LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
dormlq.f
Go to the documentation of this file.
00001 *> \brief \b DORMLQ
00002 *
00003 *  =========== DOCUMENTATION ===========
00004 *
00005 * Online html documentation available at 
00006 *            http://www.netlib.org/lapack/explore-html/ 
00007 *
00008 *> \htmlonly
00009 *> Download DORMLQ + dependencies 
00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dormlq.f"> 
00011 *> [TGZ]</a> 
00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dormlq.f"> 
00013 *> [ZIP]</a> 
00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dormlq.f"> 
00015 *> [TXT]</a>
00016 *> \endhtmlonly 
00017 *
00018 *  Definition:
00019 *  ===========
00020 *
00021 *       SUBROUTINE DORMLQ( 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 *       DOUBLE PRECISION   A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
00030 *       ..
00031 *  
00032 *
00033 *> \par Purpose:
00034 *  =============
00035 *>
00036 *> \verbatim
00037 *>
00038 *> DORMLQ 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(k) . . . H(2) H(1)
00048 *>
00049 *> as returned by DGELQF. 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] A
00092 *> \verbatim
00093 *>          A is DOUBLE PRECISION array, dimension
00094 *>                               (LDA,M) if SIDE = 'L',
00095 *>                               (LDA,N) if SIDE = 'R'
00096 *>          The i-th row must contain the vector which defines the
00097 *>          elementary reflector H(i), for i = 1,2,...,k, as returned by
00098 *>          DGELQF in the first k rows of its array argument A.
00099 *> \endverbatim
00100 *>
00101 *> \param[in] LDA
00102 *> \verbatim
00103 *>          LDA is INTEGER
00104 *>          The leading dimension of the array A. LDA >= max(1,K).
00105 *> \endverbatim
00106 *>
00107 *> \param[in] TAU
00108 *> \verbatim
00109 *>          TAU is DOUBLE PRECISION array, dimension (K)
00110 *>          TAU(i) must contain the scalar factor of the elementary
00111 *>          reflector H(i), as returned by DGELQF.
00112 *> \endverbatim
00113 *>
00114 *> \param[in,out] C
00115 *> \verbatim
00116 *>          C is DOUBLE PRECISION array, dimension (LDC,N)
00117 *>          On entry, the M-by-N matrix C.
00118 *>          On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q.
00119 *> \endverbatim
00120 *>
00121 *> \param[in] LDC
00122 *> \verbatim
00123 *>          LDC is INTEGER
00124 *>          The leading dimension of the array C. LDC >= max(1,M).
00125 *> \endverbatim
00126 *>
00127 *> \param[out] WORK
00128 *> \verbatim
00129 *>          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
00130 *>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
00131 *> \endverbatim
00132 *>
00133 *> \param[in] LWORK
00134 *> \verbatim
00135 *>          LWORK is INTEGER
00136 *>          The dimension of the array WORK.
00137 *>          If SIDE = 'L', LWORK >= max(1,N);
00138 *>          if SIDE = 'R', LWORK >= max(1,M).
00139 *>          For optimum performance LWORK >= N*NB if SIDE = 'L', and
00140 *>          LWORK >= M*NB if SIDE = 'R', where NB is the optimal
00141 *>          blocksize.
00142 *>
00143 *>          If LWORK = -1, then a workspace query is assumed; the routine
00144 *>          only calculates the optimal size of the WORK array, returns
00145 *>          this value as the first entry of the WORK array, and no error
00146 *>          message related to LWORK is issued by XERBLA.
00147 *> \endverbatim
00148 *>
00149 *> \param[out] INFO
00150 *> \verbatim
00151 *>          INFO is INTEGER
00152 *>          = 0:  successful exit
00153 *>          < 0:  if INFO = -i, the i-th argument had an illegal value
00154 *> \endverbatim
00155 *
00156 *  Authors:
00157 *  ========
00158 *
00159 *> \author Univ. of Tennessee 
00160 *> \author Univ. of California Berkeley 
00161 *> \author Univ. of Colorado Denver 
00162 *> \author NAG Ltd. 
00163 *
00164 *> \date November 2011
00165 *
00166 *> \ingroup doubleOTHERcomputational
00167 *
00168 *  =====================================================================
00169       SUBROUTINE DORMLQ( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
00170      $                   WORK, LWORK, INFO )
00171 *
00172 *  -- LAPACK computational routine (version 3.4.0) --
00173 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00174 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00175 *     November 2011
00176 *
00177 *     .. Scalar Arguments ..
00178       CHARACTER          SIDE, TRANS
00179       INTEGER            INFO, K, LDA, LDC, LWORK, M, N
00180 *     ..
00181 *     .. Array Arguments ..
00182       DOUBLE PRECISION   A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
00183 *     ..
00184 *
00185 *  =====================================================================
00186 *
00187 *     .. Parameters ..
00188       INTEGER            NBMAX, LDT
00189       PARAMETER          ( NBMAX = 64, LDT = NBMAX+1 )
00190 *     ..
00191 *     .. Local Scalars ..
00192       LOGICAL            LEFT, LQUERY, NOTRAN
00193       CHARACTER          TRANST
00194       INTEGER            I, I1, I2, I3, IB, IC, IINFO, IWS, JC, LDWORK,
00195      $                   LWKOPT, MI, NB, NBMIN, NI, NQ, NW
00196 *     ..
00197 *     .. Local Arrays ..
00198       DOUBLE PRECISION   T( LDT, NBMAX )
00199 *     ..
00200 *     .. External Functions ..
