N).

XACT

          XACT is COMPLEX array, dimension (LDX,NRHS)
          The exact solution vectors.  Each vector is stored as a
          column of the matrix XACT.

LDXACT

          LDXACT is INTEGER
          The leading dimension of the array XACT.  LDXACT >= max(1,N).

FERR

          FERR is REAL array, dimension (NRHS)
          The estimated forward error bounds for each solution vector
          X.  If XTRUE is the true solution, FERR bounds the magnitude
          of the largest entry in (X - XTRUE) divided by the magnitude
          of the largest entry in X.

BERR

          BERR is REAL array, dimension (NRHS)
          The componentwise relative backward error of each solution
          vector (i.e., the smallest relative change in any entry of A
          or B that makes X an exact solution).

RESLTS

          RESLTS is REAL array, dimension (2)
          The maximum over the NRHS solution vectors of the ratios:
          RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR )
          RESLTS(2) = BERR / ( (n+1)*EPS + (*) )

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine cpst01 (character UPLO, integer N, complex, dimension( lda, * ) A, integer LDA, complex, dimension( ldafac, * ) AFAC, integer LDAFAC, complex, dimension( ldperm, * ) PERM, integer LDPERM, integer, dimension( * ) PIV, real, dimension( * ) RWORK, real RESID, integer RANK)

CPST01

Purpose:

 CPST01 reconstructs an Hermitian positive semidefinite matrix A
 from its L or U factors and the permutation matrix P and computes
 the residual
    norm( P*L*L'*P' - A ) / ( N * norm(A) * EPS ) or
    norm( P*U'*U*P' - A ) / ( N * norm(A) * EPS ),
 where EPS is the machine epsilon, L' is the conjugate transpose of L,
 and U' is the conjugate transpose of U.

Parameters:

UPLO

          UPLO is CHARACTER*1
          Specifies whether the upper or lower triangular part of the
          Hermitian matrix A is stored:
          = 'U':  Upper triangular
          = 'L':  Lower triangular

          N is INTEGER
          The number of rows and columns of the matrix A.  N >= 0.

          A is COMPLEX array, dimension (LDA,N)
          The original Hermitian matrix A.

LDA

          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N)

AFAC

          AFAC is COMPLEX array, dimension (LDAFAC,N)
          The factor L or U from the L*L' or U'*U
          factorization of A.

LDAFAC

          LDAFAC is INTEGER
          The leading dimension of the array AFAC.  LDAFAC >= max(1,N).

PERM

          PERM is COMPLEX array, dimension (LDPERM,N)
          Overwritten with the reconstructed matrix, and then with the
          difference P*L*L'*P' - A (or P*U'*U*P' - A)

LDPERM

          LDPERM is INTEGER
          The leading dimension of the array PERM.
          LDAPERM >= max(1,N).

PIV

          PIV is INTEGER array, dimension (N)
          PIV is such that the nonzero entries are
          P( PIV( K ), K ) = 1.

RWORK

          RWORK is REAL array, dimension (N)

RESID

          RESID is REAL
          If UPLO = 'L', norm(L*L' - A) / ( N * norm(A) * EPS )
          If UPLO = 'U', norm(U'*U - A) / ( N * norm(A) * EPS )

RANK

          RANK is INTEGER
          number of nonzero singular values of A.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine cptt01 (integer N, real, dimension( * ) D, complex, dimension( * ) E, real, dimension( * ) DF, complex, dimension( * ) EF, complex, dimension( * ) WORK, real RESID)

CPTT01

Purpose:

 CPTT01 reconstructs a tridiagonal matrix A from its L*D*L'
 factorization and computes the residual
    norm(L*D*L' - A) / ( n * norm(A) * EPS ),
 where EPS is the machine epsilon.

Parameters:

          N is INTEGTER
          The order of the matrix A.

          D is REAL array, dimension (N)
          The n diagonal elements of the tridiagonal matrix A.

          E is COMPLEX array, dimension (N-1)
          The (n-1) subdiagonal elements of the tridiagonal matrix A.

          DF is REAL array, dimension (N)
          The n diagonal elements of the factor L from the L*D*L'
          factorization of A.

          EF is COMPLEX array, dimension (N-1)
          The (n-1) subdiagonal elements of the factor L from the
          L*D*L' factorization of A.

WORK

          WORK is COMPLEX array, dimension (2*N)

RESID

          RESID is REAL
          norm(L*D*L' - A) / (n * norm(A) * EPS)

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine cptt02 (character UPLO, integer N, integer NRHS, real, dimension( * ) D, complex, dimension( * ) E, complex, dimension( ldx, * ) X, integer LDX, complex, dimension( ldb, * ) B, integer LDB, real RESID)

CPTT02

Purpose:

 CPTT02 computes the residual for the solution to a symmetric
 tridiagonal system of equations:
    RESID = norm(B - A*X) / (norm(A) * norm(X) * EPS),
 where EPS is the machine epsilon.

Parameters:

UPLO

          UPLO is CHARACTER*1
          Specifies whether the superdiagonal or the subdiagonal of the
          tridiagonal matrix A is stored.
          = 'U':  E is the superdiagonal of A
          = 'L':  E is the subdiagonal of A

          N is INTEGTER
          The order of the matrix A.

NRHS

          NRHS is INTEGER
          The number of right hand sides, i.e., the number of columns
          of the matrices B and X.  NRHS >= 0.

          D is REAL array, dimension (N)
          The n diagonal elements of the tridiagonal matrix A.

          E is COMPLEX array, dimension (N-1)
          The (n-1) subdiagonal elements of the tridiagonal matrix A.

          X is COMPLEX array, dimension (LDX,NRHS)
          The n by nrhs matrix of solution vectors X.

LDX

          LDX is INTEGER
          The leading dimension of the array X.  LDX >= max(1,N).

          B is COMPLEX array, dimension (LDB,NRHS)
          On entry, the n by nrhs matrix of right hand side vectors B.
          On exit, B is overwritten with the difference B - A*X.

LDB

          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,N).

RESID

          RESID is REAL
          norm(B - A*X) / (norm(A) * norm(X) * EPS)

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine cptt05 (integer N, integer NRHS, real, dimension( * ) D, complex, dimension( * ) E, complex, dimension( ldb, * ) B, integer LDB, complex, dimension( ldx, * ) X, integer LDX, complex, dimension( ldxact, * ) XACT, integer LDXACT, real, dimension( * ) FERR, real, dimension( * ) BERR, real, dimension( * ) RESLTS)

CPTT05

Purpose:

 CPTT05 tests the error bounds from iterative refinement for the
 computed solution to a system of equations A*X = B, where A is a
 Hermitian tridiagonal matrix of order n.
 RESLTS(1) = test of the error bound
           = norm(X - XACT) / ( norm(X) * FERR )
 A large value is returned if this ratio is not less than one.
 RESLTS(2) = residual from the iterative refinement routine
           = the maximum of BERR / ( NZ*EPS + (*) ), where
             (*) = NZ*UNFL / (min_i (abs(A)*abs(X) +abs(b))_i )
             and NZ = max. number of nonzeros in any row of A, plus 1

Parameters:

          N is INTEGER
          The number of rows of the matrices X, B, and XACT, and the
          order of the matrix A.  N >= 0.

NRHS

          NRHS is INTEGER
          The number of columns of the matrices X, B, and XACT.
          NRHS >= 0.

          D is REAL array, dimension (N)
          The n diagonal elements of the tridiagonal matrix A.

          E is COMPLEX array, dimension (N-1)
          The (n-1) subdiagonal elements of the tridiagonal matrix A.

          B is COMPLEX array, dimension (LDB,NRHS)
          The right hand side vectors for the system of linear
          equations.

LDB

          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,N).

          X is COMPLEX array, dimension (LDX,NRHS)
          The computed solution vectors.  Each vector is stored as a
          column of the matrix X.

LDX

          LDX is INTEGER
          The leading dimension of the array X.  LDX >= max(1,N).

XACT

          XACT is COMPLEX array, dimension (LDX,NRHS)
          The exact solution vectors.  Each vector is stored as a
          column of the matrix XACT.

LDXACT

          LDXACT is INTEGER
          The leading dimension of the array XACT.  LDXACT >= max(1,N).

FERR

          FERR is REAL array, dimension (NRHS)
          The estimated forward error bounds for each solution vector
          X.  If XTRUE is the true solution, FERR bounds the magnitude
          of the largest entry in (X - XTRUE) divided by the magnitude
          of the largest entry in X.

BERR

          BERR is REAL array, dimension (NRHS)
          The componentwise relative backward error of each solution
          vector (i.e., the smallest relative change in any entry of A
          or B that makes X an exact solution).

RESLTS

          RESLTS is REAL array, dimension (2)
          The maximum over the NRHS solution vectors of the ratios:
          RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR )
          RESLTS(2) = BERR / ( NZ*EPS + (*) )

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine cqlt01 (integer M, integer N, complex, dimension( lda, * ) A, complex, dimension( lda, * ) AF, complex, dimension( lda, * ) Q, complex, dimension( lda, * ) L, integer LDA, complex, dimension( * ) TAU, complex, dimension( lwork ) WORK, integer LWORK, real, dimension( * ) RWORK, real, dimension( * ) RESULT)

CQLT01

Purpose:

 CQLT01 tests CGEQLF, which computes the QL factorization of an m-by-n
 matrix A, and partially tests CUNGQL which forms the m-by-m
 orthogonal matrix Q.
 CQLT01 compares L with Q'*A, and checks that Q is orthogonal.

Parameters:

          M is INTEGER
          The number of rows of the matrix A.  M >= 0.

          N is INTEGER
          The number of columns of the matrix A.  N >= 0.

          A is COMPLEX array, dimension (LDA,N)
          The m-by-n matrix A.

          AF is COMPLEX array, dimension (LDA,N)
          Details of the QL factorization of A, as returned by CGEQLF.
          See CGEQLF for further details.

          Q is COMPLEX array, dimension (LDA,M)
          The m-by-m orthogonal matrix Q.

          L is COMPLEX array, dimension (LDA,max(M,N))

LDA

          LDA is INTEGER
          The leading dimension of the arrays A, AF, Q and R.
          LDA >= max(M,N).

TAU

          TAU is COMPLEX array, dimension (min(M,N))
          The scalar factors of the elementary reflectors, as returned
          by CGEQLF.

WORK

          WORK is COMPLEX array, dimension (LWORK)

LWORK

          LWORK is INTEGER
          The dimension of the array WORK.

RWORK

          RWORK is REAL array, dimension (M)

RESULT

          RESULT is REAL array, dimension (2)
          The test ratios:
          RESULT(1) = norm( L - Q'*A ) / ( M * norm(A) * EPS )
          RESULT(2) = norm( I - Q'*Q ) / ( M * EPS )

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine cqlt02 (integer M, integer N, integer K, complex, dimension( lda, * ) A, complex, dimension( lda, * ) AF, complex, dimension( lda, * ) Q, complex, dimension( lda, * ) L, integer LDA, complex, dimension( * ) TAU, complex, dimension( lwork ) WORK, integer LWORK, real, dimension( * ) RWORK, real, dimension( * ) RESULT)

CQLT02

Purpose:

 CQLT02 tests CUNGQL, which generates an m-by-n matrix Q with
 orthonornmal columns that is defined as the product of k elementary
 reflectors.
 Given the QL factorization of an m-by-n matrix A, CQLT02 generates
 the orthogonal matrix Q defined by the factorization of the last k
 columns of A; it compares L(m-n+1:m,n-k+1:n) with
 Q(1:m,m-n+1:m)'*A(1:m,n-k+1:n), and checks that the columns of Q are
 orthonormal.

Parameters:

          M is INTEGER
          The number of rows of the matrix Q to be generated.  M >= 0.

          N is INTEGER
          The number of columns of the matrix Q to be generated.
          M >= N >= 0.

          K is INTEGER
          The number of elementary reflectors whose product defines the
          matrix Q. N >= K >= 0.

          A is COMPLEX array, dimension (LDA,N)
          The m-by-n matrix A which was factorized by CQLT01.

          AF is COMPLEX array, dimension (LDA,N)
          Details of the QL factorization of A, as returned by CGEQLF.
          See CGEQLF for further details.

          Q is COMPLEX array, dimension (LDA,N)

          L is COMPLEX array, dimension (LDA,N)

LDA

          LDA is INTEGER
          The leading dimension of the arrays A, AF, Q and L. LDA >= M.

TAU

          TAU is COMPLEX array, dimension (N)
          The scalar factors of the elementary reflectors corresponding
          to the QL factorization in AF.

WORK

          WORK is COMPLEX array, dimension (LWORK)

LWORK

          LWORK is INTEGER
          The dimension of the array WORK.

RWORK

          RWORK is REAL array, dimension (M)

RESULT

          RESULT is REAL array, dimension (2)
          The test ratios:
          RESULT(1) = norm( L - Q'*A ) / ( M * norm(A) * EPS )
          RESULT(2) = norm( I - Q'*Q ) / ( M * EPS )

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine cqlt03 (integer M, integer N, integer K, complex, dimension( lda, * ) AF, complex, dimension( lda, * ) C, complex, dimension( lda, * ) CC, complex, dimension( lda, * ) Q, integer LDA, complex, dimension( * ) TAU, complex, dimension( lwork ) WORK, integer LWORK, real, dimension( * ) RWORK, real, dimension( * ) RESULT)

CQLT03

Purpose:

 CQLT03 tests CUNMQL, which computes Q*C, Q'*C, C*Q or C*Q'.
 CQLT03 compares the results of a call to CUNMQL with the results of
 forming Q explicitly by a call to CUNGQL and then performing matrix
 multiplication by a call to CGEMM.

Parameters:

          M is INTEGER
          The order of the orthogonal matrix Q.  M >= 0.

          N is INTEGER
          The number of rows or columns of the matrix C; C is m-by-n if
          Q is applied from the left, or n-by-m if Q is applied from
          the right.  N >= 0.

          K is INTEGER
          The number of elementary reflectors whose product defines the
          orthogonal matrix Q.  M >= K >= 0.

          AF is COMPLEX array, dimension (LDA,N)
          Details of the QL factorization of an m-by-n matrix, as
          returned by CGEQLF. See CGEQLF for further details.

          C is COMPLEX array, dimension (LDA,N)

          CC is COMPLEX array, dimension (LDA,N)

          Q is COMPLEX array, dimension (LDA,M)

LDA

          LDA is INTEGER
          The leading dimension of the arrays AF, C, CC, and Q.

TAU

          TAU is COMPLEX array, dimension (min(M,N))
          The scalar factors of the elementary reflectors corresponding
          to the QL factorization in AF.

WORK

          WORK is COMPLEX array, dimension (LWORK)

LWORK

          LWORK is INTEGER
          The length of WORK.  LWORK must be at least M, and should be
          M*NB, where NB is the blocksize for this environment.

