Contents
sgtrfs - 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
SUBROUTINE SGTRFS(TRANSA, N, NRHS, LOW, DIAG, UP, LOWF, DIAGF, 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(*), DIAG(*), UP(*), LOWF(*), DIAGF(*), UPF1(*),
UPF2(*), B(LDB,*), X(LDX,*), FERR(*), BERR(*), WORK(*)
SUBROUTINE SGTRFS_64(TRANSA, N, NRHS, LOW, DIAG, UP, LOWF, DIAGF,
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(*), DIAG(*), UP(*), LOWF(*), DIAGF(*), UPF1(*),
UPF2(*), B(LDB,*), X(LDX,*), FERR(*), BERR(*), WORK(*)
F95 INTERFACE
SUBROUTINE GTRFS([TRANSA], [N], [NRHS], LOW, DIAG, UP, LOWF, DIAGF,
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, DIAG, UP, LOWF, DIAGF, UPF1,
UPF2, FERR, BERR, WORK
REAL, DIMENSION(:,:) :: B, X
SUBROUTINE GTRFS_64([TRANSA], [N], [NRHS], LOW, DIAG, UP, LOWF,
DIAGF, 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, DIAG, UP, LOWF, DIAGF, 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
*diag, float *up, float *lowf, float *diagf, 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 *diag, float *up, float *lowf, float *diagf,
float *upf1, float *upf2, long *ipivot, float *b,
long ldb, float *x, long ldx, float *ferr, float
*berr, long *info);
sgtrfs 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.
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 = Tran-
spose)
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.
DIAG (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.
DIAGF (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 solu-
tion 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 ele-
ment in (X(j) - XTRUE) divided by the magnitude of
the largest element 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 element 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 ille-
gal value