LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
zunmbr.f
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00001 *> \brief \b ZUNMBR
00002 *
00003 *  =========== DOCUMENTATION ===========
00004 *
00005 * Online html documentation available at 
00006 *            http://www.netlib.org/lapack/explore-html/ 
00007 *
00008 *> \htmlonly
00009 *> Download ZUNMBR + 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/zunmbr.f"> 
00015 *> [TXT]</a>
00016 *> \endhtmlonly 
00017 *
00018 *  Definition:
00019 *  ===========
00020 *
00021 *       SUBROUTINE ZUNMBR( 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*16         A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
00030 *       ..
00031 *  
00032 *
00033 *> \par Purpose:
00034 *  =============
00035 *>
00036 *> \verbatim
00037 *>
00038 *> If VECT = 'Q', ZUNMBR overwrites the general complex M-by-N matrix C
00039 *> with
00040 *>                 SIDE = 'L'     SIDE = 'R'
00041 *> TRANS = 'N':      Q * C          C * Q
00042 *> TRANS = 'C':      Q**H * C       C * Q**H
00043 *>
00044 *> If VECT = 'P', ZUNMBR overwrites the general complex M-by-N matrix C
00045 *> with
00046 *>                 SIDE = 'L'     SIDE = 'R'
00047 *> TRANS = 'N':      P * C          C * P
00048 *> TRANS = 'C':      P**H * C       C * P**H
00049 *>
00050 *> Here Q and P**H are the unitary matrices determined by ZGEBRD when
00051 *> reducing a complex matrix A to bidiagonal form: A = Q * B * P**H. Q
00052 *> and P**H are defined as products of elementary reflectors H(i) and
00053 *> G(i) respectively.
00054 *>
00055 *> Let nq = m if SIDE = 'L' and nq = n if SIDE = 'R'. Thus nq is the
00056 *> order of the unitary matrix Q or P**H that is applied.
00057 *>
00058 *> If VECT = 'Q', A is assumed to have been an NQ-by-K matrix:
00059 *> if nq >= k, Q = H(1) H(2) . . . H(k);
00060 *> if nq < k, Q = H(1) H(2) . . . H(nq-1).
00061 *>
00062 *> If VECT = 'P', A is assumed to have been a K-by-NQ matrix:
00063 *> if k < nq, P = G(1) G(2) . . . G(k);
00064 *> if k >= nq, P = G(1) G(2) . . . G(nq-1).
00065 *> \endverbatim
00066 *
00067 *  Arguments:
00068 *  ==========
00069 *
00070 *> \param[in] VECT
00071 *> \verbatim
00072 *>          VECT is CHARACTER*1
00073 *>          = 'Q': apply Q or Q**H;
00074 *>          = 'P': apply P or P**H.
00075 *> \endverbatim
00076 *>
00077 *> \param[in] SIDE
00078 *> \verbatim
00079 *>          SIDE is CHARACTER*1
00080 *>          = 'L': apply Q, Q**H, P or P**H from the Left;
00081 *>          = 'R': apply Q, Q**H, P or P**H from the Right.
00082 *> \endverbatim
00083 *>
00084 *> \param[in] TRANS
00085 *> \verbatim
00086 *>          TRANS is CHARACTER*1
00087 *>          = 'N':  No transpose, apply Q or P;
00088 *>          = 'C':  Conjugate transpose, apply Q**H or P**H.
00089 *> \endverbatim
00090 *>
00091 *> \param[in] M
00092 *> \verbatim
00093 *>          M is INTEGER
00094 *>          The number of rows of the matrix C. M >= 0.
00095 *> \endverbatim
00096 *>
00097 *> \param[in] N
00098 *> \verbatim
00099 *>          N is INTEGER
00100 *>          The number of columns of the matrix C. N >= 0.
00101 *> \endverbatim
00102 *>
00103 *> \param[in] K
00104 *> \verbatim
00105 *>          K is INTEGER
00106 *>          If VECT = 'Q', the number of columns in the original
00107 *>          matrix reduced by ZGEBRD.
00108 *>          If VECT = 'P', the number of rows in the original
00109 *>          matrix reduced by ZGEBRD.
00110 *>          K >= 0.
00111 *> \endverbatim
00112 *>
00113 *> \param[in] A
00114 *> \verbatim
00115 *>          A is COMPLEX*16 array, dimension
00116 *>                                (LDA,min(nq,K)) if VECT = 'Q'
00117 *>                                (LDA,nq)        if VECT = 'P'
00118 *>          The vectors which define the elementary reflectors H(i) and
00119 *>          G(i), whose products determine the matrices Q and P, as
00120 *>          returned by ZGEBRD.
00121 *> \endverbatim
00122 *>
00123 *> \param[in] LDA
00124 *> \verbatim
00125 *>          LDA is INTEGER
00126 *>          The leading dimension of the array A.
00127 *>          If VECT = 'Q', LDA >= max(1,nq);
00128 *>          if VECT = 'P', LDA >= max(1,min(nq,K)).
