LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
cunmbr.f
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00001 *> \brief \b CUNMBR
00002 *
00003 *  =========== DOCUMENTATION ===========
00004 *
00005 * Online html documentation available at 
00006 *            http://www.netlib.org/lapack/explore-html/ 
00007 *
00008 *> \htmlonly
00009 *> Download CUNMBR + 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/cunmbr.f"> 
00015 *> [TXT]</a>
00016 *> \endhtmlonly 
00017 *
00018 *  Definition:
00019 *  ===========
00020 *
00021 *       SUBROUTINE CUNMBR( VECT, SIDE, TRANS, M, N, K, A, LDA, TAU, C,
00022 *                          LDC, WORK, LWORK, INFO )
00023 * 
00024 *       .. Scalar Arguments ..
00025 *       CHARACTER          SIDE, TRANS, VECT
00026 *       INTEGER            INFO, K, LDA, LDC, LWORK, M, N
00027 *       ..
00028 *       .. Array Arguments ..
00029 *       COMPLEX            A( LDA, * ), C( LDC, * ), TAU( * ),
00030 *      $                   WORK( * )
00031 *       ..
00032 *  
00033 *
00034 *> \par Purpose:
00035 *  =============
00036 *>
00037 *> \verbatim
00038 *>
00039 *> If VECT = 'Q', CUNMBR overwrites the general complex M-by-N matrix C
00040 *> with
00041 *>                 SIDE = 'L'     SIDE = 'R'
00042 *> TRANS = 'N':      Q * C          C * Q
00043 *> TRANS = 'C':      Q**H * C       C * Q**H
00044 *>
00045 *> If VECT = 'P', CUNMBR overwrites the general complex M-by-N matrix C
00046 *> with
00047 *>                 SIDE = 'L'     SIDE = 'R'
00048 *> TRANS = 'N':      P * C          C * P
00049 *> TRANS = 'C':      P**H * C       C * P**H
00050 *>
00051 *> Here Q and P**H are the unitary matrices determined by CGEBRD when
00052 *> reducing a complex matrix A to bidiagonal form: A = Q * B * P**H. Q
00053 *> and P**H are defined as products of elementary reflectors H(i) and
00054 *> G(i) respectively.
00055 *>
00056 *> Let nq = m if SIDE = 'L' and nq = n if SIDE = 'R'. Thus nq is the
00057 *> order of the unitary matrix Q or P**H that is applied.
00058 *>
00059 *> If VECT = 'Q', A is assumed to have been an NQ-by-K matrix:
00060 *> if nq >= k, Q = H(1) H(2) . . . H(k);
00061 *> if nq < k, Q = H(1) H(2) . . . H(nq-1).
00062 *>
00063 *> If VECT = 'P', A is assumed to have been a K-by-NQ matrix:
00064 *> if k < nq, P = G(1) G(2) . . . G(k);
00065 *> if k >= nq, P = G(1) G(2) . . . G(nq-1).
00066 *> \endverbatim
00067 *
00068 *  Arguments:
00069 *  ==========
00070 *
00071 *> \param[in] VECT
00072 *> \verbatim
00073 *>          VECT is CHARACTER*1
00074 *>          = 'Q': apply Q or Q**H;
00075 *>          = 'P': apply P or P**H.
00076 *> \endverbatim
00077 *>
00078 *> \param[in] SIDE
00079 *> \verbatim
00080 *>          SIDE is CHARACTER*1
00081 *>          = 'L': apply Q, Q**H, P or P**H from the Left;
00082 *>          = 'R': apply Q, Q**H, P or P**H from the Right.
00083 *> \endverbatim
00084 *>
00085 *> \param[in] TRANS
00086 *> \verbatim
00087 *>          TRANS is CHARACTER*1
00088 *>          = 'N':  No transpose, apply Q or P;
00089 *>          = 'C':  Conjugate transpose, apply Q**H or P**H.
