LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
sormqr.f
Go to the documentation of this file.
00001 *> \brief \b SORMQR
00002 *
00003 *  =========== DOCUMENTATION ===========
00004 *
00005 * Online html documentation available at 
00006 *            http://www.netlib.org/lapack/explore-html/ 
00007 *
00008 *> \htmlonly
00009 *> Download SORMQR + dependencies 
00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/sormqr.f"> 
00011 *> [TGZ]</a> 
00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/sormqr.f"> 
00013 *> [ZIP]</a> 
00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/sormqr.f"> 
00015 *> [TXT]</a>
00016 *> \endhtmlonly 
00017 *
00018 *  Definition:
00019 *  ===========
00020 *
00021 *       SUBROUTINE SORMQR( 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 *       REAL               A( LDA, * ), C( LDC, * ), TAU( * ),
00030 *      $                   WORK( * )
00031 *       ..
00032 *  
00033 *
00034 *> \par Purpose:
00035 *  =============
00036 *>
00037 *> \verbatim
00038 *>
00039 *> SORMQR 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 defined as the product of k
00046 *> elementary reflectors
00047 *>
00048 *>       Q = H(1) H(2) . . . H(k)
00049 *>
00050 *> as returned by SGEQRF. Q is of order M if SIDE = 'L' and of order N
00051 *> if SIDE = 'R'.
00052 *> \endverbatim
00053 *
00054 *  Arguments:
00055 *  ==========
00056 *
00057 *> \param[in] SIDE
00058 *> \verbatim
00059 *>          SIDE is CHARACTER*1
00060 *>          = 'L': apply Q or Q**T from the Left;
00061 *>          = 'R': apply Q or Q**T from the Right.
00062 *> \endverbatim
00063 *>
00064 *> \param[in] TRANS
00065 *> \verbatim
00066 *>          TRANS is CHARACTER*1
00067 *>          = 'N':  No transpose, apply Q;
00068 *>          = 'T':  Transpose, apply Q**T.
00069 *> \endverbatim
00070 *>
00071 *> \param[in] M
00072 *> \verbatim
00073 *>          M is INTEGER
00074 *>          The number of rows of the matrix C. M >= 0.
00075 *> \endverbatim
00076 *>
00077 *> \param[in] N
00078 *> \verbatim
00079 *>          N is INTEGER
00080 *>          The number of columns of the matrix C. N >= 0.
00081 *> \endverbatim
00082 *>
00083 *> \param[in] K
00084 *> \verbatim
00085 *>          K is INTEGER
00086 *>          The number of elementary reflectors whose product defines
00087 *>          the matrix Q.
00088 *>          If SIDE = 'L', M >= K >= 0;
00089 *>          if SIDE = 'R', N >= K >= 0.
00090 *> \endverbatim
00091 *>
00092 *> \param[in] A
00093 *> \verbatim
00094 *>          A is REAL array, dimension (LDA,K)
00095 *>          The i-th column must contain the vector which defines the
00096 *>          elementary reflector H(i), for i = 1,2,...,k, as returned by
00097 *>          SGEQRF in the first k columns of its array argument A.
00098 *> \endverbatim
00099 *>
00100 *> \param[in] LDA
00101 *> \verbatim
00102 *>          LDA is INTEGER
00103 *>          The leading dimension of the array A.
00104 *>          If SIDE = 'L', LDA >= max(1,M);
00105 *>          if SIDE = 'R', LDA >= max(1,N).
00106 *> \endverbatim
00107 *>
00108 *> \param[in] TAU
00109 *> \verbatim
00110 *>          TAU is REAL array, dimension (K)
00111 *>          TAU(i) must contain the scalar factor of the elementary
00112 *>          reflector H(i), as returned by SGEQRF.
00113 *> \endverbatim
00114 *>
00115 *> \param[in,out] C
00116 *> \verbatim
00117 *>          C is REAL array, dimension (LDC,N)
00118 *>          On entry, the M-by-N matrix C.
00119 *>          On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q.
00120 *> \endverbatim
00121 *>
00122 *> \param[in] LDC
00123 *> \verbatim
00124 *>          LDC is INTEGER
00125 *>          The leading dimension of the array C. LDC >= max(1,M).