RWORK

          RWORK is REAL array, dimension (M)

RESULT

          RESULT is REAL array, dimension (4)
          The test ratios compare two techniques for multiplying a
          random matrix C by an m-by-m orthogonal matrix Q.
          RESULT(1) = norm( Q*C - Q*C )  / ( M * norm(C) * EPS )
          RESULT(2) = norm( C*Q - C*Q )  / ( M * norm(C) * EPS )
          RESULT(3) = norm( Q'*C - Q'*C )/ ( M * norm(C) * EPS )
          RESULT(4) = norm( C*Q' - C*Q' )/ ( M * norm(C) * EPS )

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

real function cqpt01 (integer M, integer N, integer K, complex, dimension( lda, * ) A, complex, dimension( lda, * ) AF, integer LDA, complex, dimension( * ) TAU, integer, dimension( * ) JPVT, complex, dimension( lwork ) WORK, integer LWORK)

CQPT01

Purpose:

 CQPT01 tests the QR-factorization with pivoting of a matrix A.  The
 array AF contains the (possibly partial) QR-factorization of A, where
 the upper triangle of AF(1:k,1:k) is a partial triangular factor,
 the entries below the diagonal in the first k columns are the
 Householder vectors, and the rest of AF contains a partially updated
 matrix.
 This function returns ||A*P - Q*R||/(||norm(A)||*eps*M)

Parameters:

          M is INTEGER
          The number of rows of the matrices A and AF.

          N is INTEGER
          The number of columns of the matrices A and AF.

          K is INTEGER
          The number of columns of AF that have been reduced
          to upper triangular form.

          A is COMPLEX array, dimension (LDA, N)
          The original matrix A.

          AF is COMPLEX array, dimension (LDA,N)
          The (possibly partial) output of CGEQPF.  The upper triangle
          of AF(1:k,1:k) is a partial triangular factor, the entries
          below the diagonal in the first k columns are the Householder
          vectors, and the rest of AF contains a partially updated
          matrix.

LDA

          LDA is INTEGER
          The leading dimension of the arrays A and AF.

TAU

          TAU is COMPLEX array, dimension (K)
          Details of the Householder transformations as returned by
          CGEQPF.

JPVT

          JPVT is INTEGER array, dimension (N)
          Pivot information as returned by CGEQPF.

WORK

          WORK is COMPLEX array, dimension (LWORK)

LWORK

          LWORK is INTEGER
          The length of the array WORK.  LWORK >= M*N+N.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine cqrt01 (integer M, integer N, complex, dimension( lda, * ) A, complex, dimension( lda, * ) AF, complex, dimension( lda, * ) Q, complex, dimension( lda, * ) R, integer LDA, complex, dimension( * ) TAU, complex, dimension( lwork ) WORK, integer LWORK, real, dimension( * ) RWORK, real, dimension( * ) RESULT)

CQRT01

Purpose:

 CQRT01 tests CGEQRF, which computes the QR factorization of an m-by-n
 matrix A, and partially tests CUNGQR which forms the m-by-m
 orthogonal matrix Q.
 CQRT01 compares R with Q'*A, and checks that Q is orthogonal.

Parameters:

          M is INTEGER
          The number of rows of the matrix A.  M >= 0.

          N is INTEGER
          The number of columns of the matrix A.  N >= 0.

          A is COMPLEX array, dimension (LDA,N)
          The m-by-n matrix A.

          AF is COMPLEX array, dimension (LDA,N)
          Details of the QR factorization of A, as returned by CGEQRF.
          See CGEQRF for further details.

          Q is COMPLEX array, dimension (LDA,M)
          The m-by-m orthogonal matrix Q.

          R is COMPLEX array, dimension (LDA,max(M,N))

LDA

          LDA is INTEGER
          The leading dimension of the arrays A, AF, Q and R.
          LDA >= max(M,N).

TAU

          TAU is COMPLEX array, dimension (min(M,N))
          The scalar factors of the elementary reflectors, as returned
          by CGEQRF.

WORK

          WORK is COMPLEX array, dimension (LWORK)

LWORK

          LWORK is INTEGER
          The dimension of the array WORK.

RWORK

          RWORK is REAL array, dimension (M)

RESULT

          RESULT is REAL array, dimension (2)
          The test ratios:
          RESULT(1) = norm( R - Q'*A ) / ( M * norm(A) * EPS )
          RESULT(2) = norm( I - Q'*Q ) / ( M * EPS )

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine cqrt01p (integer M, integer N, complex, dimension( lda, * ) A, complex, dimension( lda, * ) AF, complex, dimension( lda, * ) Q, complex, dimension( lda, * ) R, integer LDA, complex, dimension( * ) TAU, complex, dimension( lwork ) WORK, integer LWORK, real, dimension( * ) RWORK, real, dimension( * ) RESULT)

CQRT01P

Purpose:

 CQRT01P tests CGEQRFP, which computes the QR factorization of an m-by-n
 matrix A, and partially tests CUNGQR which forms the m-by-m
 orthogonal matrix Q.
 CQRT01P compares R with Q'*A, and checks that Q is orthogonal.

Parameters:

          M is INTEGER
          The number of rows of the matrix A.  M >= 0.

          N is INTEGER
          The number of columns of the matrix A.  N >= 0.

          A is COMPLEX array, dimension (LDA,N)
          The m-by-n matrix A.

          AF is COMPLEX array, dimension (LDA,N)
          Details of the QR factorization of A, as returned by CGEQRFP.
          See CGEQRFP for further details.

          Q is COMPLEX array, dimension (LDA,M)
          The m-by-m orthogonal matrix Q.

          R is COMPLEX array, dimension (LDA,max(M,N))

LDA

          LDA is INTEGER
          The leading dimension of the arrays A, AF, Q and R.
          LDA >= max(M,N).

TAU

          TAU is COMPLEX array, dimension (min(M,N))
          The scalar factors of the elementary reflectors, as returned
          by CGEQRFP.

WORK

          WORK is COMPLEX array, dimension (LWORK)

LWORK

          LWORK is INTEGER
          The dimension of the array WORK.

RWORK

          RWORK is REAL array, dimension (M)

RESULT

          RESULT is REAL array, dimension (2)
          The test ratios:
          RESULT(1) = norm( R - Q'*A ) / ( M * norm(A) * EPS )
          RESULT(2) = norm( I - Q'*Q ) / ( M * EPS )

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine cqrt02 (integer M, integer N, integer K, complex, dimension( lda, * ) A, complex, dimension( lda, * ) AF, complex, dimension( lda, * ) Q, complex, dimension( lda, * ) R, integer LDA, complex, dimension( * ) TAU, complex, dimension( lwork ) WORK, integer LWORK, real, dimension( * ) RWORK, real, dimension( * ) RESULT)

CQRT02

Purpose:

 CQRT02 tests CUNGQR, which generates an m-by-n matrix Q with
 orthonornmal columns that is defined as the product of k elementary
 reflectors.
 Given the QR factorization of an m-by-n matrix A, CQRT02 generates
 the orthogonal matrix Q defined by the factorization of the first k
 columns of A; it compares R(1:n,1:k) with Q(1:m,1:n)'*A(1:m,1:k),
 and checks that the columns of Q are orthonormal.

Parameters:

          M is INTEGER
          The number of rows of the matrix Q to be generated.  M >= 0.

          N is INTEGER
          The number of columns of the matrix Q to be generated.
          M >= N >= 0.

          K is INTEGER
          The number of elementary reflectors whose product defines the
          matrix Q. N >= K >= 0.

          A is COMPLEX array, dimension (LDA,N)
          The m-by-n matrix A which was factorized by CQRT01.

          AF is COMPLEX array, dimension (LDA,N)
          Details of the QR factorization of A, as returned by CGEQRF.
          See CGEQRF for further details.

          Q is COMPLEX array, dimension (LDA,N)

          R is COMPLEX array, dimension (LDA,N)

LDA

          LDA is INTEGER
          The leading dimension of the arrays A, AF, Q and R. LDA >= M.

TAU

          TAU is COMPLEX array, dimension (N)
          The scalar factors of the elementary reflectors corresponding
          to the QR factorization in AF.

WORK

          WORK is COMPLEX array, dimension (LWORK)

LWORK

          LWORK is INTEGER
          The dimension of the array WORK.

RWORK

          RWORK is REAL array, dimension (M)

RESULT

          RESULT is REAL array, dimension (2)
          The test ratios:
          RESULT(1) = norm( R - Q'*A ) / ( M * norm(A) * EPS )
          RESULT(2) = norm( I - Q'*Q ) / ( M * EPS )

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine cqrt03 (integer M, integer N, integer K, complex, dimension( lda, * ) AF, complex, dimension( lda, * ) C, complex, dimension( lda, * ) CC, complex, dimension( lda, * ) Q, integer LDA, complex, dimension( * ) TAU, complex, dimension( lwork ) WORK, integer LWORK, real, dimension( * ) RWORK, real, dimension( * ) RESULT)

CQRT03

Purpose:

 CQRT03 tests CUNMQR, which computes Q*C, Q'*C, C*Q or C*Q'.
 CQRT03 compares the results of a call to CUNMQR with the results of
 forming Q explicitly by a call to CUNGQR and then performing matrix
 multiplication by a call to CGEMM.

Parameters:

          M is INTEGER
          The order of the orthogonal matrix Q.  M >= 0.

          N is INTEGER
          The number of rows or columns of the matrix C; C is m-by-n if
          Q is applied from the left, or n-by-m if Q is applied from
          the right.  N >= 0.

          K is INTEGER
          The number of elementary reflectors whose product defines the
          orthogonal matrix Q.  M >= K >= 0.

          AF is COMPLEX array, dimension (LDA,N)
          Details of the QR factorization of an m-by-n matrix, as
          returned by CGEQRF. See CGEQRF for further details.

          C is COMPLEX array, dimension (LDA,N)

          CC is COMPLEX array, dimension (LDA,N)

          Q is COMPLEX array, dimension (LDA,M)

LDA

          LDA is INTEGER
          The leading dimension of the arrays AF, C, CC, and Q.

TAU

          TAU is COMPLEX array, dimension (min(M,N))
          The scalar factors of the elementary reflectors corresponding
          to the QR factorization in AF.

WORK

          WORK is COMPLEX array, dimension (LWORK)

LWORK

          LWORK is INTEGER
          The length of WORK.  LWORK must be at least M, and should be
          M*NB, where NB is the blocksize for this environment.

RWORK

          RWORK is REAL array, dimension (M)

RESULT

          RESULT is REAL array, dimension (4)
          The test ratios compare two techniques for multiplying a
          random matrix C by an m-by-m orthogonal matrix Q.
          RESULT(1) = norm( Q*C - Q*C )  / ( M * norm(C) * EPS )
          RESULT(2) = norm( C*Q - C*Q )  / ( M * norm(C) * EPS )
          RESULT(3) = norm( Q'*C - Q'*C )/ ( M * norm(C) * EPS )
          RESULT(4) = norm( C*Q' - C*Q' )/ ( M * norm(C) * EPS )

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2015

subroutine cqrt04 (integer M, integer N, integer NB, real, dimension(6) RESULT)

CQRT04

Purpose:

 CQRT04 tests CGEQRT and CGEMQRT.

Parameters:

          M is INTEGER
          Number of rows in test matrix.

          N is INTEGER
          Number of columns in test matrix.

          NB is INTEGER
          Block size of test matrix.  NB <= Min(M,N).

RESULT

          RESULT is REAL array, dimension (6)
          Results of each of the six tests below.
          RESULT(1) = | A - Q R |
          RESULT(2) = | I - Q^H Q |
          RESULT(3) = | Q C - Q C |
          RESULT(4) = | Q^H C - Q^H C |
          RESULT(5) = | C Q - C Q | 
          RESULT(6) = | C Q^H - C Q^H |

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: April 2012

subroutine cqrt05 (integer M, integer N, integer L, integer NB, real, dimension(6) RESULT)

CQRT05

Purpose:

 CQRT05 tests CTPQRT and CTPMQRT.

Parameters:

          M is INTEGER
          Number of rows in lower part of the test matrix.

          N is INTEGER
          Number of columns in test matrix.

          L is INTEGER
          The number of rows of the upper trapezoidal part the
          lower test matrix.  0 <= L <= M.

          NB is INTEGER
          Block size of test matrix.  NB <= N.

RESULT

          RESULT is REAL array, dimension (6)
          Results of each of the six tests below.
          RESULT(1) = | A - Q R |
          RESULT(2) = | I - Q^H Q |
          RESULT(3) = | Q C - Q C |
          RESULT(4) = | Q^H C - Q^H C |
          RESULT(5) = | C Q - C Q | 
          RESULT(6) = | C Q^H - C Q^H |

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: April 2012

real function cqrt11 (integer M, integer K, complex, dimension( lda, * ) A, integer LDA, complex, dimension( * ) TAU, complex, dimension( lwork ) WORK, integer LWORK)

CQRT11

Purpose:

 CQRT11 computes the test ratio
       || Q'*Q - I || / (eps * m)
 where the orthogonal matrix Q is represented as a product of
 elementary transformations.  Each transformation has the form
    H(k) = I - tau(k) v(k) v(k)'
 where tau(k) is stored in TAU(k) and v(k) is an m-vector of the form
 [ 0 ... 0 1 x(k) ]', where x(k) is a vector of length m-k stored
 in A(k+1:m,k).

Parameters:

          M is INTEGER
          The number of rows of the matrix A.

          K is INTEGER
          The number of columns of A whose subdiagonal entries
          contain information about orthogonal transformations.

          A is COMPLEX array, dimension (LDA,K)
          The (possibly partial) output of a QR reduction routine.

LDA

          LDA is INTEGER
          The leading dimension of the array A.

TAU

          TAU is COMPLEX array, dimension (K)
          The scaling factors tau for the elementary transformations as
          computed by the QR factorization routine.

WORK

          WORK is COMPLEX array, dimension (LWORK)

LWORK

          LWORK is INTEGER
          The length of the array WORK.  LWORK >= M*M + M.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

real function cqrt12 (integer M, integer N, complex, dimension( lda, * ) A, integer LDA, real, dimension( * ) S, complex, dimension( lwork ) WORK, integer LWORK, real, dimension( * ) RWORK)

CQRT12

Purpose:

 CQRT12 computes the singular values `svlues' of the upper trapezoid
 of A(1:M,1:N) and returns the ratio
      || s - svlues||/(||svlues||*eps*max(M,N))

Parameters:

          M is INTEGER
          The number of rows of the matrix A.

          N is INTEGER
          The number of columns of the matrix A.

          A is COMPLEX array, dimension (LDA,N)
          The M-by-N matrix A. Only the upper trapezoid is referenced.

