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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b SORMR3 00002 * 00003 * =========== DOCUMENTATION =========== 00004 * 00005 * Online html documentation available at 00006 * http://www.netlib.org/lapack/explore-html/ 00007 * 00008 *> \htmlonly 00009 *> Download SORMR3 + dependencies 00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/sormr3.f"> 00011 *> [TGZ]</a> 00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/sormr3.f"> 00013 *> [ZIP]</a> 00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/sormr3.f"> 00015 *> [TXT]</a> 00016 *> \endhtmlonly 00017 * 00018 * Definition: 00019 * =========== 00020 * 00021 * SUBROUTINE SORMR3( SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC, 00022 * WORK, INFO ) 00023 * 00024 * .. Scalar Arguments .. 00025 * CHARACTER SIDE, TRANS 00026 * INTEGER INFO, K, L, LDA, LDC, 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 *> SORMR3 overwrites the general real m by n matrix C with 00039 *> 00040 *> Q * C if SIDE = 'L' and TRANS = 'N', or 00041 *> 00042 *> Q**T* C if SIDE = 'L' and TRANS = 'C', or 00043 *> 00044 *> C * Q if SIDE = 'R' and TRANS = 'N', or 00045 *> 00046 *> C * Q**T if SIDE = 'R' and TRANS = 'C', 00047 *> 00048 *> where Q is a real orthogonal matrix defined as the product of k 00049 *> elementary reflectors 00050 *> 00051 *> Q = H(1) H(2) . . . H(k) 00052 *> 00053 *> as returned by STZRZF. Q is of order m if SIDE = 'L' and of order n 00054 *> if SIDE = 'R'. 00055 *> \endverbatim 00056 * 00057 * Arguments: 00058 * ========== 00059 * 00060 *> \param[in] SIDE 00061 *> \verbatim 00062 *> SIDE is CHARACTER*1 00063 *> = 'L': apply Q or Q**T from the Left 00064 *> = 'R': apply Q or Q**T from the Right 00065 *> \endverbatim 00066 *> 00067 *> \param[in] TRANS 00068 *> \verbatim 00069 *> TRANS is CHARACTER*1 00070 *> = 'N': apply Q (No transpose) 00071 *> = 'T': apply Q**T (Transpose) 00072 *> \endverbatim 00073 *> 00074 *> \param[in] M 00075 *> \verbatim 00076 *> M is INTEGER 00077 *> The number of rows of the matrix C. M >= 0. 00078 *> \endverbatim 00079 *> 00080 *> \param[in] N 00081 *> \verbatim 00082 *> N is INTEGER 00083 *> The number of columns of the matrix C. N >= 0. 00084 *> \endverbatim 00085 *> 00086 *> \param[in] K 00087 *> \verbatim 00088 *> K is INTEGER 00089 *> The number of elementary reflectors whose product defines 00090 *> the matrix Q. 00091 *> If SIDE = 'L', M >= K >= 0; 00092 *> if SIDE = 'R', N >= K >= 0. 00093 *> \endverbatim 00094 *> 00095 *> \param[in] L 00096 *> \verbatim 00097 *> L is INTEGER 00098 *> The number of columns of the matrix A containing 00099 *> the meaningful part of the Householder reflectors. 00100 *> If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0. 00101 *> \endverbatim 00102 *> 00103 *> \param[in] A 00104 *> \verbatim 00105 *> A is REAL array, dimension 00106 *> (LDA,M) if SIDE = 'L', 00107 *> (LDA,N) if SIDE = 'R' 00108 *> The i-th row must contain the vector which defines the 00109 *> elementary reflector H(i), for i = 1,2,...,k, as returned by 00110 *> STZRZF in the last k rows of its array argument A. 00111 *> A is modified by the routine but restored on exit. 00112 *> \endverbatim 00113 *> 00114 *> \param[in] LDA 00115 *> \verbatim 00116 *> LDA is INTEGER 00117 *> The leading dimension of the array A. LDA >= max(1,K). 00118 *> \endverbatim 00119 *> 00120 *> \param[in] TAU 00121 *> \verbatim 00122 *> TAU is REAL array, dimension (K) 00123 *> TAU(i) must contain the scalar factor of the elementary 00124 *> reflector H(i), as returned by STZRZF. 00125 *> \endverbatim 00126 *> 00127 *> \param[in,out] C 00128 *> \verbatim 00129 *> C is REAL array, dimension (LDC,N) 00130 *> On entry, the m-by-n matrix C. 00131 *> On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q. 00132 *> \endverbatim 00133 *> 00134 *> \param[in] LDC 00135 *> \verbatim 00136 *> LDC is INTEGER 00137 *> The leading dimension of the array C. LDC >= max(1,M). 