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SUBROUTINE SRQT01( M, N, A, AF, Q, R, LDA, TAU, WORK, LWORK,
$ RWORK, RESULT )
*
* -- LAPACK test routine (version 3.0) --
* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
* Courant Institute, Argonne National Lab, and Rice University
* September 30, 1994
*
* .. Scalar Arguments ..
INTEGER LDA, LWORK, M, N
* ..
* .. Array Arguments ..
REAL A( LDA, * ), AF( LDA, * ), Q( LDA, * ),
$ R( LDA, * ), RESULT( * ), RWORK( * ), TAU( * ),
$ WORK( LWORK )
* ..
*
* Purpose
* =======
*
* SRQT01 tests SGERQF, which computes the RQ factorization of an m-by-n
* matrix A, and partially tests SORGRQ which forms the n-by-n
* orthogonal matrix Q.
*
* SRQT01 compares R with A*Q', and checks that Q is orthogonal.
*
* Arguments
* =========
*
* M (input) INTEGER
* The number of rows of the matrix A. M >= 0.
*
* N (input) INTEGER
* The number of columns of the matrix A. N >= 0.
*
* A (input) REAL array, dimension (LDA,N)
* The m-by-n matrix A.
*
* AF (output) REAL array, dimension (LDA,N)
* Details of the RQ factorization of A, as returned by SGERQF.
* See SGERQF for further details.
*
* Q (output) REAL array, dimension (LDA,N)
* The n-by-n orthogonal matrix Q.
*
* R (workspace) REAL array, dimension (LDA,max(M,N))
*
* LDA (input) INTEGER
* The leading dimension of the arrays A, AF, Q and L.
* LDA >= max(M,N).
*
* TAU (output) REAL array, dimension (min(M,N))
* The scalar factors of the elementary reflectors, as returned
* by SGERQF.
*
* WORK (workspace) REAL array, dimension (LWORK)
*
* LWORK (input) INTEGER
* The dimension of the array WORK.
*
* RWORK (workspace) REAL array, dimension (max(M,N))
*
* RESULT (output) REAL array, dimension (2)
* The test ratios:
* RESULT(1) = norm( R - A*Q' ) / ( N * norm(A) * EPS )
* RESULT(2) = norm( I - Q*Q' ) / ( N * EPS )
*
* =====================================================================
*
* .. Parameters ..
REAL ZERO, ONE
PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 )
REAL ROGUE
PARAMETER ( ROGUE = -1.0E+10 )
* ..
* .. Local Scalars ..
INTEGER INFO, MINMN
REAL ANORM, EPS, RESID
* ..
* .. External Functions ..
REAL SLAMCH, SLANGE, SLANSY
EXTERNAL SLAMCH, SLANGE, SLANSY
* ..
* .. External Subroutines ..
EXTERNAL SGEMM, SGERQF, SLACPY, SLASET, SORGRQ, SSYRK
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX, MIN, REAL
* ..
* .. Scalars in Common ..
CHARACTER*6 SRNAMT
* ..
* .. Common blocks ..
COMMON / SRNAMC / SRNAMT
* ..
* .. Executable Statements ..
*
MINMN = MIN( M, N )
EPS = SLAMCH( 'Epsilon' )
*
* Copy the matrix A to the array AF.
*
CALL SLACPY( 'Full', M, N, A, LDA, AF, LDA )
*
* Factorize the matrix A in the array AF.
*
SRNAMT = 'SGERQF'
CALL SGERQF( M, N, AF, LDA, TAU, WORK, LWORK, INFO )
*
* Copy details of Q
*
CALL SLASET( 'Full', N, N, ROGUE, ROGUE, Q, LDA )
IF( M.LE.N ) THEN
IF( M.GT.0 .AND. M.LT.N )
$ CALL SLACPY( 'Full', M, N-M, AF, LDA, Q( N-M+1, 1 ), LDA )
IF( M.GT.1 )
$ CALL SLACPY( 'Lower', M-1, M-1, AF( 2, N-M+1 ), LDA,
$ Q( N-M+2, N-M+1 ), LDA )
ELSE
IF( N.GT.1 )
$ CALL SLACPY( 'Lower', N-1, N-1, AF( M-N+2, 1 ), LDA,
$ Q( 2, 1 ), LDA )
END IF
*
* Generate the n-by-n matrix Q
*
SRNAMT = 'SORGRQ'
CALL SORGRQ( N, N, MINMN, Q, LDA, TAU, WORK, LWORK, INFO )
*
* Copy R
*
CALL SLASET( 'Full', M, N, ZERO, ZERO, R, LDA )
IF( M.LE.N ) THEN
IF( M.GT.0 )
$ CALL SLACPY( 'Upper', M, M, AF( 1, N-M+1 ), LDA,
$ R( 1, N-M+1 ), LDA )
ELSE
IF( M.GT.N .AND. N.GT.0 )
$ CALL SLACPY( 'Full', M-N, N, AF, LDA, R, LDA )
IF( N.GT.0 )
$ CALL SLACPY( 'Upper', N, N, AF( M-N+1, 1 ), LDA,
$ R( M-N+1, 1 ), LDA )
END IF
*
* Compute R - A*Q'
*
CALL SGEMM( 'No transpose', 'Transpose', M, N, N, -ONE, A, LDA, Q,
$ LDA, ONE, R, LDA )
*
* Compute norm( R - Q'*A ) / ( N * norm(A) * EPS ) .
*
ANORM = SLANGE( '1', M, N, A, LDA, RWORK )
RESID = SLANGE( '1', M, N, R, LDA, RWORK )
IF( ANORM.GT.ZERO ) THEN
RESULT( 1 ) = ( ( RESID / REAL( MAX( 1, N ) ) ) / ANORM ) / EPS
ELSE
RESULT( 1 ) = ZERO
END IF
*
* Compute I - Q*Q'
*
CALL SLASET( 'Full', N, N, ZERO, ONE, R, LDA )
CALL SSYRK( 'Upper', 'No transpose', N, N, -ONE, Q, LDA, ONE, R,
$ LDA )
*
* Compute norm( I - Q*Q' ) / ( N * EPS ) .
*
RESID = SLANSY( '1', 'Upper', N, R, LDA, RWORK )
*
RESULT( 2 ) = ( RESID / REAL( MAX( 1, N ) ) ) / EPS
*
RETURN
*
* End of SRQT01
*
END
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