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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b DORMBR 00002 * 00003 * =========== DOCUMENTATION =========== 00004 * 00005 * Online html documentation available at 00006 * http://www.netlib.org/lapack/explore-html/ 00007 * 00008 *> \htmlonly 00009 *> Download DORMBR + dependencies 00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dormbr.f"> 00011 *> [TGZ]</a> 00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dormbr.f"> 00013 *> [ZIP]</a> 00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dormbr.f"> 00015 *> [TXT]</a> 00016 *> \endhtmlonly 00017 * 00018 * Definition: 00019 * =========== 00020 * 00021 * SUBROUTINE DORMBR( VECT, SIDE, TRANS, M, N, K, A, LDA, TAU, C, 00022 * LDC, WORK, LWORK, INFO ) 00023 * 00024 * .. Scalar Arguments .. 00025 * CHARACTER SIDE, TRANS, VECT 00026 * INTEGER INFO, K, LDA, LDC, LWORK, M, N 00027 * .. 00028 * .. Array Arguments .. 00029 * DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) 00030 * .. 00031 * 00032 * 00033 *> \par Purpose: 00034 * ============= 00035 *> 00036 *> \verbatim 00037 *> 00038 *> If VECT = 'Q', DORMBR overwrites the general real M-by-N matrix C 00039 *> with 00040 *> SIDE = 'L' SIDE = 'R' 00041 *> TRANS = 'N': Q * C C * Q 00042 *> TRANS = 'T': Q**T * C C * Q**T 00043 *> 00044 *> If VECT = 'P', DORMBR overwrites the general real M-by-N matrix C 00045 *> with 00046 *> SIDE = 'L' SIDE = 'R' 00047 *> TRANS = 'N': P * C C * P 00048 *> TRANS = 'T': P**T * C C * P**T 00049 *> 00050 *> Here Q and P**T are the orthogonal matrices determined by DGEBRD when 00051 *> reducing a real matrix A to bidiagonal form: A = Q * B * P**T. Q and 00052 *> P**T are defined as products of elementary reflectors H(i) and G(i) 00053 *> respectively. 00054 *> 00055 *> Let nq = m if SIDE = 'L' and nq = n if SIDE = 'R'. Thus nq is the 00056 *> order of the orthogonal matrix Q or P**T that is applied. 00057 *> 00058 *> If VECT = 'Q', A is assumed to have been an NQ-by-K matrix: 00059 *> if nq >= k, Q = H(1) H(2) . . . H(k); 00060 *> if nq < k, Q = H(1) H(2) . . . H(nq-1). 00061 *> 00062 *> If VECT = 'P', A is assumed to have been a K-by-NQ matrix: 00063 *> if k < nq, P = G(1) G(2) . . . G(k); 00064 *> if k >= nq, P = G(1) G(2) . . . G(nq-1). 00065 *> \endverbatim 00066 * 00067 * Arguments: 00068 * ========== 00069 * 00070 *> \param[in] VECT 00071 *> \verbatim 00072 *> VECT is CHARACTER*1 00073 *> = 'Q': apply Q or Q**T; 00074 *> = 'P': apply P or P**T. 00075 *> \endverbatim 00076 *> 00077 *> \param[in] SIDE 00078 *> \verbatim 00079 *> SIDE is CHARACTER*1 00080 *> = 'L': apply Q, Q**T, P or P**T from the Left; 00081 *> = 'R': apply Q, Q**T, P or P**T from the Right. 00082 *> \endverbatim 00083 *> 00084 *> \param[in] TRANS 00085 *> \verbatim 00086 *> TRANS is CHARACTER*1 00087 *> = 'N': No transpose, apply Q or P; 00088 *> = 'T': Transpose, apply Q**T or P**T. 00089 *> \endverbatim 00090 *> 00091 *> \param[in] M 00092 *> \verbatim 00093 *> M is INTEGER 00094 *> The number of rows of the matrix C. M >= 0. 00095 *> \endverbatim 00096 *> 00097 *> \param[in] N 00098 *> \verbatim 00099 *> N is INTEGER 00100 *> The number of columns of the matrix C. N >= 0. 00101 *> \endverbatim 00102 *> 00103 *> \param[in] K 00104 *> \verbatim 00105 *> K is INTEGER 00106 *> If VECT = 'Q', the number of columns in the original 00107 *> matrix reduced by DGEBRD. 00108 *> If VECT = 'P', the number of rows in the original 00109 *> matrix reduced by DGEBRD. 00110 *> K >= 0. 