LDA

          LDA is INTEGER
          The leading dimension of the array A.

          S is REAL array, dimension (min(M,N))
          The singular values of the matrix A.

WORK

          WORK is COMPLEX array, dimension (LWORK)

LWORK

          LWORK is INTEGER
          The length of the array WORK. LWORK >= M*N + 2*min(M,N) +
          max(M,N).

RWORK

          RWORK is REAL array, dimension (4*min(M,N))

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine cqrt13 (integer SCALE, integer M, integer N, complex, dimension( lda, * ) A, integer LDA, real NORMA, integer, dimension( 4 ) ISEED)

CQRT13

Purpose:

 CQRT13 generates a full-rank matrix that may be scaled to have large
 or small norm.

Parameters:

SCALE

          SCALE is INTEGER
          SCALE = 1: normally scaled matrix
          SCALE = 2: matrix scaled up
          SCALE = 3: matrix scaled down

          M is INTEGER
          The number of rows of the matrix A.

          N is INTEGER
          The number of columns of A.

          A is COMPLEX array, dimension (LDA,N)
          The M-by-N matrix A.

LDA

          LDA is INTEGER
          The leading dimension of the array A.

NORMA

          NORMA is REAL
          The one-norm of A.

ISEED

          ISEED is integer array, dimension (4)
          Seed for random number generator

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

real function cqrt14 (character TRANS, integer M, integer N, integer NRHS, complex, dimension( lda, * ) A, integer LDA, complex, dimension( ldx, * ) X, integer LDX, complex, dimension( lwork ) WORK, integer LWORK)

CQRT14

Purpose:

 CQRT14 checks whether X is in the row space of A or A'.  It does so
 by scaling both X and A such that their norms are in the range
 [sqrt(eps), 1/sqrt(eps)], then computing a QR factorization of [A,X]
 (if TRANS = 'C') or an LQ factorization of [A',X]' (if TRANS = 'N'),
 and returning the norm of the trailing triangle, scaled by
 MAX(M,N,NRHS)*eps.

Parameters:

TRANS

          TRANS is CHARACTER*1
          = 'N':  No transpose, check for X in the row space of A
          = 'C':  Conjugate transpose, check for X in row space of A'.

          M is INTEGER
          The number of rows of the matrix A.

          N is INTEGER
          The number of columns of the matrix A.

NRHS

          NRHS is INTEGER
          The number of right hand sides, i.e., the number of columns
          of X.

          A is COMPLEX array, dimension (LDA,N)
          The M-by-N matrix A.

LDA

          LDA is INTEGER
          The leading dimension of the array A.

          X is COMPLEX array, dimension (LDX,NRHS)
          If TRANS = 'N', the N-by-NRHS matrix X.
          IF TRANS = 'C', the M-by-NRHS matrix X.

LDX

          LDX is INTEGER
          The leading dimension of the array X.

WORK

          WORK is COMPLEX array dimension (LWORK)

LWORK

          LWORK is INTEGER
          length of workspace array required
          If TRANS = 'N', LWORK >= (M+NRHS)*(N+2);
          if TRANS = 'C', LWORK >= (N+NRHS)*(M+2).

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine cqrt15 (integer SCALE, integer RKSEL, integer M, integer N, integer NRHS, complex, dimension( lda, * ) A, integer LDA, complex, dimension( ldb, * ) B, integer LDB, real, dimension( * ) S, integer RANK, real NORMA, real NORMB, integer, dimension( 4 ) ISEED, complex, dimension( lwork ) WORK, integer LWORK)

CQRT15

Purpose:

 CQRT15 generates a matrix with full or deficient rank and of various
 norms.

Parameters:

SCALE

          SCALE is INTEGER
          SCALE = 1: normally scaled matrix
          SCALE = 2: matrix scaled up
          SCALE = 3: matrix scaled down

RKSEL

          RKSEL is INTEGER
          RKSEL = 1: full rank matrix
          RKSEL = 2: rank-deficient matrix

          M is INTEGER
          The number of rows of the matrix A.

          N is INTEGER
          The number of columns of A.

NRHS

          NRHS is INTEGER
          The number of columns of B.

          A is COMPLEX array, dimension (LDA,N)
          The M-by-N matrix A.

LDA

          LDA is INTEGER
          The leading dimension of the array A.

          B is COMPLEX array, dimension (LDB, NRHS)
          A matrix that is in the range space of matrix A.

LDB

          LDB is INTEGER
          The leading dimension of the array B.

          S is REAL array, dimension MIN(M,N)
          Singular values of A.

RANK

          RANK is INTEGER
          number of nonzero singular values of A.

NORMA

          NORMA is REAL
          one-norm norm of A.

NORMB

          NORMB is REAL
          one-norm norm of B.

ISEED

          ISEED is integer array, dimension (4)
          seed for random number generator.

WORK

          WORK is COMPLEX array, dimension (LWORK)

LWORK

          LWORK is INTEGER
          length of work space required.
          LWORK >= MAX(M+MIN(M,N),NRHS*MIN(M,N),2*N+M)

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine cqrt16 (character TRANS, integer M, integer N, integer NRHS, complex, dimension( lda, * ) A, integer LDA, complex, dimension( ldx, * ) X, integer LDX, complex, dimension( ldb, * ) B, integer LDB, real, dimension( * ) RWORK, real RESID)

CQRT16

Purpose:

 CQRT16 computes the residual for a solution of a system of linear
 equations  A*x = b  or  A'*x = b:
    RESID = norm(B - A*X) / ( max(m,n) * norm(A) * norm(X) * EPS ),
 where EPS is the machine epsilon.

Parameters:

TRANS

          TRANS is CHARACTER*1
          Specifies the form of the system of equations:
          = 'N':  A *x = b
          = 'T':  A^T*x = b, where A^T is the transpose of A
          = 'C':  A^H*x = b, where A^H is the conjugate transpose of A

          M is INTEGER
          The number of rows of the matrix A.  M >= 0.

          N is INTEGER
          The number of columns of the matrix A.  N >= 0.

NRHS

          NRHS is INTEGER
          The number of columns of B, the matrix of right hand sides.
          NRHS >= 0.

          A is COMPLEX array, dimension (LDA,N)
          The original M x N matrix A.

LDA

          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,M).

          X is COMPLEX array, dimension (LDX,NRHS)
          The computed solution vectors for the system of linear
          equations.

LDX

          LDX is INTEGER
          The leading dimension of the array X.  If TRANS = 'N',
          LDX >= max(1,N); if TRANS = 'T' or 'C', LDX >= max(1,M).

          B is COMPLEX array, dimension (LDB,NRHS)
          On entry, the right hand side vectors for the system of
          linear equations.
          On exit, B is overwritten with the difference B - A*X.

LDB

          LDB is INTEGER
          The leading dimension of the array B.  IF TRANS = 'N',
          LDB >= max(1,M); if TRANS = 'T' or 'C', LDB >= max(1,N).

RWORK

          RWORK is REAL array, dimension (M)

RESID

          RESID is REAL
          The maximum over the number of right hand sides of
          norm(B - A*X) / ( max(m,n) * norm(A) * norm(X) * EPS ).

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

real function cqrt17 (character TRANS, integer IRESID, integer M, integer N, integer NRHS, complex, dimension( lda, * ) A, integer LDA, complex, dimension( ldx, * ) X, integer LDX, complex, dimension( ldb, * ) B, integer LDB, complex, dimension( ldb, * ) C, complex, dimension( lwork ) WORK, integer LWORK)

CQRT17

Purpose:

 CQRT17 computes the ratio
    || R'*op(A) ||/(||A||*alpha*max(M,N,NRHS)*eps)
 where R = op(A)*X - B, op(A) is A or A', and
    alpha = ||B|| if IRESID = 1 (zero-residual problem)
    alpha = ||R|| if IRESID = 2 (otherwise).

Parameters:

TRANS

          TRANS is CHARACTER*1
          Specifies whether or not the transpose of A is used.
          = 'N':  No transpose, op(A) = A.
          = 'C':  Conjugate transpose, op(A) = A'.

IRESID

          IRESID is INTEGER
          IRESID = 1 indicates zero-residual problem.
          IRESID = 2 indicates non-zero residual.

          M is INTEGER
          The number of rows of the matrix A.
          If TRANS = 'N', the number of rows of the matrix B.
          If TRANS = 'C', the number of rows of the matrix X.

          N is INTEGER
          The number of columns of the matrix  A.
          If TRANS = 'N', the number of rows of the matrix X.
          If TRANS = 'C', the number of rows of the matrix B.

NRHS

          NRHS is INTEGER
          The number of columns of the matrices X and B.

          A is COMPLEX array, dimension (LDA,N)
          The m-by-n matrix A.

LDA

          LDA is INTEGER
          The leading dimension of the array A. LDA >= M.

          X is COMPLEX array, dimension (LDX,NRHS)
          If TRANS = 'N', the n-by-nrhs matrix X.
          If TRANS = 'C', the m-by-nrhs matrix X.

LDX

          LDX is INTEGER
          The leading dimension of the array X.
          If TRANS = 'N', LDX >= N.
          If TRANS = 'C', LDX >= M.

          B is COMPLEX array, dimension (LDB,NRHS)
          If TRANS = 'N', the m-by-nrhs matrix B.
          If TRANS = 'C', the n-by-nrhs matrix B.

LDB

          LDB is INTEGER
          The leading dimension of the array B.
          If TRANS = 'N', LDB >= M.
          If TRANS = 'C', LDB >= N.

          C is COMPLEX array, dimension (LDB,NRHS)

WORK

          WORK is COMPLEX array, dimension (LWORK)

LWORK

          LWORK is INTEGER
          The length of the array WORK.  LWORK >= NRHS*(M+N).

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2015

subroutine crqt01 (integer M, integer N, complex, dimension( lda, * ) A, complex, dimension( lda, * ) AF, complex, dimension( lda, * ) Q, complex, dimension( lda, * ) R, integer LDA, complex, dimension( * ) TAU, complex, dimension( lwork ) WORK, integer LWORK, real, dimension( * ) RWORK, real, dimension( * ) RESULT)

CRQT01

Purpose:

 CRQT01 tests CGERQF, which computes the RQ factorization of an m-by-n
 matrix A, and partially tests CUNGRQ which forms the n-by-n
 orthogonal matrix Q.
 CRQT01 compares R with A*Q', and checks that Q is orthogonal.

Parameters:

          M is INTEGER
          The number of rows of the matrix A.  M >= 0.

          N is INTEGER
          The number of columns of the matrix A.  N >= 0.

          A is COMPLEX array, dimension (LDA,N)
          The m-by-n matrix A.

          AF is COMPLEX array, dimension (LDA,N)
          Details of the RQ factorization of A, as returned by CGERQF.
          See CGERQF for further details.

          Q is COMPLEX array, dimension (LDA,N)
          The n-by-n orthogonal matrix Q.

          R is COMPLEX array, dimension (LDA,max(M,N))

LDA

          LDA is INTEGER
          The leading dimension of the arrays A, AF, Q and L.
          LDA >= max(M,N).

TAU

          TAU is COMPLEX array, dimension (min(M,N))
          The scalar factors of the elementary reflectors, as returned
          by CGERQF.

WORK

          WORK is COMPLEX array, dimension (LWORK)

LWORK

          LWORK is INTEGER
          The dimension of the array WORK.

RWORK

          RWORK is REAL array, dimension (max(M,N))

RESULT

          RESULT is REAL array, dimension (2)
          The test ratios:
          RESULT(1) = norm( R - A*Q' ) / ( N * norm(A) * EPS )
          RESULT(2) = norm( I - Q*Q' ) / ( N * EPS )

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine crqt02 (integer M, integer N, integer K, complex, dimension( lda, * ) A, complex, dimension( lda, * ) AF, complex, dimension( lda, * ) Q, complex, dimension( lda, * ) R, integer LDA, complex, dimension( * ) TAU, complex, dimension( lwork ) WORK, integer LWORK, real, dimension( * ) RWORK, real, dimension( * ) RESULT)

CRQT02

Purpose:

 CRQT02 tests CUNGRQ, which generates an m-by-n matrix Q with
 orthonornmal rows that is defined as the product of k elementary
 reflectors.
 Given the RQ factorization of an m-by-n matrix A, CRQT02 generates
 the orthogonal matrix Q defined by the factorization of the last k
 rows of A; it compares R(m-k+1:m,n-m+1:n) with
 A(m-k+1:m,1:n)*Q(n-m+1:n,1:n)', and checks that the rows of Q are
 orthonormal.

Parameters:

          M is INTEGER
          The number of rows of the matrix Q to be generated.  M >= 0.

          N is INTEGER
          The number of columns of the matrix Q to be generated.
          N >= M >= 0.

          K is INTEGER
          The number of elementary reflectors whose product defines the
          matrix Q. M >= K >= 0.

          A is COMPLEX array, dimension (LDA,N)
          The m-by-n matrix A which was factorized by CRQT01.

          AF is COMPLEX array, dimension (LDA,N)
          Details of the RQ factorization of A, as returned by CGERQF.
          See CGERQF for further details.

          Q is COMPLEX array, dimension (LDA,N)

          R is COMPLEX array, dimension (LDA,M)

LDA

          LDA is INTEGER
          The leading dimension of the arrays A, AF, Q and L. LDA >= N.

TAU

          TAU is COMPLEX array, dimension (M)
          The scalar factors of the elementary reflectors corresponding
          to the RQ factorization in AF.

WORK

          WORK is COMPLEX array, dimension (LWORK)

LWORK

          LWORK is INTEGER
          The dimension of the array WORK.

RWORK

          RWORK is REAL array, dimension (M)

RESULT

          RESULT is REAL array, dimension (2)
          The test ratios:
          RESULT(1) = norm( R - A*Q' ) / ( N * norm(A) * EPS )
          RESULT(2) = norm( I - Q*Q' ) / ( N * EPS )

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine crqt03 (integer M, integer N, integer K, complex, dimension( lda, * ) AF, complex, dimension( lda, * ) C, complex, dimension( lda, * ) CC, complex, dimension( lda, * ) Q, integer LDA, complex, dimension( * ) TAU, complex, dimension( lwork ) WORK, integer LWORK, real, dimension( * ) RWORK, real, dimension( * ) RESULT)

CRQT03

Purpose:

 CRQT03 tests CUNMRQ, which computes Q*C, Q'*C, C*Q or C*Q'.
 CRQT03 compares the results of a call to CUNMRQ with the results of
 forming Q explicitly by a call to CUNGRQ and then performing matrix
 multiplication by a call to CGEMM.

Parameters:

          M is INTEGER
          The number of rows or columns of the matrix C; C is n-by-m if
          Q is applied from the left, or m-by-n if Q is applied from
          the right.  M >= 0.

