*> \brief \b SRZT01 * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * REAL FUNCTION SRZT01( M, N, A, AF, LDA, TAU, WORK, * LWORK ) * * .. Scalar Arguments .. * INTEGER LDA, LWORK, M, N * .. * .. Array Arguments .. * REAL A( LDA, * ), AF( LDA, * ), TAU( * ), * \$ WORK( LWORK ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> SRZT01 returns *> || A - R*Q || / ( M * eps * ||A|| ) *> for an upper trapezoidal A that was factored with STZRZF. *> \endverbatim * * Arguments: * ========== * *> \param[in] M *> \verbatim *> M is INTEGER *> The number of rows of the matrices A and AF. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The number of columns of the matrices A and AF. *> \endverbatim *> *> \param[in] A *> \verbatim *> A is REAL array, dimension (LDA,N) *> The original upper trapezoidal M by N matrix A. *> \endverbatim *> *> \param[in] AF *> \verbatim *> AF is REAL array, dimension (LDA,N) *> The output of STZRZF for input matrix A. *> The lower triangle is not referenced. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the arrays A and AF. *> \endverbatim *> *> \param[in] TAU *> \verbatim *> TAU is REAL array, dimension (M) *> Details of the Householder transformations as returned by *> STZRZF. *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is REAL array, dimension (LWORK) *> \endverbatim *> *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER *> The length of the array WORK. LWORK >= m*n + m*nb. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \ingroup single_lin * * ===================================================================== REAL FUNCTION SRZT01( M, N, A, AF, 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 LDA, LWORK, M, N * .. * .. Array Arguments .. REAL A( LDA, * ), AF( LDA, * ), TAU( * ), \$ WORK( LWORK ) * .. * * ===================================================================== * * .. Parameters .. REAL ZERO, ONE PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 ) * .. * .. Local Scalars .. INTEGER I, INFO, J REAL NORMA * .. * .. Local Arrays .. REAL RWORK( 1 ) * .. * .. External Functions .. REAL SLAMCH, SLANGE EXTERNAL SLAMCH, SLANGE * .. * .. External Subroutines .. EXTERNAL SAXPY, SLASET, SORMRZ, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC MAX, REAL * .. * .. Executable Statements .. * SRZT01 = ZERO * IF( LWORK.LT.M*N+M ) THEN CALL XERBLA( 'SRZT01', 8 ) RETURN END IF * * Quick return if possible * IF( M.LE.0 .OR. N.LE.0 ) \$ RETURN * NORMA = SLANGE( 'One-norm', M, N, A, LDA, RWORK ) * * Copy upper triangle R * CALL SLASET( 'Full', M, N, ZERO, ZERO, WORK, M ) DO 20 J = 1, M DO 10 I = 1, J WORK( ( J-1 )*M+I ) = AF( I, J ) 10 CONTINUE 20 CONTINUE * * R = R * P(1) * ... *P(m) * CALL SORMRZ( 'Right', 'No tranpose', M, N, M, N-M, AF, LDA, TAU, \$ WORK, M, WORK( M*N+1 ), LWORK-M*N, INFO ) * * R = R - A * DO 30 I = 1, N CALL SAXPY( M, -ONE, A( 1, I ), 1, WORK( ( I-1 )*M+1 ), 1 ) 30 CONTINUE * SRZT01 = SLANGE( 'One-norm', M, N, WORK, M, RWORK ) * SRZT01 = SRZT01 / ( SLAMCH( 'Epsilon' )*REAL( MAX( M, N ) ) ) IF( NORMA.NE.ZERO ) \$ SRZT01 = SRZT01 / NORMA * RETURN * * End of SRZT01 * END