00126 *> \endverbatim
00127 *>
00128 *> \param[out] WORK
00129 *> \verbatim
00130 *>          WORK is REAL array, dimension (MAX(1,LWORK))
00131 *>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
00132 *> \endverbatim
00133 *>
00134 *> \param[in] LWORK
00135 *> \verbatim
00136 *>          LWORK is INTEGER
00137 *>          The dimension of the array WORK.
00138 *>          If SIDE = 'L', LWORK >= max(1,N);
00139 *>          if SIDE = 'R', LWORK >= max(1,M).
00140 *>          For optimum performance LWORK >= N*NB if SIDE = 'L', and
00141 *>          LWORK >= M*NB if SIDE = 'R', where NB is the optimal
00142 *>          blocksize.
00143 *>
00144 *>          If LWORK = -1, then a workspace query is assumed; the routine
00145 *>          only calculates the optimal size of the WORK array, returns
00146 *>          this value as the first entry of the WORK array, and no error
00147 *>          message related to LWORK is issued by XERBLA.
00148 *> \endverbatim
00149 *>
00150 *> \param[out] INFO
00151 *> \verbatim
00152 *>          INFO is INTEGER
00153 *>          = 0:  successful exit
00154 *>          < 0:  if INFO = -i, the i-th argument had an illegal value
00155 *> \endverbatim
00156 *
00157 *  Authors:
00158 *  ========
00159 *
00160 *> \author Univ. of Tennessee 
00161 *> \author Univ. of California Berkeley 
00162 *> \author Univ. of Colorado Denver 
00163 *> \author NAG Ltd. 
00164 *
00165 *> \date November 2011
00166 *
00167 *> \ingroup realOTHERcomputational
00168 *
00169 *  =====================================================================
00170       SUBROUTINE SORMQR( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
00171      $                   WORK, LWORK, INFO )
00172 *
00173 *  -- LAPACK computational routine (version 3.4.0) --
00174 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00175 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00176 *     November 2011
00177 *
00178 *     .. Scalar Arguments ..
00179       CHARACTER          SIDE, TRANS
00180       INTEGER            INFO, K, LDA, LDC, LWORK, M, N
00181 *     ..
00182 *     .. Array Arguments ..
00183       REAL               A( LDA, * ), C( LDC, * ), TAU( * ),
00184      $                   WORK( * )
00185 *     ..
00186 *
00187 *  =====================================================================
00188 *
00189 *     .. Parameters ..
00190       INTEGER            NBMAX, LDT
00191       PARAMETER          ( NBMAX = 64, LDT = NBMAX+1 )
00192 *     ..
00193 *     .. Local Scalars ..
00194       LOGICAL            LEFT, LQUERY, NOTRAN
00195       INTEGER            I, I1, I2, I3, IB, IC, IINFO, IWS, JC, LDWORK,
00196      $                   LWKOPT, MI, NB, NBMIN, NI, NQ, NW
00197 *     ..
00198 *     .. Local Arrays ..
00199       REAL               T( LDT, NBMAX )
00200 *     ..
00201 *     .. External Functions ..
00202       LOGICAL            LSAME
00203       INTEGER            ILAENV
00204       EXTERNAL           LSAME, ILAENV
00205 *     ..
00206 *     .. External Subroutines ..
00207       EXTERNAL           SLARFB, SLARFT, SORM2R, XERBLA
00208 *     ..
00209 *     .. Intrinsic Functions ..
00210       INTRINSIC          MAX, MIN
00211 *     ..
00212 *     .. Executable Statements ..
00213 *
00214 *     Test the input arguments
00215 *
00216       INFO = 0
00217       LEFT = LSAME( SIDE, 'L' )
00218       NOTRAN = LSAME( TRANS, 'N' )
00219       LQUERY = ( LWORK.EQ.-1 )
00220 *
00221 *     NQ is the order of Q and NW is the minimum dimension of WORK
00222 *
00223       IF( LEFT ) THEN
00224          NQ = M
00225          NW = N
00226       ELSE
00227          NQ = N
00228          NW = M
00229       END IF
00230       IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN
00231          INFO = -1
00232       ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) ) THEN
00233          INFO = -2
00234       ELSE IF( M.LT.0 ) THEN
00235          INFO = -3
00236       ELSE IF( N.LT.0 ) THEN
00237          INFO = -4
00238       ELSE IF( K.LT.0 .OR. K.GT.NQ ) THEN
00239          INFO = -5
00240       ELSE IF( LDA.LT.MAX( 1, NQ ) ) THEN
00241          INFO = -7
00242       ELSE IF( LDC.LT.MAX( 1, M ) ) THEN
00243          INFO = -10
00244       ELSE IF( LWORK.LT.MAX( 1, NW ) .AND. .NOT.LQUERY ) THEN
00245          INFO = -12
00246       END IF
00247 *
00248       IF( INFO.EQ.0 ) THEN
00249 *
00250 *        Determine the block size.  NB may be at most NBMAX, where NBMAX
00251 *        is used to define the local array T.
