1*> \brief \b CQRT12 2* 3* =========== DOCUMENTATION =========== 4* 5* Online html documentation available at 6* http://www.netlib.org/lapack/explore-html/ 7* 8* Definition: 9* =========== 10* 11* REAL FUNCTION CQRT12( M, N, A, LDA, S, WORK, LWORK, 12* RWORK ) 13* 14* .. Scalar Arguments .. 15* INTEGER LDA, LWORK, M, N 16* .. 17* .. Array Arguments .. 18* REAL RWORK( * ), S( * ) 19* COMPLEX A( LDA, * ), WORK( LWORK ) 20* .. 21* 22* 23*> \par Purpose: 24* ============= 25*> 26*> \verbatim 27*> 28*> CQRT12 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 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 REAL 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 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 REAL array, dimension (4*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 complex_lin 95* 96* ===================================================================== 97 REAL FUNCTION CQRT12( 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 REAL RWORK( * ), S( * ) 110 COMPLEX A( LDA, * ), WORK( LWORK ) 111* .. 112* 113* ===================================================================== 114* 115* .. Parameters .. 116 REAL ZERO, ONE 117 PARAMETER ( ZERO = 0.0E0, ONE = 1.0E0 ) 118* .. 119* .. Local Scalars .. 120 INTEGER I, INFO, ISCL, J, MN 121 REAL ANRM, BIGNUM, NRMSVL, SMLNUM 122* .. 123* .. Local Arrays .. 124 REAL DUMMY( 1 ) 125* .. 126* .. External Functions .. 127 REAL CLANGE, SASUM, SLAMCH, SNRM2 128 EXTERNAL CLANGE, SASUM, SLAMCH, SNRM2 129* .. 130* .. External Subroutines .. 131 EXTERNAL CGEBD2, CLASCL, CLASET, SAXPY, SBDSQR, SLABAD, 132 $ SLASCL, XERBLA 133* .. 134* .. Intrinsic Functions .. 135 INTRINSIC CMPLX, MAX, MIN, REAL 136* .. 137* .. Executable Statements .. 138* 139 CQRT12 = 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( 'CQRT12', 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 = SNRM2( MN, S, 1 ) 155* 156* Copy upper triangle of A into work 157* 158 CALL CLASET( 'Full', M, N, CMPLX( ZERO ), CMPLX( ZERO ), WORK, M ) 159 DO 20 J = 1, N 160 DO 10 I = 1, MIN( J, M ) 161 WORK( ( J-1 )*M+I ) = A( I, J ) 162 10 CONTINUE 163 20 CONTINUE 164* 165* Get machine parameters 166* 167 SMLNUM = SLAMCH( 'S' ) / SLAMCH( 'P' ) 168 BIGNUM = ONE / SMLNUM 169 CALL SLABAD( SMLNUM, BIGNUM ) 170* 171* Scale work if max entry outside range [SMLNUM,BIGNUM] 172* 173 ANRM = CLANGE( 'M', M, N, WORK, M, DUMMY ) 174 ISCL = 0 175 IF( ANRM.GT.ZERO .AND. ANRM.LT.SMLNUM ) THEN 176* 177* Scale matrix norm up to SMLNUM 178* 179 CALL CLASCL( 'G', 0, 0, ANRM, SMLNUM, M, N, WORK, M, INFO ) 180 ISCL = 1 181 ELSE IF( ANRM.GT.BIGNUM ) THEN 182* 183* Scale matrix norm down to BIGNUM 184* 185 CALL CLASCL( 'G', 0, 0, ANRM, BIGNUM, M, N, WORK, M, INFO ) 186 ISCL = 1 187 END IF 188* 189 IF( ANRM.NE.ZERO ) THEN 190* 191* Compute SVD of work 192* 193 CALL CGEBD2( M, N, WORK, M, RWORK( 1 ), RWORK( MN+1 ), 194 $ WORK( M*N+1 ), WORK( M*N+MN+1 ), 195 $ WORK( M*N+2*MN+1 ), INFO ) 196 CALL SBDSQR( 'Upper', MN, 0, 0, 0, RWORK( 1 ), RWORK( MN+1 ), 197 $ DUMMY, MN, DUMMY, 1, DUMMY, MN, RWORK( 2*MN+1 ), 198 $ INFO ) 199* 200 IF( ISCL.EQ.1 ) THEN 201 IF( ANRM.GT.BIGNUM ) THEN 202 CALL SLASCL( 'G', 0, 0, BIGNUM, ANRM, MN, 1, RWORK( 1 ), 203 $ MN, INFO ) 204 END IF 205 IF( ANRM.LT.SMLNUM ) THEN 206 CALL SLASCL( 'G', 0, 0, SMLNUM, ANRM, MN, 1, RWORK( 1 ), 207 $ MN, INFO ) 208 END IF 209 END IF 210* 211 ELSE 212* 213 DO 30 I = 1, MN 214 RWORK( I ) = ZERO 215 30 CONTINUE 216 END IF 217* 218* Compare s and singular values of work 219* 220 CALL SAXPY( MN, -ONE, S, 1, RWORK( 1 ), 1 ) 221 CQRT12 = SASUM( MN, RWORK( 1 ), 1 ) / 222 $ ( SLAMCH( 'Epsilon' )*REAL( MAX( M, N ) ) ) 223 IF( NRMSVL.NE.ZERO ) 224 $ CQRT12 = CQRT12 / NRMSVL 225* 226 RETURN 227* 228* End of CQRT12 229* 230 END 231