00090 *> \endverbatim
00091 *>
00092 *> \param[in] M
00093 *> \verbatim
00094 *>          M is INTEGER
00095 *>          The number of rows of the matrix C. M >= 0.
00096 *> \endverbatim
00097 *>
00098 *> \param[in] N
00099 *> \verbatim
00100 *>          N is INTEGER
00101 *>          The number of columns of the matrix C. N >= 0.
00102 *> \endverbatim
00103 *>
00104 *> \param[in] K
00105 *> \verbatim
00106 *>          K is INTEGER
00107 *>          If VECT = 'Q', the number of columns in the original
00108 *>          matrix reduced by CGEBRD.
00109 *>          If VECT = 'P', the number of rows in the original
00110 *>          matrix reduced by CGEBRD.
00111 *>          K >= 0.
00112 *> \endverbatim
00113 *>
00114 *> \param[in] A
00115 *> \verbatim
00116 *>          A is COMPLEX array, dimension
00117 *>                                (LDA,min(nq,K)) if VECT = 'Q'
00118 *>                                (LDA,nq)        if VECT = 'P'
00119 *>          The vectors which define the elementary reflectors H(i) and
00120 *>          G(i), whose products determine the matrices Q and P, as
00121 *>          returned by CGEBRD.
00122 *> \endverbatim
00123 *>
00124 *> \param[in] LDA
00125 *> \verbatim
00126 *>          LDA is INTEGER
00127 *>          The leading dimension of the array A.
00128 *>          If VECT = 'Q', LDA >= max(1,nq);
00129 *>          if VECT = 'P', LDA >= max(1,min(nq,K)).
00130 *> \endverbatim
00131 *>
00132 *> \param[in] TAU
00133 *> \verbatim
00134 *>          TAU is COMPLEX array, dimension (min(nq,K))
00135 *>          TAU(i) must contain the scalar factor of the elementary
00136 *>          reflector H(i) or G(i) which determines Q or P, as returned
00137 *>          by CGEBRD in the array argument TAUQ or TAUP.
00138 *> \endverbatim
00139 *>
00140 *> \param[in,out] C
00141 *> \verbatim
00142 *>          C is COMPLEX array, dimension (LDC,N)
00143 *>          On entry, the M-by-N matrix C.
00144 *>          On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q
00145 *>          or P*C or P**H*C or C*P or C*P**H.
00146 *> \endverbatim
00147 *>
00148 *> \param[in] LDC
00149 *> \verbatim
00150 *>          LDC is INTEGER
00151 *>          The leading dimension of the array C. LDC >= max(1,M).
00152 *> \endverbatim
00153 *>
00154 *> \param[out] WORK
00155 *> \verbatim
00156 *>          WORK is COMPLEX array, dimension (MAX(1,LWORK))
00157 *>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
00158 *> \endverbatim
00159 *>
00160 *> \param[in] LWORK
00161 *> \verbatim
00162 *>          LWORK is INTEGER
00163 *>          The dimension of the array WORK.
00164 *>          If SIDE = 'L', LWORK >= max(1,N);
00165 *>          if SIDE = 'R', LWORK >= max(1,M);
00166 *>          if N = 0 or M = 0, LWORK >= 1.
00167 *>          For optimum performance LWORK >= max(1,N*NB) if SIDE = 'L',
00168 *>          and LWORK >= max(1,M*NB) if SIDE = 'R', where NB is the
00169 *>          optimal blocksize. (NB = 0 if M = 0 or N = 0.)
00170 *>
00171 *>          If LWORK = -1, then a workspace query is assumed; the routine
00172 *>          only calculates the optimal size of the WORK array, returns
00173 *>          this value as the first entry of the WORK array, and no error
00174 *>          message related to LWORK is issued by XERBLA.
