1*> \brief \b ZQRT01 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 ZQRT01( 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*> ZQRT01 tests ZGEQRF, 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*> ZQRT01 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 ZGEQRF. 61*> See ZGEQRF 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 ZGEQRF. 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*> \ingroup complex16_lin 122* 123* ===================================================================== 124 SUBROUTINE ZQRT01( M, N, A, AF, Q, R, LDA, TAU, WORK, LWORK, 125 $ RWORK, RESULT ) 126* 127* -- LAPACK test routine -- 128* -- LAPACK is a software package provided by Univ. of Tennessee, -- 129* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 130* 131* .. Scalar Arguments .. 132 INTEGER LDA, LWORK, M, N 133* .. 134* .. Array Arguments .. 135 DOUBLE PRECISION RESULT( * ), RWORK( * ) 136 COMPLEX*16 A( LDA, * ), AF( LDA, * ), Q( LDA, * ), 137 $ R( LDA, * ), TAU( * ), WORK( LWORK ) 138* .. 139* 140* ===================================================================== 141* 142* .. Parameters .. 143 DOUBLE PRECISION ZERO, ONE 144 PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) 145 COMPLEX*16 ROGUE 146 PARAMETER ( ROGUE = ( -1.0D+10, -1.0D+10 ) ) 147* .. 148* .. Local Scalars .. 149 INTEGER INFO, MINMN 150 DOUBLE PRECISION ANORM, EPS, RESID 151* .. 152* .. External Functions .. 153 DOUBLE PRECISION DLAMCH, ZLANGE, ZLANSY 154 EXTERNAL DLAMCH, ZLANGE, ZLANSY 155* .. 156* .. External Subroutines .. 157 EXTERNAL ZGEMM, ZGEQRF, ZHERK, ZLACPY, ZLASET, ZUNGQR 158* .. 159* .. Intrinsic Functions .. 160 INTRINSIC DBLE, DCMPLX, MAX, MIN 161* .. 162* .. Scalars in Common .. 163 CHARACTER*32 SRNAMT 164* .. 165* .. Common blocks .. 166 COMMON / SRNAMC / SRNAMT 167* .. 168* .. Executable Statements .. 169* 170 MINMN = MIN( M, N ) 171 EPS = DLAMCH( 'Epsilon' ) 172* 173* Copy the matrix A to the array AF. 174* 175 CALL ZLACPY( 'Full', M, N, A, LDA, AF, LDA ) 176* 177* Factorize the matrix A in the array AF. 178* 179 SRNAMT = 'ZGEQRF' 180 CALL ZGEQRF( M, N, AF, LDA, TAU, WORK, LWORK, INFO ) 181* 182* Copy details of Q 183* 184 CALL ZLASET( 'Full', M, M, ROGUE, ROGUE, Q, LDA ) 185 CALL ZLACPY( 'Lower', M-1, N, AF( 2, 1 ), LDA, Q( 2, 1 ), LDA ) 186* 187* Generate the m-by-m matrix Q 188* 189 SRNAMT = 'ZUNGQR' 190 CALL ZUNGQR( M, M, MINMN, Q, LDA, TAU, WORK, LWORK, INFO ) 191* 192* Copy R 193* 194 CALL ZLASET( 'Full', M, N, DCMPLX( ZERO ), DCMPLX( ZERO ), R, 195 $ LDA ) 196 CALL ZLACPY( 'Upper', M, N, AF, LDA, R, LDA ) 197* 198* Compute R - Q'*A 199* 200 CALL ZGEMM( 'Conjugate transpose', 'No transpose', M, N, M, 201 $ DCMPLX( -ONE ), Q, LDA, A, LDA, DCMPLX( ONE ), R, 202 $ LDA ) 203* 204* Compute norm( R - Q'*A ) / ( M * norm(A) * EPS ) . 205* 206 ANORM = ZLANGE( '1', M, N, A, LDA, RWORK ) 207 RESID = ZLANGE( '1', M, N, R, LDA, RWORK ) 208 IF( ANORM.GT.ZERO ) THEN 209 RESULT( 1 ) = ( ( RESID / DBLE( MAX( 1, M ) ) ) / ANORM ) / EPS 210 ELSE 211 RESULT( 1 ) = ZERO 212 END IF 213* 214* Compute I - Q'*Q 215* 216 CALL ZLASET( 'Full', M, M, DCMPLX( ZERO ), DCMPLX( ONE ), R, LDA ) 217 CALL ZHERK( 'Upper', 'Conjugate transpose', M, M, -ONE, Q, LDA, 218 $ ONE, R, LDA ) 219* 220* Compute norm( I - Q'*Q ) / ( M * EPS ) . 221* 222 RESID = ZLANSY( '1', 'Upper', M, R, LDA, RWORK ) 223* 224 RESULT( 2 ) = ( RESID / DBLE( MAX( 1, M ) ) ) / EPS 225* 226 RETURN 227* 228* End of ZQRT01 229* 230 END 231