LAPACK 3.3.1
Linear Algebra PACKage

cunmbr.f

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00001       SUBROUTINE CUNMBR( VECT, SIDE, TRANS, M, N, K, A, LDA, TAU, C,
00002      $                   LDC, WORK, LWORK, INFO )
00003 *
00004 *  -- LAPACK routine (version 3.2) --
00005 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00006 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00007 *     November 2006
00008 *
00009 *     .. Scalar Arguments ..
00010       CHARACTER          SIDE, TRANS, VECT
00011       INTEGER            INFO, K, LDA, LDC, LWORK, M, N
00012 *     ..
00013 *     .. Array Arguments ..
00014       COMPLEX            A( LDA, * ), C( LDC, * ), TAU( * ),
00015      $                   WORK( * )
00016 *     ..
00017 *
00018 *  Purpose
00019 *  =======
00020 *
00021 *  If VECT = 'Q', CUNMBR overwrites the general complex M-by-N matrix C
00022 *  with
00023 *                  SIDE = 'L'     SIDE = 'R'
00024 *  TRANS = 'N':      Q * C          C * Q
00025 *  TRANS = 'C':      Q**H * C       C * Q**H
00026 *
00027 *  If VECT = 'P', CUNMBR overwrites the general complex M-by-N matrix C
00028 *  with
00029 *                  SIDE = 'L'     SIDE = 'R'
00030 *  TRANS = 'N':      P * C          C * P
00031 *  TRANS = 'C':      P**H * C       C * P**H
00032 *
00033 *  Here Q and P**H are the unitary matrices determined by CGEBRD when
00034 *  reducing a complex matrix A to bidiagonal form: A = Q * B * P**H. Q
00035 *  and P**H are defined as products of elementary reflectors H(i) and
00036 *  G(i) respectively.
00037 *
00038 *  Let nq = m if SIDE = 'L' and nq = n if SIDE = 'R'. Thus nq is the
00039 *  order of the unitary matrix Q or P**H that is applied.
00040 *
00041 *  If VECT = 'Q', A is assumed to have been an NQ-by-K matrix:
00042 *  if nq >= k, Q = H(1) H(2) . . . H(k);
00043 *  if nq < k, Q = H(1) H(2) . . . H(nq-1).
00044 *
00045 *  If VECT = 'P', A is assumed to have been a K-by-NQ matrix:
00046 *  if k < nq, P = G(1) G(2) . . . G(k);
00047 *  if k >= nq, P = G(1) G(2) . . . G(nq-1).
00048 *
00049 *  Arguments
00050 *  =========
00051 *
00052 *  VECT    (input) CHARACTER*1
00053 *          = 'Q': apply Q or Q**H;
00054 *          = 'P': apply P or P**H.
00055 *
00056 *  SIDE    (input) CHARACTER*1
00057 *          = 'L': apply Q, Q**H, P or P**H from the Left;
00058 *          = 'R': apply Q, Q**H, P or P**H from the Right.
00059 *
00060 *  TRANS   (input) CHARACTER*1
00061 *          = 'N':  No transpose, apply Q or P;
00062 *          = 'C':  Conjugate transpose, apply Q**H or P**H.
00063 *
00064 *  M       (input) INTEGER
00065 *          The number of rows of the matrix C. M >= 0.
00066 *
00067 *  N       (input) INTEGER
00068 *          The number of columns of the matrix C. N >= 0.
00069 *
00070 *  K       (input) INTEGER
00071 *          If VECT = 'Q', the number of columns in the original
00072 *          matrix reduced by CGEBRD.
00073 *          If VECT = 'P', the number of rows in the original
00074 *          matrix reduced by CGEBRD.
00075 *          K >= 0.
00076 *
00077 *  A       (input) COMPLEX array, dimension
00078 *                                (LDA,min(nq,K)) if VECT = 'Q'
00079 *                                (LDA,nq)        if VECT = 'P'
00080 *          The vectors which define the elementary reflectors H(i) and
00081 *          G(i), whose products determine the matrices Q and P, as
00082 *          returned by CGEBRD.
00083 *
00084 *  LDA     (input) INTEGER
00085 *          The leading dimension of the array A.
