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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b SORMHR 00002 * 00003 * =========== DOCUMENTATION =========== 00004 * 00005 * Online html documentation available at 00006 * http://www.netlib.org/lapack/explore-html/ 00007 * 00008 *> \htmlonly 00009 *> Download SORMHR + dependencies 00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/sormhr.f"> 00011 *> [TGZ]</a> 00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/sormhr.f"> 00013 *> [ZIP]</a> 00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/sormhr.f"> 00015 *> [TXT]</a> 00016 *> \endhtmlonly 00017 * 00018 * Definition: 00019 * =========== 00020 * 00021 * SUBROUTINE SORMHR( SIDE, TRANS, M, N, ILO, IHI, A, LDA, TAU, C, 00022 * LDC, WORK, LWORK, INFO ) 00023 * 00024 * .. Scalar Arguments .. 00025 * CHARACTER SIDE, TRANS 00026 * INTEGER IHI, ILO, INFO, LDA, LDC, LWORK, M, N 00027 * .. 00028 * .. Array Arguments .. 00029 * REAL A( LDA, * ), C( LDC, * ), TAU( * ), 00030 * $ WORK( * ) 00031 * .. 00032 * 00033 * 00034 *> \par Purpose: 00035 * ============= 00036 *> 00037 *> \verbatim 00038 *> 00039 *> SORMHR overwrites the general real M-by-N matrix C with 00040 *> 00041 *> SIDE = 'L' SIDE = 'R' 00042 *> TRANS = 'N': Q * C C * Q 00043 *> TRANS = 'T': Q**T * C C * Q**T 00044 *> 00045 *> where Q is a real orthogonal matrix of order nq, with nq = m if 00046 *> SIDE = 'L' and nq = n if SIDE = 'R'. Q is defined as the product of 00047 *> IHI-ILO elementary reflectors, as returned by SGEHRD: 00048 *> 00049 *> Q = H(ilo) H(ilo+1) . . . H(ihi-1). 00050 *> \endverbatim 00051 * 00052 * Arguments: 00053 * ========== 00054 * 00055 *> \param[in] SIDE 00056 *> \verbatim 00057 *> SIDE is CHARACTER*1 00058 *> = 'L': apply Q or Q**T from the Left; 00059 *> = 'R': apply Q or Q**T from the Right. 00060 *> \endverbatim 00061 *> 00062 *> \param[in] TRANS 00063 *> \verbatim 00064 *> TRANS is CHARACTER*1 00065 *> = 'N': No transpose, apply Q; 00066 *> = 'T': Transpose, apply Q**T. 00067 *> \endverbatim 00068 *> 00069 *> \param[in] M 00070 *> \verbatim 00071 *> M is INTEGER 00072 *> The number of rows of the matrix C. M >= 0. 00073 *> \endverbatim 00074 *> 00075 *> \param[in] N 00076 *> \verbatim 00077 *> N is INTEGER 00078 *> The number of columns of the matrix C. N >= 0. 00079 *> \endverbatim 00080 *> 00081 *> \param[in] ILO 00082 *> \verbatim 00083 *> ILO is INTEGER 00084 *> \endverbatim 00085 *> 00086 *> \param[in] IHI 00087 *> \verbatim 00088 *> IHI is INTEGER 00089 *> 00090 *> ILO and IHI must have the same values as in the previous call 00091 *> of SGEHRD. Q is equal to the unit matrix except in the 00092 *> submatrix Q(ilo+1:ihi,ilo+1:ihi). 00093 *> If SIDE = 'L', then 1 <= ILO <= IHI <= M, if M > 0, and 00094 *> ILO = 1 and IHI = 0, if M = 0; 00095 *> if SIDE = 'R', then 1 <= ILO <= IHI <= N, if N > 0, and 00096 *> ILO = 1 and IHI = 0, if N = 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 vectors which define the elementary reflectors, as 00105 *> returned by SGEHRD. 00106 *> \endverbatim 00107 *> 00108 *> \param[in] LDA 00109 *> \verbatim 00110 *> LDA is INTEGER 00111 *> The leading dimension of the array A. 00112 *> LDA >= max(1,M) if SIDE = 'L'; LDA >= max(1,N) if SIDE = 'R'. 00113 *> \endverbatim 00114 *> 00115 *> \param[in] TAU 00116 *> \verbatim 00117 *> TAU is REAL array, dimension 00118 *> (M-1) if SIDE = 'L' 00119 *> (N-1) if SIDE = 'R' 00120 *> TAU(i) must contain the scalar factor of the elementary 00121 *> reflector H(i), as returned by SGEHRD. 00122 *> \endverbatim 00123 *> 00124 *> \param[in,out] C 00125 *> \verbatim 00126 *> C is REAL array, dimension (LDC,N) 00127 *> On entry, the M-by-N matrix C. 00128 *> On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q. 00129 *> \endverbatim 00130 *> 00131 *> \param[in] LDC 00132 *> \verbatim 00133 *> LDC is INTEGER 00134 *> The leading dimension of the array C. LDC >= max(1,M). 00135 *> \endverbatim 00136 *> 00137 *> \param[out] WORK 00138 *> \verbatim 00139 *> WORK is REAL array, dimension (MAX(1,LWORK)) 00140 *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. 