1*> \brief \b ZQRT12 2* 3* =========== DOCUMENTATION =========== 4* 5* Online html documentation available at 6* http://www.netlib.org/lapack/explore-html/ 7* 8* Definition: 9* =========== 10* 11* DOUBLE PRECISION FUNCTION ZQRT12( M, N, A, LDA, S, WORK, LWORK, 12* RWORK ) 13* 14* .. Scalar Arguments .. 15* INTEGER LDA, LWORK, M, N 16* .. 17* .. Array Arguments .. 18* DOUBLE PRECISION RWORK( * ), S( * ) 19* COMPLEX*16 A( LDA, * ), WORK( LWORK ) 20* .. 21* 22* 23*> \par Purpose: 24* ============= 25*> 26*> \verbatim 27*> 28*> ZQRT12 computes the singular values `svlues' of the upper trapezoid 29*> of A(1:M,1:N) and returns the ratio 30*> 31*> || s - svlues||/(||svlues||*eps*max(M,N)) 32*> \endverbatim 33* 34* Arguments: 35* ========== 36* 37*> \param[in] M 38*> \verbatim 39*> M is INTEGER 40*> The number of rows of the matrix A. 41*> \endverbatim 42*> 43*> \param[in] N 44*> \verbatim 45*> N is INTEGER 46*> The number of columns of the matrix A. 47*> \endverbatim 48*> 49*> \param[in] A 50*> \verbatim 51*> A is COMPLEX*16 array, dimension (LDA,N) 52*> The M-by-N matrix A. Only the upper trapezoid is referenced. 53*> \endverbatim 54*> 55*> \param[in] LDA 56*> \verbatim 57*> LDA is INTEGER 58*> The leading dimension of the array A. 59*> \endverbatim 60*> 61*> \param[in] S 62*> \verbatim 63*> S is DOUBLE PRECISION array, dimension (min(M,N)) 64*> The singular values of the matrix A. 65*> \endverbatim 66*> 67*> \param[out] WORK 68*> \verbatim 69*> WORK is COMPLEX*16 array, dimension (LWORK) 70*> \endverbatim 71*> 72*> \param[in] LWORK 73*> \verbatim 74*> LWORK is INTEGER 75*> The length of the array WORK. LWORK >= M*N + 2*min(M,N) + 76*> max(M,N). 77*> \endverbatim 78*> 79*> \param[out] RWORK 80*> \verbatim 81*> RWORK is DOUBLE PRECISION array, dimension (2*min(M,N)) 82*> \endverbatim 83* 84* Authors: 85* ======== 86* 87*> \author Univ. of Tennessee 88*> \author Univ. of California Berkeley 89*> \author Univ. of Colorado Denver 90*> \author NAG Ltd. 91* 92*> \date November 2011 93* 94*> \ingroup complex16_lin 95* 96* ===================================================================== 97 DOUBLE PRECISION FUNCTION ZQRT12( M, N, A, LDA, S, WORK, LWORK, 98 $ RWORK ) 99* 100* -- LAPACK test routine (version 3.4.0) -- 101* -- LAPACK is a software package provided by Univ. of Tennessee, -- 102* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 103* November 2011 104* 105* .. Scalar Arguments .. 106 INTEGER LDA, LWORK, M, N 107* .. 108* .. Array Arguments .. 109 DOUBLE PRECISION RWORK( * ), S( * ) 110 COMPLEX*16 A( LDA, * ), WORK( LWORK ) 111* .. 112* 113* ===================================================================== 114* 115* .. Parameters .. 116 DOUBLE PRECISION ZERO, ONE 117 PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 ) 118* .. 