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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b DORMQR 00002 * 00003 * =========== DOCUMENTATION =========== 00004 * 00005 * Online html documentation available at 00006 * http://www.netlib.org/lapack/explore-html/ 00007 * 00008 *> \htmlonly 00009 *> Download DORMQR + dependencies 00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dormqr.f"> 00011 *> [TGZ]</a> 00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dormqr.f"> 00013 *> [ZIP]</a> 00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dormqr.f"> 00015 *> [TXT]</a> 00016 *> \endhtmlonly 00017 * 00018 * Definition: 00019 * =========== 00020 * 00021 * SUBROUTINE DORMQR( 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 *> DORMQR 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 DGEQRF. 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 (LDA,K) 00094 *> The i-th column must contain the vector which defines the 00095 *> elementary reflector H(i), for i = 1,2,...,k, as returned by 00096 *> DGEQRF in the first k columns of its array argument A. 00097 *> \endverbatim 00098 *> 00099 *> \param[in] LDA 00100 *> \verbatim 00101 *> LDA is INTEGER 00102 *> The leading dimension of the array A. 00103 *> If SIDE = 'L', LDA >= max(1,M); 00104 *> if SIDE = 'R', LDA >= max(1,N). 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 DGEQRF. 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 DORMQR( 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 INTEGER I, I1, I2, I3, IB, IC, IINFO, IWS, JC, LDWORK, 00194 $ LWKOPT, MI, NB, NBMIN, NI, NQ, NW 00195 * .. 00196 * .. Local Arrays .. 00197 DOUBLE PRECISION T( LDT, NBMAX ) 00198 * .. 00199 * .. External Functions .. 00200 LOGICAL LSAME 00201 INTEGER ILAENV 00202 EXTERNAL LSAME, ILAENV 00203 * .. 00204 * .. External Subroutines .. 00205 EXTERNAL DLARFB, DLARFT, DORM2R, XERBLA 00206 * .. 00207 * .. Intrinsic Functions .. 00208 INTRINSIC MAX, MIN 00209 * .. 00210 * .. Executable Statements .. 00211 * 00212 * Test the input arguments 00213 * 00214 INFO = 0 00215 LEFT = LSAME( SIDE, 'L' ) 00216 NOTRAN = LSAME( TRANS, 'N' ) 00217 LQUERY = ( LWORK.EQ.-1 ) 00218 * 00219 * NQ is the order of Q and NW is the minimum dimension of WORK 00220 * 00221 IF( LEFT ) THEN 00222 NQ = M 00223 NW = N 00224 ELSE 00225 NQ = N 00226 NW = M 00227 END IF 00228 IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN 00229 INFO = -1 00230 ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) ) THEN 00231 INFO = -2 00232 ELSE IF( M.LT.0 ) THEN 00233 INFO = -3 00234 ELSE IF( N.LT.0 ) THEN 00235 INFO = -4 00236 ELSE IF( K.LT.0 .OR. K.GT.NQ ) THEN 00237 INFO = -5 00238 ELSE IF( LDA.LT.MAX( 1, NQ ) ) THEN 00239 INFO = -7 00240 ELSE IF( LDC.LT.MAX( 1, M ) ) THEN 00241 INFO = -10 00242 ELSE IF( LWORK.LT.MAX( 1, NW ) .AND. .NOT.LQUERY ) THEN 00243 INFO = -12 00244 END IF 00245 * 00246 IF( INFO.EQ.0 ) THEN 00247 * 00248 * Determine the block size. NB may be at most NBMAX, where NBMAX 00249 * is used to define the local array T. 00250 * 00251 NB = MIN( NBMAX, ILAENV( 1, 'DORMQR', SIDE // TRANS, M, N, K, 00252 $ -1 ) ) 00253 LWKOPT = MAX( 1, NW )*NB 00254 WORK( 1 ) = LWKOPT 00255 END IF 00256 * 00257 IF( INFO.NE.0 ) THEN 00258 CALL XERBLA( 'DORMQR', -INFO ) 00259 RETURN 00260 ELSE IF( LQUERY ) THEN 00261 RETURN 00262 END IF 00263 * 00264 * Quick return if possible 00265 * 00266 IF( M.EQ.0 .OR. N.EQ.0 .OR. K.EQ.0 ) THEN 00267 WORK( 1 ) = 1 00268 RETURN 00269 END IF 00270 * 00271 NBMIN = 2 00272 LDWORK = NW 00273 IF( NB.GT.1 .AND. NB.LT.K ) THEN 00274 IWS = NW*NB 00275 IF( LWORK.LT.IWS ) THEN 00276 NB = LWORK / LDWORK 00277 NBMIN = MAX( 2, ILAENV( 2, 'DORMQR', SIDE // TRANS, M, N, K, 00278 $ -1 ) ) 00279 END IF 00280 ELSE 00281 IWS = NW 00282 END IF 00283 * 00284 IF( NB.LT.NBMIN .OR. NB.GE.K ) THEN 00285 * 00286 * Use unblocked code 00287 * 00288 CALL DORM2R( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, 00289 $ IINFO ) 00290 ELSE 00291 * 00292 * Use blocked code 00293 * 00294 IF( ( LEFT .AND. .NOT.NOTRAN ) .OR. 00295 $ ( .NOT.LEFT .AND. NOTRAN ) ) THEN 00296 I1 = 1 00297 I2 = K 00298 I3 = NB 00299 ELSE 00300 I1 = ( ( K-1 ) / NB )*NB + 1 00301 I2 = 1 00302 I3 = -NB 00303 END IF 00304 * 00305 IF( LEFT ) THEN 00306 NI = N 00307 JC = 1 00308 ELSE 00309 MI = M 00310 IC = 1 00311 END IF 00312 * 00313 DO 10 I = I1, I2, I3 00314 IB = MIN( NB, K-I+1 ) 00315 * 00316 * Form the triangular factor of the block reflector 00317 * H = H(i) H(i+1) . . . H(i+ib-1) 00318 * 00319 CALL DLARFT( 'Forward', 'Columnwise', NQ-I+1, IB, A( I, I ), 00320 $ LDA, TAU( I ), T, LDT ) 00321 IF( LEFT ) THEN 00322 * 00323 * H or H**T is applied to C(i:m,1:n) 00324 * 00325 MI = M - I + 1 00326 IC = I 00327 ELSE 00328 * 00329 * H or H**T is applied to C(1:m,i:n) 00330 * 00331 NI = N - I + 1 00332 JC = I 00333 END IF 00334 * 00335 * Apply H or H**T 00336 * 00337 CALL DLARFB( SIDE, TRANS, 'Forward', 'Columnwise', MI, NI, 00338 $ IB, A( I, I ), LDA, T, LDT, C( IC, JC ), LDC, 00339 $ WORK, LDWORK ) 00340 10 CONTINUE 00341 END IF 00342 WORK( 1 ) = LWKOPT 00343 RETURN 00344 * 00345 * End of DORMQR 00346 * 00347 END