1*> \brief \b ZQRT01P 2* 3* =========== DOCUMENTATION =========== 4* 5* Online html documentation available at 6* http://www.netlib.org/lapack/explore-html/ 7* 8* Definition: 9* =========== 10* 11* SUBROUTINE ZQRT01P( M, N, A, AF, Q, R, LDA, TAU, WORK, LWORK, 12* RWORK, RESULT ) 13* 14* .. Scalar Arguments .. 15* INTEGER LDA, LWORK, M, N 16* .. 17* .. Array Arguments .. 18* DOUBLE PRECISION RESULT( * ), RWORK( * ) 19* COMPLEX*16 A( LDA, * ), AF( LDA, * ), Q( LDA, * ), 20* $ R( LDA, * ), TAU( * ), WORK( LWORK ) 21* .. 22* 23* 24*> \par Purpose: 25* ============= 26*> 27*> \verbatim 28*> 29*> ZQRT01P tests ZGEQRFP, which computes the QR factorization of an m-by-n 30*> matrix A, and partially tests ZUNGQR which forms the m-by-m 31*> orthogonal matrix Q. 32*> 33*> ZQRT01P compares R with Q'*A, and checks that Q is orthogonal. 34*> \endverbatim 35* 36* Arguments: 37* ========== 38* 39*> \param[in] M 40*> \verbatim 41*> M is INTEGER 42*> The number of rows of the matrix A. M >= 0. 43*> \endverbatim 44*> 45*> \param[in] N 46*> \verbatim 47*> N is INTEGER 48*> The number of columns of the matrix A. N >= 0. 49*> \endverbatim 50*> 51*> \param[in] A 52*> \verbatim 53*> A is COMPLEX*16 array, dimension (LDA,N) 54*> The m-by-n matrix A. 55*> \endverbatim 56*> 57*> \param[out] AF 58*> \verbatim 59*> AF is COMPLEX*16 array, dimension (LDA,N) 60*> Details of the QR factorization of A, as returned by ZGEQRFP. 61*> See ZGEQRFP for further details. 62*> \endverbatim 63*> 64*> \param[out] Q 65*> \verbatim 66*> Q is COMPLEX*16 array, dimension (LDA,M) 67*> The m-by-m orthogonal matrix Q. 68*> \endverbatim 69*> 70*> \param[out] R 71*> \verbatim 72*> R is COMPLEX*16 array, dimension (LDA,max(M,N)) 73*> \endverbatim 74*> 75*> \param[in] LDA 76*> \verbatim 77*> LDA is INTEGER 78*> The leading dimension of the arrays A, AF, Q and R. 79*> LDA >= max(M,N). 80*> \endverbatim 81*> 82*> \param[out] TAU 83*> \verbatim 84*> TAU is COMPLEX*16 array, dimension (min(M,N)) 85*> The scalar factors of the elementary reflectors, as returned 86*> by ZGEQRFP. 87*> \endverbatim 88*> 89*> \param[out] WORK 90*> \verbatim 91*> WORK is COMPLEX*16 array, dimension (LWORK) 92*> \endverbatim 93*> 94*> \param[in] LWORK 95*> \verbatim 96*> LWORK is INTEGER 97*> The dimension of the array WORK. 98*> \endverbatim 99*> 100*> \param[out] RWORK 101*> \verbatim 102*> RWORK is DOUBLE PRECISION array, dimension (M) 103*> \endverbatim 104*> 105*> \param[out] RESULT 106*> \verbatim 107*> RESULT is DOUBLE PRECISION array, dimension (2) 108*> The test ratios: 109*> RESULT(1) = norm( R - Q'*A ) / ( M * norm(A) * EPS ) 110*> RESULT(2) = norm( I - Q'*Q ) / ( M * EPS ) 111*> \endverbatim 112* 113* Authors: 114* ======== 115* 116*> \author Univ. of Tennessee 117*> \author Univ. of California Berkeley 118*> \author Univ. of Colorado Denver 119*> \author NAG Ltd. 120* 121*> \date December 2016 122* 123*> \ingroup complex16_lin 124* 125* ===================================================================== 126 SUBROUTINE ZQRT01P( M, N, A, AF, Q, R, LDA, TAU, WORK, LWORK, 127 $ RWORK, RESULT ) 128* 129* -- LAPACK test routine (version 3.7.0) -- 130* -- LAPACK is a software package provided by Univ. of Tennessee, -- 131* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 132* December 2016 133* 134* .. Scalar Arguments .. 