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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b DORMRQ 00002 * 00003 * =========== DOCUMENTATION =========== 00004 * 00005 * Online html documentation available at 00006 * http://www.netlib.org/lapack/explore-html/ 00007 * 00008 *> \htmlonly 00009 *> Download DORMRQ + dependencies 00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dormrq.f"> 00011 *> [TGZ]</a> 00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dormrq.f"> 00013 *> [ZIP]</a> 00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dormrq.f"> 00015 *> [TXT]</a> 00016 *> \endhtmlonly 00017 * 00018 * Definition: 00019 * =========== 00020 * 00021 * SUBROUTINE DORMRQ( 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 * DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) 00030 * .. 00031 * 00032 * 00033 *> \par Purpose: 00034 * ============= 00035 *> 00036 *> \verbatim 00037 *> 00038 *> DORMRQ overwrites the general real M-by-N matrix C with 00039 *> 00040 *> SIDE = 'L' SIDE = 'R' 00041 *> TRANS = 'N': Q * C C * Q 00042 *> TRANS = 'T': Q**T * C C * Q**T 00043 *> 00044 *> where Q is a real orthogonal matrix defined as the product of k 00045 *> elementary reflectors 00046 *> 00047 *> Q = H(1) H(2) . . . H(k) 00048 *> 00049 *> as returned by DGERQF. Q is of order M if SIDE = 'L' and of order N 00050 *> if SIDE = 'R'. 00051 *> \endverbatim 00052 * 00053 * Arguments: 00054 * ========== 00055 * 00056 *> \param[in] SIDE 00057 *> \verbatim 00058 *> SIDE is CHARACTER*1 00059 *> = 'L': apply Q or Q**T from the Left; 00060 *> = 'R': apply Q or Q**T from the Right. 00061 *> \endverbatim 00062 *> 00063 *> \param[in] TRANS 00064 *> \verbatim 00065 *> TRANS is CHARACTER*1 00066 *> = 'N': No transpose, apply Q; 00067 *> = 'T': Transpose, apply Q**T. 00068 *> \endverbatim 00069 *> 00070 *> \param[in] M 00071 *> \verbatim 00072 *> M is INTEGER 00073 *> The number of rows of the matrix C. M >= 0. 00074 *> \endverbatim 00075 *> 00076 *> \param[in] N 00077 *> \verbatim 00078 *> N is INTEGER 00079 *> The number of columns of the matrix C. N >= 0. 00080 *> \endverbatim 00081 *> 00082 *> \param[in] K 00083 *> \verbatim 00084 *> K is INTEGER 00085 *> The number of elementary reflectors whose product defines 00086 *> the matrix Q. 00087 *> If SIDE = 'L', M >= K >= 0; 00088 *> if SIDE = 'R', N >= K >= 0. 00089 *> \endverbatim 00090 *> 00091 *> \param[in] A 00092 *> \verbatim 00093 *> A is DOUBLE PRECISION array, dimension 00094 *> (LDA,M) if SIDE = 'L', 00095 *> (LDA,N) if SIDE = 'R' 00096 *> The i-th row must contain the vector which defines the 00097 *> elementary reflector H(i), for i = 1,2,...,k, as returned by 00098 *> DGERQF in the last k rows of its array argument A. 00099 *> \endverbatim 00100 *> 00101 *> \param[in] LDA 00102 *> \verbatim 00103 *> LDA is INTEGER 00104 *> The leading dimension of the array A. LDA >= max(1,K). 00105 *> \endverbatim 00106 *> 00107 *> \param[in] TAU 00108 *> \verbatim 00109 *> TAU is DOUBLE PRECISION array, dimension (K) 00110 *> TAU(i) must contain the scalar factor of the elementary 00111 *> reflector H(i), as returned by DGERQF. 