# dtprfs.f - Man Page

## Synopsis

### Functions/Subroutines

subroutine **dtprfs** (UPLO, TRANS, DIAG, **N**, **NRHS**, AP, B, **LDB**, X, LDX, FERR, BERR, WORK, IWORK, INFO)**DTPRFS**

## Function/Subroutine Documentation

### subroutine dtprfs (character UPLO, character TRANS, character DIAG, integer N, integer NRHS, double precision, dimension( * ) AP, double precision, dimension( ldb, * ) B, integer LDB, double precision, dimension( ldx, * ) X, integer LDX, double precision, dimension( * ) FERR, double precision, dimension( * ) BERR, double precision, dimension( * ) WORK, integer, dimension( * ) IWORK, integer INFO)

**DTPRFS**

**Purpose:**

DTPRFS 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 DTPTRS or some other means before entering this routine. DTPRFS does not do iterative refinement because doing so cannot improve the backward error.

**Parameters:***UPLO*UPLO is CHARACTER*1 = 'U': A is upper triangular; = 'L': A is lower triangular.

*TRANS*TRANS is 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*DIAG is CHARACTER*1 = 'N': A is non-unit triangular; = 'U': A is unit triangular.

*N*N is INTEGER The order of the matrix A. N >= 0.

*NRHS*NRHS is INTEGER The number of right hand sides, i.e., the number of columns of the matrices B and X. NRHS >= 0.

*AP*AP is 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*B is DOUBLE PRECISION array, dimension (LDB,NRHS) The right hand side matrix B.

*LDB*LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).

*X*X is DOUBLE PRECISION array, dimension (LDX,NRHS) The solution matrix X.

*LDX*LDX is INTEGER The leading dimension of the array X. LDX >= max(1,N).

*FERR*FERR is 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*BERR is 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*WORK is DOUBLE PRECISION array, dimension (3*N)

*IWORK*IWORK is INTEGER array, dimension (N)

*INFO*INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value

**Author:**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Date:**December 2016

Definition at line 177 of file dtprfs.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page dtprfs(3) is an alias of dtprfs.f(3).

Tue Nov 14 2017 Version 3.8.0 LAPACK