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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b DORMTR 00002 * 00003 * =========== DOCUMENTATION =========== 00004 * 00005 * Online html documentation available at 00006 * http://www.netlib.org/lapack/explore-html/ 00007 * 00008 *> \htmlonly 00009 *> Download DORMTR + dependencies 00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dormtr.f"> 00011 *> [TGZ]</a> 00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dormtr.f"> 00013 *> [ZIP]</a> 00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dormtr.f"> 00015 *> [TXT]</a> 00016 *> \endhtmlonly 00017 * 00018 * Definition: 00019 * =========== 00020 * 00021 * SUBROUTINE DORMTR( 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 * DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) 00030 * .. 00031 * 00032 * 00033 *> \par Purpose: 00034 * ============= 00035 *> 00036 *> \verbatim 00037 *> 00038 *> DORMTR 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 of order nq, with nq = m if 00045 *> SIDE = 'L' and nq = n if SIDE = 'R'. Q is defined as the product of 00046 *> nq-1 elementary reflectors, as returned by DSYTRD: 00047 *> 00048 *> if UPLO = 'U', Q = H(nq-1) . . . H(2) H(1); 00049 *> 00050 *> if UPLO = 'L', Q = H(1) H(2) . . . H(nq-1). 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] UPLO 00064 *> \verbatim 00065 *> UPLO is CHARACTER*1 00066 *> = 'U': Upper triangle of A contains elementary reflectors 00067 *> from DSYTRD; 00068 *> = 'L': Lower triangle of A contains elementary reflectors 00069 *> from DSYTRD. 00070 *> \endverbatim 00071 *> 00072 *> \param[in] TRANS 00073 *> \verbatim 00074 *> TRANS is CHARACTER*1 00075 *> = 'N': No transpose, apply Q; 00076 *> = 'T': Transpose, apply Q**T. 00077 *> \endverbatim 00078 *> 00079 *> \param[in] M 00080 *> \verbatim 00081 *> M is INTEGER 00082 *> The number of rows of the matrix C. M >= 0. 00083 *> \endverbatim 00084 *> 00085 *> \param[in] N 00086 *> \verbatim 00087 *> N is INTEGER 00088 *> The number of columns of the matrix C. N >= 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 vectors which define the elementary reflectors, as 00097 *> returned by DSYTRD. 00098 *> \endverbatim 00099 *> 00100 *> \param[in] LDA 00101 *> \verbatim 00102 *> LDA is INTEGER 00103 *> The leading dimension of the array A. 00104 *> LDA >= max(1,M) if SIDE = 'L'; LDA >= max(1,N) if SIDE = 'R'. 00105 *> \endverbatim 00106 *> 00107 *> \param[in] TAU 00108 *> \verbatim 00109 *> TAU is DOUBLE PRECISION array, dimension 00110 *> (M-1) if SIDE = 'L' 00111 *> (N-1) if SIDE = 'R' 00112 *> TAU(i) must contain the scalar factor of the elementary 00113 *> reflector H(i), as returned by DSYTRD. 00114 *> \endverbatim 00115 *> 00116 *> \param[in,out] C 00117 *> \verbatim 00118 *> C is DOUBLE PRECISION array, dimension (LDC,N) 00119 *> On entry, the M-by-N matrix C. 00120 *> On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q. 00121 *> \endverbatim 00122 *> 00123 *> \param[in] LDC 00124 *> \verbatim 00125 *> LDC is INTEGER 00126 *> The leading dimension of the array C. LDC >= max(1,M). 00127 *> \endverbatim 00128 *> 00129 *> \param[out] WORK 00130 *> \verbatim 00131 *> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) 00132 *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. 00133 *> \endverbatim 00134 *> 00135 *> \param[in] LWORK 00136 *> \verbatim 00137 *> LWORK is INTEGER 00138 *> The dimension of the array WORK. 00139 *> If SIDE = 'L', LWORK >= max(1,N); 00140 *> if SIDE = 'R', LWORK >= max(1,M). 00141 *> For optimum performance LWORK >= N*NB if SIDE = 'L', and 00142 *> LWORK >= M*NB if SIDE = 'R', where NB is the optimal 00143 *> blocksize. 00144 *> 00145 *> If LWORK = -1, then a workspace query is assumed; the routine 00146 *> only calculates the optimal size of the WORK array, returns 00147 *> this value as the first entry of the WORK array, and no error 00148 *> message related to LWORK is issued by XERBLA. 