*> \brief \b DQRT11 * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * DOUBLE PRECISION FUNCTION DQRT11( M, K, A, LDA, TAU, WORK, LWORK ) * * .. Scalar Arguments .. * INTEGER K, LDA, LWORK, M * .. * .. Array Arguments .. * DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( LWORK ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DQRT11 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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. * *> \date December 2016 * *> \ingroup double_lin * * ===================================================================== DOUBLE PRECISION FUNCTION DQRT11( M, K, A, LDA, TAU, WORK, LWORK ) * * -- LAPACK test routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. INTEGER K, LDA, LWORK, M * .. * .. Array Arguments .. DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( LWORK ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, ONE PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 ) * .. * .. Local Scalars .. INTEGER INFO, J * .. * .. External Functions .. DOUBLE PRECISION DLAMCH, DLANGE EXTERNAL DLAMCH, DLANGE * .. * .. External Subroutines .. EXTERNAL DLASET, DORM2R, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC DBLE * .. * .. Local Arrays .. DOUBLE PRECISION RDUMMY( 1 ) * .. * .. Executable Statements .. * DQRT11 = ZERO * * Test for sufficient workspace * IF( LWORK.LT.M*M+M ) THEN CALL XERBLA( 'DQRT11', 7 ) RETURN END IF * * Quick return if possible * IF( M.LE.0 ) $ RETURN * CALL DLASET( 'Full', M, M, ZERO, ONE, WORK, M ) * * Form Q * CALL DORM2R( 'Left', 'No transpose', M, M, K, A, LDA, TAU, WORK, $ M, WORK( M*M+1 ), INFO ) * * Form Q'*Q * CALL DORM2R( 'Left', '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 * DQRT11 = DLANGE( 'One-norm', M, M, WORK, M, RDUMMY ) / $ ( DBLE( M )*DLAMCH( 'Epsilon' ) ) * RETURN * * End of DQRT11 * END