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 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*16 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*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