00175 *> \endverbatim
00176 *>
00177 *> \param[out] INFO
00178 *> \verbatim
00179 *>          INFO is INTEGER
00180 *>          = 0:  successful exit
00181 *>          < 0:  if INFO = -i, the i-th argument had an illegal value
00182 *> \endverbatim
00183 *
00184 *  Authors:
00185 *  ========
00186 *
00187 *> \author Univ. of Tennessee 
00188 *> \author Univ. of California Berkeley 
00189 *> \author Univ. of Colorado Denver 
00190 *> \author NAG Ltd. 
00191 *
00192 *> \date November 2011
00193 *
00194 *> \ingroup complexOTHERcomputational
00195 *
00196 *  =====================================================================
00197       SUBROUTINE CUNMBR( VECT, SIDE, TRANS, M, N, K, A, LDA, TAU, C,
00198      $                   LDC, WORK, LWORK, INFO )
00199 *
00200 *  -- LAPACK computational routine (version 3.4.0) --
00201 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00202 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00203 *     November 2011
00204 *
00205 *     .. Scalar Arguments ..
00206       CHARACTER          SIDE, TRANS, VECT
00207       INTEGER            INFO, K, LDA, LDC, LWORK, M, N
00208 *     ..
00209 *     .. Array Arguments ..
00210       COMPLEX            A( LDA, * ), C( LDC, * ), TAU( * ),
00211      $                   WORK( * )
00212 *     ..
00213 *
00214 *  =====================================================================
00215 *
00216 *     .. Local Scalars ..
00217       LOGICAL            APPLYQ, LEFT, LQUERY, NOTRAN
00218       CHARACTER          TRANST
00219       INTEGER            I1, I2, IINFO, LWKOPT, MI, NB, NI, NQ, NW
00220 *     ..
00221 *     .. External Functions ..
00222       LOGICAL            LSAME
00223       INTEGER            ILAENV
00224       EXTERNAL           ILAENV, LSAME
00225 *     ..
00226 *     .. External Subroutines ..
00227       EXTERNAL           CUNMLQ, CUNMQR, XERBLA
00228 *     ..
00229 *     .. Intrinsic Functions ..
00230       INTRINSIC          MAX, MIN
00231 *     ..
00232 *     .. Executable Statements ..
