numeric-linalg
Educational material on the SciPy implementation of numerical linear algebra algorithms
| Name | Size | Mode | |
| .. | |||
| lapack/SRC/cunbdb5.f | 8117B | -rw-r--r-- |
001 002 003 004 005 006 007 008 009 010 011 012 013 014 015 016 017 018 019 020 021 022 023 024 025 026 027 028 029 030 031 032 033 034 035 036 037 038 039 040 041 042 043 044 045 046 047 048 049 050 051 052 053 054 055 056 057 058 059 060 061 062 063 064 065 066 067 068 069 070 071 072 073 074 075 076 077 078 079 080 081 082 083 084 085 086 087 088 089 090 091 092 093 094 095 096 097 098 099 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292
*> \brief \b CUNBDB5 * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download CUNBDB5 + dependencies *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cunbdb5.f"> *> [TGZ]</a> *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cunbdb5.f"> *> [ZIP]</a> *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cunbdb5.f"> *> [TXT]</a> *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE CUNBDB5( M1, M2, N, X1, INCX1, X2, INCX2, Q1, LDQ1, Q2, * LDQ2, WORK, LWORK, INFO ) * * .. Scalar Arguments .. * INTEGER INCX1, INCX2, INFO, LDQ1, LDQ2, LWORK, M1, M2, * $ N * .. * .. Array Arguments .. * COMPLEX Q1(LDQ1,*), Q2(LDQ2,*), WORK(*), X1(*), X2(*) * .. * * *> \par Purpose: * ============= *> *>\verbatim *> *> CUNBDB5 orthogonalizes the column vector *> X = [ X1 ] *> [ X2 ] *> with respect to the columns of *> Q = [ Q1 ] . *> [ Q2 ] *> The columns of Q must be orthonormal. *> *> If the projection is zero according to Kahan's "twice is enough" *> criterion, then some other vector from the orthogonal complement *> is returned. This vector is chosen in an arbitrary but deterministic *> way. *> *>\endverbatim * * Arguments: * ========== * *> \param[in] M1 *> \verbatim *> M1 is INTEGER *> The dimension of X1 and the number of rows in Q1. 0 <= M1. *> \endverbatim *> *> \param[in] M2 *> \verbatim *> M2 is INTEGER *> The dimension of X2 and the number of rows in Q2. 0 <= M2. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The number of columns in Q1 and Q2. 0 <= N. *> \endverbatim *> *> \param[in,out] X1 *> \verbatim *> X1 is COMPLEX array, dimension (M1) *> On entry, the top part of the vector to be orthogonalized. *> On exit, the top part of the projected vector. *> \endverbatim *> *> \param[in] INCX1 *> \verbatim *> INCX1 is INTEGER *> Increment for entries of X1. *> \endverbatim *> *> \param[in,out] X2 *> \verbatim *> X2 is COMPLEX array, dimension (M2) *> On entry, the bottom part of the vector to be *> orthogonalized. On exit, the bottom part of the projected *> vector. *> \endverbatim *> *> \param[in] INCX2 *> \verbatim *> INCX2 is INTEGER *> Increment for entries of X2. *> \endverbatim *> *> \param[in] Q1 *> \verbatim *> Q1 is COMPLEX array, dimension (LDQ1, N) *> The top part of the orthonormal basis matrix. *> \endverbatim *> *> \param[in] LDQ1 *> \verbatim *> LDQ1 is INTEGER *> The leading dimension of Q1. LDQ1 >= M1. *> \endverbatim *> *> \param[in] Q2 *> \verbatim *> Q2 is COMPLEX array, dimension (LDQ2, N) *> The bottom part of the orthonormal basis matrix. *> \endverbatim *> *> \param[in] LDQ2 *> \verbatim *> LDQ2 is INTEGER *> The leading dimension of Q2. LDQ2 >= M2. *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is COMPLEX array, dimension (LWORK) *> \endverbatim *> *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER *> The dimension of the array WORK. LWORK >= N. *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit. *> < 0: if INFO = -i, the i-th argument had an illegal value. