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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b CQRT15 00002 * 00003 * =========== DOCUMENTATION =========== 00004 * 00005 * Online html documentation available at 00006 * http://www.netlib.org/lapack/explore-html/ 00007 * 00008 * Definition: 00009 * =========== 00010 * 00011 * SUBROUTINE CQRT15( SCALE, RKSEL, M, N, NRHS, A, LDA, B, LDB, S, 00012 * RANK, NORMA, NORMB, ISEED, WORK, LWORK ) 00013 * 00014 * .. Scalar Arguments .. 00015 * INTEGER LDA, LDB, LWORK, M, N, NRHS, RANK, RKSEL, SCALE 00016 * REAL NORMA, NORMB 00017 * .. 00018 * .. Array Arguments .. 00019 * INTEGER ISEED( 4 ) 00020 * REAL S( * ) 00021 * COMPLEX A( LDA, * ), B( LDB, * ), WORK( LWORK ) 00022 * .. 00023 * 00024 * 00025 *> \par Purpose: 00026 * ============= 00027 *> 00028 *> \verbatim 00029 *> 00030 *> CQRT15 generates a matrix with full or deficient rank and of various 00031 *> norms. 00032 *> \endverbatim 00033 * 00034 * Arguments: 00035 * ========== 00036 * 00037 *> \param[in] SCALE 00038 *> \verbatim 00039 *> SCALE is INTEGER 00040 *> SCALE = 1: normally scaled matrix 00041 *> SCALE = 2: matrix scaled up 00042 *> SCALE = 3: matrix scaled down 00043 *> \endverbatim 00044 *> 00045 *> \param[in] RKSEL 00046 *> \verbatim 00047 *> RKSEL is INTEGER 00048 *> RKSEL = 1: full rank matrix 00049 *> RKSEL = 2: rank-deficient matrix 00050 *> \endverbatim 00051 *> 00052 *> \param[in] M 00053 *> \verbatim 00054 *> M is INTEGER 00055 *> The number of rows of the matrix A. 00056 *> \endverbatim 00057 *> 00058 *> \param[in] N 00059 *> \verbatim 00060 *> N is INTEGER 00061 *> The number of columns of A. 00062 *> \endverbatim 00063 *> 00064 *> \param[in] NRHS 00065 *> \verbatim 00066 *> NRHS is INTEGER 00067 *> The number of columns of B. 00068 *> \endverbatim 00069 *> 00070 *> \param[out] A 00071 *> \verbatim 00072 *> A is COMPLEX array, dimension (LDA,N) 00073 *> The M-by-N matrix A. 00074 *> \endverbatim 00075 *> 00076 *> \param[in] LDA 00077 *> \verbatim 00078 *> LDA is INTEGER 00079 *> The leading dimension of the array A. 00080 *> \endverbatim 00081 *> 00082 *> \param[out] B 00083 *> \verbatim 00084 *> B is COMPLEX array, dimension (LDB, NRHS) 00085 *> A matrix that is in the range space of matrix A. 00086 *> \endverbatim 00087 *> 00088 *> \param[in] LDB 00089 *> \verbatim 00090 *> LDB is INTEGER 00091 *> The leading dimension of the array B. 00092 *> \endverbatim 00093 *> 00094 *> \param[out] S 00095 *> \verbatim 00096 *> S is REAL array, dimension MIN(M,N) 00097 *> Singular values of A. 00098 *> \endverbatim 00099 *> 00100 *> \param[out] RANK 00101 *> \verbatim 00102 *> RANK is INTEGER 00103 *> number of nonzero singular values of A. 00104 *> \endverbatim 00105 *> 00106 *> \param[out] NORMA 00107 *> \verbatim 00108 *> NORMA is REAL 00109 *> one-norm norm of A. 00110 *> \endverbatim 00111 *> 00112 *> \param[out] NORMB 00113 *> \verbatim 00114 *> NORMB is REAL 00115 *> one-norm norm of B. 00116 *> \endverbatim 00117 *> 00118 *> \param[in,out] ISEED 00119 *> \verbatim 00120 *> ISEED is integer array, dimension (4) 00121 *> seed for random number generator. 