00111 *> \endverbatim 00112 *> 00113 *> \param[in] A 00114 *> \verbatim 00115 *> A is DOUBLE PRECISION array, dimension 00116 *> (LDA,min(nq,K)) if VECT = 'Q' 00117 *> (LDA,nq) if VECT = 'P' 00118 *> The vectors which define the elementary reflectors H(i) and 00119 *> G(i), whose products determine the matrices Q and P, as 00120 *> returned by DGEBRD. 00121 *> \endverbatim 00122 *> 00123 *> \param[in] LDA 00124 *> \verbatim 00125 *> LDA is INTEGER 00126 *> The leading dimension of the array A. 00127 *> If VECT = 'Q', LDA >= max(1,nq); 00128 *> if VECT = 'P', LDA >= max(1,min(nq,K)). 00129 *> \endverbatim 00130 *> 00131 *> \param[in] TAU 00132 *> \verbatim 00133 *> TAU is DOUBLE PRECISION array, dimension (min(nq,K)) 00134 *> TAU(i) must contain the scalar factor of the elementary 00135 *> reflector H(i) or G(i) which determines Q or P, as returned 00136 *> by DGEBRD in the array argument TAUQ or TAUP. 00137 *> \endverbatim 00138 *> 00139 *> \param[in,out] C 00140 *> \verbatim 00141 *> C is DOUBLE PRECISION array, dimension (LDC,N) 00142 *> On entry, the M-by-N matrix C. 00143 *> On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q 00144 *> or P*C or P**T*C or C*P or C*P**T. 00145 *> \endverbatim 00146 *> 00147 *> \param[in] LDC 00148 *> \verbatim 00149 *> LDC is INTEGER 00150 *> The leading dimension of the array C. LDC >= max(1,M). 00151 *> \endverbatim 00152 *> 00153 *> \param[out] WORK 00154 *> \verbatim 00155 *> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) 00156 *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. 00157 *> \endverbatim 00158 *> 00159 *> \param[in] LWORK 00160 *> \verbatim 00161 *> LWORK is INTEGER 00162 *> The dimension of the array WORK. 00163 *> If SIDE = 'L', LWORK >= max(1,N); 00164 *> if SIDE = 'R', LWORK >= max(1,M). 00165 *> For optimum performance LWORK >= N*NB if SIDE = 'L', and 00166 *> LWORK >= M*NB if SIDE = 'R', where NB is the optimal 00167 *> blocksize. 00168 *> 00169 *> If LWORK = -1, then a workspace query is assumed; the routine 00170 *> only calculates the optimal size of the WORK array, returns 00171 *> this value as the first entry of the WORK array, and no error 00172 *> message related to LWORK is issued by XERBLA. 00173 *> \endverbatim 00174 *> 00175 *> \param[out] INFO 00176 *> \verbatim 00177 *> INFO is INTEGER 00178 *> = 0: successful exit 00179 *> < 0: if INFO = -i, the i-th argument had an illegal value 00180 *> \endverbatim 00181 * 00182 * Authors: 00183 * ======== 00184 * 00185 *> \author Univ. of Tennessee 00186 *> \author Univ. of California Berkeley 00187 *> \author Univ. of Colorado Denver 00188 *> \author NAG Ltd. 00189 * 00190 *> \date November 2011 00191 * 00192 *> \ingroup doubleOTHERcomputational 00193 * 00194 * ===================================================================== 00195 SUBROUTINE DORMBR( VECT, SIDE, TRANS, M, N, K, A, LDA, TAU, C, 00196 $ LDC, WORK, LWORK, INFO ) 00197 * 00198 * -- LAPACK computational routine (version 3.4.0) -- 00199 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00200 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00201 * November 2011 00202 * 00203 * .. Scalar Arguments .. 00204 CHARACTER SIDE, TRANS, VECT 00205 INTEGER INFO, K, LDA, LDC, LWORK, M, N 00206 * .. 00207 * .. Array Arguments .. 00208 DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) 00209 * .. 00210 * 00211 * ===================================================================== 00212 * 00213 * .. Local Scalars .. 00214 LOGICAL APPLYQ, LEFT, LQUERY, NOTRAN 00215 CHARACTER TRANST 00216 INTEGER I1, I2, IINFO, LWKOPT, MI, NB, NI, NQ, NW 00217 * .. 00218 * .. External Functions .. 