sptrfs(3P) Sun Performance Library sptrfs(3P)NAMEsptrfs - improve 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
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);
PURPOSEsptrfs 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
6 Mar 2009 sptrfs(3P)