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \ingroup unbdb5 * * ===================================================================== SUBROUTINE CUNBDB5( M1, M2, N, X1, INCX1, X2, INCX2, Q1, LDQ1, $ Q2, $ LDQ2, WORK, LWORK, INFO ) * * -- LAPACK computational routine -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * * .. Scalar Arguments .. INTEGER INCX1, INCX2, INFO, LDQ1, LDQ2, LWORK, M1, M2, $ N * .. * .. Array Arguments .. COMPLEX Q1(LDQ1,*), Q2(LDQ2,*), WORK(*), X1(*), X2(*) * .. * * ===================================================================== * * .. Parameters .. REAL REALZERO PARAMETER ( REALZERO = 0.0E0 ) COMPLEX ONE, ZERO PARAMETER ( ONE = (1.0E0,0.0E0), ZERO = (0.0E0,0.0E0) ) * .. * .. Local Scalars .. INTEGER CHILDINFO, I, J REAL EPS, NORM, SCL, SSQ * .. * .. External Subroutines .. EXTERNAL CLASSQ, CUNBDB6, CSCAL, XERBLA * .. * .. External Functions .. REAL SLAMCH, SCNRM2 EXTERNAL SLAMCH, SCNRM2 * .. * .. Intrinsic Function .. INTRINSIC MAX * .. * .. Executable Statements .. * * Test input arguments * INFO = 0 IF( M1 .LT. 0 ) THEN INFO = -1 ELSE IF( M2 .LT. 0 ) THEN INFO = -2 ELSE IF( N .LT. 0 ) THEN INFO = -3 ELSE IF( INCX1 .LT. 1 ) THEN INFO = -5 ELSE IF( INCX2 .LT. 1 ) THEN INFO = -7 ELSE IF( LDQ1 .LT. MAX( 1, M1 ) ) THEN INFO = -9 ELSE IF( LDQ2 .LT. MAX( 1, M2 ) ) THEN INFO = -11 ELSE IF( LWORK .LT. N ) THEN INFO = -13 END IF * IF( INFO .NE. 0 ) THEN CALL XERBLA( 'CUNBDB5', -INFO ) RETURN END IF * EPS = SLAMCH( 'Precision' ) * * Project X onto the orthogonal complement of Q if X is nonzero * SCL = REALZERO SSQ = REALZERO CALL CLASSQ( M1, X1, INCX1, SCL, SSQ ) CALL CLASSQ( M2, X2, INCX2, SCL, SSQ ) NORM = SCL * SQRT( SSQ ) * IF( NORM .GT. REAL( N ) * EPS ) THEN * Scale vector to unit norm to avoid problems in the caller code. * Computing the reciprocal is undesirable but * * xLASCL cannot be used because of the vector increments and * * the round-off error has a negligible impact on * orthogonalization. CALL CSCAL( M1, ONE / NORM, X1, INCX1 ) CALL CSCAL( M2, ONE / NORM, X2, INCX2 ) CALL CUNBDB6( M1, M2, N, X1, INCX1, X2, INCX2, Q1, LDQ1, Q2, $ LDQ2, WORK, LWORK, CHILDINFO ) * * If the projection is nonzero, then return * IF( SCNRM2(M1,X1,INCX1) .NE. REALZERO $ .OR. SCNRM2(M2,X2,INCX2) .NE. REALZERO ) THEN RETURN END IF END IF * * Project each standard basis vector e_1,...,e_M1 in turn, stopping * when a nonzero projection is found * DO I = 1, M1 DO J = 1, M1 X1(J) = ZERO END DO X1(I) = ONE DO J = 1, M2 X2(J) = ZERO END DO CALL CUNBDB6( M1, M2, N, X1, INCX1, X2, INCX2, Q1, LDQ1, Q2, $ LDQ2, WORK, LWORK, CHILDINFO ) IF( SCNRM2(M1,X1,INCX1) .NE. REALZERO $ .OR. SCNRM2(M2,X2,INCX2) .NE. REALZERO ) THEN RETURN END IF END DO * * Project each standard basis vector e_(M1+1),...,e_(M1+M2) in turn, * stopping when a nonzero projection is found * DO I = 1, M2 DO J = 1, M1 X1(J) = ZERO END DO DO J = 1, M2 X2(J) = ZERO END DO X2(I) = ONE CALL CUNBDB6( M1, M2, N, X1, INCX1, X2, INCX2, Q1, LDQ1, Q2, $ LDQ2, WORK, LWORK, CHILDINFO ) IF( SCNRM2(M1,X1,INCX1) .NE. REALZERO $ .OR. SCNRM2(M2,X2,INCX2) .NE. REALZERO ) THEN RETURN END IF END DO * RETURN * * End of CUNBDB5 * END