00122 *> \endverbatim 00123 *> 00124 *> \param[out] WORK 00125 *> \verbatim 00126 *> WORK is COMPLEX array, dimension (LWORK) 00127 *> \endverbatim 00128 *> 00129 *> \param[in] LWORK 00130 *> \verbatim 00131 *> LWORK is INTEGER 00132 *> length of work space required. 00133 *> LWORK >= MAX(M+MIN(M,N),NRHS*MIN(M,N),2*N+M) 00134 *> \endverbatim 00135 * 00136 * Authors: 00137 * ======== 00138 * 00139 *> \author Univ. of Tennessee 00140 *> \author Univ. of California Berkeley 00141 *> \author Univ. of Colorado Denver 00142 *> \author NAG Ltd. 00143 * 00144 *> \date November 2011 00145 * 00146 *> \ingroup complex_lin 00147 * 00148 * ===================================================================== 00149 SUBROUTINE CQRT15( SCALE, RKSEL, M, N, NRHS, A, LDA, B, LDB, S, 00150 $ RANK, NORMA, NORMB, ISEED, WORK, LWORK ) 00151 * 00152 * -- LAPACK test routine (version 3.4.0) -- 00153 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00154 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00155 * November 2011 00156 * 00157 * .. Scalar Arguments .. 00158 INTEGER LDA, LDB, LWORK, M, N, NRHS, RANK, RKSEL, SCALE 00159 REAL NORMA, NORMB 00160 * .. 00161 * .. Array Arguments .. 00162 INTEGER ISEED( 4 ) 00163 REAL S( * ) 00164 COMPLEX A( LDA, * ), B( LDB, * ), WORK( LWORK ) 00165 * .. 00166 * 00167 * ===================================================================== 00168 * 00169 * .. Parameters .. 00170 REAL ZERO, ONE, TWO, SVMIN 00171 PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0, TWO = 2.0E+0, 00172 $ SVMIN = 0.1E+0 ) 00173 COMPLEX CZERO, CONE 00174 PARAMETER ( CZERO = ( 0.0E+0, 0.0E+0 ), 00175 $ CONE = ( 1.0E+0, 0.0E+0 ) ) 00176 * .. 00177 * .. Local Scalars .. 00178 INTEGER INFO, J, MN 00179 REAL BIGNUM, EPS, SMLNUM, TEMP 00180 * .. 00181 * .. Local Arrays .. 00182 REAL DUMMY( 1 ) 00183 * .. 00184 * .. External Functions .. 00185 REAL CLANGE, SASUM, SCNRM2, SLAMCH, SLARND 00186 EXTERNAL CLANGE, SASUM, SCNRM2, SLAMCH, SLARND 00187 * .. 00188 * .. External Subroutines .. 00189 EXTERNAL CGEMM, CLARF, CLARNV, CLAROR, CLASCL, CLASET, 00190 $ CSSCAL, SLABAD, SLAORD, SLASCL, XERBLA 00191 * .. 00192 * .. Intrinsic Functions .. 00193 INTRINSIC ABS, CMPLX, MAX, MIN 00194 * .. 00195 * .. Executable Statements .. 