00112 *> \endverbatim 00113 *> 00114 *> \param[in,out] C 00115 *> \verbatim 00116 *> C is DOUBLE PRECISION array, dimension (LDC,N) 00117 *> On entry, the M-by-N matrix C. 00118 *> On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q. 00119 *> \endverbatim 00120 *> 00121 *> \param[in] LDC 00122 *> \verbatim 00123 *> LDC is INTEGER 00124 *> The leading dimension of the array C. LDC >= max(1,M). 00125 *> \endverbatim 00126 *> 00127 *> \param[out] WORK 00128 *> \verbatim 00129 *> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) 00130 *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. 00131 *> \endverbatim 00132 *> 00133 *> \param[in] LWORK 00134 *> \verbatim 00135 *> LWORK is INTEGER 00136 *> The dimension of the array WORK. 00137 *> If SIDE = 'L', LWORK >= max(1,N); 00138 *> if SIDE = 'R', LWORK >= max(1,M). 00139 *> For optimum performance LWORK >= N*NB if SIDE = 'L', and 00140 *> LWORK >= M*NB if SIDE = 'R', where NB is the optimal 00141 *> blocksize. 00142 *> 00143 *> If LWORK = -1, then a workspace query is assumed; the routine 00144 *> only calculates the optimal size of the WORK array, returns 00145 *> this value as the first entry of the WORK array, and no error 00146 *> message related to LWORK is issued by XERBLA. 00147 *> \endverbatim 00148 *> 00149 *> \param[out] INFO 00150 *> \verbatim 00151 *> INFO is INTEGER 00152 *> = 0: successful exit 00153 *> < 0: if INFO = -i, the i-th argument had an illegal value 00154 *> \endverbatim 00155 * 00156 * Authors: 00157 * ======== 00158 * 00159 *> \author Univ. of Tennessee 00160 *> \author Univ. of California Berkeley 00161 *> \author Univ. of Colorado Denver 00162 *> \author NAG Ltd. 00163 * 00164 *> \date November 2011 00165 * 00166 *> \ingroup doubleOTHERcomputational 00167 * 00168 * ===================================================================== 00169 SUBROUTINE DORMRQ( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, 00170 $ WORK, LWORK, INFO ) 00171 * 00172 * -- LAPACK computational routine (version 3.4.0) -- 00173 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00174 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00175 * November 2011 00176 * 00177 * .. Scalar Arguments .. 00178 CHARACTER SIDE, TRANS 00179 INTEGER INFO, K, LDA, LDC, LWORK, M, N 00180 * .. 00181 * .. Array Arguments .. 00182 DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) 00183 * .. 00184 * 00185 * ===================================================================== 00186 * 00187 * .. Parameters .. 00188 INTEGER NBMAX, LDT 00189 PARAMETER ( NBMAX = 64, LDT = NBMAX+1 ) 00190 * .. 00191 * .. Local Scalars .. 00192 LOGICAL LEFT, LQUERY, NOTRAN 00193 CHARACTER TRANST 00194 INTEGER I, I1, I2, I3, IB, IINFO, IWS, LDWORK, LWKOPT, 00195 $ MI, NB, NBMIN, NI, NQ, NW 00196 * .. 00197 * .. Local Arrays .. 00198 DOUBLE PRECISION T( LDT, NBMAX ) 00199 * .. 00200 * .. External Functions .. 00201 LOGICAL LSAME 00202 INTEGER ILAENV 00203 EXTERNAL LSAME, ILAENV 00204 * .. 00205 * .. External Subroutines .. 00206 EXTERNAL DLARFB, DLARFT, DORMR2, XERBLA 00207 * .. 00208 * .. Intrinsic Functions .. 00209 INTRINSIC MAX, MIN 00210 * .. 00211 * .. Executable Statements .. 