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