ztbrfs - provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular band coeffi- cient matrix
SUBROUTINE ZTBRFS(UPLO, TRANSA, DIAG, N, KD, NRHS, A, LDA, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER*1 UPLO, TRANSA, DIAG DOUBLE COMPLEX A(LDA,*), B(LDB,*), X(LDX,*), WORK(*) INTEGER N, KD, NRHS, LDA, LDB, LDX, INFO DOUBLE PRECISION FERR(*), BERR(*), WORK2(*) SUBROUTINE ZTBRFS_64(UPLO, TRANSA, DIAG, N, KD, NRHS, A, LDA, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER*1 UPLO, TRANSA, DIAG DOUBLE COMPLEX A(LDA,*), B(LDB,*), X(LDX,*), WORK(*) INTEGER*8 N, KD, NRHS, LDA, LDB, LDX, INFO DOUBLE PRECISION FERR(*), BERR(*), WORK2(*) F95 INTERFACE SUBROUTINE TBRFS(UPLO, TRANSA, DIAG, N, KD, NRHS, A, LDA, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER(LEN=1) :: UPLO, TRANSA, DIAG COMPLEX(8), DIMENSION(:) :: WORK COMPLEX(8), DIMENSION(:,:) :: A, B, X INTEGER :: N, KD, NRHS, LDA, LDB, LDX, INFO REAL(8), DIMENSION(:) :: FERR, BERR, WORK2 SUBROUTINE TBRFS_64(UPLO, TRANSA, DIAG, N, KD, NRHS, A, LDA, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER(LEN=1) :: UPLO, TRANSA, DIAG COMPLEX(8), DIMENSION(:) :: WORK COMPLEX(8), DIMENSION(:,:) :: A, B, X INTEGER(8) :: N, KD, NRHS, LDA, LDB, LDX, INFO REAL(8), DIMENSION(:) :: FERR, BERR, WORK2 C INTERFACE #include <sunperf.h> void ztbrfs(char uplo, char transa, char diag, int n, int kd, int nrhs, doublecomplex *a, int lda, doublecomplex *b, int ldb, double- complex *x, int ldx, double *ferr, double *berr, int *info); void ztbrfs_64(char uplo, char transa, char diag, long n, long kd, long nrhs, doublecomplex *a, long lda, doublecomplex *b, long ldb, doublecomplex *x, long ldx, double *ferr, double *berr, long *info);
Oracle Solaris Studio Performance Library ztbrfs(3P) NAME ztbrfs - provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular band coeffi- cient matrix SYNOPSIS SUBROUTINE ZTBRFS(UPLO, TRANSA, DIAG, N, KD, NRHS, A, LDA, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER*1 UPLO, TRANSA, DIAG DOUBLE COMPLEX A(LDA,*), B(LDB,*), X(LDX,*), WORK(*) INTEGER N, KD, NRHS, LDA, LDB, LDX, INFO DOUBLE PRECISION FERR(*), BERR(*), WORK2(*) SUBROUTINE ZTBRFS_64(UPLO, TRANSA, DIAG, N, KD, NRHS, A, LDA, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER*1 UPLO, TRANSA, DIAG DOUBLE COMPLEX A(LDA,*), B(LDB,*), X(LDX,*), WORK(*) INTEGER*8 N, KD, NRHS, LDA, LDB, LDX, INFO DOUBLE PRECISION FERR(*), BERR(*), WORK2(*) F95 INTERFACE SUBROUTINE TBRFS(UPLO, TRANSA, DIAG, N, KD, NRHS, A, LDA, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER(LEN=1) :: UPLO, TRANSA, DIAG COMPLEX(8), DIMENSION(:) :: WORK COMPLEX(8), DIMENSION(:,:) :: A, B, X INTEGER :: N, KD, NRHS, LDA, LDB, LDX, INFO REAL(8), DIMENSION(:) :: FERR, BERR, WORK2 SUBROUTINE TBRFS_64(UPLO, TRANSA, DIAG, N, KD, NRHS, A, LDA, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER(LEN=1) :: UPLO, TRANSA, DIAG COMPLEX(8), DIMENSION(:) :: WORK COMPLEX(8), DIMENSION(:,:) :: A, B, X INTEGER(8) :: N, KD, NRHS, LDA, LDB, LDX, INFO REAL(8), DIMENSION(:) :: FERR, BERR, WORK2 C INTERFACE #include <sunperf.h> void ztbrfs(char uplo, char transa, char diag, int n, int kd, int nrhs, doublecomplex *a, int lda, doublecomplex *b, int ldb, double- complex *x, int ldx, double *ferr, double *berr, int *info); void ztbrfs_64(char uplo, char transa, char diag, long n, long kd, long nrhs, doublecomplex *a, long lda, doublecomplex *b, long ldb, doublecomplex *x, long ldx, double *ferr, double *berr, long *info); PURPOSE ztbrfs provides error bounds and backward error estimates for the solu- tion to a system of linear equations with a triangular band coefficient matrix. The solution matrix X must be computed by ZTBTRS or some other means before entering this routine. ZTBRFS does not do iterative refinement because doing so cannot improve the backward error. ARGUMENTS UPLO (input) = 'U': A is upper triangular; = 'L': A is lower triangular. 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) DIAG (input) = 'N': A is non-unit triangular; = 'U': A is unit triangular. N (input) The order of the matrix A. N >= 0. KD (input) The number of superdiagonals or subdiagonals of the triangu- lar band matrix A. KD >= 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 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 A as follows: if UPLO = 'U', A(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; if UPLO = 'L', A(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. LDA (input) The leading dimension of the array A. LDA >= KD+1. B (input) The right hand side matrix B. LDB (input) The leading dimension of the array B. LDB >= max(1,N). X (input) The 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 ztbrfs(3P)