
ZTPRFS(l) ) ZTPRFS(l)
NAME
ZTPRFS  provide error bounds and backward error estimates for the solution to a system of
linear equations with a triangular packed coefficient matrix
SYNOPSIS
SUBROUTINE ZTPRFS( 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
DOUBLE PRECISION BERR( * ), FERR( * ), RWORK( * )
COMPLEX*16 AP( * ), B( LDB, * ), WORK( * ), X( LDX, * )
PURPOSE
ZTPRFS provides error bounds and backward error estimates for the solution to a system of
linear equations with a triangular packed coefficient matrix. The solution matrix X must
be computed by ZTPTRS or some other means before entering this routine. ZTPRFS 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 nonunit 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*16 array, dimension (N*(N+1)/2)
The upper or lower triangular matrix A, packed columnwise in a linear array. The
jth column of A is stored in the array AP as follows: if UPLO = 'U', AP(i +
(j1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j1)*(2nj)/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*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 jth 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 esti
mate is as reliable as the estimate for RCOND, and is almost always a slight over
estimate 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 solu
tion).
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 ith argument had an illegal value
LAPACK version 3.0 15 June 2000 ZTPRFS(l) 
