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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b CUNMTR 00002 * 00003 * =========== DOCUMENTATION =========== 00004 * 00005 * Online html documentation available at 00006 * http://www.netlib.org/lapack/explore-html/ 00007 * 00008 *> \htmlonly 00009 *> Download CUNMTR + dependencies 00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cunmtr.f"> 00011 *> [TGZ]</a> 00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cunmtr.f"> 00013 *> [ZIP]</a> 00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cunmtr.f"> 00015 *> [TXT]</a> 00016 *> \endhtmlonly 00017 * 00018 * Definition: 00019 * =========== 00020 * 00021 * SUBROUTINE CUNMTR( SIDE, UPLO, TRANS, M, N, A, LDA, TAU, C, LDC, 00022 * WORK, LWORK, INFO ) 00023 * 00024 * .. Scalar Arguments .. 00025 * CHARACTER SIDE, TRANS, UPLO 00026 * INTEGER INFO, 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 *> CUNMTR 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 of order nq, with nq = m if 00046 *> SIDE = 'L' and nq = n if SIDE = 'R'. Q is defined as the product of 00047 *> nq-1 elementary reflectors, as returned by CHETRD: 00048 *> 00049 *> if UPLO = 'U', Q = H(nq-1) . . . H(2) H(1); 00050 *> 00051 *> if UPLO = 'L', Q = H(1) H(2) . . . H(nq-1). 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] UPLO 00065 *> \verbatim 00066 *> UPLO is CHARACTER*1 00067 *> = 'U': Upper triangle of A contains elementary reflectors 00068 *> from CHETRD; 00069 *> = 'L': Lower triangle of A contains elementary reflectors 00070 *> from CHETRD. 00071 *> \endverbatim 00072 *> 00073 *> \param[in] TRANS 00074 *> \verbatim 00075 *> TRANS is CHARACTER*1 00076 *> = 'N': No transpose, apply Q; 00077 *> = 'C': Conjugate transpose, apply Q**H. 00078 *> \endverbatim 00079 *> 00080 *> \param[in] M 00081 *> \verbatim 00082 *> M is INTEGER 00083 *> The number of rows of the matrix C. M >= 0. 00084 *> \endverbatim 00085 *> 00086 *> \param[in] N 00087 *> \verbatim 00088 *> N is INTEGER 00089 *> The number of columns of the matrix C. N >= 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 vectors which define the elementary reflectors, as 00098 *> returned by CHETRD. 00099 *> \endverbatim 00100 *> 00101 *> \param[in] LDA 00102 *> \verbatim 00103 *> LDA is INTEGER 00104 *> The leading dimension of the array A. 00105 *> LDA >= max(1,M) if SIDE = 'L'; LDA >= max(1,N) if SIDE = 'R'. 00106 *> \endverbatim 00107 *> 00108 *> \param[in] TAU 00109 *> \verbatim 00110 *> TAU is COMPLEX array, dimension 00111 *> (M-1) if SIDE = 'L' 00112 *> (N-1) if SIDE = 'R' 00113 *> TAU(i) must contain the scalar factor of the elementary 00114 *> reflector H(i), as returned by CHETRD. 00115 *> \endverbatim 00116 *> 00117 *> \param[in,out] C 00118 *> \verbatim 00119 *> C is COMPLEX array, dimension (LDC,N) 00120 *> On entry, the M-by-N matrix C. 00121 *> On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q. 00122 *> \endverbatim 00123 *> 00124 *> \param[in] LDC 00125 *> \verbatim 00126 *> LDC is INTEGER 00127 *> The leading dimension of the array C. LDC >= max(1,M). 00128 *> \endverbatim 00129 *> 00130 *> \param[out] WORK 00131 *> \verbatim 00132 *> WORK is COMPLEX array, dimension (MAX(1,LWORK)) 00133 *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. 00134 *> \endverbatim 00135 *> 00136 *> \param[in] LWORK 00137 *> \verbatim 00138 *> LWORK is INTEGER 00139 *> The dimension of the array WORK. 00140 *> If SIDE = 'L', LWORK >= max(1,N); 00141 *> if SIDE = 'R', LWORK >= max(1,M). 00142 *> For optimum performance LWORK >= N*NB if SIDE = 'L', and 00143 *> LWORK >=M*NB if SIDE = 'R', where NB is the optimal 00144 *> blocksize. 00145 *> 00146 *> If LWORK = -1, then a workspace query is assumed; the routine 00147 *> only calculates the optimal size of the WORK array, returns 00148 *> this value as the first entry of the WORK array, and no error 00149 *> message related to LWORK is issued by XERBLA. 