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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b CUNMLQ 00002 * 00003 * =========== DOCUMENTATION =========== 00004 * 00005 * Online html documentation available at 00006 * http://www.netlib.org/lapack/explore-html/ 00007 * 00008 *> \htmlonly 00009 *> Download CUNMLQ + dependencies 00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cunmlq.f"> 00011 *> [TGZ]</a> 00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cunmlq.f"> 00013 *> [ZIP]</a> 00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cunmlq.f"> 00015 *> [TXT]</a> 00016 *> \endhtmlonly 00017 * 00018 * Definition: 00019 * =========== 00020 * 00021 * SUBROUTINE CUNMLQ( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, 00022 * WORK, LWORK, INFO ) 00023 * 00024 * .. Scalar Arguments .. 00025 * CHARACTER SIDE, TRANS 00026 * INTEGER INFO, K, LDA, LDC, LWORK, M, N 00027 * .. 00028 * .. Array Arguments .. 00029 * COMPLEX A( LDA, * ), C( LDC, * ), TAU( * ), 00030 * $ WORK( * ) 00031 * .. 00032 * 00033 * 00034 *> \par Purpose: 00035 * ============= 00036 *> 00037 *> \verbatim 00038 *> 00039 *> CUNMLQ overwrites the general complex M-by-N matrix C with 00040 *> 00041 *> SIDE = 'L' SIDE = 'R' 00042 *> TRANS = 'N': Q * C C * Q 00043 *> TRANS = 'C': Q**H * C C * Q**H 00044 *> 00045 *> where Q is a complex unitary matrix defined as the product of k 00046 *> elementary reflectors 00047 *> 00048 *> Q = H(k)**H . . . H(2)**H H(1)**H 00049 *> 00050 *> as returned by CGELQF. Q is of order M if SIDE = 'L' and of order N 00051 *> if SIDE = 'R'. 00052 *> \endverbatim 00053 * 00054 * Arguments: 00055 * ========== 00056 * 00057 *> \param[in] SIDE 00058 *> \verbatim 00059 *> SIDE is CHARACTER*1 00060 *> = 'L': apply Q or Q**H from the Left; 00061 *> = 'R': apply Q or Q**H from the Right. 00062 *> \endverbatim 00063 *> 00064 *> \param[in] TRANS 00065 *> \verbatim 00066 *> TRANS is CHARACTER*1 00067 *> = 'N': No transpose, apply Q; 00068 *> = 'C': Conjugate transpose, apply Q**H. 00069 *> \endverbatim 00070 *> 00071 *> \param[in] M 00072 *> \verbatim 00073 *> M is INTEGER 00074 *> The number of rows of the matrix C. M >= 0. 00075 *> \endverbatim 00076 *> 00077 *> \param[in] N 00078 *> \verbatim 00079 *> N is INTEGER 00080 *> The number of columns of the matrix C. N >= 0. 00081 *> \endverbatim 00082 *> 00083 *> \param[in] K 00084 *> \verbatim 00085 *> K is INTEGER 00086 *> The number of elementary reflectors whose product defines 00087 *> the matrix Q. 00088 *> If SIDE = 'L', M >= K >= 0; 00089 *> if SIDE = 'R', N >= K >= 0. 00090 *> \endverbatim 00091 *> 00092 *> \param[in] A 00093 *> \verbatim 00094 *> A is COMPLEX array, dimension 00095 *> (LDA,M) if SIDE = 'L', 00096 *> (LDA,N) if SIDE = 'R' 00097 *> The i-th row must contain the vector which defines the 00098 *> elementary reflector H(i), for i = 1,2,...,k, as returned by 00099 *> CGELQF in the first k rows of its array argument A. 00100 *> \endverbatim 00101 *> 00102 *> \param[in] LDA 00103 *> \verbatim 00104 *> LDA is INTEGER 00105 *> The leading dimension of the array A. LDA >= max(1,K). 00106 *> \endverbatim 00107 *> 00108 *> \param[in] TAU 00109 *> \verbatim 00110 *> TAU is COMPLEX array, dimension (K) 00111 *> TAU(i) must contain the scalar factor of the elementary 00112 *> reflector H(i), as returned by CGELQF. 