# sqrt16.f - Man Page

TESTING/LIN/sqrt16.f

## Synopsis

### Functions/Subroutines

subroutine **sqrt16** (trans, m, n, nrhs, a, lda, x, ldx, b, ldb, rwork, resid)**SQRT16**

## Function/Subroutine Documentation

### subroutine sqrt16 (character trans, integer m, integer n, integer nrhs, real, dimension( lda, * ) a, integer lda, real, dimension( ldx, * ) x, integer ldx, real, dimension( ldb, * ) b, integer ldb, real, dimension( * ) rwork, real resid)

**SQRT16**

**Purpose:**

SQRT16 computes the residual for a solution of a system of linear equations A*x = b or A'*x = b: RESID = norm(B - A*X) / ( max(m,n) * norm(A) * norm(X) * EPS ), where EPS is the machine epsilon.

**Parameters***TRANS*TRANS is CHARACTER*1 Specifies the form of the system of equations: = 'N': A *x = b = 'T': A'*x = b, where A' is the transpose of A = 'C': A'*x = b, where A' is the transpose of A

*M*M is INTEGER The number of rows of the matrix A. M >= 0.

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

*NRHS*NRHS is INTEGER The number of columns of B, the matrix of right hand sides. NRHS >= 0.

*A*A is REAL array, dimension (LDA,N) The original M x N matrix A.

*LDA*LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).

*X*X is REAL array, dimension (LDX,NRHS) The computed solution vectors for the system of linear equations.

*LDX*LDX is INTEGER The leading dimension of the array X. If TRANS = 'N', LDX >= max(1,N); if TRANS = 'T' or 'C', LDX >= max(1,M).

*B*B is REAL array, dimension (LDB,NRHS) On entry, the right hand side vectors for the system of linear equations. On exit, B is overwritten with the difference B - A*X.

*LDB*LDB is INTEGER The leading dimension of the array B. IF TRANS = 'N', LDB >= max(1,M); if TRANS = 'T' or 'C', LDB >= max(1,N).

*RWORK*RWORK is REAL array, dimension (M)

*RESID*RESID is REAL The maximum over the number of right hand sides of norm(B - A*X) / ( max(m,n) * norm(A) * norm(X) * EPS ).

**Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **131** of file **sqrt16.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page sqrt16(3) is an alias of sqrt16.f(3).

Tue Nov 28 2023 12:08:43 Version 3.12.0 LAPACK