00141 *> \endverbatim 00142 *> 00143 *> \param[in] LWORK 00144 *> \verbatim 00145 *> LWORK is INTEGER 00146 *> The dimension of the array WORK. 00147 *> If SIDE = 'L', LWORK >= max(1,N); 00148 *> if SIDE = 'R', LWORK >= max(1,M). 00149 *> For optimum performance LWORK >= N*NB if SIDE = 'L', and 00150 *> LWORK >= M*NB if SIDE = 'R', where NB is the optimal 00151 *> blocksize. 00152 *> 00153 *> If LWORK = -1, then a workspace query is assumed; the routine 00154 *> only calculates the optimal size of the WORK array, returns 00155 *> this value as the first entry of the WORK array, and no error 00156 *> message related to LWORK is issued by XERBLA. 00157 *> \endverbatim 00158 *> 00159 *> \param[out] INFO 00160 *> \verbatim 00161 *> INFO is INTEGER 00162 *> = 0: successful exit 00163 *> < 0: if INFO = -i, the i-th argument had an illegal value 00164 *> \endverbatim 00165 * 00166 * Authors: 00167 * ======== 00168 * 00169 *> \author Univ. of Tennessee 00170 *> \author Univ. of California Berkeley 00171 *> \author Univ. of Colorado Denver 00172 *> \author NAG Ltd. 00173 * 00174 *> \date November 2011 00175 * 00176 *> \ingroup realOTHERcomputational 00177 * 00178 * ===================================================================== 00179 SUBROUTINE SORMHR( SIDE, TRANS, M, N, ILO, IHI, A, LDA, TAU, C, 00180 $ LDC, WORK, LWORK, INFO ) 00181 * 00182 * -- LAPACK computational routine (version 3.4.0) -- 00183 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00184 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00185 * November 2011 00186 * 00187 * .. Scalar Arguments .. 00188 CHARACTER SIDE, TRANS 00189 INTEGER IHI, ILO, INFO, LDA, LDC, LWORK, M, N 00190 * .. 00191 * .. Array Arguments .. 00192 REAL A( LDA, * ), C( LDC, * ), TAU( * ), 00193 $ WORK( * ) 00194 * .. 00195 * 00196 * ===================================================================== 00197 * 00198 * .. Local Scalars .. 00199 LOGICAL LEFT, LQUERY 00200 INTEGER I1, I2, IINFO, LWKOPT, MI, NB, NH, NI, NQ, NW 00201 * .. 00202 * .. External Functions .. 00203 LOGICAL LSAME 00204 INTEGER ILAENV 00205 EXTERNAL ILAENV, LSAME 00206 * .. 00207 * .. External Subroutines .. 00208 EXTERNAL SORMQR, XERBLA 00209 * .. 00210 * .. Intrinsic Functions .. 00211 INTRINSIC MAX, MIN 00212 * .. 00213 * .. Executable Statements .. 00214 * 00215 * Test the input arguments 00216 * 00217 INFO = 0 00218 NH = IHI - ILO 00219 LEFT = LSAME( SIDE, 'L' ) 00220 LQUERY = ( LWORK.EQ.-1 ) 00221 * 00222 * NQ is the order of Q and NW is the minimum dimension of WORK 00223 * 00224 IF( LEFT ) THEN 00225 NQ = M 00226 NW = N 00227 ELSE 00228 NQ = N 00229 NW = M 00230 END IF 00231 IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN 00232 INFO = -1 00233 ELSE IF( .NOT.LSAME( TRANS, 'N' ) .AND. .NOT.LSAME( TRANS, 'T' ) ) 00234 $ THEN 00235 INFO = -2 00236 ELSE IF( M.LT.0 ) THEN 00237 INFO = -3 00238 ELSE IF( N.LT.0 ) THEN 00239 INFO = -4 00240 ELSE IF( ILO.LT.1 .OR. ILO.GT.MAX( 1, NQ ) ) THEN 00241 INFO = -5 00242 ELSE IF( IHI.LT.MIN( ILO, NQ ) .OR. IHI.GT.NQ ) THEN 00243 INFO = -6 00244 ELSE IF( LDA.LT.MAX( 1, NQ ) ) THEN 00245 INFO = -8 00246 ELSE IF( LDC.LT.MAX( 1, M ) ) THEN 00247 INFO = -11 00248 ELSE IF( LWORK.LT.MAX( 1, NW ) .AND. .NOT.LQUERY ) THEN 00249 INFO = -13 00250 END IF 00251 * 00252 IF( INFO.EQ.0 ) THEN 00253 IF( LEFT ) THEN 00254 NB = ILAENV( 1, 'SORMQR', SIDE // TRANS, NH, N, NH, -1 ) 00255 ELSE 00256 NB = ILAENV( 1, 'SORMQR', SIDE // TRANS, M, NH, NH, -1 ) 00257 END IF 00258 LWKOPT = MAX( 1, NW )*NB 00259 WORK( 1 ) = LWKOPT 00260 END IF 00261 * 00262 IF( INFO.NE.0 ) THEN 00263 CALL XERBLA( 'SORMHR', -INFO ) 00264 RETURN 00265 ELSE IF( LQUERY ) THEN 00266 RETURN 00267 END IF 00268 * 00269 * Quick return if possible 00270 * 00271 IF( M.EQ.0 .OR. N.EQ.0 .OR. NH.EQ.0 ) THEN 00272 WORK( 1 ) = 1 00273 RETURN 00274 END IF 00275 * 00276 IF( LEFT ) THEN 00277 MI = NH 00278 NI = N 00279 I1 = ILO + 1 00280 I2 = 1 00281 ELSE 00282 MI = M 00283 NI = NH 00284 I1 = 1 00285 I2 = ILO + 1 00286 END IF 00287 * 00288 CALL SORMQR( SIDE, TRANS, MI, NI, NH, A( ILO+1, ILO ), LDA, 00289 $ TAU( ILO ), C( I1, I2 ), LDC, WORK, LWORK, IINFO ) 00290 * 00291 WORK( 1 ) = LWKOPT 00292 RETURN 00293 * 00294 * End of SORMHR 00295 * 00296 END