00201       LOGICAL            LSAME
00202       INTEGER            ILAENV
00203       EXTERNAL           LSAME, ILAENV
00204 *     ..
00205 *     .. External Subroutines ..
00206       EXTERNAL           DLARFB, DLARFT, DORML2, XERBLA
00207 *     ..
00208 *     .. Intrinsic Functions ..
00209       INTRINSIC          MAX, MIN
00210 *     ..
00211 *     .. Executable Statements ..
00212 *
00213 *     Test the input arguments
00214 *
00215       INFO = 0
00216       LEFT = LSAME( SIDE, 'L' )
00217       NOTRAN = LSAME( TRANS, 'N' )
00218       LQUERY = ( LWORK.EQ.-1 )
00219 *
00220 *     NQ is the order of Q and NW is the minimum dimension of WORK
00221 *
00222       IF( LEFT ) THEN
00223          NQ = M
00224          NW = N
00225       ELSE
00226          NQ = N
00227          NW = M
00228       END IF
00229       IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN
00230          INFO = -1
00231       ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) ) THEN
00232          INFO = -2
00233       ELSE IF( M.LT.0 ) THEN
00234          INFO = -3
00235       ELSE IF( N.LT.0 ) THEN
00236          INFO = -4
00237       ELSE IF( K.LT.0 .OR. K.GT.NQ ) THEN
00238          INFO = -5
00239       ELSE IF( LDA.LT.MAX( 1, K ) ) THEN
00240          INFO = -7
00241       ELSE IF( LDC.LT.MAX( 1, M ) ) THEN
00242          INFO = -10
00243       ELSE IF( LWORK.LT.MAX( 1, NW ) .AND. .NOT.LQUERY ) THEN
00244          INFO = -12
00245       END IF
00246 *
00247       IF( INFO.EQ.0 ) THEN
00248 *
00249 *        Determine the block size.  NB may be at most NBMAX, where NBMAX
00250 *        is used to define the local array T.
00251 *
00252          NB = MIN( NBMAX, ILAENV( 1, 'DORMLQ', SIDE // TRANS, M, N, K,
00253      $        -1 ) )
00254          LWKOPT = MAX( 1, NW )*NB
00255          WORK( 1 ) = LWKOPT
00256       END IF
00257 *
00258       IF( INFO.NE.0 ) THEN
00259          CALL XERBLA( 'DORMLQ', -INFO )
00260          RETURN
00261       ELSE IF( LQUERY ) THEN
00262          RETURN
00263       END IF
00264 *
00265 *     Quick return if possible
00266 *
00267       IF( M.EQ.0 .OR. N.EQ.0 .OR. K.EQ.0 ) THEN
00268          WORK( 1 ) = 1
00269          RETURN
00270       END IF
00271 *
00272       NBMIN = 2
00273       LDWORK = NW
00274       IF( NB.GT.1 .AND. NB.LT.K ) THEN
00275          IWS = NW*NB
00276          IF( LWORK.LT.IWS ) THEN
00277             NB = LWORK / LDWORK
00278             NBMIN = MAX( 2, ILAENV( 2, 'DORMLQ', SIDE // TRANS, M, N, K,
00279      $              -1 ) )
00280          END IF
00281       ELSE
00282          IWS = NW
00283       END IF
00284 *
00285       IF( NB.LT.NBMIN .OR. NB.GE.K ) THEN
00286 *
00287 *        Use unblocked code
00288 *
00289          CALL DORML2( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK,
00290      $                IINFO )
00291       ELSE
00292 *
00293 *        Use blocked code
00294 *
00295          IF( ( LEFT .AND. NOTRAN ) .OR.
00296      $       ( .NOT.LEFT .AND. .NOT.NOTRAN ) ) THEN
00297             I1 = 1
00298             I2 = K
00299             I3 = NB
00300          ELSE
00301             I1 = ( ( K-1 ) / NB )*NB + 1
00302             I2 = 1
00303             I3 = -NB
00304          END IF
00305 *
00306          IF( LEFT ) THEN
00307             NI = N
00308             JC = 1
00309          ELSE
00310             MI = M
00311             IC = 1
00312          END IF
00313 *
00314          IF( NOTRAN ) THEN
00315             TRANST = 'T'
00316          ELSE
00317             TRANST = 'N'
00318          END IF
00319 *
00320          DO 10 I = I1, I2, I3
00321             IB = MIN( NB, K-I+1 )
00322 *
00323 *           Form the triangular factor of the block reflector
00324 *           H = H(i) H(i+1) . . . H(i+ib-1)
00325 *
00326             CALL DLARFT( 'Forward', 'Rowwise', NQ-I+1, IB, A( I, I ),
00327      $                   LDA, TAU( I ), T, LDT )
00328             IF( LEFT ) THEN
00329 *
00330 *              H or H**T is applied to C(i:m,1:n)
00331 *
00332                MI = M - I + 1
00333                IC = I
00334             ELSE
00335 *
00336 *              H or H**T is applied to C(1:m,i:n)
00337 *
00338                NI = N - I + 1
00339                JC = I
00340             END IF
00341 *
00342 *           Apply H or H**T
00343 *
00344             CALL DLARFB( SIDE, TRANST, 'Forward', 'Rowwise', MI, NI, IB,
00345      $                   A( I, I ), LDA, T, LDT, C( IC, JC ), LDC, WORK,
00346      $                   LDWORK )
00347    10    CONTINUE
00348       END IF
00349       WORK( 1 ) = LWKOPT
00350       RETURN
00351 *
00352 *     End of DORMLQ
00353 *
00354       END
 All Files Functions