dtprfs - provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular packed coef- ficient matrix
SUBROUTINE DTPRFS(UPLO, TRANSA, DIAG, N, NRHS, A, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER*1 UPLO, TRANSA, DIAG INTEGER N, NRHS, LDB, LDX, INFO INTEGER WORK2(*) DOUBLE PRECISION A(*), B(LDB,*), X(LDX,*), FERR(*), BERR(*), WORK(*) SUBROUTINE DTPRFS_64(UPLO, TRANSA, DIAG, N, NRHS, A, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER*1 UPLO, TRANSA, DIAG INTEGER*8 N, NRHS, LDB, LDX, INFO INTEGER*8 WORK2(*) DOUBLE PRECISION A(*), B(LDB,*), X(LDX,*), FERR(*), BERR(*), WORK(*) F95 INTERFACE SUBROUTINE TPRFS(UPLO, TRANSA, DIAG, N, NRHS, A, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER(LEN=1) :: UPLO, TRANSA, DIAG INTEGER :: N, NRHS, LDB, LDX, INFO INTEGER, DIMENSION(:) :: WORK2 REAL(8), DIMENSION(:) :: A, FERR, BERR, WORK REAL(8), DIMENSION(:,:) :: B, X SUBROUTINE TPRFS_64(UPLO, TRANSA, DIAG, N, NRHS, A, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER(LEN=1) :: UPLO, TRANSA, DIAG INTEGER(8) :: N, NRHS, LDB, LDX, INFO INTEGER(8), DIMENSION(:) :: WORK2 REAL(8), DIMENSION(:) :: A, FERR, BERR, WORK REAL(8), DIMENSION(:,:) :: B, X C INTERFACE #include <sunperf.h> void dtprfs(char uplo, char transa, char diag, int n, int nrhs, double *a, double *b, int ldb, double *x, int ldx, double *ferr, double *berr, int *info); void dtprfs_64(char uplo, char transa, char diag, long n, long nrhs, double *a, double *b, long ldb, double *x, long ldx, double *ferr, double *berr, long *info);
Oracle Solaris Studio Performance Library dtprfs(3P) NAME dtprfs - provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular packed coef- ficient matrix SYNOPSIS SUBROUTINE DTPRFS(UPLO, TRANSA, DIAG, N, NRHS, A, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER*1 UPLO, TRANSA, DIAG INTEGER N, NRHS, LDB, LDX, INFO INTEGER WORK2(*) DOUBLE PRECISION A(*), B(LDB,*), X(LDX,*), FERR(*), BERR(*), WORK(*) SUBROUTINE DTPRFS_64(UPLO, TRANSA, DIAG, N, NRHS, A, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER*1 UPLO, TRANSA, DIAG INTEGER*8 N, NRHS, LDB, LDX, INFO INTEGER*8 WORK2(*) DOUBLE PRECISION A(*), B(LDB,*), X(LDX,*), FERR(*), BERR(*), WORK(*) F95 INTERFACE SUBROUTINE TPRFS(UPLO, TRANSA, DIAG, N, NRHS, A, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER(LEN=1) :: UPLO, TRANSA, DIAG INTEGER :: N, NRHS, LDB, LDX, INFO INTEGER, DIMENSION(:) :: WORK2 REAL(8), DIMENSION(:) :: A, FERR, BERR, WORK REAL(8), DIMENSION(:,:) :: B, X SUBROUTINE TPRFS_64(UPLO, TRANSA, DIAG, N, NRHS, A, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER(LEN=1) :: UPLO, TRANSA, DIAG INTEGER(8) :: N, NRHS, LDB, LDX, INFO INTEGER(8), DIMENSION(:) :: WORK2 REAL(8), DIMENSION(:) :: A, FERR, BERR, WORK REAL(8), DIMENSION(:,:) :: B, X C INTERFACE #include <sunperf.h> void dtprfs(char uplo, char transa, char diag, int n, int nrhs, double *a, double *b, int ldb, double *x, int ldx, double *ferr, double *berr, int *info); void dtprfs_64(char uplo, char transa, char diag, long n, long nrhs, double *a, double *b, long ldb, double *x, long ldx, double *ferr, double *berr, long *info); PURPOSE dtprfs provides error bounds and backward error estimates for the solu- tion to a system of linear equations with a triangular packed coeffi- cient matrix. The solution matrix X must be computed by DTPTRS or some other means before entering this routine. DTPRFS 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 = Transpose) DIAG (input) = 'N': A is non-unit triangular; = 'U': A is unit triangular. N (input) The order of the matrix A. N >= 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) DOUBLE PRECISION 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 A as follows: if UPLO = 'U', A(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', A(i + (j-1)*(2*n-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 (input) DOUBLE PRECISION array, dimension (LDB,NRHS) The right hand side matrix B. LDB (input) The leading dimension of the array B. LDB >= max(1,N). X (input) DOUBLE PRECISION array, dimension (LDX,NRHS) The solution matrix X. LDX (input) 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 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) DOUBLE PRECISION array, dimension (NRHS) 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) DOUBLE PRECISION array, dimension(3*N) WORK2 (workspace) INTEGER array, dimension(N) INFO (output) = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value 7 Nov 2015 dtprfs(3P)