00219 LOGICAL LSAME 00220 INTEGER ILAENV 00221 EXTERNAL LSAME, ILAENV 00222 * .. 00223 * .. External Subroutines .. 00224 EXTERNAL DORMLQ, DORMQR, XERBLA 00225 * .. 00226 * .. Intrinsic Functions .. 00227 INTRINSIC MAX, MIN 00228 * .. 00229 * .. Executable Statements .. 00230 * 00231 * Test the input arguments 00232 * 00233 INFO = 0 00234 APPLYQ = LSAME( VECT, 'Q' ) 00235 LEFT = LSAME( SIDE, 'L' ) 00236 NOTRAN = LSAME( TRANS, 'N' ) 00237 LQUERY = ( LWORK.EQ.-1 ) 00238 * 00239 * NQ is the order of Q or P and NW is the minimum dimension of WORK 00240 * 00241 IF( LEFT ) THEN 00242 NQ = M 00243 NW = N 00244 ELSE 00245 NQ = N 00246 NW = M 00247 END IF 00248 IF( .NOT.APPLYQ .AND. .NOT.LSAME( VECT, 'P' ) ) THEN 00249 INFO = -1 00250 ELSE IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN 00251 INFO = -2 00252 ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) ) THEN 00253 INFO = -3 00254 ELSE IF( M.LT.0 ) THEN 00255 INFO = -4 00256 ELSE IF( N.LT.0 ) THEN 00257 INFO = -5 00258 ELSE IF( K.LT.0 ) THEN 00259 INFO = -6 00260 ELSE IF( ( APPLYQ .AND. LDA.LT.MAX( 1, NQ ) ) .OR. 00261 $ ( .NOT.APPLYQ .AND. LDA.LT.MAX( 1, MIN( NQ, K ) ) ) ) 00262 $ THEN 00263 INFO = -8 00264 ELSE IF( LDC.LT.MAX( 1, M ) ) THEN 00265 INFO = -11 00266 ELSE IF( LWORK.LT.MAX( 1, NW ) .AND. .NOT.LQUERY ) THEN 00267 INFO = -13 00268 END IF 00269 * 00270 IF( INFO.EQ.0 ) THEN 00271 IF( APPLYQ ) THEN 00272 IF( LEFT ) THEN 00273 NB = ILAENV( 1, 'DORMQR', SIDE // TRANS, M-1, N, M-1, 00274 $ -1 ) 00275 ELSE 00276 NB = ILAENV( 1, 'DORMQR', SIDE // TRANS, M, N-1, N-1, 00277 $ -1 ) 00278 END IF 00279 ELSE 00280 IF( LEFT ) THEN 00281 NB = ILAENV( 1, 'DORMLQ', SIDE // TRANS, M-1, N, M-1, 00282 $ -1 ) 00283 ELSE 00284 NB = ILAENV( 1, 'DORMLQ', SIDE // TRANS, M, N-1, N-1, 00285 $ -1 ) 00286 END IF 00287 END IF 00288 LWKOPT = MAX( 1, NW )*NB 00289 WORK( 1 ) = LWKOPT 00290 END IF 00291 * 00292 IF( INFO.NE.0 ) THEN 00293 CALL XERBLA( 'DORMBR', -INFO ) 00294 RETURN 00295 ELSE IF( LQUERY ) THEN 00296 RETURN 00297 END IF 00298 * 00299 * Quick return if possible 00300 * 00301 WORK( 1 ) = 1 00302 IF( M.EQ.0 .OR. N.EQ.0 ) 00303 $ RETURN 00304 * 00305 IF( APPLYQ ) THEN 00306 * 00307 * Apply Q 00308 * 00309 IF( NQ.GE.K ) THEN 00310 * 00311 * Q was determined by a call to DGEBRD with nq >= k 00312 * 00313 CALL DORMQR( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, 00314 $ WORK, LWORK, IINFO ) 00315 ELSE IF( NQ.GT.1 ) THEN 00316 * 00317 * Q was determined by a call to DGEBRD with nq < k 00318 * 00319 IF( LEFT ) THEN 00320 MI = M - 1 00321 NI = N 00322 I1 = 2 00323 I2 = 1 00324 ELSE 00325 MI = M 00326 NI = N - 1 00327 I1 = 1 00328 I2 = 2 00329 END IF 00330 CALL DORMQR( SIDE, TRANS, MI, NI, NQ-1, A( 2, 1 ), LDA, TAU, 00331 $ C( I1, I2 ), LDC, WORK, LWORK, IINFO ) 00332 END IF 00333 ELSE 00334 * 00335 * Apply P 00336 * 00337 IF( NOTRAN ) THEN 00338 TRANST = 'T' 00339 ELSE 00340 TRANST = 'N' 00341 END IF 00342 IF( NQ.GT.K ) THEN 00343 * 00344 * P was determined by a call to DGEBRD with nq > k 00345 * 00346 CALL DORMLQ( SIDE, TRANST, M, N, K, A, LDA, TAU, C, LDC, 00347 $ WORK, LWORK, IINFO ) 00348 ELSE IF( NQ.GT.1 ) THEN 00349 * 00350 * P was determined by a call to DGEBRD with nq <= k 00351 * 00352 IF( LEFT ) THEN 00353 MI = M - 1 00354 NI = N 00355 I1 = 2 00356 I2 = 1 00357 ELSE 00358 MI = M 00359 NI = N - 1 00360 I1 = 1 00361 I2 = 2 00362 END IF 00363 CALL DORMLQ( SIDE, TRANST, MI, NI, NQ-1, A( 1, 2 ), LDA, 00364 $ TAU, C( I1, I2 ), LDC, WORK, LWORK, IINFO ) 00365 END IF 00366 END IF 00367 WORK( 1 ) = LWKOPT 00368 RETURN 00369 * 00370 * End of DORMBR 00371 * 00372 END