00113 *> \endverbatim 00114 *> 00115 *> \param[in,out] C 00116 *> \verbatim 00117 *> C is COMPLEX array, dimension (LDC,N) 00118 *> On entry, the M-by-N matrix C. 00119 *> On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q. 00120 *> \endverbatim 00121 *> 00122 *> \param[in] LDC 00123 *> \verbatim 00124 *> LDC is INTEGER 00125 *> The leading dimension of the array C. LDC >= max(1,M). 00126 *> \endverbatim 00127 *> 00128 *> \param[out] WORK 00129 *> \verbatim 00130 *> WORK is COMPLEX array, dimension (MAX(1,LWORK)) 00131 *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. 00132 *> \endverbatim 00133 *> 00134 *> \param[in] LWORK 00135 *> \verbatim 00136 *> LWORK is INTEGER 00137 *> The dimension of the array WORK. 00138 *> If SIDE = 'L', LWORK >= max(1,N); 00139 *> if SIDE = 'R', LWORK >= max(1,M). 00140 *> For optimum performance LWORK >= N*NB if SIDE 'L', and 00141 *> LWORK >= M*NB if SIDE = 'R', where NB is the optimal 00142 *> blocksize. 00143 *> 00144 *> If LWORK = -1, then a workspace query is assumed; the routine 00145 *> only calculates the optimal size of the WORK array, returns 00146 *> this value as the first entry of the WORK array, and no error 00147 *> message related to LWORK is issued by XERBLA. 00148 *> \endverbatim 00149 *> 00150 *> \param[out] INFO 00151 *> \verbatim 00152 *> INFO is INTEGER 00153 *> = 0: successful exit 00154 *> < 0: if INFO = -i, the i-th argument had an illegal value 00155 *> \endverbatim 00156 * 00157 * Authors: 00158 * ======== 00159 * 00160 *> \author Univ. of Tennessee 00161 *> \author Univ. of California Berkeley 00162 *> \author Univ. of Colorado Denver 00163 *> \author NAG Ltd. 00164 * 00165 *> \date November 2011 00166 * 00167 *> \ingroup complexOTHERcomputational 00168 * 00169 * ===================================================================== 00170 SUBROUTINE CUNMLQ( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, 00171 $ WORK, LWORK, INFO ) 00172 * 00173 * -- LAPACK computational routine (version 3.4.0) -- 00174 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00175 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00176 * November 2011 00177 * 00178 * .. Scalar Arguments .. 00179 CHARACTER SIDE, TRANS 00180 INTEGER INFO, K, LDA, LDC, LWORK, M, N 00181 * .. 00182 * .. Array Arguments .. 00183 COMPLEX A( LDA, * ), C( LDC, * ), TAU( * ), 00184 $ WORK( * ) 00185 * .. 00186 * 00187 * ===================================================================== 00188 * 00189 * .. Parameters .. 00190 INTEGER NBMAX, LDT 00191 PARAMETER ( NBMAX = 64, LDT = NBMAX+1 ) 00192 * .. 00193 * .. Local Scalars .. 00194 LOGICAL LEFT, LQUERY, NOTRAN 00195 CHARACTER TRANST 00196 INTEGER I, I1, I2, I3, IB, IC, IINFO, IWS, JC, LDWORK, 00197 $ LWKOPT, MI, NB, NBMIN, NI, NQ, NW 00198 * .. 00199 * .. Local Arrays .. 00200 COMPLEX T( LDT, NBMAX ) 00201 * .. 00202 * .. External Functions .. 00203 LOGICAL LSAME 00204 INTEGER ILAENV 00205 EXTERNAL LSAME, ILAENV 00206 * .. 00207 * .. External Subroutines .. 00208 EXTERNAL CLARFB, CLARFT, CUNML2, XERBLA 00209 * .. 00210 * .. Intrinsic Functions .. 00211 INTRINSIC MAX, MIN 00212 * .. 