cgtrfs(3P) Sun Performance Library cgtrfs(3P)NAMEcgtrfs - 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 CGTRFS(TRANSA, N, NRHS, LOW, D, UP, LOWF, DF, UPF1,
UPF2, IPIVOT, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO)
CHARACTER * 1 TRANSA
COMPLEX LOW(*), D(*), UP(*), LOWF(*), DF(*), UPF1(*), UPF2(*),
B(LDB,*), X(LDX,*), WORK(*)
INTEGER N, NRHS, LDB, LDX, INFO
INTEGER IPIVOT(*)
REAL FERR(*), BERR(*), WORK2(*)
SUBROUTINE CGTRFS_64(TRANSA, N, NRHS, LOW, D, UP, LOWF, DF,
UPF1, UPF2, IPIVOT, B, LDB, X, LDX, FERR, BERR, WORK, WORK2,
INFO)
CHARACTER * 1 TRANSA
COMPLEX LOW(*), D(*), UP(*), LOWF(*), DF(*), UPF1(*), UPF2(*),
B(LDB,*), X(LDX,*), WORK(*)
INTEGER*8 N, NRHS, LDB, LDX, INFO
INTEGER*8 IPIVOT(*)
REAL FERR(*), BERR(*), WORK2(*)
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
COMPLEX, DIMENSION(:) :: LOW, D, UP, LOWF, DF, UPF1, UPF2, WORK
COMPLEX, DIMENSION(:,:) :: B, X
INTEGER :: N, NRHS, LDB, LDX, INFO
INTEGER, DIMENSION(:) :: IPIVOT
REAL, DIMENSION(:) :: FERR, BERR, WORK2
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
COMPLEX, DIMENSION(:) :: LOW, D, UP, LOWF, DF, UPF1, UPF2, WORK
COMPLEX, DIMENSION(:,:) :: B, X
INTEGER(8) :: N, NRHS, LDB, LDX, INFO
INTEGER(8), DIMENSION(:) :: IPIVOT
REAL, DIMENSION(:) :: FERR, BERR, WORK2
C INTERFACE
#include <sunperf.h>
void cgtrfs(char transa, int n, int nrhs, complex *low, complex *d,
complex *up, complex *lowf, complex *df, complex *upf1, com‐
plex *upf2, int *ipivot, complex *b, int ldb, complex *x, int
ldx, float *ferr, float *berr, int *info);
void cgtrfs_64(char transa, long n, long nrhs, complex *low, complex
*d, complex *up, complex *lowf, complex *df, complex *upf1,
complex *upf2, long *ipivot, complex *b, long ldb, complex
*x, long ldx, float *ferr, float *berr, long *info);
PURPOSEcgtrfs 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)
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 CGTTRF.
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 CGTTRS. 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(2*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 cgtrfs(3P)