00150 *> \endverbatim 00151 *> 00152 *> \param[out] INFO 00153 *> \verbatim 00154 *> INFO is INTEGER 00155 *> = 0: successful exit 00156 *> < 0: if INFO = -i, the i-th argument had an illegal value 00157 *> \endverbatim 00158 * 00159 * Authors: 00160 * ======== 00161 * 00162 *> \author Univ. of Tennessee 00163 *> \author Univ. of California Berkeley 00164 *> \author Univ. of Colorado Denver 00165 *> \author NAG Ltd. 00166 * 00167 *> \date November 2011 00168 * 00169 *> \ingroup complexOTHERcomputational 00170 * 00171 * ===================================================================== 00172 SUBROUTINE CUNMTR( SIDE, UPLO, TRANS, M, N, A, LDA, TAU, C, LDC, 00173 $ WORK, LWORK, INFO ) 00174 * 00175 * -- LAPACK computational routine (version 3.4.0) -- 00176 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00177 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00178 * November 2011 00179 * 00180 * .. Scalar Arguments .. 00181 CHARACTER SIDE, TRANS, UPLO 00182 INTEGER INFO, LDA, LDC, LWORK, M, N 00183 * .. 00184 * .. Array Arguments .. 00185 COMPLEX A( LDA, * ), C( LDC, * ), TAU( * ), 00186 $ WORK( * ) 00187 * .. 00188 * 00189 * ===================================================================== 00190 * 00191 * .. Local Scalars .. 00192 LOGICAL LEFT, LQUERY, UPPER 00193 INTEGER I1, I2, IINFO, LWKOPT, MI, NB, NI, NQ, NW 00194 * .. 00195 * .. External Functions .. 00196 LOGICAL LSAME 00197 INTEGER ILAENV 00198 EXTERNAL ILAENV, LSAME 00199 * .. 00200 * .. External Subroutines .. 00201 EXTERNAL CUNMQL, CUNMQR, XERBLA 00202 * .. 00203 * .. Intrinsic Functions .. 00204 INTRINSIC MAX 00205 * .. 00206 * .. Executable Statements .. 00207 * 00208 * Test the input arguments 00209 * 00210 INFO = 0 00211 LEFT = LSAME( SIDE, 'L' ) 00212 UPPER = LSAME( UPLO, 'U' ) 00213 LQUERY = ( LWORK.EQ.-1 ) 00214 * 00215 * NQ is the order of Q and NW is the minimum dimension of WORK 00216 * 00217 IF( LEFT ) THEN 00218 NQ = M 00219 NW = N 00220 ELSE 00221 NQ = N 00222 NW = M 00223 END IF 00224 IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN 00225 INFO = -1 00226 ELSE IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN 00227 INFO = -2 00228 ELSE IF( .NOT.LSAME( TRANS, 'N' ) .AND. .NOT.LSAME( TRANS, 'C' ) ) 00229 $ THEN 00230 INFO = -3 00231 ELSE IF( M.LT.0 ) THEN 00232 INFO = -4 00233 ELSE IF( N.LT.0 ) THEN 00234 INFO = -5 00235 ELSE IF( LDA.LT.MAX( 1, NQ ) ) THEN 00236 INFO = -7 00237 ELSE IF( LDC.LT.MAX( 1, M ) ) THEN 00238 INFO = -10 00239 ELSE IF( LWORK.LT.MAX( 1, NW ) .AND. .NOT.LQUERY ) THEN 00240 INFO = -12 00241 END IF 00242 * 00243 IF( INFO.EQ.0 ) THEN 00244 IF( UPPER ) THEN 00245 IF( LEFT ) THEN 00246 NB = ILAENV( 1, 'CUNMQL', SIDE // TRANS, M-1, N, M-1, 00247 $ -1 ) 00248 ELSE 00249 NB = ILAENV( 1, 'CUNMQL', SIDE // TRANS, M, N-1, N-1, 00250 $ -1 ) 00251 END IF 00252 ELSE 00253 IF( LEFT ) THEN 00254 NB = ILAENV( 1, 'CUNMQR', SIDE // TRANS, M-1, N, M-1, 00255 $ -1 ) 00256 ELSE 00257 NB = ILAENV( 1, 'CUNMQR', SIDE // TRANS, M, N-1, N-1, 00258 $ -1 ) 00259 END IF 00260 END IF 00261 LWKOPT = MAX( 1, NW )*NB 00262 WORK( 1 ) = LWKOPT 00263 END IF 00264 * 00265 IF( INFO.NE.0 ) THEN 00266 CALL XERBLA( 'CUNMTR', -INFO ) 00267 RETURN 00268 ELSE IF( LQUERY ) THEN 00269 RETURN 00270 END IF 00271 * 00272 * Quick return if possible 00273 * 00274 IF( M.EQ.0 .OR. N.EQ.0 .OR. NQ.EQ.1 ) THEN 00275 WORK( 1 ) = 1 00276 RETURN 00277 END IF 00278 * 00279 IF( LEFT ) THEN 00280 MI = M - 1 00281 NI = N 00282 ELSE 00283 MI = M 00284 NI = N - 1 00285 END IF 00286 * 00287 IF( UPPER ) THEN 00288 * 00289 * Q was determined by a call to CHETRD with UPLO = 'U' 00290 * 00291 CALL CUNMQL( SIDE, TRANS, MI, NI, NQ-1, A( 1, 2 ), LDA, TAU, C, 00292 $ LDC, WORK, LWORK, IINFO ) 00293 ELSE 00294 * 00295 * Q was determined by a call to CHETRD with UPLO = 'L' 00296 * 00297 IF( LEFT ) THEN 00298 I1 = 2 00299 I2 = 1 00300 ELSE 00301 I1 = 1 00302 I2 = 2 00303 END IF 00304 CALL CUNMQR( SIDE, TRANS, MI, NI, NQ-1, A( 2, 1 ), LDA, TAU, 00305 $ C( I1, I2 ), LDC, WORK, LWORK, IINFO ) 00306 END IF 00307 WORK( 1 ) = LWKOPT 00308 RETURN 00309 * 00310 * End of CUNMTR 00311 * 00312 END