00233 *
00234 *     Test the input arguments
00235 *
00236       INFO = 0
00237       APPLYQ = LSAME( VECT, 'Q' )
00238       LEFT = LSAME( SIDE, 'L' )
00239       NOTRAN = LSAME( TRANS, 'N' )
00240       LQUERY = ( LWORK.EQ.-1 )
00241 *
00242 *     NQ is the order of Q or P and NW is the minimum dimension of WORK
00243 *
00244       IF( LEFT ) THEN
00245          NQ = M
00246          NW = N
00247       ELSE
00248          NQ = N
00249          NW = M
00250       END IF
00251       IF( M.EQ.0 .OR. N.EQ.0 ) THEN
00252          NW = 0
00253       END IF
00254       IF( .NOT.APPLYQ .AND. .NOT.LSAME( VECT, 'P' ) ) THEN
00255          INFO = -1
00256       ELSE IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN
00257          INFO = -2
00258       ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'C' ) ) THEN
00259          INFO = -3
00260       ELSE IF( M.LT.0 ) THEN
00261          INFO = -4
00262       ELSE IF( N.LT.0 ) THEN
00263          INFO = -5
00264       ELSE IF( K.LT.0 ) THEN
00265          INFO = -6
00266       ELSE IF( ( APPLYQ .AND. LDA.LT.MAX( 1, NQ ) ) .OR.
00267      $         ( .NOT.APPLYQ .AND. LDA.LT.MAX( 1, MIN( NQ, K ) ) ) )
00268      $          THEN
00269          INFO = -8
00270       ELSE IF( LDC.LT.MAX( 1, M ) ) THEN
00271          INFO = -11
00272       ELSE IF( LWORK.LT.MAX( 1, NW ) .AND. .NOT.LQUERY ) THEN
00273          INFO = -13
00274       END IF
00275 *
00276       IF( INFO.EQ.0 ) THEN
00277          IF( NW.GT.0 ) THEN
00278             IF( APPLYQ ) THEN
00279                IF( LEFT ) THEN
00280                   NB = ILAENV( 1, 'CUNMQR', SIDE // TRANS, M-1, N, M-1,
00281      $                         -1 )
00282                ELSE
00283                   NB = ILAENV( 1, 'CUNMQR', SIDE // TRANS, M, N-1, N-1,
00284      $                         -1 )
00285                END IF
00286             ELSE
00287                IF( LEFT ) THEN
00288                   NB = ILAENV( 1, 'CUNMLQ', SIDE // TRANS, M-1, N, M-1,
00289      $                         -1 )
00290                ELSE
00291                   NB = ILAENV( 1, 'CUNMLQ', SIDE // TRANS, M, N-1, N-1,
00292      $                         -1 )
00293                END IF
00294             END IF
00295             LWKOPT = MAX( 1, NW*NB )
00296          ELSE
00297             LWKOPT = 1
00298          END IF
00299          WORK( 1 ) = LWKOPT
00300       END IF
00301 *
00302       IF( INFO.NE.0 ) THEN
00303          CALL XERBLA( 'CUNMBR', -INFO )
00304          RETURN
00305       ELSE IF( LQUERY ) THEN
00306          RETURN
00307       END IF
00308 *
00309 *     Quick return if possible
00310 *
00311       IF( M.EQ.0 .OR. N.EQ.0 )
00312      $   RETURN
00313 *
00314       IF( APPLYQ ) THEN
00315 *
00316 *        Apply Q
00317 *
00318          IF( NQ.GE.K ) THEN
00319 *
00320 *           Q was determined by a call to CGEBRD with nq >= k
00321 *
00322             CALL CUNMQR( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
00323      $                   WORK, LWORK, IINFO )
00324          ELSE IF( NQ.GT.1 ) THEN
00325 *
00326 *           Q was determined by a call to CGEBRD with nq < k
00327 *
00328             IF( LEFT ) THEN
00329                MI = M - 1
00330                NI = N
00331                I1 = 2
00332                I2 = 1
00333             ELSE
00334                MI = M
00335                NI = N - 1
00336                I1 = 1
00337                I2 = 2
00338             END IF
00339             CALL CUNMQR( SIDE, TRANS, MI, NI, NQ-1, A( 2, 1 ), LDA, TAU,
00340      $                   C( I1, I2 ), LDC, WORK, LWORK, IINFO )
00341          END IF
00342       ELSE
00343 *
00344 *        Apply P
00345 *
00346          IF( NOTRAN ) THEN
00347             TRANST = 'C'
00348          ELSE
00349             TRANST = 'N'
00350          END IF
00351          IF( NQ.GT.K ) THEN
00352 *
00353 *           P was determined by a call to CGEBRD with nq > k
00354 *
00355             CALL CUNMLQ( SIDE, TRANST, M, N, K, A, LDA, TAU, C, LDC,
00356      $                   WORK, LWORK, IINFO )
00357          ELSE IF( NQ.GT.1 ) THEN
00358 *
00359 *           P was determined by a call to CGEBRD with nq <= k
00360 *
00361             IF( LEFT ) THEN
00362                MI = M - 1
00363                NI = N
00364                I1 = 2
00365                I2 = 1
00366             ELSE
00367                MI = M
00368                NI = N - 1
00369                I1 = 1
00370                I2 = 2
00371             END IF
00372             CALL CUNMLQ( SIDE, TRANST, MI, NI, NQ-1, A( 1, 2 ), LDA,
00373      $                   TAU, C( I1, I2 ), LDC, WORK, LWORK, IINFO )
00374          END IF
00375       END IF
00376       WORK( 1 ) = LWKOPT
00377       RETURN
00378 *
00379 *     End of CUNMBR
00380 *
00381       END
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