00212 * 00213 * Test the input arguments 00214 * 00215 INFO = 0 00216 LEFT = LSAME( SIDE, 'L' ) 00217 NOTRAN = LSAME( TRANS, 'N' ) 00218 LQUERY = ( LWORK.EQ.-1 ) 00219 * 00220 * NQ is the order of Q and NW is the minimum dimension of WORK 00221 * 00222 IF( LEFT ) THEN 00223 NQ = M 00224 NW = MAX( 1, N ) 00225 ELSE 00226 NQ = N 00227 NW = MAX( 1, M ) 00228 END IF 00229 IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN 00230 INFO = -1 00231 ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) ) THEN 00232 INFO = -2 00233 ELSE IF( M.LT.0 ) THEN 00234 INFO = -3 00235 ELSE IF( N.LT.0 ) THEN 00236 INFO = -4 00237 ELSE IF( K.LT.0 .OR. K.GT.NQ ) THEN 00238 INFO = -5 00239 ELSE IF( LDA.LT.MAX( 1, K ) ) THEN 00240 INFO = -7 00241 ELSE IF( LDC.LT.MAX( 1, M ) ) THEN 00242 INFO = -10 00243 END IF 00244 * 00245 IF( INFO.EQ.0 ) THEN 00246 IF( M.EQ.0 .OR. N.EQ.0 ) THEN 00247 LWKOPT = 1 00248 ELSE 00249 * 00250 * Determine the block size. NB may be at most NBMAX, where 00251 * NBMAX is used to define the local array T. 00252 * 00253 NB = MIN( NBMAX, ILAENV( 1, 'DORMRQ', SIDE // TRANS, M, N, 00254 $ K, -1 ) ) 00255 LWKOPT = NW*NB 00256 END IF 00257 WORK( 1 ) = LWKOPT 00258 * 00259 IF( LWORK.LT.NW .AND. .NOT.LQUERY ) THEN 00260 INFO = -12 00261 END IF 00262 END IF 00263 * 00264 IF( INFO.NE.0 ) THEN 00265 CALL XERBLA( 'DORMRQ', -INFO ) 00266 RETURN 00267 ELSE IF( LQUERY ) THEN 00268 RETURN 00269 END IF 00270 * 00271 * Quick return if possible 00272 * 00273 IF( M.EQ.0 .OR. N.EQ.0 ) THEN 00274 RETURN 00275 END IF 00276 * 00277 NBMIN = 2 00278 LDWORK = NW 00279 IF( NB.GT.1 .AND. NB.LT.K ) THEN 00280 IWS = NW*NB 00281 IF( LWORK.LT.IWS ) THEN 00282 NB = LWORK / LDWORK 00283 NBMIN = MAX( 2, ILAENV( 2, 'DORMRQ', SIDE // TRANS, M, N, K, 00284 $ -1 ) ) 00285 END IF 00286 ELSE 00287 IWS = NW 00288 END IF 00289 * 00290 IF( NB.LT.NBMIN .OR. NB.GE.K ) THEN 00291 * 00292 * Use unblocked code 00293 * 00294 CALL DORMR2( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, 00295 $ IINFO ) 00296 ELSE 00297 * 00298 * Use blocked code 00299 * 00300 IF( ( LEFT .AND. .NOT.NOTRAN ) .OR. 00301 $ ( .NOT.LEFT .AND. NOTRAN ) ) THEN 00302 I1 = 1 00303 I2 = K 00304 I3 = NB 00305 ELSE 00306 I1 = ( ( K-1 ) / NB )*NB + 1 00307 I2 = 1 00308 I3 = -NB 00309 END IF 00310 * 00311 IF( LEFT ) THEN 00312 NI = N 00313 ELSE 00314 MI = M 00315 END IF 00316 * 00317 IF( NOTRAN ) THEN 00318 TRANST = 'T' 00319 ELSE 00320 TRANST = 'N' 00321 END IF 00322 * 00323 DO 10 I = I1, I2, I3 00324 IB = MIN( NB, K-I+1 ) 00325 * 00326 * Form the triangular factor of the block reflector 00327 * H = H(i+ib-1) . . . H(i+1) H(i) 00328 * 00329 CALL DLARFT( 'Backward', 'Rowwise', NQ-K+I+IB-1, IB, 00330 $ A( I, 1 ), LDA, TAU( I ), T, LDT ) 00331 IF( LEFT ) THEN 00332 * 00333 * H or H**T is applied to C(1:m-k+i+ib-1,1:n) 00334 * 00335 MI = M - K + I + IB - 1 00336 ELSE 00337 * 00338 * H or H**T is applied to C(1:m,1:n-k+i+ib-1) 00339 * 00340 NI = N - K + I + IB - 1 00341 END IF 00342 * 00343 * Apply H or H**T 00344 * 00345 CALL DLARFB( SIDE, TRANST, 'Backward', 'Rowwise', MI, NI, 00346 $ IB, A( I, 1 ), LDA, T, LDT, C, LDC, WORK, 00347 $ LDWORK ) 00348 10 CONTINUE 00349 END IF 00350 WORK( 1 ) = LWKOPT 00351 RETURN 00352 * 00353 * End of DORMRQ 00354 * 00355 END