00138 *> \endverbatim 00139 *> 00140 *> \param[out] WORK 00141 *> \verbatim 00142 *> WORK is REAL array, dimension 00143 *> (N) if SIDE = 'L', 00144 *> (M) if SIDE = 'R' 00145 *> \endverbatim 00146 *> 00147 *> \param[out] INFO 00148 *> \verbatim 00149 *> INFO is INTEGER 00150 *> = 0: successful exit 00151 *> < 0: if INFO = -i, the i-th argument had an illegal value 00152 *> \endverbatim 00153 * 00154 * Authors: 00155 * ======== 00156 * 00157 *> \author Univ. of Tennessee 00158 *> \author Univ. of California Berkeley 00159 *> \author Univ. of Colorado Denver 00160 *> \author NAG Ltd. 00161 * 00162 *> \date November 2011 00163 * 00164 *> \ingroup realOTHERcomputational 00165 * 00166 *> \par Contributors: 00167 * ================== 00168 *> 00169 *> A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA 00170 * 00171 *> \par Further Details: 00172 * ===================== 00173 *> 00174 *> \verbatim 00175 *> \endverbatim 00176 *> 00177 * ===================================================================== 00178 SUBROUTINE SORMR3( SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC, 00179 $ WORK, INFO ) 00180 * 00181 * -- LAPACK computational routine (version 3.4.0) -- 00182 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00183 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00184 * November 2011 00185 * 00186 * .. Scalar Arguments .. 00187 CHARACTER SIDE, TRANS 00188 INTEGER INFO, K, L, LDA, LDC, M, N 00189 * .. 00190 * .. Array Arguments .. 00191 REAL A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) 00192 * .. 00193 * 00194 * ===================================================================== 00195 * 00196 * .. Local Scalars .. 00197 LOGICAL LEFT, NOTRAN 00198 INTEGER I, I1, I2, I3, IC, JA, JC, MI, NI, NQ 00199 * .. 00200 * .. External Functions .. 00201 LOGICAL LSAME 00202 EXTERNAL LSAME 00203 * .. 00204 * .. External Subroutines .. 00205 EXTERNAL SLARZ, XERBLA 00206 * .. 00207 * .. Intrinsic Functions .. 00208 INTRINSIC MAX 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 * 00218 * NQ is the order of Q 00219 * 00220 IF( LEFT ) THEN 00221 NQ = M 00222 ELSE 00223 NQ = N 00224 END IF 00225 IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN 00226 INFO = -1 00227 ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) ) THEN 00228 INFO = -2 00229 ELSE IF( M.LT.0 ) THEN 00230 INFO = -3 00231 ELSE IF( N.LT.0 ) THEN 00232 INFO = -4 00233 ELSE IF( K.LT.0 .OR. K.GT.NQ ) THEN 00234 INFO = -5 00235 ELSE IF( L.LT.0 .OR. ( LEFT .AND. ( L.GT.M ) ) .OR. 00236 $ ( .NOT.LEFT .AND. ( L.GT.N ) ) ) THEN 00237 INFO = -6 00238 ELSE IF( LDA.LT.MAX( 1, K ) ) THEN 00239 INFO = -8 00240 ELSE IF( LDC.LT.MAX( 1, M ) ) THEN 00241 INFO = -11 00242 END IF 00243 IF( INFO.NE.0 ) THEN 00244 CALL XERBLA( 'SORMR3', -INFO ) 00245 RETURN 00246 END IF 00247 * 00248 * Quick return if possible 00249 * 00250 IF( M.EQ.0 .OR. N.EQ.0 .OR. K.EQ.0 ) 00251 $ RETURN 00252 * 00253 IF( ( LEFT .AND. .NOT.NOTRAN .OR. .NOT.LEFT .AND. NOTRAN ) ) THEN 00254 I1 = 1 00255 I2 = K 00256 I3 = 1 00257 ELSE 00258 I1 = K 00259 I2 = 1 00260 I3 = -1 00261 END IF 00262 * 00263 IF( LEFT ) THEN 00264 NI = N 00265 JA = M - L + 1 00266 JC = 1 00267 ELSE 00268 MI = M 00269 JA = N - L + 1 00270 IC = 1 00271 END IF 00272 * 00273 DO 10 I = I1, I2, I3 00274 IF( LEFT ) THEN 00275 * 00276 * H(i) or H(i)**T is applied to C(i:m,1:n) 00277 * 00278 MI = M - I + 1 00279 IC = I 00280 ELSE 00281 * 00282 * H(i) or H(i)**T is applied to C(1:m,i:n) 00283 * 00284 NI = N - I + 1 00285 JC = I 00286 END IF 00287 * 00288 * Apply H(i) or H(i)**T 00289 * 00290 CALL SLARZ( SIDE, MI, NI, L, A( I, JA ), LDA, TAU( I ), 00291 $ C( IC, JC ), LDC, WORK ) 00292 * 00293 10 CONTINUE 00294 * 00295 RETURN 00296 * 00297 * End of SORMR3 00298 * 00299 END