dptrfs (3p)

Name

dptrfs - 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 DPTRFS(N, NRHS, D, E, DF, EF, B, LDB, X, LDX,
FERR, BERR, WORK, INFO)

INTEGER N, NRHS, LDB, LDX, INFO
DOUBLE PRECISION D(*), E(*), DF(*), EF(*), B(LDB,*), X(LDX,*), FERR(*),
BERR(*), WORK(*)

SUBROUTINE DPTRFS_64(N, NRHS, D, E, DF, EF, B, LDB, X,
LDX, FERR, BERR, WORK, INFO)

INTEGER*8 N, NRHS, LDB, LDX, INFO
DOUBLE PRECISION 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(8), DIMENSION(:) :: D, E, DF, EF, FERR, BERR, WORK
REAL(8), 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(8), DIMENSION(:) :: D, E, DF, EF, FERR, BERR, WORK
REAL(8), DIMENSION(:,:) :: B, X




C INTERFACE
#include <sunperf.h>

void dptrfs(int n, int nrhs, double *d, double *e, double  *df,  double
*ef,  double  *b,  int ldb, double *x, int ldx, double *ferr,
double *berr, int *info);

void dptrfs_64(long n, long nrhs, double *d,  double  *e,  double  *df,
double  *ef, double *b, long ldb, double *x, long ldx, double
*ferr, double *berr, long *info);

Description

Oracle Solaris Studio Performance Library                           dptrfs(3P)



NAME
       dptrfs  - 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 DPTRFS(N, NRHS, D, E, DF, EF, B, LDB, X, LDX,
             FERR, BERR, WORK, INFO)

       INTEGER N, NRHS, LDB, LDX, INFO
       DOUBLE PRECISION D(*), E(*), DF(*), EF(*), B(LDB,*), X(LDX,*), FERR(*),
       BERR(*), WORK(*)

       SUBROUTINE DPTRFS_64(N, NRHS, D, E, DF, EF, B, LDB, X,
             LDX, FERR, BERR, WORK, INFO)

       INTEGER*8 N, NRHS, LDB, LDX, INFO
       DOUBLE PRECISION 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(8), DIMENSION(:) :: D, E, DF, EF, FERR, BERR, WORK
       REAL(8), 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(8), DIMENSION(:) :: D, E, DF, EF, FERR, BERR, WORK
       REAL(8), DIMENSION(:,:) :: B, X




   C INTERFACE
       #include <sunperf.h>

       void dptrfs(int n, int nrhs, double *d, double *e, double  *df,  double
                 *ef,  double  *b,  int ldb, double *x, int ldx, double *ferr,
                 double *berr, int *info);

       void dptrfs_64(long n, long nrhs, double *d,  double  *e,  double  *df,
                 double  *ef, double *b, long ldb, double *x, long ldx, double
                 *ferr, double *berr, long *info);



PURPOSE
       dptrfs 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 DPTTRF.


       EF (input)
                 The  (n-1) subdiagonal elements of the unit bidiagonal factor
                 L from the factorization computed by DPTTRF.


       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  DPTTRS.   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                        dptrfs(3P)