- SUBROUTINE ZGBRFS(
- TRANS, N, KL, KU, NRHS, AB, LDAB, AFB, LDAFB, IPIV, B, LDB, X, LDX, FERR, BERR, WORK, RWORK, INFO )
- CHARACTER TRANS
- INTEGER INFO, KL, KU, LDAB, LDAFB, LDB, LDX, N, NRHS
- INTEGER IPIV( * )
- DOUBLE PRECISION BERR( * ), FERR( * ), RWORK( * )
- COMPLEX*16 AB( LDAB, * ), AFB( LDAFB, * ), B( LDB, * ), WORK( * ), X( LDX, * )
PURPOSEZGBRFS improves the computed solution to a system of linear equations when the coefficient matrix is banded, and provides error bounds and backward error estimates for the solution.
- TRANS (input) 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)
- N (input) INTEGER
- The order of the matrix A. N >= 0.
- KL (input) INTEGER
- The number of subdiagonals within the band of A. KL >= 0.
- KU (input) INTEGER
- The number of superdiagonals within the band of A. KU >= 0.
- NRHS (input) INTEGER
- The number of right hand sides, i.e., the number of columns of the matrices B and X. NRHS >= 0.
- AB (input) COMPLEX*16 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 (input) INTEGER
- The leading dimension of the array AB. LDAB >= KL+KU+1.
- AFB (input) COMPLEX*16 array, dimension (LDAFB,N)
- Details of the LU factorization of the band matrix A, as computed by ZGBTRF. 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.
- LDAFB (input) INTEGER
- The leading dimension of the array AFB. LDAFB >= 2*KL*KU+1.
- IPIV (input) INTEGER array, dimension (N)
- The pivot indices from ZGBTRF; for 1<=i<=N, row i of the matrix was interchanged with row IPIV(i).
- B (input) COMPLEX*16 array, dimension (LDB,NRHS)
- The right hand side matrix B.
- LDB (input) INTEGER
- The leading dimension of the array B. LDB >= max(1,N).
- X (input/output) COMPLEX*16 array, dimension (LDX,NRHS)
- On entry, the solution matrix X, as computed by ZGBTRS. On exit, the improved solution matrix X.
- LDX (input) INTEGER
- The leading dimension of the array X. LDX >= max(1,N).
- FERR (output) DOUBLE PRECISION array, dimension (NRHS)
- The estimated forward error bound for each solution vector X(j) (the j-th 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.
- BERR (output) 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).
- WORK (workspace) COMPLEX*16 array, dimension (2*N)
- RWORK (workspace) DOUBLE PRECISION array, dimension (N)
- INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
PARAMETERSITMAX is the maximum number of steps of iterative refinement.