00213 * .. Executable Statements .. 00214 * 00215 * Test the input arguments 00216 * 00217 INFO = 0 00218 LEFT = LSAME( SIDE, 'L' ) 00219 NOTRAN = LSAME( TRANS, 'N' ) 00220 LQUERY = ( LWORK.EQ.-1 ) 00221 * 00222 * NQ is the order of Q and NW is the minimum dimension of WORK 00223 * 00224 IF( LEFT ) THEN 00225 NQ = M 00226 NW = N 00227 ELSE 00228 NQ = N 00229 NW = M 00230 END IF 00231 IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN 00232 INFO = -1 00233 ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'C' ) ) THEN 00234 INFO = -2 00235 ELSE IF( M.LT.0 ) THEN 00236 INFO = -3 00237 ELSE IF( N.LT.0 ) THEN 00238 INFO = -4 00239 ELSE IF( K.LT.0 .OR. K.GT.NQ ) THEN 00240 INFO = -5 00241 ELSE IF( LDA.LT.MAX( 1, K ) ) THEN 00242 INFO = -7 00243 ELSE IF( LDC.LT.MAX( 1, M ) ) THEN 00244 INFO = -10 00245 ELSE IF( LWORK.LT.MAX( 1, NW ) .AND. .NOT.LQUERY ) THEN 00246 INFO = -12 00247 END IF 00248 * 00249 IF( INFO.EQ.0 ) THEN 00250 * 00251 * Determine the block size. NB may be at most NBMAX, where NBMAX 00252 * is used to define the local array T. 00253 * 00254 NB = MIN( NBMAX, ILAENV( 1, 'CUNMLQ', SIDE // TRANS, M, N, K, 00255 $ -1 ) ) 00256 LWKOPT = MAX( 1, NW )*NB 00257 WORK( 1 ) = LWKOPT 00258 END IF 00259 * 00260 IF( INFO.NE.0 ) THEN 00261 CALL XERBLA( 'CUNMLQ', -INFO ) 00262 RETURN 00263 ELSE IF( LQUERY ) THEN 00264 RETURN 00265 END IF 00266 * 00267 * Quick return if possible 00268 * 00269 IF( M.EQ.0 .OR. N.EQ.0 .OR. K.EQ.0 ) THEN 00270 WORK( 1 ) = 1 00271 RETURN 00272 END IF 00273 * 00274 NBMIN = 2 00275 LDWORK = NW 00276 IF( NB.GT.1 .AND. NB.LT.K ) THEN 00277 IWS = NW*NB 00278 IF( LWORK.LT.IWS ) THEN 00279 NB = LWORK / LDWORK 00280 NBMIN = MAX( 2, ILAENV( 2, 'CUNMLQ', SIDE // TRANS, M, N, K, 00281 $ -1 ) ) 00282 END IF 00283 ELSE 00284 IWS = NW 00285 END IF 00286 * 00287 IF( NB.LT.NBMIN .OR. NB.GE.K ) THEN 00288 * 00289 * Use unblocked code 00290 * 00291 CALL CUNML2( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, 00292 $ IINFO ) 00293 ELSE 00294 * 00295 * Use blocked code 00296 * 00297 IF( ( LEFT .AND. NOTRAN ) .OR. 00298 $ ( .NOT.LEFT .AND. .NOT.NOTRAN ) ) THEN 00299 I1 = 1 00300 I2 = K 00301 I3 = NB 00302 ELSE 00303 I1 = ( ( K-1 ) / NB )*NB + 1 00304 I2 = 1 00305 I3 = -NB 00306 END IF 00307 * 00308 IF( LEFT ) THEN 00309 NI = N 00310 JC = 1 00311 ELSE 00312 MI = M 00313 IC = 1 00314 END IF 00315 * 00316 IF( NOTRAN ) THEN 00317 TRANST = 'C' 00318 ELSE 00319 TRANST = 'N' 00320 END IF 00321 * 00322 DO 10 I = I1, I2, I3 00323 IB = MIN( NB, K-I+1 ) 00324 * 00325 * Form the triangular factor of the block reflector 00326 * H = H(i) H(i+1) . . . H(i+ib-1) 00327 * 00328 CALL CLARFT( 'Forward', 'Rowwise', NQ-I+1, IB, A( I, I ), 00329 $ LDA, TAU( I ), T, LDT ) 00330 IF( LEFT ) THEN 00331 * 00332 * H or H**H is applied to C(i:m,1:n) 00333 * 00334 MI = M - I + 1 00335 IC = I 00336 ELSE 00337 * 00338 * H or H**H is applied to C(1:m,i:n) 00339 * 00340 NI = N - I + 1 00341 JC = I 00342 END IF 00343 * 00344 * Apply H or H**H 00345 * 00346 CALL CLARFB( SIDE, TRANST, 'Forward', 'Rowwise', MI, NI, IB, 00347 $ A( I, I ), LDA, T, LDT, C( IC, JC ), LDC, WORK, 00348 $ LDWORK ) 00349 10 CONTINUE 00350 END IF 00351 WORK( 1 ) = LWKOPT 00352 RETURN 00353 * 00354 * End of CUNMLQ 00355 * 00356 END