00149 *> \endverbatim 00150 *> 00151 *> \param[out] INFO 00152 *> \verbatim 00153 *> INFO is INTEGER 00154 *> = 0: successful exit 00155 *> < 0: if INFO = -i, the i-th argument had an illegal value 00156 *> \endverbatim 00157 * 00158 * Authors: 00159 * ======== 00160 * 00161 *> \author Univ. of Tennessee 00162 *> \author Univ. of California Berkeley 00163 *> \author Univ. of Colorado Denver 00164 *> \author NAG Ltd. 00165 * 00166 *> \date November 2011 00167 * 00168 *> \ingroup doubleOTHERcomputational 00169 * 00170 * ===================================================================== 00171 SUBROUTINE DORMTR( SIDE, UPLO, TRANS, M, N, A, LDA, TAU, C, LDC, 00172 $ WORK, LWORK, INFO ) 00173 * 00174 * -- LAPACK computational routine (version 3.4.0) -- 00175 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00176 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00177 * November 2011 00178 * 00179 * .. Scalar Arguments .. 00180 CHARACTER SIDE, TRANS, UPLO 00181 INTEGER INFO, LDA, LDC, LWORK, M, N 00182 * .. 00183 * .. Array Arguments .. 00184 DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) 00185 * .. 00186 * 00187 * ===================================================================== 00188 * 00189 * .. Local Scalars .. 00190 LOGICAL LEFT, LQUERY, UPPER 00191 INTEGER I1, I2, IINFO, LWKOPT, MI, NB, NI, NQ, NW 00192 * .. 00193 * .. External Functions .. 00194 LOGICAL LSAME 00195 INTEGER ILAENV 00196 EXTERNAL LSAME, ILAENV 00197 * .. 00198 * .. External Subroutines .. 00199 EXTERNAL DORMQL, DORMQR, XERBLA 00200 * .. 00201 * .. Intrinsic Functions .. 00202 INTRINSIC MAX 00203 * .. 00204 * .. Executable Statements .. 00205 * 00206 * Test the input arguments 00207 * 00208 INFO = 0 00209 LEFT = LSAME( SIDE, 'L' ) 00210 UPPER = LSAME( UPLO, 'U' ) 00211 LQUERY = ( LWORK.EQ.-1 ) 00212 * 00213 * NQ is the order of Q and NW is the minimum dimension of WORK 00214 * 00215 IF( LEFT ) THEN 00216 NQ = M 00217 NW = N 00218 ELSE 00219 NQ = N 00220 NW = M 00221 END IF 00222 IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN 00223 INFO = -1 00224 ELSE IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN 00225 INFO = -2 00226 ELSE IF( .NOT.LSAME( TRANS, 'N' ) .AND. .NOT.LSAME( TRANS, 'T' ) ) 00227 $ THEN 00228 INFO = -3 00229 ELSE IF( M.LT.0 ) THEN 00230 INFO = -4 00231 ELSE IF( N.LT.0 ) THEN 00232 INFO = -5 00233 ELSE IF( LDA.LT.MAX( 1, NQ ) ) THEN 00234 INFO = -7 00235 ELSE IF( LDC.LT.MAX( 1, M ) ) THEN 00236 INFO = -10 00237 ELSE IF( LWORK.LT.MAX( 1, NW ) .AND. .NOT.LQUERY ) THEN 00238 INFO = -12 00239 END IF 00240 * 00241 IF( INFO.EQ.0 ) THEN 00242 IF( UPPER ) THEN 00243 IF( LEFT ) THEN 00244 NB = ILAENV( 1, 'DORMQL', SIDE // TRANS, M-1, N, M-1, 00245 $ -1 ) 00246 ELSE 00247 NB = ILAENV( 1, 'DORMQL', SIDE // TRANS, M, N-1, N-1, 00248 $ -1 ) 00249 END IF 00250 ELSE 00251 IF( LEFT ) THEN 00252 NB = ILAENV( 1, 'DORMQR', SIDE // TRANS, M-1, N, M-1, 00253 $ -1 ) 00254 ELSE 00255 NB = ILAENV( 1, 'DORMQR', SIDE // TRANS, M, N-1, N-1, 00256 $ -1 ) 00257 END IF 00258 END IF 00259 LWKOPT = MAX( 1, NW )*NB 00260 WORK( 1 ) = LWKOPT 00261 END IF 00262 * 00263 IF( INFO.NE.0 ) THEN 00264 CALL XERBLA( 'DORMTR', -INFO ) 00265 RETURN 00266 ELSE IF( LQUERY ) THEN 00267 RETURN 00268 END IF 00269 * 00270 * Quick return if possible 00271 * 00272 IF( M.EQ.0 .OR. N.EQ.0 .OR. NQ.EQ.1 ) THEN 00273 WORK( 1 ) = 1 00274 RETURN 00275 END IF 00276 * 00277 IF( LEFT ) THEN 00278 MI = M - 1 00279 NI = N 00280 ELSE 00281 MI = M 00282 NI = N - 1 00283 END IF 00284 * 00285 IF( UPPER ) THEN 00286 * 00287 * Q was determined by a call to DSYTRD with UPLO = 'U' 00288 * 00289 CALL DORMQL( SIDE, TRANS, MI, NI, NQ-1, A( 1, 2 ), LDA, TAU, C, 00290 $ LDC, WORK, LWORK, IINFO ) 00291 ELSE 00292 * 00293 * Q was determined by a call to DSYTRD with UPLO = 'L' 00294 * 00295 IF( LEFT ) THEN 00296 I1 = 2 00297 I2 = 1 00298 ELSE 00299 I1 = 1 00300 I2 = 2 00301 END IF 00302 CALL DORMQR( SIDE, TRANS, MI, NI, NQ-1, A( 2, 1 ), LDA, TAU, 00303 $ C( I1, I2 ), LDC, WORK, LWORK, IINFO ) 00304 END IF 00305 WORK( 1 ) = LWKOPT 00306 RETURN 00307 * 00308 * End of DORMTR 00309 * 00310 END