00086 *          If VECT = 'Q', LDA >= max(1,nq);
00087 *          if VECT = 'P', LDA >= max(1,min(nq,K)).
00088 *
00089 *  TAU     (input) COMPLEX array, dimension (min(nq,K))
00090 *          TAU(i) must contain the scalar factor of the elementary
00091 *          reflector H(i) or G(i) which determines Q or P, as returned
00092 *          by CGEBRD in the array argument TAUQ or TAUP.
00093 *
00094 *  C       (input/output) COMPLEX array, dimension (LDC,N)
00095 *          On entry, the M-by-N matrix C.
00096 *          On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q
00097 *          or P*C or P**H*C or C*P or C*P**H.
00098 *
00099 *  LDC     (input) INTEGER
00100 *          The leading dimension of the array C. LDC >= max(1,M).
00101 *
00102 *  WORK    (workspace/output) COMPLEX array, dimension (MAX(1,LWORK))
00103 *          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
00104 *
00105 *  LWORK   (input) INTEGER
00106 *          The dimension of the array WORK.
00107 *          If SIDE = 'L', LWORK >= max(1,N);
00108 *          if SIDE = 'R', LWORK >= max(1,M);
00109 *          if N = 0 or M = 0, LWORK >= 1.
00110 *          For optimum performance LWORK >= max(1,N*NB) if SIDE = 'L',
00111 *          and LWORK >= max(1,M*NB) if SIDE = 'R', where NB is the
00112 *          optimal blocksize. (NB = 0 if M = 0 or N = 0.)
00113 *
00114 *          If LWORK = -1, then a workspace query is assumed; the routine
00115 *          only calculates the optimal size of the WORK array, returns
00116 *          this value as the first entry of the WORK array, and no error
00117 *          message related to LWORK is issued by XERBLA.
00118 *
00119 *  INFO    (output) INTEGER
00120 *          = 0:  successful exit
00121 *          < 0:  if INFO = -i, the i-th argument had an illegal value
00122 *
00123 *  =====================================================================
00124 *
00125 *     .. Local Scalars ..
00126       LOGICAL            APPLYQ, LEFT, LQUERY, NOTRAN
00127       CHARACTER          TRANST
00128       INTEGER            I1, I2, IINFO, LWKOPT, MI, NB, NI, NQ, NW
00129 *     ..
00130 *     .. External Functions ..
00131       LOGICAL            LSAME
00132       INTEGER            ILAENV
00133       EXTERNAL           ILAENV, LSAME
00134 *     ..
00135 *     .. External Subroutines ..
00136       EXTERNAL           CUNMLQ, CUNMQR, XERBLA
00137 *     ..
00138 *     .. Intrinsic Functions ..
00139       INTRINSIC          MAX, MIN
00140 *     ..
00141 *     .. Executable Statements ..