00196 * 00197 MN = MIN( M, N ) 00198 IF( LWORK.LT.MAX( M+MN, MN*NRHS, 2*N+M ) ) THEN 00199 CALL XERBLA( 'CQRT15', 16 ) 00200 RETURN 00201 END IF 00202 * 00203 SMLNUM = SLAMCH( 'Safe minimum' ) 00204 BIGNUM = ONE / SMLNUM 00205 CALL SLABAD( SMLNUM, BIGNUM ) 00206 EPS = SLAMCH( 'Epsilon' ) 00207 SMLNUM = ( SMLNUM / EPS ) / EPS 00208 BIGNUM = ONE / SMLNUM 00209 * 00210 * Determine rank and (unscaled) singular values 00211 * 00212 IF( RKSEL.EQ.1 ) THEN 00213 RANK = MN 00214 ELSE IF( RKSEL.EQ.2 ) THEN 00215 RANK = ( 3*MN ) / 4 00216 DO 10 J = RANK + 1, MN 00217 S( J ) = ZERO 00218 10 CONTINUE 00219 ELSE 00220 CALL XERBLA( 'CQRT15', 2 ) 00221 END IF 00222 * 00223 IF( RANK.GT.0 ) THEN 00224 * 00225 * Nontrivial case 00226 * 00227 S( 1 ) = ONE 00228 DO 30 J = 2, RANK 00229 20 CONTINUE 00230 TEMP = SLARND( 1, ISEED ) 00231 IF( TEMP.GT.SVMIN ) THEN 00232 S( J ) = ABS( TEMP ) 00233 ELSE 00234 GO TO 20 00235 END IF 00236 30 CONTINUE 00237 CALL SLAORD( 'Decreasing', RANK, S, 1 ) 00238 * 00239 * Generate 'rank' columns of a random orthogonal matrix in A 00240 * 00241 CALL CLARNV( 2, ISEED, M, WORK ) 00242 CALL CSSCAL( M, ONE / SCNRM2( M, WORK, 1 ), WORK, 1 ) 00243 CALL CLASET( 'Full', M, RANK, CZERO, CONE, A, LDA ) 00244 CALL CLARF( 'Left', M, RANK, WORK, 1, CMPLX( TWO ), A, LDA, 00245 $ WORK( M+1 ) ) 00246 * 00247 * workspace used: m+mn 00248 * 00249 * Generate consistent rhs in the range space of A 00250 * 00251 CALL CLARNV( 2, ISEED, RANK*NRHS, WORK ) 00252 CALL CGEMM( 'No transpose', 'No transpose', M, NRHS, RANK, 00253 $ CONE, A, LDA, WORK, RANK, CZERO, B, LDB ) 00254 * 00255 * work space used: <= mn *nrhs 00256 * 00257 * generate (unscaled) matrix A 00258 * 00259 DO 40 J = 1, RANK 00260 CALL CSSCAL( M, S( J ), A( 1, J ), 1 ) 00261 40 CONTINUE 00262 IF( RANK.LT.N ) 00263 $ CALL CLASET( 'Full', M, N-RANK, CZERO, CZERO, 00264 $ A( 1, RANK+1 ), LDA ) 00265 CALL CLAROR( 'Right', 'No initialization', M, N, A, LDA, ISEED, 00266 $ WORK, INFO ) 00267 * 00268 ELSE 00269 * 00270 * work space used 2*n+m 00271 * 00272 * Generate null matrix and rhs 00273 * 00274 DO 50 J = 1, MN 00275 S( J ) = ZERO 00276 50 CONTINUE 00277 CALL CLASET( 'Full', M, N, CZERO, CZERO, A, LDA ) 00278 CALL CLASET( 'Full', M, NRHS, CZERO, CZERO, B, LDB ) 00279 * 00280 END IF 00281 * 00282 * Scale the matrix 00283 * 00284 IF( SCALE.NE.1 ) THEN 00285 NORMA = CLANGE( 'Max', M, N, A, LDA, DUMMY ) 00286 IF( NORMA.NE.ZERO ) THEN 00287 IF( SCALE.EQ.2 ) THEN 00288 * 00289 * matrix scaled up 00290 * 00291 CALL CLASCL( 'General', 0, 0, NORMA, BIGNUM, M, N, A, 00292 $ LDA, INFO ) 00293 CALL SLASCL( 'General', 0, 0, NORMA, BIGNUM, MN, 1, S, 00294 $ MN, INFO ) 00295 CALL CLASCL( 'General', 0, 0, NORMA, BIGNUM, M, NRHS, B, 00296 $ LDB, INFO ) 00297 ELSE IF( SCALE.EQ.3 ) THEN 00298 * 00299 * matrix scaled down 00300 * 00301 CALL CLASCL( 'General', 0, 0, NORMA, SMLNUM, M, N, A, 00302 $ LDA, INFO ) 00303 CALL SLASCL( 'General', 0, 0, NORMA, SMLNUM, MN, 1, S, 00304 $ MN, INFO ) 00305 CALL CLASCL( 'General', 0, 0, NORMA, SMLNUM, M, NRHS, B, 00306 $ LDB, INFO ) 00307 ELSE 00308 CALL XERBLA( 'CQRT15', 1 ) 00309 RETURN 00310 END IF 00311 END IF 00312 END IF 00313 * 00314 NORMA = SASUM( MN, S, 1 ) 00315 NORMB = CLANGE( 'One-norm', M, NRHS, B, LDB, DUMMY ) 00316 * 00317 RETURN 00318 * 00319 * End of CQRT15 00320 * 00321 END