135 INTEGER LDA, LWORK, M, N 136* .. 137* .. Array Arguments .. 138 DOUBLE PRECISION RESULT( * ), RWORK( * ) 139 COMPLEX*16 A( LDA, * ), AF( LDA, * ), Q( LDA, * ), 140 $ R( LDA, * ), TAU( * ), WORK( LWORK ) 141* .. 142* 143* ===================================================================== 144* 145* .. Parameters .. 146 DOUBLE PRECISION ZERO, ONE 147 PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) 148 COMPLEX*16 ROGUE 149 PARAMETER ( ROGUE = ( -1.0D+10, -1.0D+10 ) ) 150* .. 151* .. Local Scalars .. 152 INTEGER INFO, MINMN 153 DOUBLE PRECISION ANORM, EPS, RESID 154* .. 155* .. External Functions .. 156 DOUBLE PRECISION DLAMCH, ZLANGE, ZLANSY 157 EXTERNAL DLAMCH, ZLANGE, ZLANSY 158* .. 159* .. External Subroutines .. 160 EXTERNAL ZGEMM, ZGEQRFP, ZHERK, ZLACPY, ZLASET, ZUNGQR 161* .. 162* .. Intrinsic Functions .. 163 INTRINSIC DBLE, DCMPLX, MAX, MIN 164* .. 165* .. Scalars in Common .. 166 CHARACTER*32 SRNAMT 167* .. 168* .. Common blocks .. 169 COMMON / SRNAMC / SRNAMT 170* .. 171* .. Executable Statements .. 172* 173 MINMN = MIN( M, N ) 174 EPS = DLAMCH( 'Epsilon' ) 175* 176* Copy the matrix A to the array AF. 177* 178 CALL ZLACPY( 'Full', M, N, A, LDA, AF, LDA ) 179* 180* Factorize the matrix A in the array AF. 181* 182 SRNAMT = 'ZGEQRFP' 183 CALL ZGEQRFP( M, N, AF, LDA, TAU, WORK, LWORK, INFO ) 184* 185* Copy details of Q 186* 187 CALL ZLASET( 'Full', M, M, ROGUE, ROGUE, Q, LDA ) 188 CALL ZLACPY( 'Lower', M-1, N, AF( 2, 1 ), LDA, Q( 2, 1 ), LDA ) 189* 190* Generate the m-by-m matrix Q 191* 192 SRNAMT = 'ZUNGQR' 193 CALL ZUNGQR( M, M, MINMN, Q, LDA, TAU, WORK, LWORK, INFO ) 194* 195* Copy R 196* 197 CALL ZLASET( 'Full', M, N, DCMPLX( ZERO ), DCMPLX( ZERO ), R, 198 $ LDA ) 199 CALL ZLACPY( 'Upper', M, N, AF, LDA, R, LDA ) 200* 201* Compute R - Q'*A 202* 203 CALL ZGEMM( 'Conjugate transpose', 'No transpose', M, N, M, 204 $ DCMPLX( -ONE ), Q, LDA, A, LDA, DCMPLX( ONE ), R, 205 $ LDA ) 206* 207* Compute norm( R - Q'*A ) / ( M * norm(A) * EPS ) . 208* 209 ANORM = ZLANGE( '1', M, N, A, LDA, RWORK ) 210 RESID = ZLANGE( '1', M, N, R, LDA, RWORK ) 211 IF( ANORM.GT.ZERO ) THEN 212 RESULT( 1 ) = ( ( RESID / DBLE( MAX( 1, M ) ) ) / ANORM ) / EPS 213 ELSE 214 RESULT( 1 ) = ZERO 215 END IF 216* 217* Compute I - Q'*Q 218* 219 CALL ZLASET( 'Full', M, M, DCMPLX( ZERO ), DCMPLX( ONE ), R, LDA ) 220 CALL ZHERK( 'Upper', 'Conjugate transpose', M, M, -ONE, Q, LDA, 221 $ ONE, R, LDA ) 222* 223* Compute norm( I - Q'*Q ) / ( M * EPS ) . 224* 225 RESID = ZLANSY( '1', 'Upper', M, R, LDA, RWORK ) 226* 227 RESULT( 2 ) = ( RESID / DBLE( MAX( 1, M ) ) ) / EPS 228* 229 RETURN 230* 231* End of ZQRT01P 232* 233 END 234