ZTRRFS(3)
provides error bounds and backward error estimates for the solution to a system of linear equations with a triangular coefficient matrix
SYNOPSIS
- SUBROUTINE ZTRRFS(
-
UPLO, TRANS, DIAG, N, NRHS, A, LDA, B, LDB, X,
LDX, FERR, BERR, WORK, RWORK, INFO )
-
CHARACTER
DIAG, TRANS, UPLO
-
INTEGER
INFO, LDA, LDB, LDX, N, NRHS
-
DOUBLE
PRECISION BERR( * ), FERR( * ), RWORK( * )
-
COMPLEX*16
A( LDA, * ), B( LDB, * ), WORK( * ),
X( LDX, * )
PURPOSE
ZTRRFS provides error bounds and backward error estimates for the
solution to a system of linear equations with a triangular
coefficient matrix.
The solution matrix X must be computed by ZTRTRS or some other
means before entering this routine. ZTRRFS does not do iterative
refinement because doing so cannot improve the backward error.
ARGUMENTS
- UPLO (input) CHARACTER*1
-
= 'U': A is upper triangular;
= 'L': A is lower triangular.
- TRANS (input) CHARACTER*1
-
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)
- DIAG (input) CHARACTER*1
-
= 'N': A is non-unit triangular;
= 'U': A is unit triangular.
- N (input) INTEGER
-
The order of the matrix A. N >= 0.
- NRHS (input) INTEGER
-
The number of right hand sides, i.e., the number of columns
of the matrices B and X. NRHS >= 0.
- A (input) COMPLEX*16 array, dimension (LDA,N)
-
The triangular matrix A. If UPLO = 'U', the leading N-by-N
upper triangular part of the array A contains the upper
triangular matrix, and the strictly lower triangular part of
A is not referenced. If UPLO = 'L', the leading N-by-N lower
triangular part of the array A contains the lower triangular
matrix, and the strictly upper triangular part of A is not
referenced. If DIAG = 'U', the diagonal elements of A are
also not referenced and are assumed to be 1.
- LDA (input) INTEGER
-
The leading dimension of the array A. LDA >= max(1,N).
- B (input) COMPLEX*16 array, dimension (LDB,NRHS)
-
The right hand side matrix B.
- LDB (input) INTEGER
-
The leading dimension of the array B. LDB >= max(1,N).
- X (input) COMPLEX*16 array, dimension (LDX,NRHS)
-
The solution matrix X.
- LDX (input) INTEGER
-
The leading dimension of the array X. LDX >= max(1,N).
- FERR (output) DOUBLE PRECISION array, dimension (NRHS)
-
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 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). The estimate is as reliable as
the estimate for RCOND, and is almost always a slight
overestimate of the true error.
- BERR (output) DOUBLE PRECISION array, dimension (NRHS)
-
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) COMPLEX*16 array, dimension (2*N)
-
- RWORK (workspace) DOUBLE PRECISION array, dimension (N)
-
- INFO (output) INTEGER
-
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value