00129 *> \endverbatim
00130 *>
00131 *> \param[in] TAU
00132 *> \verbatim
00133 *>          TAU is COMPLEX*16 array, dimension (min(nq,K))
00134 *>          TAU(i) must contain the scalar factor of the elementary
00135 *>          reflector H(i) or G(i) which determines Q or P, as returned
00136 *>          by ZGEBRD in the array argument TAUQ or TAUP.
00137 *> \endverbatim
00138 *>
00139 *> \param[in,out] C
00140 *> \verbatim
00141 *>          C is COMPLEX*16 array, dimension (LDC,N)
00142 *>          On entry, the M-by-N matrix C.
00143 *>          On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q
00144 *>          or P*C or P**H*C or C*P or C*P**H.
00145 *> \endverbatim
00146 *>
00147 *> \param[in] LDC
00148 *> \verbatim
00149 *>          LDC is INTEGER
00150 *>          The leading dimension of the array C. LDC >= max(1,M).
00151 *> \endverbatim
00152 *>
00153 *> \param[out] WORK
00154 *> \verbatim
00155 *>          WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
00156 *>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
00157 *> \endverbatim
00158 *>
00159 *> \param[in] LWORK
00160 *> \verbatim
00161 *>          LWORK is INTEGER
00162 *>          The dimension of the array WORK.
00163 *>          If SIDE = 'L', LWORK >= max(1,N);
00164 *>          if SIDE = 'R', LWORK >= max(1,M);
00165 *>          if N = 0 or M = 0, LWORK >= 1.
00166 *>          For optimum performance LWORK >= max(1,N*NB) if SIDE = 'L',
00167 *>          and LWORK >= max(1,M*NB) if SIDE = 'R', where NB is the
00168 *>          optimal blocksize. (NB = 0 if M = 0 or N = 0.)
00169 *>
00170 *>          If LWORK = -1, then a workspace query is assumed; the routine
00171 *>          only calculates the optimal size of the WORK array, returns
00172 *>          this value as the first entry of the WORK array, and no error
00173 *>          message related to LWORK is issued by XERBLA.
00174 *> \endverbatim
00175 *>
00176 *> \param[out] INFO
00177 *> \verbatim
00178 *>          INFO is INTEGER
00179 *>          = 0:  successful exit
00180 *>          < 0:  if INFO = -i, the i-th argument had an illegal value
00181 *> \endverbatim
00182 *
00183 *  Authors:
00184 *  ========
00185 *
00186 *> \author Univ. of Tennessee 
00187 *> \author Univ. of California Berkeley 
00188 *> \author Univ. of Colorado Denver 
00189 *> \author NAG Ltd. 
00190 *
00191 *> \date November 2011
00192 *
00193 *> \ingroup complex16OTHERcomputational
00194 *
00195 *  =====================================================================
00196       SUBROUTINE ZUNMBR( VECT, SIDE, TRANS, M, N, K, A, LDA, TAU, C,
00197      $                   LDC, WORK, LWORK, INFO )
00198 *
00199 *  -- LAPACK computational routine (version 3.4.0) --
00200 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00201 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00202 *     November 2011
00203 *
00204 *     .. Scalar Arguments ..
00205       CHARACTER          SIDE, TRANS, VECT
00206       INTEGER            INFO, K, LDA, LDC, LWORK, M, N
00207 *     ..
00208 *     .. Array Arguments ..
00209       COMPLEX*16         A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
00210 *     ..
00211 *
00212 *  =====================================================================
00213 *
00214 *     .. Local Scalars ..
00215       LOGICAL            APPLYQ, LEFT, LQUERY, NOTRAN
00216       CHARACTER          TRANST
00217       INTEGER            I1, I2, IINFO, LWKOPT, MI, NB, NI, NQ, NW
00218 *     ..
00219 *     .. External Functions ..
00220       LOGICAL            LSAME
00221       INTEGER            ILAENV
00222       EXTERNAL           LSAME, ILAENV
00223 *     ..
00224 *     .. External Subroutines ..
00225       EXTERNAL           XERBLA, ZUNMLQ, ZUNMQR
00226 *     ..
00227 *     .. Intrinsic Functions ..
00228       INTRINSIC          MAX, MIN
00229 *     ..
00230 *     .. Executable Statements ..
