• NAME
• SYNOPSIS
• F95 INTERFACE
• C INTERFACE
• PURPOSE
• ARGUMENTS

NAME

sptrfs - improve the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite and tridiagonal, and provides error bounds and backward error estimates for the solution

SYNOPSIS

  SUBROUTINE SPTRFS( N, NRHS, DIAG, OFFD, DIAGF, OFFDF, B, LDB, X, 
 *      LDX, FERR, BERR, WORK, INFO)
  INTEGER N, NRHS, LDB, LDX, INFO
  REAL DIAG(*), OFFD(*), DIAGF(*), OFFDF(*), B(LDB,*), X(LDX,*), FERR(*), BERR(*), WORK(*)

  SUBROUTINE SPTRFS_64( N, NRHS, DIAG, OFFD, DIAGF, OFFDF, B, LDB, X, 
 *      LDX, FERR, BERR, WORK, INFO)
  INTEGER*8 N, NRHS, LDB, LDX, INFO
  REAL DIAG(*), OFFD(*), DIAGF(*), OFFDF(*), B(LDB,*), X(LDX,*), FERR(*), BERR(*), WORK(*)

F95 INTERFACE

  SUBROUTINE PTRFS( [N], [NRHS], DIAG, OFFD, DIAGF, OFFDF, B, [LDB], 
 *       X, [LDX], FERR, BERR, [WORK], [INFO])
  INTEGER :: N, NRHS, LDB, LDX, INFO
  REAL, DIMENSION(:) :: DIAG, OFFD, DIAGF, OFFDF, FERR, BERR, WORK
  REAL, DIMENSION(:,:) :: B, X

  SUBROUTINE PTRFS_64( [N], [NRHS], DIAG, OFFD, DIAGF, OFFDF, B, [LDB], 
 *       X, [LDX], FERR, BERR, [WORK], [INFO])
  INTEGER(8) :: N, NRHS, LDB, LDX, INFO
  REAL, DIMENSION(:) :: DIAG, OFFD, DIAGF, OFFDF, FERR, BERR, WORK
  REAL, DIMENSION(:,:) :: B, X

C INTERFACE

#include <sunperf.h>

void sptrfs(int n, int nrhs, float *diag, float *offd, float *diagf, float *offdf, float *b, int ldb, float *x, int ldx, float *ferr, float *berr, int *info);

void sptrfs_64(long n, long nrhs, float *diag, float *offd, float *diagf, float *offdf, 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 tridiagonal, 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.

• DIAG (input)
  The n diagonal elements of the tridiagonal matrix A.

• OFFD (input)
  The (n-1) subdiagonal elements of the tridiagonal matrix A.

• DIAGF (input)
  The n diagonal elements of the diagonal matrix DIAG from the factorization computed by SPTTRF.

• OFFDF (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 element 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