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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b SORMRZ 00002 * 00003 * =========== DOCUMENTATION =========== 00004 * 00005 * Online html documentation available at 00006 * http://www.netlib.org/lapack/explore-html/ 00007 * 00008 *> \htmlonly 00009 *> Download SORMRZ + dependencies 00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/sormrz.f"> 00011 *> [TGZ]</a> 00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/sormrz.f"> 00013 *> [ZIP]</a> 00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/sormrz.f"> 00015 *> [TXT]</a> 00016 *> \endhtmlonly 00017 * 00018 * Definition: 00019 * =========== 00020 * 00021 * SUBROUTINE SORMRZ( SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC, 00022 * WORK, LWORK, INFO ) 00023 * 00024 * .. Scalar Arguments .. 00025 * CHARACTER SIDE, TRANS 00026 * INTEGER INFO, K, L, LDA, LDC, LWORK, M, N 00027 * .. 00028 * .. Array Arguments .. 00029 * REAL A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) 00030 * .. 00031 * 00032 * 00033 *> \par Purpose: 00034 * ============= 00035 *> 00036 *> \verbatim 00037 *> 00038 *> SORMRZ 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 STZRZF. 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] L 00092 *> \verbatim 00093 *> L is INTEGER 00094 *> The number of columns of the matrix A containing 00095 *> the meaningful part of the Householder reflectors. 00096 *> If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0. 00097 *> \endverbatim 00098 *> 00099 *> \param[in] A 00100 *> \verbatim 00101 *> A is REAL array, dimension 00102 *> (LDA,M) if SIDE = 'L', 00103 *> (LDA,N) if SIDE = 'R' 00104 *> The i-th row must contain the vector which defines the 00105 *> elementary reflector H(i), for i = 1,2,...,k, as returned by 00106 *> STZRZF in the last k rows of its array argument A. 00107 *> A is modified by the routine but restored on exit. 00108 *> \endverbatim 00109 *> 00110 *> \param[in] LDA 00111 *> \verbatim 00112 *> LDA is INTEGER 00113 *> The leading dimension of the array A. LDA >= max(1,K). 00114 *> \endverbatim 00115 *> 00116 *> \param[in] TAU 00117 *> \verbatim 00118 *> TAU is REAL array, dimension (K) 00119 *> TAU(i) must contain the scalar factor of the elementary 00120 *> reflector H(i), as returned by STZRZF. 00121 *> \endverbatim 00122 *> 00123 *> \param[in,out] C 00124 *> \verbatim 00125 *> C is REAL array, dimension (LDC,N) 00126 *> On entry, the M-by-N matrix C. 00127 *> On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q. 00128 *> \endverbatim 00129 *> 00130 *> \param[in] LDC 00131 *> \verbatim 00132 *> LDC is INTEGER 00133 *> The leading dimension of the array C. LDC >= max(1,M). 00134 *> \endverbatim 00135 *> 00136 *> \param[out] WORK 00137 *> \verbatim 00138 *> WORK is REAL array, dimension (MAX(1,LWORK)) 00139 *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. 00140 *> \endverbatim 00141 *> 00142 *> \param[in] LWORK 00143 *> \verbatim 00144 *> LWORK is INTEGER 00145 *> The dimension of the array WORK. 00146 *> If SIDE = 'L', LWORK >= max(1,N); 00147 *> if SIDE = 'R', LWORK >= max(1,M). 