ctprfs - provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular packed coef- ficient matrix
SUBROUTINE CTPRFS(UPLO, TRANSA, DIAG, N, NRHS, A, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER*1 UPLO, TRANSA, DIAG COMPLEX A(*), B(LDB,*), X(LDX,*), WORK(*) INTEGER N, NRHS, LDB, LDX, INFO REAL FERR(*), BERR(*), WORK2(*) SUBROUTINE CTPRFS_64(UPLO, TRANSA, DIAG, N, NRHS, A, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER*1 UPLO, TRANSA, DIAG COMPLEX A(*), B(LDB,*), X(LDX,*), WORK(*) INTEGER*8 N, NRHS, LDB, LDX, INFO REAL FERR(*), BERR(*), WORK2(*) 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 COMPLEX, DIMENSION(:) :: A, WORK COMPLEX, DIMENSION(:,:) :: B, X INTEGER :: N, NRHS, LDB, LDX, INFO REAL, DIMENSION(:) :: FERR, BERR, WORK2 SUBROUTINE TPRFS_64(UPLO, TRANSA, DIAG, N, NRHS, A, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER(LEN=1) :: UPLO, TRANSA, DIAG COMPLEX, DIMENSION(:) :: A, WORK COMPLEX, DIMENSION(:,:) :: B, X INTEGER(8) :: N, NRHS, LDB, LDX, INFO REAL, DIMENSION(:) :: FERR, BERR, WORK2 C INTERFACE #include <sunperf.h> void ctprfs(char uplo, char transa, char diag, int n, int nrhs, complex *a, complex *b, int ldb, complex *x, int ldx, float *ferr, float *berr, int *info); void ctprfs_64(char uplo, char transa, char diag, long n, long nrhs, complex *a, complex *b, long ldb, complex *x, long ldx, float *ferr, float *berr, long *info);
Oracle Solaris Studio Performance Library ctprfs(3P) NAME ctprfs - 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 CTPRFS(UPLO, TRANSA, DIAG, N, NRHS, A, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER*1 UPLO, TRANSA, DIAG COMPLEX A(*), B(LDB,*), X(LDX,*), WORK(*) INTEGER N, NRHS, LDB, LDX, INFO REAL FERR(*), BERR(*), WORK2(*) SUBROUTINE CTPRFS_64(UPLO, TRANSA, DIAG, N, NRHS, A, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER*1 UPLO, TRANSA, DIAG COMPLEX A(*), B(LDB,*), X(LDX,*), WORK(*) INTEGER*8 N, NRHS, LDB, LDX, INFO REAL FERR(*), BERR(*), WORK2(*) 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 COMPLEX, DIMENSION(:) :: A, WORK COMPLEX, DIMENSION(:,:) :: B, X INTEGER :: N, NRHS, LDB, LDX, INFO REAL, DIMENSION(:) :: FERR, BERR, WORK2 SUBROUTINE TPRFS_64(UPLO, TRANSA, DIAG, N, NRHS, A, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO) CHARACTER(LEN=1) :: UPLO, TRANSA, DIAG COMPLEX, DIMENSION(:) :: A, WORK COMPLEX, DIMENSION(:,:) :: B, X INTEGER(8) :: N, NRHS, LDB, LDX, INFO REAL, DIMENSION(:) :: FERR, BERR, WORK2 C INTERFACE #include <sunperf.h> void ctprfs(char uplo, char transa, char diag, int n, int nrhs, complex *a, complex *b, int ldb, complex *x, int ldx, float *ferr, float *berr, int *info); void ctprfs_64(char uplo, char transa, char diag, long n, long nrhs, complex *a, complex *b, long ldb, complex *x, long ldx, float *ferr, float *berr, long *info); PURPOSE ctprfs 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 CTPTRS or some other means before entering this routine. CTPRFS 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. NRHS (input) The number of right hand sides, i.e., the number of columns of the matrices B and X. NRHS >= 0. A (input) COMPLEX 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)*(2n-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) COMPLEX 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) COMPLEX array, dimension (LDX,NRHS) The solution matrix X. LDX (input) The leading dimension of the array X. LDX >= max(1,N). FERR (output) REAL 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) REAL 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) COMPLEX array, dimension(2*N) WORK2 (workspace) REAL array, dimension(N) INFO (output) = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value 7 Nov 2015 ctprfs(3P)