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SUBROUTINE SQLT02( M, N, K, A, AF, Q, L, 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 K, LDA, LWORK, M, N
* ..
* .. Array Arguments ..
REAL A( LDA, * ), AF( LDA, * ), L( LDA, * ),
$ Q( LDA, * ), RESULT( * ), RWORK( * ), TAU( * ),
$ WORK( LWORK )
* ..
*
* Purpose
* =======
*
* SQLT02 tests SORGQL, which generates an m-by-n matrix Q with
* orthonornmal columns that is defined as the product of k elementary
* reflectors.
*
* Given the QL factorization of an m-by-n matrix A, SQLT02 generates
* the orthogonal matrix Q defined by the factorization of the last k
* columns of A; it compares L(m-n+1:m,n-k+1:n) with
* Q(1:m,m-n+1:m)'*A(1:m,n-k+1:n), and checks that the columns of Q are
* orthonormal.
*
* Arguments
* =========
*
* M (input) INTEGER
* The number of rows of the matrix Q to be generated. M >= 0.
*
* N (input) INTEGER
* The number of columns of the matrix Q to be generated.
* M >= N >= 0.
*
* K (input) INTEGER
* The number of elementary reflectors whose product defines the
* matrix Q. N >= K >= 0.
*
* A (input) REAL array, dimension (LDA,N)
* The m-by-n matrix A which was factorized by SQLT01.
*
* AF (input) REAL array, dimension (LDA,N)
* Details of the QL factorization of A, as returned by SGEQLF.
* See SGEQLF for further details.
*
* Q (workspace) REAL array, dimension (LDA,N)
*
* L (workspace) REAL array, dimension (LDA,N)
*
* LDA (input) INTEGER
* The leading dimension of the arrays A, AF, Q and L. LDA >= M.
*
* TAU (input) REAL array, dimension (N)
* The scalar factors of the elementary reflectors corresponding
* to the QL factorization in AF.
*
* WORK (workspace) REAL array, dimension (LWORK)
*
* LWORK (input) INTEGER
* The dimension of the array WORK.
*
* RWORK (workspace) REAL array, dimension (M)
*
* RESULT (output) REAL array, dimension (2)
* The test ratios:
* RESULT(1) = norm( L - Q'*A ) / ( M * norm(A) * EPS )
* RESULT(2) = norm( I - Q'*Q ) / ( M * 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
REAL ANORM, EPS, RESID
* ..
* .. External Functions ..
REAL SLAMCH, SLANGE, SLANSY
EXTERNAL SLAMCH, SLANGE, SLANSY
* ..
* .. External Subroutines ..
EXTERNAL SGEMM, SLACPY, SLASET, SORGQL, SSYRK
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX, REAL
* ..
* .. Scalars in Common ..
CHARACTER*6 SRNAMT
* ..
* .. Common blocks ..
COMMON / SRNAMC / SRNAMT
* ..
* .. Executable Statements ..
*
* Quick return if possible
*
IF( M.EQ.0 .OR. N.EQ.0 .OR. K.EQ.0 ) THEN
RESULT( 1 ) = ZERO
RESULT( 2 ) = ZERO
RETURN
END IF
*
EPS = SLAMCH( 'Epsilon' )
*
* Copy the last k columns of the factorization to the array Q
*
CALL SLASET( 'Full', M, N, ROGUE, ROGUE, Q, LDA )
IF( K.LT.M )
$ CALL SLACPY( 'Full', M-K, K, AF( 1, N-K+1 ), LDA,
$ Q( 1, N-K+1 ), LDA )
IF( K.GT.1 )
$ CALL SLACPY( 'Upper', K-1, K-1, AF( M-K+1, N-K+2 ), LDA,
$ Q( M-K+1, N-K+2 ), LDA )
*
* Generate the last n columns of the matrix Q
*
SRNAMT = 'SORGQL'
CALL SORGQL( M, N, K, Q, LDA, TAU( N-K+1 ), WORK, LWORK, INFO )
*
* Copy L(m-n+1:m,n-k+1:n)
*
CALL SLASET( 'Full', N, K, ZERO, ZERO, L( M-N+1, N-K+1 ), LDA )
CALL SLACPY( 'Lower', K, K, AF( M-K+1, N-K+1 ), LDA,
$ L( M-K+1, N-K+1 ), LDA )
*
* Compute L(m-n+1:m,n-k+1:n) - Q(1:m,m-n+1:m)' * A(1:m,n-k+1:n)
*
CALL SGEMM( 'Transpose', 'No transpose', N, K, M, -ONE, Q, LDA,
$ A( 1, N-K+1 ), LDA, ONE, L( M-N+1, N-K+1 ), LDA )
*
* Compute norm( L - Q'*A ) / ( M * norm(A) * EPS ) .
*
ANORM = SLANGE( '1', M, K, A( 1, N-K+1 ), LDA, RWORK )
RESID = SLANGE( '1', N, K, L( M-N+1, N-K+1 ), 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, L, LDA )
CALL SSYRK( 'Upper', 'Transpose', N, M, -ONE, Q, LDA, ONE, L,
$ LDA )
*
* Compute norm( I - Q'*Q ) / ( M * EPS ) .
*
RESID = SLANSY( '1', 'Upper', N, L, LDA, RWORK )
*
RESULT( 2 ) = ( RESID / REAL( MAX( 1, M ) ) ) / EPS
*
RETURN
*
* End of SQLT02
*
END
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