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172 lines
4.1 KiB
172 lines
4.1 KiB
2 years ago
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*> \brief \b CQRT11
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*
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* =========== DOCUMENTATION ===========
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*
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* Online html documentation available at
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* http://www.netlib.org/lapack/explore-html/
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*
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* Definition:
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* ===========
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*
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* REAL FUNCTION CQRT11( M, K, A, LDA, TAU, WORK, LWORK )
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*
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* .. Scalar Arguments ..
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* INTEGER K, LDA, LWORK, M
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* ..
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* .. Array Arguments ..
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* COMPLEX A( LDA, * ), TAU( * ), WORK( LWORK )
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* ..
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*
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*
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*> \par Purpose:
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* =============
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*>
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*> \verbatim
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*>
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*> CQRT11 computes the test ratio
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*>
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*> || Q'*Q - I || / (eps * m)
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*>
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*> where the orthogonal matrix Q is represented as a product of
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*> elementary transformations. Each transformation has the form
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*>
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*> H(k) = I - tau(k) v(k) v(k)'
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*>
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*> where tau(k) is stored in TAU(k) and v(k) is an m-vector of the form
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*> [ 0 ... 0 1 x(k) ]', where x(k) is a vector of length m-k stored
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*> in A(k+1:m,k).
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*> \endverbatim
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*
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* Arguments:
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* ==========
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*
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*> \param[in] M
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*> \verbatim
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*> M is INTEGER
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*> The number of rows of the matrix A.
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*> \endverbatim
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*>
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*> \param[in] K
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*> \verbatim
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*> K is INTEGER
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*> The number of columns of A whose subdiagonal entries
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*> contain information about orthogonal transformations.
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*> \endverbatim
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*>
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*> \param[in] A
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*> \verbatim
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*> A is COMPLEX array, dimension (LDA,K)
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*> The (possibly partial) output of a QR reduction routine.
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*> \endverbatim
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*>
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*> \param[in] LDA
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*> \verbatim
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*> LDA is INTEGER
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*> The leading dimension of the array A.
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*> \endverbatim
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*>
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*> \param[in] TAU
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*> \verbatim
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*> TAU is COMPLEX array, dimension (K)
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*> The scaling factors tau for the elementary transformations as
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*> computed by the QR factorization routine.
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*> \endverbatim
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*>
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*> \param[out] WORK
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*> \verbatim
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*> WORK is COMPLEX array, dimension (LWORK)
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*> \endverbatim
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*>
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*> \param[in] LWORK
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*> \verbatim
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*> LWORK is INTEGER
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*> The length of the array WORK. LWORK >= M*M + M.
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*> \endverbatim
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*
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* Authors:
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* ========
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*
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*> \author Univ. of Tennessee
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*> \author Univ. of California Berkeley
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*> \author Univ. of Colorado Denver
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*> \author NAG Ltd.
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*
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*> \ingroup complex_lin
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*
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* =====================================================================
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REAL FUNCTION CQRT11( M, K, A, LDA, TAU, WORK, LWORK )
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*
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* -- LAPACK test routine --
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* -- LAPACK is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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*
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* .. Scalar Arguments ..
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INTEGER K, LDA, LWORK, M
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* ..
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* .. Array Arguments ..
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COMPLEX A( LDA, * ), TAU( * ), WORK( LWORK )
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* ..
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*
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* =====================================================================
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*
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* .. Parameters ..
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REAL ZERO, ONE
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PARAMETER ( ZERO = 0.0E0, ONE = 1.0E0 )
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* ..
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* .. Local Scalars ..
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INTEGER INFO, J
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* ..
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* .. External Functions ..
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REAL CLANGE, SLAMCH
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EXTERNAL CLANGE, SLAMCH
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* ..
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* .. External Subroutines ..
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EXTERNAL CLASET, CUNM2R, XERBLA
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC CMPLX, REAL
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* ..
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* .. Local Arrays ..
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REAL RDUMMY( 1 )
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* ..
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* .. Executable Statements ..
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*
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CQRT11 = ZERO
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*
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* Test for sufficient workspace
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*
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IF( LWORK.LT.M*M+M ) THEN
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CALL XERBLA( 'CQRT11', 7 )
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RETURN
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END IF
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*
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* Quick return if possible
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*
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IF( M.LE.0 )
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$ RETURN
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*
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CALL CLASET( 'Full', M, M, CMPLX( ZERO ), CMPLX( ONE ), WORK, M )
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*
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* Form Q
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*
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CALL CUNM2R( 'Left', 'No transpose', M, M, K, A, LDA, TAU, WORK,
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$ M, WORK( M*M+1 ), INFO )
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*
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* Form Q'*Q
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*
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CALL CUNM2R( 'Left', 'Conjugate transpose', M, M, K, A, LDA, TAU,
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$ WORK, M, WORK( M*M+1 ), INFO )
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*
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DO 10 J = 1, M
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WORK( ( J-1 )*M+J ) = WORK( ( J-1 )*M+J ) - ONE
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10 CONTINUE
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*
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CQRT11 = CLANGE( 'One-norm', M, M, WORK, M, RDUMMY ) /
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$ ( REAL( M )*SLAMCH( 'Epsilon' ) )
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*
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RETURN
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*
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* End of CQRT11
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*
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END
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