NAME

TESTING/LIN/sqrt01.f

SYNOPSIS

Functions/Subroutines

subroutine sqrt01 (m, n, a, af, q, r, lda, tau, work, lwork, rwork, result)
SQRT01

Function/Subroutine Documentation

subroutine sqrt01 (integer m, integer n, real, dimension( lda, * ) a, real, dimension( lda, * ) af, real, dimension( lda, * ) q, real, dimension( lda, * ) r, integer lda, real, dimension( * ) tau, real, dimension( lwork ) work, integer lwork, real, dimension( * ) rwork, real, dimension( * ) result)

SQRT01

Purpose:



 SQRT01 tests SGEQRF, which computes the QR factorization of an m-by-n


 matrix A, and partially tests SORGQR which forms the m-by-m


 orthogonal matrix Q.


 SQRT01 compares R with Q'*A, and checks that Q is orthogonal.

Parameters



          M is INTEGER


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



          N is INTEGER


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



          A is REAL array, dimension (LDA,N)


          The m-by-n matrix A.



          AF is REAL array, dimension (LDA,N)


          Details of the QR factorization of A, as returned by SGEQRF.


          See SGEQRF for further details.



          Q is REAL array, dimension (LDA,M)


          The m-by-m orthogonal matrix Q.



          R is REAL array, dimension (LDA,max(M,N))

LDA



          LDA is INTEGER


          The leading dimension of the arrays A, AF, Q and R.


          LDA >= max(M,N).

TAU



          TAU is REAL array, dimension (min(M,N))


          The scalar factors of the elementary reflectors, as returned


          by SGEQRF.

WORK



          WORK is REAL array, dimension (LWORK)

LWORK



          LWORK is INTEGER


          The dimension of the array WORK.

RWORK



          RWORK is REAL array, dimension (M)

RESULT



          RESULT is REAL array, dimension (2)


          The test ratios:


          RESULT(1) = norm( R - Q'*A ) / ( M * norm(A) * EPS )


          RESULT(2) = norm( I - Q'*Q ) / ( M * EPS )

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 124 of file sqrt01.f.

Author

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