          N is INTEGER
          The order of the orthogonal matrix Q.  N >= 0.

          K is INTEGER
          The number of elementary reflectors whose product defines the
          orthogonal matrix Q.  N >= K >= 0.

          AF is COMPLEX array, dimension (LDA,N)
          Details of the RQ factorization of an m-by-n matrix, as
          returned by CGERQF. See CGERQF for further details.

          C is COMPLEX array, dimension (LDA,N)

          CC is COMPLEX array, dimension (LDA,N)

          Q is COMPLEX array, dimension (LDA,N)

LDA

          LDA is INTEGER
          The leading dimension of the arrays AF, C, CC, and Q.

TAU

          TAU is COMPLEX array, dimension (min(M,N))
          The scalar factors of the elementary reflectors corresponding
          to the RQ factorization in AF.

WORK

          WORK is COMPLEX array, dimension (LWORK)

LWORK

          LWORK is INTEGER
          The length of WORK.  LWORK must be at least M, and should be
          M*NB, where NB is the blocksize for this environment.

RWORK

          RWORK is REAL array, dimension (M)

RESULT

          RESULT is REAL array, dimension (4)
          The test ratios compare two techniques for multiplying a
          random matrix C by an n-by-n orthogonal matrix Q.
          RESULT(1) = norm( Q*C - Q*C )  / ( N * norm(C) * EPS )
          RESULT(2) = norm( C*Q - C*Q )  / ( N * norm(C) * EPS )
          RESULT(3) = norm( Q'*C - Q'*C )/ ( N * norm(C) * EPS )
          RESULT(4) = norm( C*Q' - C*Q' )/ ( N * norm(C) * EPS )

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

real function crzt01 (integer M, integer N, complex, dimension( lda, * ) A, complex, dimension( lda, * ) AF, integer LDA, complex, dimension( * ) TAU, complex, dimension( lwork ) WORK, integer LWORK)

CRZT01

Purpose:

 CRZT01 returns
      || A - R*Q || / ( M * eps * ||A|| )
 for an upper trapezoidal A that was factored with CTZRZF.

Parameters:

          M is INTEGER
          The number of rows of the matrices A and AF.

          N is INTEGER
          The number of columns of the matrices A and AF.

          A is COMPLEX array, dimension (LDA,N)
          The original upper trapezoidal M by N matrix A.

          AF is COMPLEX array, dimension (LDA,N)
          The output of CTZRZF for input matrix A.
          The lower triangle is not referenced.

LDA

          LDA is INTEGER
          The leading dimension of the arrays A and AF.

TAU

          TAU is COMPLEX array, dimension (M)
          Details of the  Householder transformations as returned by
          CTZRZF.

WORK

          WORK is COMPLEX array, dimension (LWORK)

LWORK

          LWORK is INTEGER
          The length of the array WORK.  LWORK >= m*n + m.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

real function crzt02 (integer M, integer N, complex, dimension( lda, * ) AF, integer LDA, complex, dimension( * ) TAU, complex, dimension( lwork ) WORK, integer LWORK)

CRZT02

Purpose:

 CRZT02 returns
      || I - Q'*Q || / ( M * eps)
 where the matrix Q is defined by the Householder transformations
 generated by CTZRZF.

Parameters:

          M is INTEGER
          The number of rows of the matrix AF.

          N is INTEGER
          The number of columns of the matrix AF.

          AF is COMPLEX array, dimension (LDA,N)
          The output of CTZRZF.

LDA

          LDA is INTEGER
          The leading dimension of the array AF.

TAU

          TAU is COMPLEX array, dimension (M)
          Details of the Householder transformations as returned by
          CTZRZF.

WORK

          WORK is COMPLEX array, dimension (LWORK)

LWORK

          LWORK is INTEGER
          Length of WORK array. LWORK >= N*N+N.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine csbmv (character UPLO, integer N, integer K, complex ALPHA, complex, dimension( lda, * ) A, integer LDA, complex, dimension( * ) X, integer INCX, complex BETA, complex, dimension( * ) Y, integer INCY)

CSBMV

Purpose:

 CSBMV  performs the matrix-vector  operation
    y := alpha*A*x + beta*y,
 where alpha and beta are scalars, x and y are n element vectors and
 A is an n by n symmetric band matrix, with k super-diagonals.

  UPLO   - CHARACTER*1
           On entry, UPLO specifies whether the upper or lower
           triangular part of the band matrix A is being supplied as
           follows:
              UPLO = 'U' or 'u'   The upper triangular part of A is
                                  being supplied.
              UPLO = 'L' or 'l'   The lower triangular part of A is
                                  being supplied.
           Unchanged on exit.
  N      - INTEGER
           On entry, N specifies the order of the matrix A.
           N must be at least zero.
           Unchanged on exit.
  K      - INTEGER
           On entry, K specifies the number of super-diagonals of the
           matrix A. K must satisfy  0 .le. K.
           Unchanged on exit.
  ALPHA  - COMPLEX
           On entry, ALPHA specifies the scalar alpha.
           Unchanged on exit.
  A      - COMPLEX array, dimension( LDA, N )
           Before entry with UPLO = 'U' or 'u', the leading ( k + 1 )
           by n part of the array A must contain the upper triangular
           band part of the symmetric matrix, supplied column by
           column, with the leading diagonal of the matrix in row
           ( k + 1 ) of the array, the first super-diagonal starting at
           position 2 in row k, and so on. The top left k by k triangle
           of the array A is not referenced.
           The following program segment will transfer the upper
           triangular part of a symmetric band matrix from conventional
           full matrix storage to band storage:
                 DO 20, J = 1, N
                    M = K + 1 - J
                    DO 10, I = MAX( 1, J - K ), J
                       A( M + I, J ) = matrix( I, J )
              10    CONTINUE
              20 CONTINUE
           Before entry with UPLO = 'L' or 'l', the leading ( k + 1 )
           by n part of the array A must contain the lower triangular
           band part of the symmetric matrix, supplied column by
           column, with the leading diagonal of the matrix in row 1 of
           the array, the first sub-diagonal starting at position 1 in
           row 2, and so on. The bottom right k by k triangle of the
           array A is not referenced.
           The following program segment will transfer the lower
           triangular part of a symmetric band matrix from conventional
           full matrix storage to band storage:
                 DO 20, J = 1, N
                    M = 1 - J
                    DO 10, I = J, MIN( N, J + K )
                       A( M + I, J ) = matrix( I, J )
              10    CONTINUE
              20 CONTINUE
           Unchanged on exit.
  LDA    - INTEGER
           On entry, LDA specifies the first dimension of A as declared
           in the calling (sub) program. LDA must be at least
           ( k + 1 ).
           Unchanged on exit.
  X      - COMPLEX array, dimension at least
           ( 1 + ( N - 1 )*abs( INCX ) ).
           Before entry, the incremented array X must contain the
           vector x.
           Unchanged on exit.
  INCX   - INTEGER
           On entry, INCX specifies the increment for the elements of
           X. INCX must not be zero.
           Unchanged on exit.
  BETA   - COMPLEX
           On entry, BETA specifies the scalar beta.
           Unchanged on exit.
  Y      - COMPLEX array, dimension at least
           ( 1 + ( N - 1 )*abs( INCY ) ).
           Before entry, the incremented array Y must contain the
           vector y. On exit, Y is overwritten by the updated vector y.
  INCY   - INTEGER
           On entry, INCY specifies the increment for the elements of
           Y. INCY must not be zero.
           Unchanged on exit.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine cspt01 (character UPLO, integer N, complex, dimension( * ) A, complex, dimension( * ) AFAC, integer, dimension( * ) IPIV, complex, dimension( ldc, * ) C, integer LDC, real, dimension( * ) RWORK, real RESID)

CSPT01

Purpose:

 CSPT01 reconstructs a symmetric indefinite packed matrix A from its
 diagonal pivoting factorization A = U*D*U' or A = L*D*L' and computes
 the residual
    norm( C - A ) / ( N * norm(A) * EPS ),
 where C is the reconstructed matrix and EPS is the machine epsilon.

Parameters:

UPLO

          UPLO is CHARACTER*1
          Specifies whether the upper or lower triangular part of the
          Hermitian matrix A is stored:
          = 'U':  Upper triangular
          = 'L':  Lower triangular

          N is INTEGER
          The order of the matrix A.  N >= 0.

          A is COMPLEX array, dimension (N*(N+1)/2)
          The original symmetric matrix A, stored as a packed
          triangular matrix.

AFAC

          AFAC is COMPLEX array, dimension (N*(N+1)/2)
          The factored form of the matrix A, stored as a packed
          triangular matrix.  AFAC contains the block diagonal matrix D
          and the multipliers used to obtain the factor L or U from the
          L*D*L' or U*D*U' factorization as computed by CSPTRF.

IPIV

          IPIV is INTEGER array, dimension (N)
          The pivot indices from CSPTRF.

          C is COMPLEX array, dimension (LDC,N)

LDC

          LDC is INTEGER
          The leading dimension of the array C.  LDC >= max(1,N).

RWORK

          RWORK is REAL array, dimension (N)

RESID

          RESID is REAL
          If UPLO = 'L', norm(L*D*L' - A) / ( N * norm(A) * EPS )
          If UPLO = 'U', norm(U*D*U' - A) / ( N * norm(A) * EPS )

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine cspt02 (character UPLO, integer N, integer NRHS, complex, dimension( * ) A, complex, dimension( ldx, * ) X, integer LDX, complex, dimension( ldb, * ) B, integer LDB, real, dimension( * ) RWORK, real RESID)

CSPT02

Purpose:

 CSPT02 computes the residual in the solution of a complex symmetric
 system of linear equations  A*x = b  when packed storage is used for
 the coefficient matrix.  The ratio computed is
    RESID = norm( B - A*X ) / ( norm(A) * norm(X) * EPS).
 where EPS is the machine precision.

Parameters:

UPLO

          UPLO is CHARACTER*1
          Specifies whether the upper or lower triangular part of the
          complex symmetric matrix A is stored:
          = 'U':  Upper triangular
          = 'L':  Lower triangular

          N is INTEGER
          The number of rows and columns of the matrix A.  N >= 0.

NRHS

          NRHS is INTEGER
          The number of columns of B, the matrix of right hand sides.
          NRHS >= 0.

          A is COMPLEX array, dimension (N*(N+1)/2)
          The original complex symmetric matrix A, stored as a packed
          triangular matrix.

          X is COMPLEX array, dimension (LDX,NRHS)
          The computed solution vectors for the system of linear
          equations.

LDX

          LDX is INTEGER
          The leading dimension of the array X.   LDX >= max(1,N).

          B is COMPLEX array, dimension (LDB,NRHS)
          On entry, the right hand side vectors for the system of
          linear equations.
          On exit, B is overwritten with the difference B - A*X.

LDB

          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,N).

RWORK

          RWORK is REAL array, dimension (N)

RESID

          RESID is REAL
          The maximum over the number of right hand sides of
          norm(B - A*X) / ( norm(A) * norm(X) * EPS ).

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine cspt03 (character UPLO, integer N, complex, dimension( * ) A, complex, dimension( * ) AINV, complex, dimension( ldw, * ) WORK, integer LDW, real, dimension( * ) RWORK, real RCOND, real RESID)

CSPT03

Purpose:

 CSPT03 computes the residual for a complex symmetric packed matrix
 times its inverse:
    norm( I - A*AINV ) / ( N * norm(A) * norm(AINV) * EPS ),
 where EPS is the machine epsilon.

Parameters:

UPLO

          UPLO is CHARACTER*1
          Specifies whether the upper or lower triangular part of the
          complex symmetric matrix A is stored:
          = 'U':  Upper triangular
          = 'L':  Lower triangular

          N is INTEGER
          The number of rows and columns of the matrix A.  N >= 0.

          A is COMPLEX array, dimension (N*(N+1)/2)
          The original complex symmetric matrix A, stored as a packed
          triangular matrix.

AINV

          AINV is COMPLEX array, dimension (N*(N+1)/2)
          The (symmetric) inverse of the matrix A, stored as a packed
          triangular matrix.

WORK

          WORK is COMPLEX array, dimension (LDW,N)

LDW

          LDW is INTEGER
          The leading dimension of the array WORK.  LDW >= max(1,N).

RWORK

          RWORK is REAL array, dimension (N)

RCOND

          RCOND is REAL
          The reciprocal of the condition number of A, computed as
          ( 1/norm(A) ) / norm(AINV).

RESID

          RESID is REAL
          norm(I - A*AINV) / ( N * norm(A) * norm(AINV) * EPS )

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine csyt01 (character UPLO, integer N, complex, dimension( lda, * ) A, integer LDA, complex, dimension( ldafac, * ) AFAC, integer LDAFAC, integer, dimension( * ) IPIV, complex, dimension( ldc, * ) C, integer LDC, real, dimension( * ) RWORK, real RESID)

CSYT01

Purpose:

 CSYT01 reconstructs a complex symmetric indefinite matrix A from its
 block L*D*L' or U*D*U' factorization and computes the residual
    norm( C - A ) / ( N * norm(A) * EPS ),
 where C is the reconstructed matrix, EPS is the machine epsilon,
 L' is the transpose of L, and U' is the transpose of U.

Parameters:

UPLO

          UPLO is CHARACTER*1
          Specifies whether the upper or lower triangular part of the
          complex symmetric matrix A is stored:
          = 'U':  Upper triangular
          = 'L':  Lower triangular

          N is INTEGER
          The number of rows and columns of the matrix A.  N >= 0.

          A is COMPLEX array, dimension (LDA,N)
          The original complex symmetric matrix A.

LDA

          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N)

AFAC

          AFAC is COMPLEX array, dimension (LDAFAC,N)
          The factored form of the matrix A.  AFAC contains the block
          diagonal matrix D and the multipliers used to obtain the
          factor L or U from the block L*D*L' or U*D*U' factorization
          as computed by CSYTRF.

LDAFAC

          LDAFAC is INTEGER
          The leading dimension of the array AFAC.  LDAFAC >= max(1,N).

IPIV

          IPIV is INTEGER array, dimension (N)
          The pivot indices from CSYTRF.

          C is COMPLEX array, dimension (LDC,N)

LDC

          LDC is INTEGER
          The leading dimension of the array C.  LDC >= max(1,N).

RWORK

          RWORK is REAL array, dimension (N)

RESID

          RESID is REAL
          If UPLO = 'L', norm(L*D*L' - A) / ( N * norm(A) * EPS )
          If UPLO = 'U', norm(U*D*U' - A) / ( N * norm(A) * EPS )

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2013

subroutine csyt01_rook (character UPLO, integer N, complex, dimension( lda, * ) A, integer LDA, complex, dimension( ldafac, * ) AFAC, integer LDAFAC, integer, dimension( * ) IPIV, complex, dimension( ldc, * ) C, integer LDC, real, dimension( * ) RWORK, real RESID)

CSYT01_ROOK

Purpose:

 CSYT01_ROOK reconstructs a complex symmetric indefinite matrix A from its
 block L*D*L' or U*D*U' factorization and computes the residual
    norm( C - A ) / ( N * norm(A) * EPS ),
 where C is the reconstructed matrix, EPS is the machine epsilon,
 L' is the transpose of L, and U' is the transpose of U.

