dgtrfs - improve the computed solution to a system of linear equations when the coefficient matrix is tridiagonal, provide error bounds and backward error estimates for the solution
SUBROUTINE DGTRFS(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(*) DOUBLE PRECISION LOW(*), D(*), UP(*), LOWF(*), DF(*), UPF1(*), UPF2(*), B(LDB,*), X(LDX,*), FERR(*), BERR(*), WORK(*) SUBROUTINE DGTRFS_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(*) DOUBLE PRECISION 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(8), DIMENSION(:) :: LOW, D, UP, LOWF, DF, UPF1, UPF2, FERR, BERR, WORK REAL(8), 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(8), DIMENSION(:) :: LOW, D, UP, LOWF, DF, UPF1, UPF2, FERR, BERR, WORK REAL(8), DIMENSION(:,:) :: B, X C INTERFACE #include <sunperf.h> void dgtrfs(char transa, int n, int nrhs, double *low, double *d, dou- ble *up, double *lowf, double *df, double *upf1, double *upf2, int *ipivot, double *b, int ldb, double *x, int ldx, double *ferr, double *berr, int *info); void dgtrfs_64(char transa, long n, long nrhs, double *low, double *d, double *up, double *lowf, double *df, double *upf1, double *upf2, long *ipivot, double *b, long ldb, double *x, long ldx, double *ferr, double *berr, long *info);
Oracle Solaris Studio Performance Library dgtrfs(3P)
NAME
dgtrfs - improve the computed solution to a system of linear equations
when the coefficient matrix is tridiagonal, provide error bounds and
backward error estimates for the solution
SYNOPSIS
SUBROUTINE DGTRFS(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(*)
DOUBLE PRECISION LOW(*), D(*), UP(*), LOWF(*), DF(*), UPF1(*), UPF2(*),
B(LDB,*), X(LDX,*), FERR(*), BERR(*), WORK(*)
SUBROUTINE DGTRFS_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(*)
DOUBLE PRECISION 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(8), DIMENSION(:) :: LOW, D, UP, LOWF, DF, UPF1, UPF2, FERR, BERR,
WORK
REAL(8), 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(8), DIMENSION(:) :: LOW, D, UP, LOWF, DF, UPF1, UPF2, FERR, BERR,
WORK
REAL(8), DIMENSION(:,:) :: B, X
C INTERFACE
#include <sunperf.h>
void dgtrfs(char transa, int n, int nrhs, double *low, double *d, dou-
ble *up, double *lowf, double *df, double *upf1, double
*upf2, int *ipivot, double *b, int ldb, double *x, int ldx,
double *ferr, double *berr, int *info);
void dgtrfs_64(char transa, long n, long nrhs, double *low, double *d,
double *up, double *lowf, double *df, double *upf1, double
*upf2, long *ipivot, double *b, long ldb, double *x, long
ldx, double *ferr, double *berr, long *info);
PURPOSE
dgtrfs 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)
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 DGTTRF.
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 DGTTRS. 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
7 Nov 2015 dgtrfs(3P)