1*> \brief \b ZQLT01 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 ZQLT01( M, N, A, AF, Q, L, 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, * ), L( LDA, * ), 20* $ Q( LDA, * ), TAU( * ), WORK( LWORK ) 21* .. 22* 23* 24*> \par Purpose: 25* ============= 26*> 27*> \verbatim 28*> 29*> ZQLT01 tests ZGEQLF, which computes the QL factorization of an m-by-n 30*> matrix A, and partially tests ZUNGQL which forms the m-by-m 31*> orthogonal matrix Q. 32*> 33*> ZQLT01 compares L 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 QL factorization of A, as returned by ZGEQLF. 61*> See ZGEQLF 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] L 71*> \verbatim 72*> L 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 ZGEQLF. 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( L - 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 ZQLT01( M, N, A, AF, Q, L, 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, * ), L( LDA, * ), 140 $ Q( 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, ZGEQLF, ZHERK, ZLACPY, ZLASET, ZUNGQL 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 = 'ZGEQLF' 183 CALL ZGEQLF( 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 IF( M.GE.N ) THEN 189 IF( N.LT.M .AND. N.GT.0 ) 190 $ CALL ZLACPY( 'Full', M-N, N, AF, LDA, Q( 1, M-N+1 ), LDA ) 191 IF( N.GT.1 ) 192 $ CALL ZLACPY( 'Upper', N-1, N-1, AF( M-N+1, 2 ), LDA, 193 $ Q( M-N+1, M-N+2 ), LDA ) 194 ELSE 195 IF( M.GT.1 ) 196 $ CALL ZLACPY( 'Upper', M-1, M-1, AF( 1, N-M+2 ), LDA, 197 $ Q( 1, 2 ), LDA ) 198 END IF 199* 200* Generate the m-by-m matrix Q 201* 202 SRNAMT = 'ZUNGQL' 203 CALL ZUNGQL( M, M, MINMN, Q, LDA, TAU, WORK, LWORK, INFO ) 204* 205* Copy L 206* 207 CALL ZLASET( 'Full', M, N, DCMPLX( ZERO ), DCMPLX( ZERO ), L, 208 $ LDA ) 209 IF( M.GE.N ) THEN 210 IF( N.GT.0 ) 211 $ CALL ZLACPY( 'Lower', N, N, AF( M-N+1, 1 ), LDA, 212 $ L( M-N+1, 1 ), LDA ) 213 ELSE 214 IF( N.GT.M .AND. M.GT.0 ) 215 $ CALL ZLACPY( 'Full', M, N-M, AF, LDA, L, LDA ) 216 IF( M.GT.0 ) 217 $ CALL ZLACPY( 'Lower', M, M, AF( 1, N-M+1 ), LDA, 218 $ L( 1, N-M+1 ), LDA ) 219 END IF 220* 221* Compute L - Q'*A 222* 223 CALL ZGEMM( 'Conjugate transpose', 'No transpose', M, N, M, 224 $ DCMPLX( -ONE ), Q, LDA, A, LDA, DCMPLX( ONE ), L, 225 $ LDA ) 226* 227* Compute norm( L - Q'*A ) / ( M * norm(A) * EPS ) . 228* 229 ANORM = ZLANGE( '1', M, N, A, LDA, RWORK ) 230 RESID = ZLANGE( '1', M, N, L, LDA, RWORK ) 231 IF( ANORM.GT.ZERO ) THEN 232 RESULT( 1 ) = ( ( RESID / DBLE( MAX( 1, M ) ) ) / ANORM ) / EPS 233 ELSE 234 RESULT( 1 ) = ZERO 235 END IF 236* 237* Compute I - Q'*Q 238* 239 CALL ZLASET( 'Full', M, M, DCMPLX( ZERO ), DCMPLX( ONE ), L, LDA ) 240 CALL ZHERK( 'Upper', 'Conjugate transpose', M, M, -ONE, Q, LDA, 241 $ ONE, L, LDA ) 242* 243* Compute norm( I - Q'*Q ) / ( M * EPS ) . 244* 245 RESID = ZLANSY( '1', 'Upper', M, L, LDA, RWORK ) 246* 247 RESULT( 2 ) = ( RESID / DBLE( MAX( 1, M ) ) ) / EPS 248* 249 RETURN 250* 251* End of ZQLT01 252* 253 END 254