CTPRFS(1) LAPACK routine (version 3.2) CTPRFS(1)NAME
CTPRFS - provides error bounds and backward error estimates for the
solution to a system of linear equations with a triangular packed coef‐
ficient matrix
SYNOPSIS
SUBROUTINE CTPRFS( UPLO, TRANS, DIAG, N, NRHS, AP, B, LDB, X, LDX,
FERR, BERR, WORK, RWORK, INFO )
CHARACTER DIAG, TRANS, UPLO
INTEGER INFO, LDB, LDX, N, NRHS
REAL BERR( * ), FERR( * ), RWORK( * )
COMPLEX AP( * ), B( LDB, * ), WORK( * ), X( LDX, * )
PURPOSE
CTPRFS provides error bounds and backward error estimates for the solu‐
tion to a system of linear equations with a triangular packed coeffi‐
cient matrix. The solution matrix X must be computed by CTPTRS or some
other means before entering this routine. CTPRFS 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.
AP (input) COMPLEX array, dimension (N*(N+1)/2)
The upper or lower triangular matrix A, packed columnwise in a
linear array. The j-th column of A is stored in the array AP
as follows: if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for
1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for
j<=i<=n. If DIAG = 'U', the diagonal elements of A are not
referenced and are assumed to be 1.
B (input) COMPLEX 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 array, dimension (LDX,NRHS)
The solution matrix X.
LDX (input) INTEGER
The leading dimension of the array X. LDX >= max(1,N).
FERR (output) REAL 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) REAL array, dimension (NRHS)
The componentwise relative backward error of each solution vec‐
tor 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 array, dimension (2*N)
RWORK (workspace) REAL array, dimension (N)
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
LAPACK routine (version 3.2) November 2008 CTPRFS(1)