Parameters:

UPLO

          UPLO is CHARACTER*1
          Specifies whether the upper or lower triangular part of the
          complex symmetric matrix A is stored:
          = 'U':  Upper triangular
          = 'L':  Lower triangular

          N is INTEGER
          The number of rows and columns of the matrix A.  N >= 0.

          A is COMPLEX array, dimension (LDA,N)
          The original complex symmetric matrix A.

LDA

          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N)

AFAC

          AFAC is COMPLEX array, dimension (LDAFAC,N)
          The factored form of the matrix A.  AFAC contains the block
          diagonal matrix D and the multipliers used to obtain the
          factor L or U from the block L*D*L' or U*D*U' factorization
          as computed by CSYTRF_ROOK.

LDAFAC

          LDAFAC is INTEGER
          The leading dimension of the array AFAC.  LDAFAC >= max(1,N).

IPIV

          IPIV is INTEGER array, dimension (N)
          The pivot indices from CSYTRF_ROOK.

          C is COMPLEX array, dimension (LDC,N)

LDC

          LDC is INTEGER
          The leading dimension of the array C.  LDC >= max(1,N).

RWORK

          RWORK is REAL array, dimension (N)

RESID

          RESID is REAL
          If UPLO = 'L', norm(L*D*L' - A) / ( N * norm(A) * EPS )
          If UPLO = 'U', norm(U*D*U' - A) / ( N * norm(A) * EPS )

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2013

subroutine csyt02 (character UPLO, integer N, integer NRHS, complex, dimension( lda, * ) A, integer LDA, complex, dimension( ldx, * ) X, integer LDX, complex, dimension( ldb, * ) B, integer LDB, real, dimension( * ) RWORK, real RESID)

CSYT02

Purpose:

 CSYT02 computes the residual for a solution to a complex symmetric
 system of linear equations  A*x = b:
    RESID = norm(B - A*X) / ( norm(A) * norm(X) * EPS ),
 where EPS is the machine epsilon.

Parameters:

UPLO

          UPLO is CHARACTER*1
          Specifies whether the upper or lower triangular part of the
          symmetric matrix A is stored:
          = 'U':  Upper triangular
          = 'L':  Lower triangular

          N is INTEGER
          The number of rows and columns of the matrix A.  N >= 0.

NRHS

          NRHS is INTEGER
          The number of columns of B, the matrix of right hand sides.
          NRHS >= 0.

          A is COMPLEX array, dimension (LDA,N)
          The original complex symmetric matrix A.

LDA

          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N)

          X is COMPLEX array, dimension (LDX,NRHS)
          The computed solution vectors for the system of linear
          equations.

LDX

          LDX is INTEGER
          The leading dimension of the array X.   LDX >= max(1,N).

          B is COMPLEX array, dimension (LDB,NRHS)
          On entry, the right hand side vectors for the system of
          linear equations.
          On exit, B is overwritten with the difference B - A*X.

LDB

          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,N).

RWORK

          RWORK is REAL array, dimension (N)

RESID

          RESID is REAL
          The maximum over the number of right hand sides of
          norm(B - A*X) / ( norm(A) * norm(X) * EPS ).

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine csyt03 (character UPLO, integer N, complex, dimension( lda, * ) A, integer LDA, complex, dimension( ldainv, * ) AINV, integer LDAINV, complex, dimension( ldwork, * ) WORK, integer LDWORK, real, dimension( * ) RWORK, real RCOND, real RESID)

CSYT03

Purpose:

 CSYT03 computes the residual for a complex symmetric matrix times
 its inverse:
    norm( I - A*AINV ) / ( N * norm(A) * norm(AINV) * EPS )
 where EPS is the machine epsilon.

Parameters:

UPLO

          UPLO is CHARACTER*1
          Specifies whether the upper or lower triangular part of the
          complex symmetric matrix A is stored:
          = 'U':  Upper triangular
          = 'L':  Lower triangular

          N is INTEGER
          The number of rows and columns of the matrix A.  N >= 0.

          A is COMPLEX array, dimension (LDA,N)
          The original complex symmetric matrix A.

LDA

          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N)

AINV

          AINV is COMPLEX array, dimension (LDAINV,N)
          On entry, the inverse of the matrix A, stored as a symmetric
          matrix in the same format as A.
          In this version, AINV is expanded into a full matrix and
          multiplied by A, so the opposing triangle of AINV will be
          changed; i.e., if the upper triangular part of AINV is
          stored, the lower triangular part will be used as work space.

LDAINV

          LDAINV is INTEGER
          The leading dimension of the array AINV.  LDAINV >= max(1,N).

WORK

          WORK is COMPLEX array, dimension (LDWORK,N)

LDWORK

          LDWORK is INTEGER
          The leading dimension of the array WORK.  LDWORK >= max(1,N).

RWORK

          RWORK is REAL array, dimension (N)

RCOND

          RCOND is REAL
          The reciprocal of the condition number of A, computed as
          RCOND = 1/ (norm(A) * norm(AINV)).

RESID

          RESID is REAL
          norm(I - A*AINV) / ( N * norm(A) * norm(AINV) * EPS )

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine ctbt02 (character UPLO, character TRANS, character DIAG, integer N, integer KD, integer NRHS, complex, dimension( ldab, * ) AB, integer LDAB, complex, dimension( ldx, * ) X, integer LDX, complex, dimension( ldb, * ) B, integer LDB, complex, dimension( * ) WORK, real, dimension( * ) RWORK, real RESID)

CTBT02

Purpose:

 CTBT02 computes the residual for the computed solution to a
 triangular system of linear equations  A*x = b,  A**T *x = b,  or
 A**H *x = b  when A is a triangular band matrix.  Here A**T denotes
 the transpose of A, A**H denotes the conjugate transpose of A, and
 x and b are N by NRHS matrices.  The test ratio is the maximum over
 the number of right hand sides of
    norm(b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ),
 where op(A) denotes A, A**T, or A**H, and EPS is the machine epsilon.

Parameters:

UPLO

          UPLO is CHARACTER*1
          Specifies whether the matrix A is upper or lower triangular.
          = 'U':  Upper triangular
          = 'L':  Lower triangular

TRANS

          TRANS is CHARACTER*1
          Specifies the operation applied to A.
          = 'N':  A *x = b     (No transpose)
          = 'T':  A**T *x = b  (Transpose)
          = 'C':  A**H *x = b  (Conjugate transpose)

DIAG

          DIAG is CHARACTER*1
          Specifies whether or not the matrix A is unit triangular.
          = 'N':  Non-unit triangular
          = 'U':  Unit triangular

          N is INTEGER
          The order of the matrix A.  N >= 0.

          KD is INTEGER
          The number of superdiagonals or subdiagonals of the
          triangular band matrix A.  KD >= 0.

NRHS

          NRHS is INTEGER
          The number of right hand sides, i.e., the number of columns
          of the matrices X and B.  NRHS >= 0.

          AB is COMPLEX array, dimension (LDA,N)
          The upper or lower triangular band matrix A, stored in the
          first kd+1 rows of the array. The j-th column of A is stored
          in the j-th column of the array AB as follows:
          if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).

LDAB

          LDAB is INTEGER
          The leading dimension of the array AB.  LDAB >= max(1,KD+1).

          X is COMPLEX array, dimension (LDX,NRHS)
          The computed solution vectors for the system of linear
          equations.

LDX

          LDX is INTEGER
          The leading dimension of the array X.  LDX >= max(1,N).

          B is COMPLEX array, dimension (LDB,NRHS)
          The right hand side vectors for the system of linear
          equations.

LDB

          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,N).

WORK

          WORK is COMPLEX array, dimension (N)

RWORK

          RWORK is REAL array, dimension (N)

RESID

          RESID is REAL
          The maximum over the number of right hand sides of
          norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ).

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine ctbt03 (character UPLO, character TRANS, character DIAG, integer N, integer KD, integer NRHS, complex, dimension( ldab, * ) AB, integer LDAB, real SCALE, real, dimension( * ) CNORM, real TSCAL, complex, dimension( ldx, * ) X, integer LDX, complex, dimension( ldb, * ) B, integer LDB, complex, dimension( * ) WORK, real RESID)

CTBT03

Purpose:

 CTBT03 computes the residual for the solution to a scaled triangular
 system of equations  A*x = s*b,  A**T *x = s*b,  or  A**H *x = s*b
 when A is a triangular band matrix.  Here A**T  denotes the transpose
 of A, A**H denotes the conjugate transpose of A, s is a scalar, and
 x and b are N by NRHS matrices.  The test ratio is the maximum over
 the number of right hand sides of
    norm(s*b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ),
 where op(A) denotes A, A**T, or A**H, and EPS is the machine epsilon.

Parameters:

UPLO

          UPLO is CHARACTER*1
          Specifies whether the matrix A is upper or lower triangular.
          = 'U':  Upper triangular
          = 'L':  Lower triangular

TRANS

          TRANS is CHARACTER*1
          Specifies the operation applied to A.
          = 'N':  A *x = s*b     (No transpose)
          = 'T':  A**T *x = s*b  (Transpose)
          = 'C':  A**H *x = s*b  (Conjugate transpose)

DIAG

          DIAG is CHARACTER*1
          Specifies whether or not the matrix A is unit triangular.
          = 'N':  Non-unit triangular
          = 'U':  Unit triangular

          N is INTEGER
          The order of the matrix A.  N >= 0.

          KD is INTEGER
          The number of superdiagonals or subdiagonals of the
          triangular band matrix A.  KD >= 0.

NRHS

          NRHS is INTEGER
          The number of right hand sides, i.e., the number of columns
          of the matrices X and B.  NRHS >= 0.

          AB is COMPLEX array, dimension (LDAB,N)
          The upper or lower triangular band matrix A, stored in the
          first kd+1 rows of the array. The j-th column of A is stored
          in the j-th column of the array AB as follows:
          if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).

LDAB

          LDAB is INTEGER
          The leading dimension of the array AB.  LDAB >= KD+1.

SCALE

          SCALE is REAL
          The scaling factor s used in solving the triangular system.

CNORM

          CNORM is REAL array, dimension (N)
          The 1-norms of the columns of A, not counting the diagonal.

TSCAL

          TSCAL is REAL
          The scaling factor used in computing the 1-norms in CNORM.
          CNORM actually contains the column norms of TSCAL*A.

          X is COMPLEX array, dimension (LDX,NRHS)
          The computed solution vectors for the system of linear
          equations.

LDX

          LDX is INTEGER
          The leading dimension of the array X.  LDX >= max(1,N).

          B is COMPLEX array, dimension (LDB,NRHS)
          The right hand side vectors for the system of linear
          equations.

LDB

          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,N).

WORK

          WORK is COMPLEX array, dimension (N)

RESID

          RESID is REAL
          The maximum over the number of right hand sides of
          norm(op(A)*x - s*b) / ( norm(op(A)) * norm(x) * EPS ).

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine ctbt05 (character UPLO, character TRANS, character DIAG, integer N, integer KD, integer NRHS, complex, dimension( ldab, * ) AB, integer LDAB, complex, dimension( ldb, * ) B, integer LDB, complex, dimension( ldx, * ) X, integer LDX, complex, dimension( ldxact, * ) XACT, integer LDXACT, real, dimension( * ) FERR, real, dimension( * ) BERR, real, dimension( * ) RESLTS)

CTBT05

Purpose:

 CTBT05 tests the error bounds from iterative refinement for the
 computed solution to a system of equations A*X = B, where A is a
 triangular band matrix.
 RESLTS(1) = test of the error bound
           = norm(X - XACT) / ( norm(X) * FERR )
 A large value is returned if this ratio is not less than one.
 RESLTS(2) = residual from the iterative refinement routine
           = the maximum of BERR / ( NZ*EPS + (*) ), where
             (*) = NZ*UNFL / (min_i (abs(A)*abs(X) +abs(b))_i )
             and NZ = max. number of nonzeros in any row of A, plus 1

Parameters:

UPLO

          UPLO is CHARACTER*1
          Specifies whether the matrix A is upper or lower triangular.
          = 'U':  Upper triangular
          = 'L':  Lower triangular

TRANS

          TRANS is CHARACTER*1
          Specifies the form of the system of equations.
          = 'N':  A * X = B  (No transpose)
          = 'T':  A'* X = B  (Transpose)
          = 'C':  A'* X = B  (Conjugate transpose = Transpose)

DIAG

          DIAG is CHARACTER*1
          Specifies whether or not the matrix A is unit triangular.
          = 'N':  Non-unit triangular
          = 'U':  Unit triangular

          N is INTEGER
          The number of rows of the matrices X, B, and XACT, and the
          order of the matrix A.  N >= 0.

          KD is INTEGER
          The number of super-diagonals of the matrix A if UPLO = 'U',
          or the number of sub-diagonals if UPLO = 'L'.  KD >= 0.

NRHS

          NRHS is INTEGER
          The number of columns of the matrices X, B, and XACT.
          NRHS >= 0.

          AB is COMPLEX array, dimension (LDAB,N)
          The upper or lower triangular band matrix A, stored in the
          first kd+1 rows of the array. The j-th column of A is stored
          in the j-th column of the array AB as follows:
          if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).
          If DIAG = 'U', the diagonal elements of A are not referenced
          and are assumed to be 1.

LDAB

          LDAB is INTEGER
          The leading dimension of the array AB.  LDAB >= KD+1.

          B is COMPLEX array, dimension (LDB,NRHS)
          The right hand side vectors for the system of linear
          equations.

LDB

          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,N).

          X is COMPLEX array, dimension (LDX,NRHS)
          The computed solution vectors.  Each vector is stored as a
          column of the matrix X.

LDX

          LDX is INTEGER
          The leading dimension of the array X.  LDX >= max(1,N).

XACT

          XACT is COMPLEX array, dimension (LDX,NRHS)
          The exact solution vectors.  Each vector is stored as a
          column of the matrix XACT.

LDXACT

          LDXACT is INTEGER
          The leading dimension of the array XACT.  LDXACT >= max(1,N).

FERR

          FERR is REAL array, dimension (NRHS)
          The estimated forward error bounds for each solution vector
          X.  If XTRUE is the true solution, FERR bounds the magnitude
          of the largest entry in (X - XTRUE) divided by the magnitude
          of the largest entry in X.

