Functions
subroutine zgtcon (NORM, N, DL, D, DU, DU2, IPIV, ANORM, RCOND, WORK, INFO)
ZGTCON
subroutine zgtrfs (TRANS, N, NRHS, DL, D, DU, DLF, DF, DUF, DU2, IPIV, B, LDB, X, LDX, FERR, BERR, WORK, RWORK, INFO)
ZGTRFS
subroutine zgttrf (N, DL, D, DU, DU2, IPIV, INFO)
ZGTTRF
subroutine zgttrs (TRANS, N, NRHS, DL, D, DU, DU2, IPIV, B, LDB, INFO)
ZGTTRS
subroutine zgtts2 (ITRANS, N, NRHS, DL, D, DU, DU2, IPIV, B, LDB)
ZGTTS2 solves a system of linear equations with a tridiagonal matrix using the LU factorization computed by sgttrf.
Detailed Description
This is the group of complex16 computational functions for GT matrices
Function Documentation
subroutine zgtcon (character NORM, integer N, complex*16, dimension( * ) DL, complex*16, dimension( * ) D, complex*16, dimension( * ) DU, complex*16, dimension( * ) DU2, integer, dimension( * ) IPIV, double precision ANORM, double precision RCOND, complex*16, dimension( * ) WORK, integer INFO)
ZGTCON
Purpose:

ZGTCON estimates the reciprocal of the condition number of a complex tridiagonal matrix A using the LU factorization as computed by ZGTTRF. An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
Parameters:

NORM
NORM is CHARACTER*1 Specifies whether the 1norm condition number or the infinitynorm condition number is required: = '1' or 'O': 1norm; = 'I': Infinitynorm.
NN is INTEGER The order of the matrix A. N >= 0.
DLDL is COMPLEX*16 array, dimension (N1) The (n1) multipliers that define the matrix L from the LU factorization of A as computed by ZGTTRF.
DD is COMPLEX*16 array, dimension (N) The n diagonal elements of the upper triangular matrix U from the LU factorization of A.
DUDU is COMPLEX*16 array, dimension (N1) The (n1) elements of the first superdiagonal of U.
DU2DU2 is COMPLEX*16 array, dimension (N2) The (n2) elements of the second superdiagonal of U.
IPIVIPIV 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.
ANORMANORM is DOUBLE PRECISION If NORM = '1' or 'O', the 1norm of the original matrix A. If NORM = 'I', the infinitynorm of the original matrix A.
RCONDRCOND is DOUBLE PRECISION The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an estimate of the 1norm of inv(A) computed in this routine.
WORKWORK is COMPLEX*16 array, dimension (2*N)
INFOINFO is INTEGER = 0: successful exit < 0: if INFO = i, the ith argument had an illegal value
Author:

Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
 September 2012
subroutine zgtrfs (character TRANS, integer N, integer NRHS, complex*16, dimension( * ) DL, complex*16, dimension( * ) D, complex*16, dimension( * ) DU, complex*16, dimension( * ) DLF, complex*16, dimension( * ) DF, complex*16, dimension( * ) DUF, complex*16, dimension( * ) DU2, integer, dimension( * ) IPIV, complex*16, dimension( ldb, * ) B, integer LDB, complex*16, dimension( ldx, * ) X, integer LDX, double precision, dimension( * ) FERR, double precision, dimension( * ) BERR, complex*16, dimension( * ) WORK, double precision, dimension( * ) RWORK, integer INFO)
ZGTRFS
Purpose:

ZGTRFS improves the computed solution to a system of linear equations when the coefficient matrix is tridiagonal, and provides error bounds and backward error estimates for the solution.
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)
NN is INTEGER The order of the matrix A. N >= 0.
NRHSNRHS is INTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.
DLDL is COMPLEX*16 array, dimension (N1) The (n1) subdiagonal elements of A.
DD is COMPLEX*16 array, dimension (N) The diagonal elements of A.
DUDU is COMPLEX*16 array, dimension (N1) The (n1) superdiagonal elements of A.
DLFDLF is COMPLEX*16 array, dimension (N1) The (n1) multipliers that define the matrix L from the LU factorization of A as computed by ZGTTRF.
DFDF is COMPLEX*16 array, dimension (N) The n diagonal elements of the upper triangular matrix U from the LU factorization of A.
DUFDUF is COMPLEX*16 array, dimension (N1) The (n1) elements of the first superdiagonal of U.
DU2DU2 is COMPLEX*16 array, dimension (N2) The (n2) elements of the second superdiagonal of U.
IPIVIPIV 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.
BB is COMPLEX*16 array, dimension (LDB,NRHS) The right hand side matrix B.
LDBLDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).
XX is COMPLEX*16 array, dimension (LDX,NRHS) On entry, the solution matrix X, as computed by ZGTTRS. On exit, the improved solution matrix X.
LDXLDX is INTEGER The leading dimension of the array X. LDX >= max(1,N).
FERRFERR is DOUBLE PRECISION array, dimension (NRHS) The estimated forward error bound for each solution vector X(j) (the jth column of the solution matrix X). If XTRUE is the true solution corresponding to X(j), FERR(j) is an estimated upper bound for the magnitude of the largest element in (X(j)  XTRUE) divided by the magnitude of the largest element in X(j). The estimate is as reliable as the estimate for RCOND, and is almost always a slight overestimate of the true error.
BERRBERR is DOUBLE PRECISION array, dimension (NRHS) The componentwise relative backward error of each solution vector X(j) (i.e., the smallest relative change in any element of A or B that makes X(j) an exact solution).
WORKWORK is COMPLEX*16 array, dimension (2*N)
RWORKRWORK is DOUBLE PRECISION array, dimension (N)
INFOINFO is INTEGER = 0: successful exit < 0: if INFO = i, the ith argument had an illegal value
Internal Parameters:

