sqrt02()

subroutine sqrt02	(	integer	m,
		integer	n,
		integer	k,
		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
	)

SQRT02

Purpose:

 SQRT02 tests SORGQR, which generates an m-by-n matrix Q with
 orthonormal columns that is defined as the product of k elementary
 reflectors.

 Given the QR factorization of an m-by-n matrix A, SQRT02 generates
 the orthogonal matrix Q defined by the factorization of the first k
 columns of A; it compares R(1:n,1:k) with Q(1:m,1:n)'*A(1:m,1:k),
 and checks that the columns of Q are orthonormal.

Parameters

[in]	M	M is INTEGER The number of rows of the matrix Q to be generated. M >= 0.
[in]	N	N is INTEGER The number of columns of the matrix Q to be generated. M >= N >= 0.
[in]	K	K is INTEGER The number of elementary reflectors whose product defines the matrix Q. N >= K >= 0.
[in]	A	A is REAL array, dimension (LDA,N) The m-by-n matrix A which was factorized by SQRT01.
[in]	AF	AF is REAL array, dimension (LDA,N) Details of the QR factorization of A, as returned by SGEQRF. See SGEQRF for further details.
[out]	Q	Q is REAL array, dimension (LDA,N)
[out]	R	R is REAL array, dimension (LDA,N)
[in]	LDA	LDA is INTEGER The leading dimension of the arrays A, AF, Q and R. LDA >= M.
[in]	TAU	TAU is REAL array, dimension (N) The scalar factors of the elementary reflectors corresponding to the QR factorization in AF.
[out]	WORK	WORK is REAL array, dimension (LWORK)
[in]	LWORK	LWORK is INTEGER The dimension of the array WORK.
[out]	RWORK	RWORK is REAL array, dimension (M)
[out]	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 133 of file sqrt02.f.

*
*  -- LAPACK test routine --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
*     .. Scalar Arguments ..
      INTEGER            K, LDA, LWORK, M, N
*     ..
*     .. Array Arguments ..
      REAL               A( LDA, * ), AF( LDA, * ), Q( LDA, * ),
     $                   R( LDA, * ), RESULT( * ), RWORK( * ), TAU( * ),
     $                   WORK( LWORK )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      REAL               ZERO, ONE
      parameter( zero = 0.0e+0, one = 1.0e+0 )
      REAL               ROGUE
      parameter( rogue = -1.0e+10 )
*     ..
*     .. Local Scalars ..
      INTEGER            INFO
      REAL               ANORM, EPS, RESID
*     ..
*     .. External Functions ..
      REAL               SLAMCH, SLANGE, SLANSY
      EXTERNAL           slamch, slange, slansy
*     ..
*     .. External Subroutines ..
      EXTERNAL           sgemm, slacpy, slaset, sorgqr, ssyrk
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          max, real
*     ..
*     .. Scalars in Common ..
      CHARACTER*32       SRNAMT
*     ..
*     .. Common blocks ..
      COMMON             / srnamc / srnamt
*     ..
*     .. Executable Statements ..
*
      eps = slamch( 'Epsilon' )
*
*     Copy the first k columns of the factorization to the array Q
*
      CALL slaset( 'Full', m, n, rogue, rogue, q, lda )
      CALL slacpy( 'Lower', m-1, k, af( 2, 1 ), lda, q( 2, 1 ), lda )
*
*     Generate the first n columns of the matrix Q
*
      srnamt = 'SORGQR'
      CALL sorgqr( m, n, k, q, lda, tau, work, lwork, info )
*
*     Copy R(1:n,1:k)
*
      CALL slaset( 'Full', n, k, zero, zero, r, lda )
      CALL slacpy( 'Upper', n, k, af, lda, r, lda )
*
*     Compute R(1:n,1:k) - Q(1:m,1:n)' * A(1:m,1:k)
*
      CALL sgemm( 'Transpose', 'No transpose', n, k, m, -one, q, lda, a,
     $            lda, one, r, lda )
*
*     Compute norm( R - Q'*A ) / ( M * norm(A) * EPS ) .
*
      anorm = slange( '1', m, k, a, lda, rwork )
      resid = slange( '1', n, k, r, lda, rwork )
      IF( anorm.GT.zero ) THEN
         result( 1 ) = ( ( resid / real( max( 1, m ) ) ) / anorm ) / eps
      ELSE
         result( 1 ) = zero
      END IF
*
*     Compute I - Q'*Q
*
      CALL slaset( 'Full', n, n, zero, one, r, lda )
      CALL ssyrk( 'Upper', 'Transpose', n, m, -one, q, lda, one, r,
     $            lda )
*
*     Compute norm( I - Q'*Q ) / ( M * EPS ) .
*
      resid = slansy( '1', 'Upper', n, r, lda, rwork )
*
      result( 2 ) = ( resid / real( max( 1, m ) ) ) / eps
*
      RETURN
*
*     End of SQRT02
*

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