00142 *
00143 *     Test the input arguments
00144 *
00145       INFO = 0
00146       APPLYQ = LSAME( VECT, 'Q' )
00147       LEFT = LSAME( SIDE, 'L' )
00148       NOTRAN = LSAME( TRANS, 'N' )
00149       LQUERY = ( LWORK.EQ.-1 )
00150 *
00151 *     NQ is the order of Q or P and NW is the minimum dimension of WORK
00152 *
00153       IF( LEFT ) THEN
00154          NQ = M
00155          NW = N
00156       ELSE
00157          NQ = N
00158          NW = M
00159       END IF
00160       IF( M.EQ.0 .OR. N.EQ.0 ) THEN
00161          NW = 0
00162       END IF
00163       IF( .NOT.APPLYQ .AND. .NOT.LSAME( VECT, 'P' ) ) THEN
00164          INFO = -1
00165       ELSE IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN
00166          INFO = -2
00167       ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'C' ) ) THEN
00168          INFO = -3
00169       ELSE IF( M.LT.0 ) THEN
00170          INFO = -4
00171       ELSE IF( N.LT.0 ) THEN
00172          INFO = -5
00173       ELSE IF( K.LT.0 ) THEN
00174          INFO = -6
00175       ELSE IF( ( APPLYQ .AND. LDA.LT.MAX( 1, NQ ) ) .OR.
00176      $         ( .NOT.APPLYQ .AND. LDA.LT.MAX( 1, MIN( NQ, K ) ) ) )
00177      $          THEN
00178          INFO = -8
00179       ELSE IF( LDC.LT.MAX( 1, M ) ) THEN
00180          INFO = -11
00181       ELSE IF( LWORK.LT.MAX( 1, NW ) .AND. .NOT.LQUERY ) THEN
00182          INFO = -13
00183       END IF
00184 *
00185       IF( INFO.EQ.0 ) THEN
00186          IF( NW.GT.0 ) THEN
00187             IF( APPLYQ ) THEN
00188                IF( LEFT ) THEN
00189                   NB = ILAENV( 1, 'CUNMQR', SIDE // TRANS, M-1, N, M-1,
00190      $                         -1 )
00191                ELSE
00192                   NB = ILAENV( 1, 'CUNMQR', SIDE // TRANS, M, N-1, N-1,
00193      $                         -1 )
00194                END IF
00195             ELSE
00196                IF( LEFT ) THEN
00197                   NB = ILAENV( 1, 'CUNMLQ', SIDE // TRANS, M-1, N, M-1,
00198      $                         -1 )
00199                ELSE
00200                   NB = ILAENV( 1, 'CUNMLQ', SIDE // TRANS, M, N-1, N-1,
00201      $                         -1 )
00202                END IF
00203             END IF
00204             LWKOPT = MAX( 1, NW*NB )
00205          ELSE
00206             LWKOPT = 1
00207          END IF
00208          WORK( 1 ) = LWKOPT
00209       END IF
00210 *
00211       IF( INFO.NE.0 ) THEN
00212          CALL XERBLA( 'CUNMBR', -INFO )
00213          RETURN
00214       ELSE IF( LQUERY ) THEN
00215          RETURN
00216       END IF
00217 *
00218 *     Quick return if possible
00219 *
00220       IF( M.EQ.0 .OR. N.EQ.0 )
00221      $   RETURN
00222 *
00223       IF( APPLYQ ) THEN
00224 *
00225 *        Apply Q
00226 *
00227          IF( NQ.GE.K ) THEN
00228 *
00229 *           Q was determined by a call to CGEBRD with nq >= k
00230 *
00231             CALL CUNMQR( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
00232      $                   WORK, LWORK, IINFO )
00233          ELSE IF( NQ.GT.1 ) THEN
00234 *
00235 *           Q was determined by a call to CGEBRD with nq < k
00236 *
00237             IF( LEFT ) THEN
00238                MI = M - 1
00239                NI = N
00240                I1 = 2
00241                I2 = 1
00242             ELSE
00243                MI = M
00244                NI = N - 1
00245                I1 = 1
00246                I2 = 2
00247             END IF
00248             CALL CUNMQR( SIDE, TRANS, MI, NI, NQ-1, A( 2, 1 ), LDA, TAU,
00249      $                   C( I1, I2 ), LDC, WORK, LWORK, IINFO )
00250          END IF
00251       ELSE
00252 *
00253 *        Apply P
00254 *
00255          IF( NOTRAN ) THEN
00256             TRANST = 'C'
00257          ELSE
00258             TRANST = 'N'
00259          END IF
00260          IF( NQ.GT.K ) THEN
00261 *
00262 *           P was determined by a call to CGEBRD with nq > k
00263 *
00264             CALL CUNMLQ( SIDE, TRANST, M, N, K, A, LDA, TAU, C, LDC,
00265      $                   WORK, LWORK, IINFO )
00266          ELSE IF( NQ.GT.1 ) THEN
00267 *
00268 *           P was determined by a call to CGEBRD with nq <= k
00269 *
00270             IF( LEFT ) THEN
00271                MI = M - 1
00272                NI = N
00273                I1 = 2
00274                I2 = 1
00275             ELSE
00276                MI = M
00277                NI = N - 1
00278                I1 = 1
00279                I2 = 2
00280             END IF
00281             CALL CUNMLQ( SIDE, TRANST, MI, NI, NQ-1, A( 1, 2 ), LDA,
00282      $                   TAU, C( I1, I2 ), LDC, WORK, LWORK, IINFO )
00283          END IF
00284       END IF
00285       WORK( 1 ) = LWKOPT
00286       RETURN
00287 *
00288 *     End of CUNMBR
00289 *
00290       END
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