00148 *> For optimum performance LWORK >= N*NB if SIDE = 'L', and 00149 *> LWORK >= M*NB if SIDE = 'R', where NB is the optimal 00150 *> blocksize. 00151 *> 00152 *> If LWORK = -1, then a workspace query is assumed; the routine 00153 *> only calculates the optimal size of the WORK array, returns 00154 *> this value as the first entry of the WORK array, and no error 00155 *> message related to LWORK is issued by XERBLA. 00156 *> \endverbatim 00157 *> 00158 *> \param[out] INFO 00159 *> \verbatim 00160 *> INFO is INTEGER 00161 *> = 0: successful exit 00162 *> < 0: if INFO = -i, the i-th argument had an illegal value 00163 *> \endverbatim 00164 * 00165 * Authors: 00166 * ======== 00167 * 00168 *> \author Univ. of Tennessee 00169 *> \author Univ. of California Berkeley 00170 *> \author Univ. of Colorado Denver 00171 *> \author NAG Ltd. 00172 * 00173 *> \date November 2011 00174 * 00175 *> \ingroup realOTHERcomputational 00176 * 00177 *> \par Contributors: 00178 * ================== 00179 *> 00180 *> A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA 00181 * 00182 *> \par Further Details: 00183 * ===================== 00184 *> 00185 *> \verbatim 00186 *> \endverbatim 00187 *> 00188 * ===================================================================== 00189 SUBROUTINE SORMRZ( SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC, 00190 $ WORK, LWORK, INFO ) 00191 * 00192 * -- LAPACK computational routine (version 3.4.0) -- 00193 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00194 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00195 * November 2011 00196 * 00197 * .. Scalar Arguments .. 00198 CHARACTER SIDE, TRANS 00199 INTEGER INFO, K, L, LDA, LDC, LWORK, M, N 00200 * .. 00201 * .. Array Arguments .. 00202 REAL A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) 00203 * .. 00204 * 00205 * ===================================================================== 00206 * 00207 * .. Parameters .. 00208 INTEGER NBMAX, LDT 00209 PARAMETER ( NBMAX = 64, LDT = NBMAX+1 ) 00210 * .. 00211 * .. Local Scalars .. 00212 LOGICAL LEFT, LQUERY, NOTRAN 00213 CHARACTER TRANST 00214 INTEGER I, I1, I2, I3, IB, IC, IINFO, IWS, JA, JC, 00215 $ LDWORK, LWKOPT, MI, NB, NBMIN, NI, NQ, NW 00216 * .. 00217 * .. Local Arrays .. 00218 REAL T( LDT, NBMAX ) 00219 * .. 00220 * .. External Functions .. 00221 LOGICAL LSAME 00222 INTEGER ILAENV 00223 EXTERNAL LSAME, ILAENV 00224 * .. 00225 * .. External Subroutines .. 00226 EXTERNAL SLARZB, SLARZT, SORMR3, XERBLA 00227 * .. 00228 * .. Intrinsic Functions .. 00229 INTRINSIC MAX, MIN 00230 * .. 00231 * .. Executable Statements .. 00232 * 00233 * Test the input arguments 00234 * 00235 INFO = 0 00236 LEFT = LSAME( SIDE, 'L' ) 00237 NOTRAN = LSAME( TRANS, 'N' ) 00238 LQUERY = ( LWORK.EQ.