00231 *
00232 *     Test the input arguments
00233 *
00234       INFO = 0
00235       APPLYQ = LSAME( VECT, 'Q' )
00236       LEFT = LSAME( SIDE, 'L' )
00237       NOTRAN = LSAME( TRANS, 'N' )
00238       LQUERY = ( LWORK.EQ.-1 )
00239 *
00240 *     NQ is the order of Q or P and NW is the minimum dimension of WORK
00241 *
00242       IF( LEFT ) THEN
00243          NQ = M
00244          NW = N
00245       ELSE
00246          NQ = N
00247          NW = M
00248       END IF
00249       IF( M.EQ.0 .OR. N.EQ.0 ) THEN
00250          NW = 0
00251       END IF
00252       IF( .NOT.APPLYQ .AND. .NOT.LSAME( VECT, 'P' ) ) THEN
00253          INFO = -1
00254       ELSE IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN
00255          INFO = -2
00256       ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'C' ) ) THEN
00257          INFO = -3
00258       ELSE IF( M.LT.0 ) THEN
00259          INFO = -4
00260       ELSE IF( N.LT.0 ) THEN
00261          INFO = -5
00262       ELSE IF( K.LT.0 ) THEN
00263          INFO = -6
00264       ELSE IF( ( APPLYQ .AND. LDA.LT.MAX( 1, NQ ) ) .OR.
00265      $         ( .NOT.APPLYQ .AND. LDA.LT.MAX( 1, MIN( NQ, K ) ) ) )
00266      $          THEN
00267          INFO = -8
00268       ELSE IF( LDC.LT.MAX( 1, M ) ) THEN
00269          INFO = -11
00270       ELSE IF( LWORK.LT.MAX( 1, NW ) .AND. .NOT.LQUERY ) THEN
00271          INFO = -13
00272       END IF
00273 *
00274       IF( INFO.EQ.0 ) THEN
00275          IF( NW.GT.0 ) THEN
00276             IF( APPLYQ ) THEN
00277                IF( LEFT ) THEN
00278                   NB = ILAENV( 1, 'ZUNMQR', SIDE // TRANS, M-1, N, M-1,
00279      $                 -1 )
00280                ELSE
00281                   NB = ILAENV( 1, 'ZUNMQR', SIDE // TRANS, M, N-1, N-1,
00282      $                 -1 )
00283                END IF
00284             ELSE
00285                IF( LEFT ) THEN
00286                   NB = ILAENV( 1, 'ZUNMLQ', SIDE // TRANS, M-1, N, M-1,
00287      $                 -1 )
00288                ELSE
00289                   NB = ILAENV( 1, 'ZUNMLQ', SIDE // TRANS, M, N-1, N-1,
00290      $                 -1 )
00291                END IF
00292             END IF
00293             LWKOPT = MAX( 1, NW*NB )
00294          ELSE
00295             LWKOPT = 1
00296          END IF
00297          WORK( 1 ) = LWKOPT
00298       END IF
00299 *
00300       IF( INFO.NE.0 ) THEN
00301          CALL XERBLA( 'ZUNMBR', -INFO )
00302          RETURN
00303       ELSE IF( LQUERY ) THEN
00304          RETURN
00305       END IF
00306 *
00307 *     Quick return if possible
00308 *
00309       IF( M.EQ.0 .OR. N.EQ.0 )
00310      $   RETURN
00311 *
00312       IF( APPLYQ ) THEN
00313 *
00314 *        Apply Q
00315 *
00316          IF( NQ.GE.K ) THEN
00317 *
00318 *           Q was determined by a call to ZGEBRD with nq >= k
00319 *
00320             CALL ZUNMQR( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
00321      $                   WORK, LWORK, IINFO )
00322          ELSE IF( NQ.GT.1 ) THEN
00323 *
00324 *           Q was determined by a call to ZGEBRD with nq < k
00325 *
00326             IF( LEFT ) THEN
00327                MI = M - 1
00328                NI = N
00329                I1 = 2
00330                I2 = 1
00331             ELSE
00332                MI = M
00333                NI = N - 1
00334                I1 = 1
00335                I2 = 2
00336             END IF
00337             CALL ZUNMQR( SIDE, TRANS, MI, NI, NQ-1, A( 2, 1 ), LDA, TAU,
00338      $                   C( I1, I2 ), LDC, WORK, LWORK, IINFO )
00339          END IF
00340       ELSE
00341 *
00342 *        Apply P
00343 *
00344          IF( NOTRAN ) THEN
00345             TRANST = 'C'
00346          ELSE
00347             TRANST = 'N'
00348          END IF
00349          IF( NQ.GT.K ) THEN
00350 *
00351 *           P was determined by a call to ZGEBRD with nq > k
00352 *
00353             CALL ZUNMLQ( SIDE, TRANST, M, N, K, A, LDA, TAU, C, LDC,
00354      $                   WORK, LWORK, IINFO )
00355          ELSE IF( NQ.GT.1 ) THEN
00356 *
00357 *           P was determined by a call to ZGEBRD with nq <= k
00358 *
00359             IF( LEFT ) THEN
00360                MI = M - 1
00361                NI = N
00362                I1 = 2
00363                I2 = 1
00364             ELSE
00365                MI = M
00366                NI = N - 1
00367                I1 = 1
00368                I2 = 2
00369             END IF
00370             CALL ZUNMLQ( SIDE, TRANST, MI, NI, NQ-1, A( 1, 2 ), LDA,
00371      $                   TAU, C( I1, I2 ), LDC, WORK, LWORK, IINFO )
00372          END IF
00373       END IF
00374       WORK( 1 ) = LWKOPT
00375       RETURN
00376 *
00377 *     End of ZUNMBR
00378 *
00379       END
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