LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
sormrz.f
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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 
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00011 *> [TGZ]</a> 
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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
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