-1 ) 00239 * 00240 * NQ is the order of Q and NW is the minimum dimension of WORK 00241 * 00242 IF( LEFT ) THEN 00243 NQ = M 00244 NW = MAX( 1, N ) 00245 ELSE 00246 NQ = N 00247 NW = MAX( 1, M ) 00248 END IF 00249 IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN 00250 INFO = -1 00251 ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) ) THEN 00252 INFO = -2 00253 ELSE IF( M.LT.0 ) THEN 00254 INFO = -3 00255 ELSE IF( N.LT.0 ) THEN 00256 INFO = -4 00257 ELSE IF( K.LT.0 .OR. K.GT.NQ ) THEN 00258 INFO = -5 00259 ELSE IF( L.LT.0 .OR. ( LEFT .AND. ( L.GT.M ) ) .OR. 00260 $ ( .NOT.LEFT .AND. ( L.GT.N ) ) ) THEN 00261 INFO = -6 00262 ELSE IF( LDA.LT.MAX( 1, K ) ) THEN 00263 INFO = -8 00264 ELSE IF( LDC.LT.MAX( 1, M ) ) THEN 00265 INFO = -11 00266 END IF 00267 * 00268 IF( INFO.EQ.0 ) THEN 00269 IF( M.EQ.0 .OR. N.EQ.0 ) THEN 00270 LWKOPT = 1 00271 ELSE 00272 * 00273 * Determine the block size. NB may be at most NBMAX, where 00274 * NBMAX is used to define the local array T. 00275 * 00276 NB = MIN( NBMAX, ILAENV( 1, 'SORMRQ', SIDE // TRANS, M, N, 00277 $ K, -1 ) ) 00278 LWKOPT = NW*NB 00279 END IF 00280 WORK( 1 ) = LWKOPT 00281 * 00282 IF( LWORK.LT.MAX( 1, NW ) .AND. .NOT.LQUERY ) THEN 00283 INFO = -13 00284 END IF 00285 END IF 00286 * 00287 IF( INFO.NE.0 ) THEN 00288 CALL XERBLA( 'SORMRZ', -INFO ) 00289 RETURN 00290 ELSE IF( LQUERY ) THEN 00291 RETURN 00292 END IF 00293 * 00294 * Quick return if possible 00295 * 00296 IF( M.EQ.0 .OR. N.EQ.0 ) THEN 00297 RETURN 00298 END IF 00299 * 00300 NBMIN = 2 00301 LDWORK = NW 00302 IF( NB.GT.1 .AND. NB.LT.K ) THEN 00303 IWS = NW*NB 00304 IF( LWORK.LT.IWS ) THEN 00305 NB = LWORK / LDWORK 00306 NBMIN = MAX( 2, ILAENV( 2, 'SORMRQ', SIDE // TRANS, M, N, K, 00307 $ -1 ) ) 00308 END IF 00309 ELSE 00310 IWS = NW 00311 END IF 00312 * 00313 IF( NB.LT.NBMIN .OR. NB.GE.K ) THEN 00314 * 00315 * Use unblocked code 00316 * 00317 CALL SORMR3( SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC, 00318 $ WORK, IINFO ) 00319 ELSE 00320 * 00321 * Use blocked code 00322 * 00323 IF( ( LEFT .AND. .NOT.NOTRAN ) .OR. 00324 $ ( .NOT.LEFT .AND. NOTRAN ) ) THEN 00325 I1 = 1 00326 I2 = K 00327 I3 = NB 00328 ELSE 00329 I1 = ( ( K-1 ) / NB )*NB + 1 00330 I2 = 1 00331 I3 = -NB 00332 END IF 00333 * 00334 IF( LEFT ) THEN 00335 NI = N 00336 JC = 1 00337 JA = M - L + 1 00338 ELSE 00339 MI = M 00340 IC = 1 00341 JA = N - L + 1 00342 END IF 00343 * 00344 IF( NOTRAN ) THEN 00345 TRANST = 'T' 00346 ELSE 00347 TRANST = 'N' 00348 END IF 00349 * 00350 DO 10 I = I1, I2, I3 00351 IB = MIN( NB, K-I+1 ) 00352 * 00353 * Form the triangular factor of the block reflector 00354 * H = H(i+ib-1) . . . H(i+1) H(i) 00355 * 00356 CALL SLARZT( 'Backward', 'Rowwise', L, IB, A( I, JA ), LDA, 00357 $ TAU( I ), T, LDT ) 00358 * 00359 IF( LEFT ) THEN 00360 * 00361 * H or H**T is applied to C(i:m,1:n) 00362 * 00363 MI = M - I + 1 00364 IC = I 00365 ELSE 00366 * 00367 * H or H**T is applied to C(1:m,i:n) 00368 * 00369 NI = N - I + 1 00370 JC = I 00371 END IF 00372 * 00373 * Apply H or H**T 00374 * 00375 CALL SLARZB( SIDE, TRANST, 'Backward', 'Rowwise', MI, NI, 00376 $ IB, L, A( I, JA ), LDA, T, LDT, C( IC, JC ), 00377 $ LDC, WORK, LDWORK ) 00378 10 CONTINUE 00379 * 00380 END IF 00381 * 00382 WORK( 1 ) = LWKOPT 00383 * 00384 RETURN 00385 * 00386 * End of SORMRZ 00387 * 00388 END