dtprfs(3)

NAME

DTPRFS - provide error bounds and backward error estimates

for the solution to a system of linear equations with a triangu

lar packed coefficient matrix

SYNOPSIS

SUBROUTINE DTPRFS( UPLO, TRANS, DIAG, N, NRHS, AP, B, LDB,
X, LDX, FERR, BERR, WORK, IWORK, INFO )
    CHARACTER      DIAG, TRANS, UPLO
    INTEGER        INFO, LDB, LDX, N, NRHS
    INTEGER        IWORK( * )
    DOUBLE         PRECISION AP( * ), B( LDB, * ), BERR( *
), FERR( * ), WORK( * ), X( LDX, * )

PURPOSE

DTPRFS provides error bounds and backward error estimates

for the solution to a system of linear equations with a triangu

lar packed coefficient matrix. The solution matrix X must be

computed by DTPTRS or some other means before entering this rou

tine. DTPRFS 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 =

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) DOUBLE PRECISION 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)*(2*n-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) DOUBLE PRECISION 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) DOUBLE PRECISION 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 solu

tion 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) DOUBLE PRECISION array, dimension

(3*N)

IWORK (workspace) INTEGER array, dimension (N)

INFO (output) INTEGER

= 0: successful exit
< 0: if INFO = -i, the i-th argument had an ille

gal value

LAPACK version 3.0 15 June 2000

DTPRFS(3)