sptrfs - improve the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite and tridiag- onal, provide error bounds and backward error estimates for the solu- tion
SUBROUTINE SPTRFS(N, NRHS, D, E, DF, EF, B, LDB, X, LDX, FERR, BERR, WORK, INFO) INTEGER N, NRHS, LDB, LDX, INFO REAL D(*), E(*), DF(*), EF(*), B(LDB,*), X(LDX,*), FERR(*), BERR(*), WORK(*) SUBROUTINE SPTRFS_64(N, NRHS, D, E, DF, EF, B, LDB, X, LDX, FERR, BERR, WORK, INFO) INTEGER*8 N, NRHS, LDB, LDX, INFO REAL D(*), E(*), DF(*), EF(*), B(LDB,*), X(LDX,*), FERR(*), BERR(*), WORK(*) F95 INTERFACE SUBROUTINE PTRFS(N, NRHS, D, E, DF, EF, B, LDB, X, LDX, FERR, BERR, WORK, INFO) INTEGER :: N, NRHS, LDB, LDX, INFO REAL, DIMENSION(:) :: D, E, DF, EF, FERR, BERR, WORK REAL, DIMENSION(:,:) :: B, X SUBROUTINE PTRFS_64(N, NRHS, D, E, DF, EF, B, LDB, X, LDX, FERR, BERR, WORK, INFO) INTEGER(8) :: N, NRHS, LDB, LDX, INFO REAL, DIMENSION(:) :: D, E, DF, EF, FERR, BERR, WORK REAL, DIMENSION(:,:) :: B, X C INTERFACE #include <sunperf.h> void sptrfs(int n, int nrhs, float *d, float *e, float *df, float *ef, float *b, int ldb, float *x, int ldx, float *ferr, float *berr, int *info); void sptrfs_64(long n, long nrhs, float *d, float *e, float *df, float *ef, float *b, long ldb, float *x, long ldx, float *ferr, float *berr, long *info);
Oracle Solaris Studio Performance Library sptrfs(3P) NAME sptrfs - improve the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite and tridiag- onal, provide error bounds and backward error estimates for the solu- tion SYNOPSIS SUBROUTINE SPTRFS(N, NRHS, D, E, DF, EF, B, LDB, X, LDX, FERR, BERR, WORK, INFO) INTEGER N, NRHS, LDB, LDX, INFO REAL D(*), E(*), DF(*), EF(*), B(LDB,*), X(LDX,*), FERR(*), BERR(*), WORK(*) SUBROUTINE SPTRFS_64(N, NRHS, D, E, DF, EF, B, LDB, X, LDX, FERR, BERR, WORK, INFO) INTEGER*8 N, NRHS, LDB, LDX, INFO REAL D(*), E(*), DF(*), EF(*), B(LDB,*), X(LDX,*), FERR(*), BERR(*), WORK(*) F95 INTERFACE SUBROUTINE PTRFS(N, NRHS, D, E, DF, EF, B, LDB, X, LDX, FERR, BERR, WORK, INFO) INTEGER :: N, NRHS, LDB, LDX, INFO REAL, DIMENSION(:) :: D, E, DF, EF, FERR, BERR, WORK REAL, DIMENSION(:,:) :: B, X SUBROUTINE PTRFS_64(N, NRHS, D, E, DF, EF, B, LDB, X, LDX, FERR, BERR, WORK, INFO) INTEGER(8) :: N, NRHS, LDB, LDX, INFO REAL, DIMENSION(:) :: D, E, DF, EF, FERR, BERR, WORK REAL, DIMENSION(:,:) :: B, X C INTERFACE #include <sunperf.h> void sptrfs(int n, int nrhs, float *d, float *e, float *df, float *ef, float *b, int ldb, float *x, int ldx, float *ferr, float *berr, int *info); void sptrfs_64(long n, long nrhs, float *d, float *e, float *df, float *ef, float *b, long ldb, float *x, long ldx, float *ferr, float *berr, long *info); PURPOSE sptrfs improves the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite and tridiag- onal, and provides error bounds and backward error estimates for the solution. ARGUMENTS 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 matrix B. NRHS >= 0. D (input) The n diagonal elements of the tridiagonal matrix A. E (input) The (n-1) subdiagonal elements of the tridiagonal matrix A. DF (input) The n diagonal elements of the diagonal matrix D from the factorization computed by SPTTRF. EF (input) The (n-1) subdiagonal elements of the unit bidiagonal factor L from the factorization computed by SPTTRF. 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 SPTTRS. On exit, the improved solution matrix X. LDX (input) The leading dimension of the array X. LDX >= max(1,N). FERR (output) The 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). 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) INFO (output) = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value 7 Nov 2015 sptrfs(3P)