119* .. Local Scalars .. 120 INTEGER I, INFO, ISCL, J, MN 121 DOUBLE PRECISION ANRM, BIGNUM, NRMSVL, SMLNUM 122* .. 123* .. Local Arrays .. 124 DOUBLE PRECISION DUMMY( 1 ) 125* .. 126* .. External Functions .. 127 DOUBLE PRECISION DASUM, DLAMCH, DNRM2, ZLANGE 128 EXTERNAL DASUM, DLAMCH, DNRM2, ZLANGE 129* .. 130* .. External Subroutines .. 131 EXTERNAL DAXPY, DBDSQR, DLABAD, DLASCL, XERBLA, ZGEBD2, 132 $ ZLASCL, ZLASET 133* .. 134* .. Intrinsic Functions .. 135 INTRINSIC DBLE, DCMPLX, MAX, MIN 136* .. 137* .. Executable Statements .. 138* 139 ZQRT12 = ZERO 140* 141* Test that enough workspace is supplied 142* 143 IF( LWORK.LT.M*N+2*MIN( M, N )+MAX( M, N ) ) THEN 144 CALL XERBLA( 'ZQRT12', 7 ) 145 RETURN 146 END IF 147* 148* Quick return if possible 149* 150 MN = MIN( M, N ) 151 IF( MN.LE.ZERO ) 152 $ RETURN 153* 154 NRMSVL = DNRM2( MN, S, 1 ) 155* 156* Copy upper triangle of A into work 157* 158 CALL ZLASET( 'Full', M, N, DCMPLX( ZERO ), DCMPLX( ZERO ), WORK, 159 $ M ) 160 DO 20 J = 1, N 161 DO 10 I = 1, MIN( J, M ) 162 WORK( ( J-1 )*M+I ) = A( I, J ) 163 10 CONTINUE 164 20 CONTINUE 165* 166* Get machine parameters 167* 168 SMLNUM = DLAMCH( 'S' ) / DLAMCH( 'P' ) 169 BIGNUM = ONE / SMLNUM 170 CALL DLABAD( SMLNUM, BIGNUM ) 171* 172* Scale work if max entry outside range [SMLNUM,BIGNUM] 173* 174 ANRM = ZLANGE( 'M', M, N, WORK, M, DUMMY ) 175 ISCL = 0 176 IF( ANRM.GT.ZERO .AND. ANRM.LT.SMLNUM ) THEN 177* 178* Scale matrix norm up to SMLNUM 179* 180 CALL ZLASCL( 'G', 0, 0, ANRM, SMLNUM, M, N, WORK, M, INFO ) 181 ISCL = 1 182 ELSE IF( ANRM.GT.BIGNUM ) THEN 183* 184* Scale matrix norm down to BIGNUM 185* 186 CALL ZLASCL( 'G', 0, 0, ANRM, BIGNUM, M, N, WORK, M, INFO ) 187 ISCL = 1 188 END IF 189* 190 IF( ANRM.NE.ZERO ) THEN 191* 192* Compute SVD of work 193* 194 CALL ZGEBD2( M, N, WORK, M, RWORK( 1 ), RWORK( MN+1 ), 195 $ WORK( M*N+1 ), WORK( M*N+MN+1 ), 196 $ WORK( M*N+2*MN+1 ), INFO ) 197 CALL DBDSQR( 'Upper', MN, 0, 0, 0, RWORK( 1 ), RWORK( MN+1 ), 198 $ DUMMY, MN, DUMMY, 1, DUMMY, MN, RWORK( 2*MN+1 ), 199 $ INFO ) 200* 201 IF( ISCL.EQ.1 ) THEN 202 IF( ANRM.GT.BIGNUM ) THEN 203 CALL DLASCL( 'G', 0, 0, BIGNUM, ANRM, MN, 1, RWORK( 1 ), 204 $ MN, INFO ) 205 END IF 206 IF( ANRM.LT.SMLNUM ) THEN 207 CALL DLASCL( 'G', 0, 0, SMLNUM, ANRM, MN, 1, RWORK( 1 ), 208 $ MN, INFO ) 209 END IF 210 END IF 211* 212 ELSE 213* 214 DO 30 I = 1, MN 215 RWORK( I ) = ZERO 216 30 CONTINUE 217 END IF 218* 219* Compare s and singular values of work 220* 221 CALL DAXPY( MN, -ONE, S, 1, RWORK( 1 ), 1 ) 222 ZQRT12 = DASUM( MN, RWORK( 1 ), 1 ) / 223 $ ( DLAMCH( 'Epsilon' )*DBLE( MAX( M, N ) ) ) 224 IF( NRMSVL.NE.ZERO ) 225 $ ZQRT12 = ZQRT12 / NRMSVL 226* 227 RETURN 228* 229* End of ZQRT12 230* 231 END 232