BERR

          BERR is REAL array, dimension (NRHS)
          The componentwise relative backward error of each solution
          vector (i.e., the smallest relative change in any entry of A
          or B that makes X an exact solution).

RESLTS

          RESLTS is REAL array, dimension (2)
          The maximum over the NRHS solution vectors of the ratios:
          RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR )
          RESLTS(2) = BERR / ( NZ*EPS + (*) )

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine ctbt06 (real RCOND, real RCONDC, character UPLO, character DIAG, integer N, integer KD, complex, dimension( ldab, * ) AB, integer LDAB, real, dimension( * ) RWORK, real RAT)

CTBT06

Purpose:

 CTBT06 computes a test ratio comparing RCOND (the reciprocal
 condition number of a triangular matrix A) and RCONDC, the estimate
 computed by CTBCON.  Information about the triangular matrix A is
 used if one estimate is zero and the other is non-zero to decide if
 underflow in the estimate is justified.

Parameters:

RCOND

          RCOND is REAL
          The estimate of the reciprocal condition number obtained by
          forming the explicit inverse of the matrix A and computing
          RCOND = 1/( norm(A) * norm(inv(A)) ).

RCONDC

          RCONDC is REAL
          The estimate of the reciprocal condition number computed by
          CTBCON.

UPLO

          UPLO is CHARACTER
          Specifies whether the matrix A is upper or lower triangular.
          = 'U':  Upper triangular
          = 'L':  Lower triangular

DIAG

          DIAG is CHARACTER
          Specifies whether or not the matrix A is unit triangular.
          = 'N':  Non-unit triangular
          = 'U':  Unit triangular

          N is INTEGER
          The order of the matrix A.  N >= 0.

          KD is INTEGER
          The number of superdiagonals or subdiagonals of the
          triangular band matrix A.  KD >= 0.

          AB is COMPLEX array, dimension (LDAB,N)
          The upper or lower triangular band matrix A, stored in the
          first kd+1 rows of the array. The j-th column of A is stored
          in the j-th column of the array AB as follows:
          if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).

LDAB

          LDAB is INTEGER
          The leading dimension of the array AB.  LDAB >= KD+1.

RWORK

          RWORK is REAL array, dimension (N)

RAT

          RAT is REAL
          The test ratio.  If both RCOND and RCONDC are nonzero,
             RAT = MAX( RCOND, RCONDC )/MIN( RCOND, RCONDC ) - 1.
          If RAT = 0, the two estimates are exactly the same.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine ctpt01 (character UPLO, character DIAG, integer N, complex, dimension( * ) AP, complex, dimension( * ) AINVP, real RCOND, real, dimension( * ) RWORK, real RESID)

CTPT01

Purpose:

 CTPT01 computes the residual for a triangular matrix A times its
 inverse when A is stored in packed format:
    RESID = norm(A*AINV - I) / ( N * norm(A) * norm(AINV) * EPS ),
 where EPS is the machine epsilon.

Parameters:

UPLO

          UPLO is CHARACTER*1
          Specifies whether the matrix A is upper or lower triangular.
          = 'U':  Upper triangular
          = 'L':  Lower triangular

DIAG

          DIAG is CHARACTER*1
          Specifies whether or not the matrix A is unit triangular.
          = 'N':  Non-unit triangular
          = 'U':  Unit triangular

          N is INTEGER
          The order of the matrix A.  N >= 0.

          AP is COMPLEX array, dimension (N*(N+1)/2)
          The original upper or lower triangular matrix A, packed
          columnwise in a linear array.  The j-th column of A is stored
          in the array AP as follows:
          if UPLO = 'U', AP((j-1)*j/2 + i) = A(i,j) for 1<=i<=j;
          if UPLO = 'L',
             AP((j-1)*(n-j) + j*(j+1)/2 + i-j) = A(i,j) for j<=i<=n.

AINVP

          AINVP is COMPLEX array, dimension (N*(N+1)/2)
          On entry, the (triangular) inverse of the matrix A, packed
          columnwise in a linear array as in AP.
          On exit, the contents of AINVP are destroyed.

RCOND

          RCOND is REAL
          The reciprocal condition number of A, computed as
          1/(norm(A) * norm(AINV)).

RWORK

          RWORK is REAL array, dimension (N)

RESID

          RESID is REAL
          norm(A*AINV - I) / ( N * norm(A) * norm(AINV) * EPS )

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine ctpt02 (character UPLO, character TRANS, character DIAG, integer N, integer NRHS, complex, dimension( * ) AP, complex, dimension( ldx, * ) X, integer LDX, complex, dimension( ldb, * ) B, integer LDB, complex, dimension( * ) WORK, real, dimension( * ) RWORK, real RESID)

CTPT02

Purpose:

 CTPT02 computes the residual for the computed solution to a
 triangular system of linear equations  A*x = b,  A**T *x = b,  or
 A**H *x = b, when the triangular matrix A is stored in packed format.
 Here A**T denotes the transpose of A, A**H denotes the conjugate
 transpose of A, and x and b are N by NRHS matrices.  The test ratio
 is the maximum over the number of right hand sides of
 the maximum over the number of right hand sides of
    norm(b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ),
 where op(A) denotes A, A**T, or A**H, and EPS is the machine epsilon.

Parameters:

UPLO

          UPLO is CHARACTER*1
          Specifies whether the matrix A is upper or lower triangular.
          = 'U':  Upper triangular
          = 'L':  Lower triangular

TRANS

          TRANS is CHARACTER*1
          Specifies the operation applied to A.
          = 'N':  A *x = b     (No transpose)
          = 'T':  A**T *x = b  (Transpose)
          = 'C':  A**H *x = b  (Conjugate transpose)

DIAG

          DIAG is CHARACTER*1
          Specifies whether or not the matrix A is unit triangular.
          = 'N':  Non-unit triangular
          = 'U':  Unit triangular

          N is INTEGER
          The order of the matrix A.  N >= 0.

NRHS

          NRHS is INTEGER
          The number of right hand sides, i.e., the number of columns
          of the matrices X and B.  NRHS >= 0.

          AP is COMPLEX array, dimension (N*(N+1)/2)
          The upper or lower triangular matrix A, packed columnwise in
          a linear array.  The j-th column of A is stored in the array
          AP as follows:
          if UPLO = 'U', AP((j-1)*j/2 + i) = A(i,j) for 1<=i<=j;
          if UPLO = 'L',
             AP((j-1)*(n-j) + j*(j+1)/2 + i-j) = A(i,j) for j<=i<=n.

          X is COMPLEX array, dimension (LDX,NRHS)
          The computed solution vectors for the system of linear
          equations.

LDX

          LDX is INTEGER
          The leading dimension of the array X.  LDX >= max(1,N).

          B is COMPLEX array, dimension (LDB,NRHS)
          The right hand side vectors for the system of linear
          equations.

LDB

          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,N).

WORK

          WORK is COMPLEX array, dimension (N)

RWORK

          RWORK is REAL array, dimension (N)

RESID

          RESID is REAL
          The maximum over the number of right hand sides of
          norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ).

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine ctpt03 (character UPLO, character TRANS, character DIAG, integer N, integer NRHS, complex, dimension( * ) AP, real SCALE, real, dimension( * ) CNORM, real TSCAL, complex, dimension( ldx, * ) X, integer LDX, complex, dimension( ldb, * ) B, integer LDB, complex, dimension( * ) WORK, real RESID)

CTPT03

Purpose:

 CTPT03 computes the residual for the solution to a scaled triangular
 system of equations A*x = s*b,  A**T *x = s*b,  or  A**H *x = s*b,
 when the triangular matrix A is stored in packed format.  Here A**T
 denotes the transpose of A, A**H denotes the conjugate transpose of
 A, s is a scalar, and x and b are N by NRHS matrices.  The test ratio
 is the maximum over the number of right hand sides of
    norm(s*b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ),
 where op(A) denotes A, A**T, or A**H, and EPS is the machine epsilon.

Parameters:

UPLO

          UPLO is CHARACTER*1
          Specifies whether the matrix A is upper or lower triangular.
          = 'U':  Upper triangular
          = 'L':  Lower triangular

TRANS

          TRANS is CHARACTER*1
          Specifies the operation applied to A.
          = 'N':  A *x = s*b     (No transpose)
          = 'T':  A**T *x = s*b  (Transpose)
          = 'C':  A**H *x = s*b  (Conjugate transpose)

DIAG

          DIAG is CHARACTER*1
          Specifies whether or not the matrix A is unit triangular.
          = 'N':  Non-unit triangular
          = 'U':  Unit triangular

          N is INTEGER
          The order of the matrix A.  N >= 0.

NRHS

          NRHS is INTEGER
          The number of right hand sides, i.e., the number of columns
          of the matrices X and B.  NRHS >= 0.

          AP is COMPLEX array, dimension (N*(N+1)/2)
          The upper or lower triangular matrix A, packed columnwise in
          a linear array.  The j-th column of A is stored in the array
          AP as follows:
          if UPLO = 'U', AP((j-1)*j/2 + i) = A(i,j) for 1<=i<=j;
          if UPLO = 'L',
             AP((j-1)*(n-j) + j*(j+1)/2 + i-j) = A(i,j) for j<=i<=n.

SCALE

          SCALE is REAL
          The scaling factor s used in solving the triangular system.

CNORM

          CNORM is REAL array, dimension (N)
          The 1-norms of the columns of A, not counting the diagonal.

TSCAL

          TSCAL is REAL
          The scaling factor used in computing the 1-norms in CNORM.
          CNORM actually contains the column norms of TSCAL*A.

          X is COMPLEX array, dimension (LDX,NRHS)
          The computed solution vectors for the system of linear
          equations.

LDX

          LDX is INTEGER
          The leading dimension of the array X.  LDX >= max(1,N).

          B is COMPLEX array, dimension (LDB,NRHS)
          The right hand side vectors for the system of linear
          equations.

LDB

          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,N).

WORK

          WORK is COMPLEX array, dimension (N)

RESID

          RESID is REAL
          The maximum over the number of right hand sides of
          norm(op(A)*x - s*b) / ( norm(op(A)) * norm(x) * EPS ).

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine ctpt05 (character UPLO, character TRANS, character DIAG, integer N, integer NRHS, complex, dimension( * ) AP, complex, dimension( ldb, * ) B, integer LDB, complex, dimension( ldx, * ) X, integer LDX, complex, dimension( ldxact, * ) XACT, integer LDXACT, real, dimension( * ) FERR, real, dimension( * ) BERR, real, dimension( * ) RESLTS)

CTPT05

Purpose:

 CTPT05 tests the error bounds from iterative refinement for the
 computed solution to a system of equations A*X = B, where A is a
 triangular matrix in packed storage format.
 RESLTS(1) = test of the error bound
           = norm(X - XACT) / ( norm(X) * FERR )
 A large value is returned if this ratio is not less than one.
 RESLTS(2) = residual from the iterative refinement routine
           = the maximum of BERR / ( (n+1)*EPS + (*) ), where
             (*) = (n+1)*UNFL / (min_i (abs(A)*abs(X) +abs(b))_i )

Parameters:

UPLO

          UPLO is CHARACTER*1
          Specifies whether the matrix A is upper or lower triangular.
          = 'U':  Upper triangular
          = 'L':  Lower triangular

TRANS

          TRANS is CHARACTER*1
          Specifies the form of the system of equations.
          = 'N':  A * X = B  (No transpose)
          = 'T':  A'* X = B  (Transpose)
          = 'C':  A'* X = B  (Conjugate transpose = Transpose)

DIAG

          DIAG is CHARACTER*1
          Specifies whether or not the matrix A is unit triangular.
          = 'N':  Non-unit triangular
          = 'U':  Unit triangular

          N is INTEGER
          The number of rows of the matrices X, B, and XACT, and the
          order of the matrix A.  N >= 0.

NRHS

          NRHS is INTEGER
          The number of columns of the matrices X, B, and XACT.
          NRHS >= 0.

          AP is COMPLEX array, dimension (N*(N+1)/2)
          The upper or lower triangular matrix A, packed columnwise in
          a linear array.  The j-th column of A is stored in the array
          AP as follows:
          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
          If DIAG = 'U', the diagonal elements of A are not referenced
          and are assumed to be 1.

          B is COMPLEX array, dimension (LDB,NRHS)
          The right hand side vectors for the system of linear
          equations.

LDB

          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,N).

          X is COMPLEX array, dimension (LDX,NRHS)
          The computed solution vectors.  Each vector is stored as a
          column of the matrix X.

LDX

          LDX is INTEGER
          The leading dimension of the array X.  LDX >= max(1,N).

XACT

          XACT is COMPLEX array, dimension (LDX,NRHS)
          The exact solution vectors.  Each vector is stored as a
          column of the matrix XACT.

LDXACT

          LDXACT is INTEGER
          The leading dimension of the array XACT.  LDXACT >= max(1,N).

FERR

          FERR is REAL array, dimension (NRHS)
          The estimated forward error bounds for each solution vector
          X.  If XTRUE is the true solution, FERR bounds the magnitude
          of the largest entry in (X - XTRUE) divided by the magnitude
          of the largest entry in X.

BERR

          BERR is REAL array, dimension (NRHS)
          The componentwise relative backward error of each solution
          vector (i.e., the smallest relative change in any entry of A
          or B that makes X an exact solution).

RESLTS

          RESLTS is REAL array, dimension (2)
          The maximum over the NRHS solution vectors of the ratios:
          RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR )
          RESLTS(2) = BERR / ( (n+1)*EPS + (*) )

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine ctpt06 (real RCOND, real RCONDC, character UPLO, character DIAG, integer N, complex, dimension( * ) AP, real, dimension( * ) RWORK, real RAT)

CTPT06

Purpose:

 CTPT06 computes a test ratio comparing RCOND (the reciprocal
 condition number of the triangular matrix A) and RCONDC, the estimate
 computed by CTPCON.  Information about the triangular matrix is used
 if one estimate is zero and the other is non-zero to decide if
 underflow in the estimate is justified.

Parameters:

RCOND

          RCOND is REAL
          The estimate of the reciprocal condition number obtained by
          forming the explicit inverse of the matrix A and computing
          RCOND = 1/( norm(A) * norm(inv(A)) ).

RCONDC

          RCONDC is REAL
          The estimate of the reciprocal condition number computed by
          CTPCON.

UPLO

          UPLO is CHARACTER
          Specifies whether the matrix A is upper or lower triangular.
          = 'U':  Upper triangular
          = 'L':  Lower triangular

DIAG

          DIAG is CHARACTER
          Specifies whether or not the matrix A is unit triangular.
          = 'N':  Non-unit triangular
          = 'U':  Unit triangular

          N is INTEGER
          The order of the matrix A.  N >= 0.