00252 *
00253          NB = MIN( NBMAX, ILAENV( 1, 'SORMQR', SIDE // TRANS, M, N, K,
00254      $        -1 ) )
00255          LWKOPT = MAX( 1, NW )*NB
00256          WORK( 1 ) = LWKOPT
00257       END IF
00258 *
00259       IF( INFO.NE.0 ) THEN
00260          CALL XERBLA( 'SORMQR', -INFO )
00261          RETURN
00262       ELSE IF( LQUERY ) THEN
00263          RETURN
00264       END IF
00265 *
00266 *     Quick return if possible
00267 *
00268       IF( M.EQ.0 .OR. N.EQ.0 .OR. K.EQ.0 ) THEN
00269          WORK( 1 ) = 1
00270          RETURN
00271       END IF
00272 *
00273       NBMIN = 2
00274       LDWORK = NW
00275       IF( NB.GT.1 .AND. NB.LT.K ) THEN
00276          IWS = NW*NB
00277          IF( LWORK.LT.IWS ) THEN
00278             NB = LWORK / LDWORK
00279             NBMIN = MAX( 2, ILAENV( 2, 'SORMQR', SIDE // TRANS, M, N, K,
00280      $              -1 ) )
00281          END IF
00282       ELSE
00283          IWS = NW
00284       END IF
00285 *
00286       IF( NB.LT.NBMIN .OR. NB.GE.K ) THEN
00287 *
00288 *        Use unblocked code
00289 *
00290          CALL SORM2R( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK,
00291      $                IINFO )
00292       ELSE
00293 *
00294 *        Use blocked code
00295 *
00296          IF( ( LEFT .AND. .NOT.NOTRAN ) .OR.
00297      $       ( .NOT.LEFT .AND. NOTRAN ) ) THEN
00298             I1 = 1
00299             I2 = K
00300             I3 = NB
00301          ELSE
00302             I1 = ( ( K-1 ) / NB )*NB + 1
00303             I2 = 1
00304             I3 = -NB
00305          END IF
00306 *
00307          IF( LEFT ) THEN
00308             NI = N
00309             JC = 1
00310          ELSE
00311             MI = M
00312             IC = 1
00313          END IF
00314 *
00315          DO 10 I = I1, I2, I3
00316             IB = MIN( NB, K-I+1 )
00317 *
00318 *           Form the triangular factor of the block reflector
00319 *           H = H(i) H(i+1) . . . H(i+ib-1)
00320 *
00321             CALL SLARFT( 'Forward', 'Columnwise', NQ-I+1, IB, A( I, I ),
00322      $                   LDA, TAU( I ), T, LDT )
00323             IF( LEFT ) THEN
00324 *
00325 *              H or H**T is applied to C(i:m,1:n)
00326 *
00327                MI = M - I + 1
00328                IC = I
00329             ELSE
00330 *
00331 *              H or H**T is applied to C(1:m,i:n)
00332 *
00333                NI = N - I + 1
00334                JC = I
00335             END IF
00336 *
00337 *           Apply H or H**T
00338 *
00339             CALL SLARFB( SIDE, TRANS, 'Forward', 'Columnwise', MI, NI,
00340      $                   IB, A( I, I ), LDA, T, LDT, C( IC, JC ), LDC,
00341      $                   WORK, LDWORK )
00342    10    CONTINUE
00343       END IF
00344       WORK( 1 ) = LWKOPT
00345       RETURN
00346 *
00347 *     End of SORMQR
00348 *
00349       END
 All Files Functions