sgtrfs(3P) Sun Performance Library sgtrfs(3P)NAMEsgtrfs - improve the computed solution to a system of linear equations
when the coefficient matrix is tridiagonal, and provides error bounds
and backward error estimates for the solution
SYNOPSIS
SUBROUTINE SGTRFS(TRANSA, N, NRHS, LOW, D, UP, LOWF, DF, UPF1,
UPF2, IPIVOT, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO)
CHARACTER * 1 TRANSA
INTEGER N, NRHS, LDB, LDX, INFO
INTEGER IPIVOT(*), WORK2(*)
REAL LOW(*), D(*), UP(*), LOWF(*), DF(*), UPF1(*), UPF2(*), B(LDB,*),
X(LDX,*), FERR(*), BERR(*), WORK(*)
SUBROUTINE SGTRFS_64(TRANSA, N, NRHS, LOW, D, UP, LOWF, DF,
UPF1, UPF2, IPIVOT, B, LDB, X, LDX, FERR, BERR, WORK, WORK2,
INFO)
CHARACTER * 1 TRANSA
INTEGER*8 N, NRHS, LDB, LDX, INFO
INTEGER*8 IPIVOT(*), WORK2(*)
REAL LOW(*), D(*), UP(*), LOWF(*), DF(*), UPF1(*), UPF2(*), B(LDB,*),
X(LDX,*), FERR(*), BERR(*), WORK(*)
F95 INTERFACE
SUBROUTINE GTRFS([TRANSA], [N], [NRHS], LOW, D, UP, LOWF, DF,
UPF1, UPF2, IPIVOT, B, [LDB], X, [LDX], FERR, BERR, [WORK],
[WORK2], [INFO])
CHARACTER(LEN=1) :: TRANSA
INTEGER :: N, NRHS, LDB, LDX, INFO
INTEGER, DIMENSION(:) :: IPIVOT, WORK2
REAL, DIMENSION(:) :: LOW, D, UP, LOWF, DF, UPF1, UPF2, FERR, BERR,
WORK
REAL, DIMENSION(:,:) :: B, X
SUBROUTINE GTRFS_64([TRANSA], [N], [NRHS], LOW, D, UP, LOWF,
DF, UPF1, UPF2, IPIVOT, B, [LDB], X, [LDX], FERR, BERR, [WORK],
[WORK2], [INFO])
CHARACTER(LEN=1) :: TRANSA
INTEGER(8) :: N, NRHS, LDB, LDX, INFO
INTEGER(8), DIMENSION(:) :: IPIVOT, WORK2
REAL, DIMENSION(:) :: LOW, D, UP, LOWF, DF, UPF1, UPF2, FERR, BERR,
WORK
REAL, DIMENSION(:,:) :: B, X
C INTERFACE
#include <sunperf.h>
void sgtrfs(char transa, int n, int nrhs, float *low, float *d, float
*up, float *lowf, float *df, float *upf1, float *upf2, int
*ipivot, float *b, int ldb, float *x, int ldx, float *ferr,
float *berr, int *info);
void sgtrfs_64(char transa, long n, long nrhs, float *low, float *d,
float *up, float *lowf, float *df, float *upf1, float *upf2,
long *ipivot, float *b, long ldb, float *x, long ldx, float
*ferr, float *berr, long *info);
PURPOSEsgtrfs improves the computed solution to a system of linear equations
when the coefficient matrix is tridiagonal, and provides error bounds
and backward error estimates for the solution.
ARGUMENTS
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 = Transpose)
TRANSA is defaulted to 'N' for F95 INTERFACE.
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.
LOW (input)
The (n-1) subdiagonal elements of A.
D (input) The diagonal elements of A.
UP (input)
The (n-1) superdiagonal elements of A.
LOWF (input)
The (n-1) multipliers that define the matrix L from the LU
factorization of A as computed by SGTTRF.
DF (input)
The n diagonal elements of the upper triangular matrix U from
the LU factorization of A.
UPF1 (input)
The (n-1) elements of the first superdiagonal of U.
UPF2 (input)
The (n-2) elements of the second superdiagonal of U.
IPIVOT (input)
The pivot indices; for 1 <= i <= n, row i of the matrix was
interchanged with row IPIVOT(i). IPIVOT(i) will always be
either i or i+1; IPIVOT(i) = i indicates a row interchange
was not required.
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 SGTTRS. On
exit, the improved solution matrix X.
LDX (input)
The leading dimension of the array X. LDX >= max(1,N).
FERR (output)
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)
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(3*N)
WORK2 (workspace)
dimension(N)
INFO (output)
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
6 Mar 2009 sgtrfs(3P)