          AP is COMPLEX array, dimension (N*(N+1)/2)
          The upper or lower triangular matrix A, packed columnwise in
          a linear array.  The j-th column of A is stored in the array
          AP as follows:
          if UPLO = 'U', AP((j-1)*j/2 + i) = A(i,j) for 1<=i<=j;
          if UPLO = 'L',
             AP((j-1)*(n-j) + j*(j+1)/2 + i-j) = A(i,j) for j<=i<=n.

RWORK

          RWORK is REAL array, dimension (N)

RAT

          RAT is REAL
          The test ratio.  If both RCOND and RCONDC are nonzero,
             RAT = MAX( RCOND, RCONDC )/MIN( RCOND, RCONDC ) - 1.
          If RAT = 0, the two estimates are exactly the same.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine ctrt01 (character UPLO, character DIAG, integer N, complex, dimension( lda, * ) A, integer LDA, complex, dimension( ldainv, * ) AINV, integer LDAINV, real RCOND, real, dimension( * ) RWORK, real RESID)

CTRT01

Purpose:

 CTRT01 computes the residual for a triangular matrix A times its
 inverse:
    RESID = norm( A*AINV - I ) / ( N * norm(A) * norm(AINV) * EPS ),
 where EPS is the machine epsilon.

Parameters:

UPLO

          UPLO is CHARACTER*1
          Specifies whether the matrix A is upper or lower triangular.
          = 'U':  Upper triangular
          = 'L':  Lower triangular

DIAG

          DIAG is CHARACTER*1
          Specifies whether or not the matrix A is unit triangular.
          = 'N':  Non-unit triangular
          = 'U':  Unit triangular

          N is INTEGER
          The order of the matrix A.  N >= 0.

          A is COMPLEX array, dimension (LDA,N)
          The triangular matrix A.  If UPLO = 'U', the leading n by n
          upper triangular part of the array A contains the upper
          triangular matrix, and the strictly lower triangular part of
          A is not referenced.  If UPLO = 'L', the leading n by n lower
          triangular part of the array A contains the lower triangular
          matrix, and the strictly upper triangular part of A is not
          referenced.  If DIAG = 'U', the diagonal elements of A are
          also not referenced and are assumed to be 1.

LDA

          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N).

AINV

          AINV is COMPLEX array, dimension (LDAINV,N)
          On entry, the (triangular) inverse of the matrix A, in the
          same storage format as A.
          On exit, the contents of AINV are destroyed.

LDAINV

          LDAINV is INTEGER
          The leading dimension of the array AINV.  LDAINV >= max(1,N).

RCOND

          RCOND is REAL
          The reciprocal condition number of A, computed as
          1/(norm(A) * norm(AINV)).

RWORK

          RWORK is REAL array, dimension (N)

RESID

          RESID is REAL
          norm(A*AINV - I) / ( N * norm(A) * norm(AINV) * EPS )

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine ctrt02 (character UPLO, character TRANS, character DIAG, integer N, integer NRHS, complex, dimension( lda, * ) A, integer LDA, complex, dimension( ldx, * ) X, integer LDX, complex, dimension( ldb, * ) B, integer LDB, complex, dimension( * ) WORK, real, dimension( * ) RWORK, real RESID)

CTRT02

Purpose:

 CTRT02 computes the residual for the computed solution to a
 triangular system of linear equations  A*x = b,  A**T *x = b,
 or A**H *x = b.  Here A is a triangular matrix, A**T is the transpose
 of A, A**H is the conjugate transpose of A, and x and b are N by NRHS
 matrices.  The test ratio is the maximum over the number of right
 hand sides of
    norm(b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ),
 where op(A) denotes A, A**T, or A**H, and EPS is the machine epsilon.

Parameters:

UPLO

          UPLO is CHARACTER*1
          Specifies whether the matrix A is upper or lower triangular.
          = 'U':  Upper triangular
          = 'L':  Lower triangular

TRANS

          TRANS is CHARACTER*1
          Specifies the operation applied to A.
          = 'N':  A *x = b     (No transpose)
          = 'T':  A**T *x = b  (Transpose)
          = 'C':  A**H *x = b  (Conjugate transpose)

DIAG

          DIAG is CHARACTER*1
          Specifies whether or not the matrix A is unit triangular.
          = 'N':  Non-unit triangular
          = 'U':  Unit triangular

          N is INTEGER
          The order of the matrix A.  N >= 0.

NRHS

          NRHS is INTEGER
          The number of right hand sides, i.e., the number of columns
          of the matrices X and B.  NRHS >= 0.

          A is COMPLEX array, dimension (LDA,N)
          The triangular matrix A.  If UPLO = 'U', the leading n by n
          upper triangular part of the array A contains the upper
          triangular matrix, and the strictly lower triangular part of
          A is not referenced.  If UPLO = 'L', the leading n by n lower
          triangular part of the array A contains the lower triangular
          matrix, and the strictly upper triangular part of A is not
          referenced.  If DIAG = 'U', the diagonal elements of A are
          also not referenced and are assumed to be 1.

LDA

          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N).

          X is COMPLEX array, dimension (LDX,NRHS)
          The computed solution vectors for the system of linear
          equations.

LDX

          LDX is INTEGER
          The leading dimension of the array X.  LDX >= max(1,N).

          B is COMPLEX array, dimension (LDB,NRHS)
          The right hand side vectors for the system of linear
          equations.

LDB

          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,N).

WORK

          WORK is COMPLEX array, dimension (N)

RWORK

          RWORK is REAL array, dimension (N)

RESID

          RESID is REAL
          The maximum over the number of right hand sides of
          norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ).

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine ctrt03 (character UPLO, character TRANS, character DIAG, integer N, integer NRHS, complex, dimension( lda, * ) A, integer LDA, real SCALE, real, dimension( * ) CNORM, real TSCAL, complex, dimension( ldx, * ) X, integer LDX, complex, dimension( ldb, * ) B, integer LDB, complex, dimension( * ) WORK, real RESID)

CTRT03

Purpose:

 CTRT03 computes the residual for the solution to a scaled triangular
 system of equations A*x = s*b,  A**T *x = s*b,  or  A**H *x = s*b.
 Here A is a triangular matrix, A**T denotes the transpose of A, A**H
 denotes the conjugate transpose of A, s is a scalar, and x and b are
 N by NRHS matrices.  The test ratio is the maximum over the number of
 right hand sides of
    norm(s*b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ),
 where op(A) denotes A, A**T, or A**H, and EPS is the machine epsilon.

Parameters:

UPLO

          UPLO is CHARACTER*1
          Specifies whether the matrix A is upper or lower triangular.
          = 'U':  Upper triangular
          = 'L':  Lower triangular

TRANS

          TRANS is CHARACTER*1
          Specifies the operation applied to A.
          = 'N':  A *x = s*b     (No transpose)
          = 'T':  A**T *x = s*b  (Transpose)
          = 'C':  A**H *x = s*b  (Conjugate transpose)

DIAG

          DIAG is CHARACTER*1
          Specifies whether or not the matrix A is unit triangular.
          = 'N':  Non-unit triangular
          = 'U':  Unit triangular

          N is INTEGER
          The order of the matrix A.  N >= 0.

NRHS

          NRHS is INTEGER
          The number of right hand sides, i.e., the number of columns
          of the matrices X and B.  NRHS >= 0.

          A is COMPLEX array, dimension (LDA,N)
          The triangular matrix A.  If UPLO = 'U', the leading n by n
          upper triangular part of the array A contains the upper
          triangular matrix, and the strictly lower triangular part of
          A is not referenced.  If UPLO = 'L', the leading n by n lower
          triangular part of the array A contains the lower triangular
          matrix, and the strictly upper triangular part of A is not
          referenced.  If DIAG = 'U', the diagonal elements of A are
          also not referenced and are assumed to be 1.

LDA

          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N).

SCALE

          SCALE is REAL
          The scaling factor s used in solving the triangular system.

CNORM

          CNORM is REAL array, dimension (N)
          The 1-norms of the columns of A, not counting the diagonal.

TSCAL

          TSCAL is REAL
          The scaling factor used in computing the 1-norms in CNORM.
          CNORM actually contains the column norms of TSCAL*A.

          X is COMPLEX array, dimension (LDX,NRHS)
          The computed solution vectors for the system of linear
          equations.

LDX

          LDX is INTEGER
          The leading dimension of the array X.  LDX >= max(1,N).

          B is COMPLEX array, dimension (LDB,NRHS)
          The right hand side vectors for the system of linear
          equations.

LDB

          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,N).

WORK

          WORK is COMPLEX array, dimension (N)

RESID

          RESID is REAL
          The maximum over the number of right hand sides of
          norm(op(A)*x - s*b) / ( norm(op(A)) * norm(x) * EPS ).

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine ctrt05 (character UPLO, character TRANS, character DIAG, integer N, integer NRHS, complex, dimension( lda, * ) A, integer LDA, complex, dimension( ldb, * ) B, integer LDB, complex, dimension( ldx, * ) X, integer LDX, complex, dimension( ldxact, * ) XACT, integer LDXACT, real, dimension( * ) FERR, real, dimension( * ) BERR, real, dimension( * ) RESLTS)

CTRT05

Purpose:

 CTRT05 tests the error bounds from iterative refinement for the
 computed solution to a system of equations A*X = B, where A is a
 triangular n by n matrix.
 RESLTS(1) = test of the error bound
           = norm(X - XACT) / ( norm(X) * FERR )
 A large value is returned if this ratio is not less than one.
 RESLTS(2) = residual from the iterative refinement routine
           = the maximum of BERR / ( (n+1)*EPS + (*) ), where
             (*) = (n+1)*UNFL / (min_i (abs(A)*abs(X) +abs(b))_i )

Parameters:

UPLO

          UPLO is CHARACTER*1
          Specifies whether the matrix A is upper or lower triangular.
          = 'U':  Upper triangular
          = 'L':  Lower triangular

TRANS

          TRANS is CHARACTER*1
          Specifies the form of the system of equations.
          = 'N':  A * X = B  (No transpose)
          = 'T':  A'* X = B  (Transpose)
          = 'C':  A'* X = B  (Conjugate transpose = Transpose)

DIAG

          DIAG is CHARACTER*1
          Specifies whether or not the matrix A is unit triangular.
          = 'N':  Non-unit triangular
          = 'U':  Unit triangular

          N is INTEGER
          The number of rows of the matrices X, B, and XACT, and the
          order of the matrix A.  N >= 0.

NRHS

          NRHS is INTEGER
          The number of columns of the matrices X, B, and XACT.
          NRHS >= 0.

          A is COMPLEX array, dimension (LDA,N)
          The triangular matrix A.  If UPLO = 'U', the leading n by n
          upper triangular part of the array A contains the upper
          triangular matrix, and the strictly lower triangular part of
          A is not referenced.  If UPLO = 'L', the leading n by n lower
          triangular part of the array A contains the lower triangular
          matrix, and the strictly upper triangular part of A is not
          referenced.  If DIAG = 'U', the diagonal elements of A are
          also not referenced and are assumed to be 1.

LDA

          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N).

          B is COMPLEX array, dimension (LDB,NRHS)
          The right hand side vectors for the system of linear
          equations.

LDB

          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,N).

          X is COMPLEX array, dimension (LDX,NRHS)
          The computed solution vectors.  Each vector is stored as a
          column of the matrix X.

LDX

          LDX is INTEGER
          The leading dimension of the array X.  LDX >= max(1,N).

XACT

          XACT is COMPLEX array, dimension (LDX,NRHS)
          The exact solution vectors.  Each vector is stored as a
          column of the matrix XACT.

LDXACT

          LDXACT is INTEGER
          The leading dimension of the array XACT.  LDXACT >= max(1,N).

FERR

          FERR is REAL array, dimension (NRHS)
          The estimated forward error bounds for each solution vector
          X.  If XTRUE is the true solution, FERR bounds the magnitude
          of the largest entry in (X - XTRUE) divided by the magnitude
          of the largest entry in X.

BERR

          BERR is REAL array, dimension (NRHS)
          The componentwise relative backward error of each solution
          vector (i.e., the smallest relative change in any entry of A
          or B that makes X an exact solution).

RESLTS

          RESLTS is REAL array, dimension (2)
          The maximum over the NRHS solution vectors of the ratios:
          RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR )
          RESLTS(2) = BERR / ( (n+1)*EPS + (*) )

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

subroutine ctrt06 (real RCOND, real RCONDC, character UPLO, character DIAG, integer N, complex, dimension( lda, * ) A, integer LDA, real, dimension( * ) RWORK, real RAT)

CTRT06

Purpose:

 CTRT06 computes a test ratio comparing RCOND (the reciprocal
 condition number of a triangular matrix A) and RCONDC, the estimate
 computed by CTRCON.  Information about the triangular matrix A is
 used if one estimate is zero and the other is non-zero to decide if
 underflow in the estimate is justified.

Parameters:

RCOND

          RCOND is REAL
          The estimate of the reciprocal condition number obtained by
          forming the explicit inverse of the matrix A and computing
          RCOND = 1/( norm(A) * norm(inv(A)) ).

RCONDC

          RCONDC is REAL
          The estimate of the reciprocal condition number computed by
          CTRCON.

UPLO

          UPLO is CHARACTER
          Specifies whether the matrix A is upper or lower triangular.
          = 'U':  Upper triangular
          = 'L':  Lower triangular

DIAG

          DIAG is CHARACTER
          Specifies whether or not the matrix A is unit triangular.
          = 'N':  Non-unit triangular
          = 'U':  Unit triangular

          N is INTEGER
          The order of the matrix A.  N >= 0.

          A is COMPLEX array, dimension (LDA,N)
          The triangular matrix A.  If UPLO = 'U', the leading n by n
          upper triangular part of the array A contains the upper
          triangular matrix, and the strictly lower triangular part of
          A is not referenced.  If UPLO = 'L', the leading n by n lower
          triangular part of the array A contains the lower triangular
          matrix, and the strictly upper triangular part of A is not
          referenced.  If DIAG = 'U', the diagonal elements of A are
          also not referenced and are assumed to be 1.

LDA

          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N).

RWORK

          RWORK is REAL array, dimension (N)

RAT

          RAT is REAL
          The test ratio.  If both RCOND and RCONDC are nonzero,
             RAT = MAX( RCOND, RCONDC )/MIN( RCOND, RCONDC ) - 1.
          If RAT = 0, the two estimates are exactly the same.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

: November 2011

Author

Generated automatically by Doxygen for LAPACK from the source code.