ITMAX is the maximum number of steps of iterative refinement.
Author:

Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
 September 2012
subroutine zgttrf (integer N, complex*16, dimension( * ) DL, complex*16, dimension( * ) D, complex*16, dimension( * ) DU, complex*16, dimension( * ) DU2, integer, dimension( * ) IPIV, integer INFO)
ZGTTRF
Purpose:

ZGTTRF computes an LU factorization of a complex tridiagonal matrix A using elimination with partial pivoting and row interchanges. The factorization has the form A = L * U where L is a product of permutation and unit lower bidiagonal matrices and U is upper triangular with nonzeros in only the main diagonal and first two superdiagonals.
Parameters:

N
N is INTEGER The order of the matrix A.
DLDL is COMPLEX*16 array, dimension (N1) On entry, DL must contain the (n1) subdiagonal elements of A. On exit, DL is overwritten by the (n1) multipliers that define the matrix L from the LU factorization of A.
DD is COMPLEX*16 array, dimension (N) On entry, D must contain the diagonal elements of A. On exit, D is overwritten by the n diagonal elements of the upper triangular matrix U from the LU factorization of A.
DUDU is COMPLEX*16 array, dimension (N1) On entry, DU must contain the (n1) superdiagonal elements of A. On exit, DU is overwritten by the (n1) elements of the first superdiagonal of U.
DU2DU2 is COMPLEX*16 array, dimension (N2) On exit, DU2 is overwritten by the (n2) elements of the second superdiagonal of U.
IPIVIPIV 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.
INFOINFO is INTEGER = 0: successful exit < 0: if INFO = k, the kth argument had an illegal value > 0: if INFO = k, U(k,k) is exactly zero. The factorization has been completed, but the factor U is exactly singular, and division by zero will occur if it is used to solve a system of equations.
Author:

Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
 September 2012
subroutine zgttrs (character TRANS, integer N, integer NRHS, complex*16, dimension( * ) DL, complex*16, dimension( * ) D, complex*16, dimension( * ) DU, complex*16, dimension( * ) DU2, integer, dimension( * ) IPIV, complex*16, dimension( ldb, * ) B, integer LDB, integer INFO)
ZGTTRS
Purpose:

ZGTTRS solves one of the systems of equations A * X = B, A**T * X = B, or A**H * X = B, with a tridiagonal matrix A using the LU factorization computed by ZGTTRF.
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)
NN is INTEGER The order of the matrix A.
NRHSNRHS is INTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.
DLDL is COMPLEX*16 array, dimension (N1) The (n1) multipliers that define the matrix L from the LU factorization of A.
DD is COMPLEX*16 array, dimension (N) The n diagonal elements of the upper triangular matrix U from the LU factorization of A.
DUDU is COMPLEX*16 array, dimension (N1) The (n1) elements of the first superdiagonal of U.
DU2DU2 is COMPLEX*16 array, dimension (N2) The (n2) elements of the second superdiagonal of U.
IPIVIPIV 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.
BB is COMPLEX*16 array, dimension (LDB,NRHS) On entry, the matrix of right hand side vectors B. On exit, B is overwritten by the solution vectors X.
LDBLDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).
INFOINFO is INTEGER = 0: successful exit < 0: if INFO = k, the kth argument had an illegal value
Author:

Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
 September 2012
subroutine zgtts2 (integer ITRANS, integer N, integer NRHS, complex*16, dimension( * ) DL, complex*16, dimension( * ) D, complex*16, dimension( * ) DU, complex*16, dimension( * ) DU2, integer, dimension( * ) IPIV, complex*16, dimension( ldb, * ) B, integer LDB)
ZGTTS2 solves a system of linear equations with a tridiagonal matrix using the LU factorization computed by sgttrf.
Purpose:

ZGTTS2 solves one of the systems of equations A * X = B, A**T * X = B, or A**H * X = B, with a tridiagonal matrix A using the LU factorization computed by ZGTTRF.
Parameters:

ITRANS
ITRANS is INTEGER Specifies the form of the system of equations. = 0: A * X = B (No transpose) = 1: A**T * X = B (Transpose) = 2: A**H * X = B (Conjugate transpose)
NN is INTEGER The order of the matrix A.
NRHSNRHS is INTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.
DLDL is COMPLEX*16 array, dimension (N1) The (n1) multipliers that define the matrix L from the LU factorization of A.
DD is COMPLEX*16 array, dimension (N) The n diagonal elements of the upper triangular matrix U from the LU factorization of A.
DUDU is COMPLEX*16 array, dimension (N1) The (n1) elements of the first superdiagonal of U.
DU2DU2 is COMPLEX*16 array, dimension (N2) The (n2) elements of the second superdiagonal of U.
IPIVIPIV 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.
BB is COMPLEX*16 array, dimension (LDB,NRHS) On entry, the matrix of right hand side vectors B. On exit, B is overwritten by the solution vectors X.
LDBLDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).
Author:

Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
 September 2012
Author
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