zgbrfs - improve the computed solution to a system of linear equations when the coefficient matrix is banded, and provide error bounds and backward error estimates for the solution
SUBROUTINE ZGBRFS(TRANSA, N, KL, KU, NRHS, A, LDA, AF, LDAF, IPIVOT, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER*1 TRANSA DOUBLE COMPLEX A(LDA,*), AF(LDAF,*), B(LDB,*), X(LDX,*), WORK(*) INTEGER N, KL, KU, NRHS, LDA, LDAF, LDB, LDX, INFO INTEGER IPIVOT(*) DOUBLE PRECISION FERR(*), BERR(*), WORK2(*) SUBROUTINE ZGBRFS_64(TRANSA, N, KL, KU, NRHS, A, LDA, AF, LDAF, IPIVOT, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER*1 TRANSA DOUBLE COMPLEX A(LDA,*), AF(LDAF,*), B(LDB,*), X(LDX,*), WORK(*) INTEGER*8 N, KL, KU, NRHS, LDA, LDAF, LDB, LDX, INFO INTEGER*8 IPIVOT(*) DOUBLE PRECISION FERR(*), BERR(*), WORK2(*) F95 INTERFACE SUBROUTINE GBRFS(TRANSA, N, KL, KU, NRHS, A, LDA, AF, LDAF, IPIVOT, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER(LEN=1) :: TRANSA COMPLEX(8), DIMENSION(:) :: WORK COMPLEX(8), DIMENSION(:,:) :: A, AF, B, X INTEGER :: N, KL, KU, NRHS, LDA, LDAF, LDB, LDX, INFO INTEGER, DIMENSION(:) :: IPIVOT REAL(8), DIMENSION(:) :: FERR, BERR, WORK2 SUBROUTINE GBRFS_64(TRANSA, N, KL, KU, NRHS, A, LDA, AF, LDAF, IPIVOT, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER(LEN=1) :: TRANSA COMPLEX(8), DIMENSION(:) :: WORK COMPLEX(8), DIMENSION(:,:) :: A, AF, B, X INTEGER(8) :: N, KL, KU, NRHS, LDA, LDAF, LDB, LDX, INFO INTEGER(8), DIMENSION(:) :: IPIVOT REAL(8), DIMENSION(:) :: FERR, BERR, WORK2 C INTERFACE #include <sunperf.h> void zgbrfs(char transa, int n, int kl, int ku, int nrhs, doublecomplex *a, int lda, doublecomplex *af, int ldaf, int *ipivot, dou- blecomplex *b, int ldb, doublecomplex *x, int ldx, double *ferr, double *berr, int *info); void zgbrfs_64(char transa, long n, long kl, long ku, long nrhs, dou- blecomplex *a, long lda, doublecomplex *af, long ldaf, long *ipivot, doublecomplex *b, long ldb, doublecomplex *x, long ldx, double *ferr, double *berr, long *info);
Oracle Solaris Studio Performance Library zgbrfs(3P) NAME zgbrfs - improve the computed solution to a system of linear equations when the coefficient matrix is banded, and provide error bounds and backward error estimates for the solution SYNOPSIS SUBROUTINE ZGBRFS(TRANSA, N, KL, KU, NRHS, A, LDA, AF, LDAF, IPIVOT, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER*1 TRANSA DOUBLE COMPLEX A(LDA,*), AF(LDAF,*), B(LDB,*), X(LDX,*), WORK(*) INTEGER N, KL, KU, NRHS, LDA, LDAF, LDB, LDX, INFO INTEGER IPIVOT(*) DOUBLE PRECISION FERR(*), BERR(*), WORK2(*) SUBROUTINE ZGBRFS_64(TRANSA, N, KL, KU, NRHS, A, LDA, AF, LDAF, IPIVOT, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER*1 TRANSA DOUBLE COMPLEX A(LDA,*), AF(LDAF,*), B(LDB,*), X(LDX,*), WORK(*) INTEGER*8 N, KL, KU, NRHS, LDA, LDAF, LDB, LDX, INFO INTEGER*8 IPIVOT(*) DOUBLE PRECISION FERR(*), BERR(*), WORK2(*) F95 INTERFACE SUBROUTINE GBRFS(TRANSA, N, KL, KU, NRHS, A, LDA, AF, LDAF, IPIVOT, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER(LEN=1) :: TRANSA COMPLEX(8), DIMENSION(:) :: WORK COMPLEX(8), DIMENSION(:,:) :: A, AF, B, X INTEGER :: N, KL, KU, NRHS, LDA, LDAF, LDB, LDX, INFO INTEGER, DIMENSION(:) :: IPIVOT REAL(8), DIMENSION(:) :: FERR, BERR, WORK2 SUBROUTINE GBRFS_64(TRANSA, N, KL, KU, NRHS, A, LDA, AF, LDAF, IPIVOT, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER(LEN=1) :: TRANSA COMPLEX(8), DIMENSION(:) :: WORK COMPLEX(8), DIMENSION(:,:) :: A, AF, B, X INTEGER(8) :: N, KL, KU, NRHS, LDA, LDAF, LDB, LDX, INFO INTEGER(8), DIMENSION(:) :: IPIVOT REAL(8), DIMENSION(:) :: FERR, BERR, WORK2 C INTERFACE #include <sunperf.h> void zgbrfs(char transa, int n, int kl, int ku, int nrhs, doublecomplex *a, int lda, doublecomplex *af, int ldaf, int *ipivot, dou- blecomplex *b, int ldb, doublecomplex *x, int ldx, double *ferr, double *berr, int *info); void zgbrfs_64(char transa, long n, long kl, long ku, long nrhs, dou- blecomplex *a, long lda, doublecomplex *af, long ldaf, long *ipivot, doublecomplex *b, long ldb, doublecomplex *x, long ldx, double *ferr, double *berr, long *info); PURPOSE zgbrfs 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. ARGUMENTS TRANSA (input) 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) The order of the matrix A. N >= 0. KL (input) The number of subdiagonals within the band of A. KL >= 0. KU (input) The number of superdiagonals within the band of A. KU >= 0. NRHS (input) The number of right hand sides, i.e., the number of columns of the matrices B and X. NRHS >= 0. A (input) 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 A as follows: A(ku+1+i-j,j) = A(i,j) for max(1,j- ku)<=i<=min(n,j+kl). LDA (input) The leading dimension of the array A. LDA >= KL+KU+1. AF (input) Details of the LU factorization of the band matrix A, as com- puted 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. LDAF (input) The leading dimension of the array AF. LDAF >= 2*KL*KU+1. IPIVOT (input) The pivot indices from ZGBTRF; for 1<=i<=N, row i of the matrix was interchanged with row IPIVOT(i). B (input) The right hand side matrix B. LDB (input) The leading dimension of the array B. LDB >= max(1,N). X (input/output) On entry, the solution matrix X, as computed by ZGBTRS. On exit, the improved solution matrix X. LDX (input) The leading dimension of the array X. LDX >= max(1,N). FERR (output) 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 esti- mated upper bound for the magnitude of the largest element in (X(j) - XTRUE) divided by the magnitude of the largest ele- ment 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) The componentwise relative backward error of each solution vector X(j) (i.e., the smallest relative change in any ele- ment of A or B that makes X(j) an exact solution). WORK (workspace) dimension(2*N) WORK2 (workspace) dimension(N) INFO (output) = 0: successful exit; < 0: if INFO = -i, the i-th argument had an illegal value. 7 Nov 2015 zgbrfs(3P)