Functions

Detailed Description

Function Documentation

program cchkaa ()

subroutine cchkeq (real THRESH, integer NOUT)

subroutine cchkqrt (real THRESH, logical TSTERR, integer NM, integer, dimension( * ) MVAL, integer NN, integer, dimension( * ) NVAL, integer NNB, integer, dimension( * ) NBVAL, integer NOUT)

subroutine cchkqrtp (real THRESH, logical TSTERR, integer NM, integer, dimension( * ) MVAL, integer NN, integer, dimension( * ) NVAL, integer NNB, integer, dimension( * ) NBVAL, integer NOUT)

program cchkrfp ()

subroutine cdrvrf1 (integer NOUT, integer NN, integer, dimension( nn ) NVAL, real THRESH, complex, dimension( lda, * ) A, integer LDA, complex, dimension( * ) ARF, real, dimension( * ) WORK)

subroutine cdrvrf2 (integer NOUT, integer NN, integer, dimension( nn ) NVAL, complex, dimension( lda, * ) A, integer LDA, complex, dimension( * ) ARF, complex, dimension(*) AP, complex, dimension( lda, * ) ASAV)

subroutine cdrvrf4 (integer NOUT, integer NN, integer, dimension( nn ) NVAL, real THRESH, complex, dimension( ldc, * ) C1, complex, dimension( ldc, *) C2, integer LDC, complex, dimension( * ) CRF, complex, dimension( lda, * ) A, integer LDA, real, dimension( * ) S_WORK_CLANGE)

subroutine cebchvxx (real THRESH, character*3 PATH)

subroutine cerrge (character*3 PATH, integer NUNIT)

subroutine cerrgt (character*3 PATH, integer NUNIT)

subroutine cerrhe (character*3 PATH, integer NUNIT)

subroutine cerrlq (character*3 PATH, integer NUNIT)

subroutine cerrls (character*3 PATH, integer NUNIT)

subroutine cerrpo (character*3 PATH, integer NUNIT)

subroutine cerrps (character*3 PATH, integer NUNIT)

subroutine cerrql (character*3 PATH, integer NUNIT)

subroutine cerrqp (character*3 PATH, integer NUNIT)

subroutine cerrqr (character*3 PATH, integer NUNIT)

subroutine cerrqrt (character*3 PATH, integer NUNIT)

subroutine cerrqrtp (character*3 PATH, integer NUNIT)

subroutine cerrrfp (integer NUNIT)

subroutine cerrrq (character*3 PATH, integer NUNIT)

subroutine cerrsy (character*3 PATH, integer NUNIT)

subroutine cerrtr (character*3 PATH, integer NUNIT)

subroutine cerrtz (character*3 PATH, integer NUNIT)

subroutine cerrvx (character*3 PATH, integer NUNIT)

subroutine cgbt01 (integer M, integer N, integer KL, integer KU, complex, dimension( lda, * ) A, integer LDA, complex, dimension( ldafac, * ) AFAC, integer LDAFAC, integer, dimension( * ) IPIV, complex, dimension( * ) WORK, real RESID)

subroutine cgbt02 (character TRANS, integer M, integer N, integer KL, integer KU, integer NRHS, complex, dimension( lda, * ) A, integer LDA, complex, dimension( ldx, * ) X, integer LDX, complex, dimension( ldb, * ) B, integer LDB, real RESID)

subroutine cgelqs (integer M, integer N, integer NRHS, complex, dimension( lda, * ) A, integer LDA, complex, dimension( * ) TAU, complex, dimension( ldb, * ) B, integer LDB, complex, dimension( lwork ) WORK, integer LWORK, integer INFO)

logical function cgennd (integer M, integer N, complex, dimension( lda, * ) A, integer LDA)

subroutine cgeqls (integer M, integer N, integer NRHS, complex, dimension( lda, * ) A, integer LDA, complex, dimension( * ) TAU, complex, dimension( ldb, * ) B, integer LDB, complex, dimension( lwork ) WORK, integer LWORK, integer INFO)

subroutine cgeqrs (integer M, integer N, integer NRHS, complex, dimension( lda, * ) A, integer LDA, complex, dimension( * ) TAU, complex, dimension( ldb, * ) B, integer LDB, complex, dimension( lwork ) WORK, integer LWORK, integer INFO)

subroutine cgerqs (integer M, integer N, integer NRHS, complex, dimension( lda, * ) A, integer LDA, complex, dimension( * ) TAU, complex, dimension( ldb, * ) B, integer LDB, complex, dimension( lwork ) WORK, integer LWORK, integer INFO)

subroutine cget01 (integer M, integer N, complex, dimension( lda, * ) A, integer LDA, complex, dimension( ldafac, * ) AFAC, integer LDAFAC, integer, dimension( * ) IPIV, real, dimension( * ) RWORK, real RESID)

subroutine cget02 (character TRANS, integer M, integer N, integer NRHS, complex, dimension( lda, * ) A, integer LDA, complex, dimension( ldx, * ) X, integer LDX, complex, dimension( ldb, * ) B, integer LDB, real, dimension( * ) RWORK, real RESID)

subroutine cget03 (integer N, complex, dimension( lda, * ) A, integer LDA, complex, dimension( ldainv, * ) AINV, integer LDAINV, complex, dimension( ldwork, * ) WORK, integer LDWORK, real, dimension( * ) RWORK, real RCOND, real RESID)

subroutine cget04 (integer N, integer NRHS, complex, dimension( ldx, * ) X, integer LDX, complex, dimension( ldxact, * ) XACT, integer LDXACT, real RCOND, real RESID)

subroutine cgtt02 (character TRANS, integer N, integer NRHS, complex, dimension( * ) DL, complex, dimension( * ) D, complex, dimension( * ) DU, complex, dimension( ldx, * ) X, integer LDX, complex, dimension( ldb, * ) B, integer LDB, real RESID)

subroutine chet01 (character UPLO, integer N, complex, dimension( lda, * ) A, integer LDA, complex, dimension( ldafac, * ) AFAC, integer LDAFAC, integer, dimension( * ) IPIV, complex, dimension( ldc, * ) C, integer LDC, real, dimension( * ) RWORK, real RESID)

subroutine chet01_rook (character UPLO, integer N, complex, dimension( lda, * ) A, integer LDA, complex, dimension( ldafac, * ) AFAC, integer LDAFAC, integer, dimension( * ) IPIV, complex, dimension( ldc, * ) C, integer LDC, real, dimension( * ) RWORK, real RESID)

subroutine chkxer (character*(*) SRNAMT, integer INFOT, integer NOUT, logical LERR, logical OK)

subroutine chpt01 (character UPLO, integer N, complex, dimension( * ) A, complex, dimension( * ) AFAC, integer, dimension( * ) IPIV, complex, dimension( ldc, * ) C, integer LDC, real, dimension( * ) RWORK, real RESID)

subroutine clahilb (integer N, integer NRHS, complex, dimension(lda,n) A, integer LDA, complex, dimension(ldx, nrhs) X, integer LDX, complex, dimension(ldb, nrhs) B, integer LDB, real, dimension(n) WORK, integer INFO, character*3 PATH)

subroutine claipd (integer N, complex, dimension( * ) A, integer INDA, integer VINDA)

subroutine claptm (character UPLO, integer N, integer NRHS, real ALPHA, real, dimension( * ) D, complex, dimension( * ) E, complex, dimension( ldx, * ) X, integer LDX, real BETA, complex, dimension( ldb, * ) B, integer LDB)

subroutine clatb4 (character*3 PATH, integer IMAT, integer M, integer N, character TYPE, integer KL, integer KU, real ANORM, integer MODE, real CNDNUM, character DIST)

subroutine clatb5 (character*3 PATH, integer IMAT, integer N, character TYPE, integer KL, integer KU, real ANORM, integer MODE, real CNDNUM, character DIST)

subroutine clatsp (character UPLO, integer N, complex, dimension( * ) X, integer, dimension( * ) ISEED)

subroutine clatsy (character UPLO, integer N, complex, dimension( ldx, * ) X, integer LDX, integer, dimension( * ) ISEED)

subroutine clattb (integer IMAT, character UPLO, character TRANS, character DIAG, integer, dimension( 4 ) ISEED, integer N, integer KD, complex, dimension( ldab, * ) AB, integer LDAB, complex, dimension( * ) B, complex, dimension( * ) WORK, real, dimension( * ) RWORK, integer INFO)

subroutine clattp (integer IMAT, character UPLO, character TRANS, character DIAG, integer, dimension( 4 ) ISEED, integer N, complex, dimension( * ) AP, complex, dimension( * ) B, complex, dimension( * ) WORK, real, dimension( * ) RWORK, integer INFO)

subroutine clattr (integer IMAT, character UPLO, character TRANS, character DIAG, integer, dimension( 4 ) ISEED, integer N, complex, dimension( lda, * ) A, integer LDA, complex, dimension( * ) B, complex, dimension( * ) WORK, real, dimension( * ) RWORK, integer INFO)

subroutine clavhe (character UPLO, character TRANS, character DIAG, integer N, integer NRHS, complex, dimension( lda, * ) A, integer LDA, integer, dimension( * ) IPIV, complex, dimension( ldb, * ) B, integer LDB, integer INFO)

subroutine clavhe_rook (character UPLO, character TRANS, character DIAG, integer N, integer NRHS, complex, dimension( lda, * ) A, integer LDA, integer, dimension( * ) IPIV, complex, dimension( ldb, * ) B, integer LDB, integer INFO)

subroutine clavhp (character UPLO, character TRANS, character DIAG, integer N, integer NRHS, complex, dimension( * ) A, integer, dimension( * ) IPIV, complex, dimension( ldb, * ) B, integer LDB, integer INFO)

subroutine clavsp (character UPLO, character TRANS, character DIAG, integer N, integer NRHS, complex, dimension( * ) A, integer, dimension( * ) IPIV, complex, dimension( ldb, * ) B, integer LDB, integer INFO)

subroutine clavsy (character UPLO, character TRANS, character DIAG, integer N, integer NRHS, complex, dimension( lda, * ) A, integer LDA, integer, dimension( * ) IPIV, complex, dimension( ldb, * ) B, integer LDB, integer INFO)

subroutine clavsy_rook (character UPLO, character TRANS, character DIAG, integer N, integer NRHS, complex, dimension( lda, * ) A, integer LDA, integer, dimension( * ) IPIV, complex, dimension( ldb, * ) B, integer LDB, integer INFO)

subroutine cpbt01 (character UPLO, integer N, integer KD, complex, dimension( lda, * ) A, integer LDA, complex, dimension( ldafac, * ) AFAC, integer LDAFAC, real, dimension( * ) RWORK, real RESID)

subroutine cpbt02 (character UPLO, integer N, integer KD, integer NRHS, complex, dimension( lda, * ) A, integer LDA, complex, dimension( ldx, * ) X, integer LDX, complex, dimension( ldb, * ) B, integer LDB, real, dimension( * ) RWORK, real RESID)

subroutine cpot01 (character UPLO, integer N, complex, dimension( lda, * ) A, integer LDA, complex, dimension( ldafac, * ) AFAC, integer LDAFAC, real, dimension( * ) RWORK, real RESID)

subroutine cpot02 (character UPLO, integer N, integer NRHS, complex, dimension( lda, * ) A, integer LDA, complex, dimension( ldx, * ) X, integer LDX, complex, dimension( ldb, * ) B, integer LDB, real, dimension( * ) RWORK, real RESID)

subroutine cpot03 (character UPLO, integer N, complex, dimension( lda, * ) A, integer LDA, complex, dimension( ldainv, * ) AINV, integer LDAINV, complex, dimension( ldwork, * ) WORK, integer LDWORK, real, dimension( * ) RWORK, real RCOND, real RESID)

subroutine cppt01 (character UPLO, integer N, complex, dimension( * ) A, complex, dimension( * ) AFAC, real, dimension( * ) RWORK, real RESID)

subroutine cppt02 (character UPLO, integer N, integer NRHS, complex, dimension( * ) A, complex, dimension( ldx, * ) X, integer LDX, complex, dimension( ldb, * ) B, integer LDB, real, dimension( * ) RWORK, real RESID)

subroutine cppt03 (character UPLO, integer N, complex, dimension( * ) A, complex, dimension( * ) AINV, complex, dimension( ldwork, * ) WORK, integer LDWORK, real, dimension( * ) RWORK, real RCOND, real RESID)

subroutine cpst01 (character UPLO, integer N, complex, dimension( lda, * ) A, integer LDA, complex, dimension( ldafac, * ) AFAC, integer LDAFAC, complex, dimension( ldperm, * ) PERM, integer LDPERM, integer, dimension( * ) PIV, real, dimension( * ) RWORK, real RESID, integer RANK)

subroutine cptt01 (integer N, real, dimension( * ) D, complex, dimension( * ) E, real, dimension( * ) DF, complex, dimension( * ) EF, complex, dimension( * ) WORK, real RESID)

subroutine cptt02 (character UPLO, integer N, integer NRHS, real, dimension( * ) D, complex, dimension( * ) E, complex, dimension( ldx, * ) X, integer LDX, complex, dimension( ldb, * ) B, integer LDB, real RESID)

real function cqpt01 (integer M, integer N, integer K, complex, dimension( lda, * ) A, complex, dimension( lda, * ) AF, integer LDA, complex, dimension( * ) TAU, integer, dimension( * ) JPVT, complex, dimension( lwork ) WORK, integer LWORK)

subroutine cqrt04 (integer M, integer N, integer NB, real, dimension(6) RESULT)

subroutine cqrt05 (integer M, integer N, integer L, integer NB, real, dimension(6) RESULT)

real function cqrt11 (integer M, integer K, complex, dimension( lda, * ) A, integer LDA, complex, dimension( * ) TAU, complex, dimension( lwork ) WORK, integer LWORK)

real function cqrt12 (integer M, integer N, complex, dimension( lda, * ) A, integer LDA, real, dimension( * ) S, complex, dimension( lwork ) WORK, integer LWORK, real, dimension( * ) RWORK)

subroutine cqrt13 (integer SCALE, integer M, integer N, complex, dimension( lda, * ) A, integer LDA, real NORMA, integer, dimension( 4 ) ISEED)

real function cqrt14 (character TRANS, integer M, integer N, integer NRHS, complex, dimension( lda, * ) A, integer LDA, complex, dimension( ldx, * ) X, integer LDX, complex, dimension( lwork ) WORK, integer LWORK)

subroutine cdrvrf2 (integer NOUT, integer NN, integer, dimension( nn ) NVAL, complex, dimension( lda, * ) A, integer LDA, complex, dimension( * ) ARF, complex, dimension() AP, complex, dimension( lda, ) ASAV)

subroutine cdrvrf4 (integer NOUT, integer NN, integer, dimension( nn ) NVAL, real THRESH, complex, dimension( ldc, * ) C1, complex, dimension( ldc, ) C2, integer LDC, complex, dimension( ) CRF, complex, dimension( lda, * ) A, integer LDA, real, dimension( * ) S_WORK_CLANGE)

subroutine chkxer (character() SRNAMT, integer INFOT, integer NOUT, logical LERR, logical OK)