LAPACK 3.3.0

zunmbr.f

Go to the documentation of this file.
00001       SUBROUTINE ZUNMBR( 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*16         A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
00015 *     ..
00016 *
00017 *  Purpose
00018 *  =======
00019 *
00020 *  If VECT = 'Q', ZUNMBR overwrites the general complex M-by-N matrix C
00021 *  with
00022 *                  SIDE = 'L'     SIDE = 'R'
00023 *  TRANS = 'N':      Q * C          C * Q
00024 *  TRANS = 'C':      Q**H * C       C * Q**H
00025 *
00026 *  If VECT = 'P', ZUNMBR overwrites the general complex M-by-N matrix C
00027 *  with
00028 *                  SIDE = 'L'     SIDE = 'R'
00029 *  TRANS = 'N':      P * C          C * P
00030 *  TRANS = 'C':      P**H * C       C * P**H
00031 *
00032 *  Here Q and P**H are the unitary matrices determined by ZGEBRD when
00033 *  reducing a complex matrix A to bidiagonal form: A = Q * B * P**H. Q
00034 *  and P**H are defined as products of elementary reflectors H(i) and
00035 *  G(i) respectively.
00036 *
00037 *  Let nq = m if SIDE = 'L' and nq = n if SIDE = 'R'. Thus nq is the
00038 *  order of the unitary matrix Q or P**H that is applied.
00039 *
00040 *  If VECT = 'Q', A is assumed to have been an NQ-by-K matrix:
00041 *  if nq >= k, Q = H(1) H(2) . . . H(k);
00042 *  if nq < k, Q = H(1) H(2) . . . H(nq-1).
00043 *
00044 *  If VECT = 'P', A is assumed to have been a K-by-NQ matrix:
00045 *  if k < nq, P = G(1) G(2) . . . G(k);
00046 *  if k >= nq, P = G(1) G(2) . . . G(nq-1).
00047 *
00048 *  Arguments
00049 *  =========
00050 *
00051 *  VECT    (input) CHARACTER*1
00052 *          = 'Q': apply Q or Q**H;
00053 *          = 'P': apply P or P**H.
00054 *
00055 *  SIDE    (input) CHARACTER*1
00056 *          = 'L': apply Q, Q**H, P or P**H from the Left;
00057 *          = 'R': apply Q, Q**H, P or P**H from the Right.
00058 *
00059 *  TRANS   (input) CHARACTER*1
00060 *          = 'N':  No transpose, apply Q or P;
00061 *          = 'C':  Conjugate transpose, apply Q**H or P**H.
00062 *
00063 *  M       (input) INTEGER
00064 *          The number of rows of the matrix C. M >= 0.
00065 *
00066 *  N       (input) INTEGER
00067 *          The number of columns of the matrix C. N >= 0.
00068 *
00069 *  K       (input) INTEGER
00070 *          If VECT = 'Q', the number of columns in the original
00071 *          matrix reduced by ZGEBRD.
00072 *          If VECT = 'P', the number of rows in the original
00073 *          matrix reduced by ZGEBRD.
00074 *          K >= 0.
00075 *
00076 *  A       (input) COMPLEX*16 array, dimension
00077 *                                (LDA,min(nq,K)) if VECT = 'Q'
00078 *                                (LDA,nq)        if VECT = 'P'
00079 *          The vectors which define the elementary reflectors H(i) and
00080 *          G(i), whose products determine the matrices Q and P, as
00081 *          returned by ZGEBRD.
00082 *
00083 *  LDA     (input) INTEGER
00084 *          The leading dimension of the array A.
00085 *          If VECT = 'Q', LDA >= max(1,nq);
00086 *          if VECT = 'P', LDA >= max(1,min(nq,K)).
00087 *
00088 *  TAU     (input) COMPLEX*16 array, dimension (min(nq,K))
00089 *          TAU(i) must contain the scalar factor of the elementary
00090 *          reflector H(i) or G(i) which determines Q or P, as returned
00091 *          by ZGEBRD in the array argument TAUQ or TAUP.
00092 *
00093 *  C       (input/output) COMPLEX*16 array, dimension (LDC,N)
00094 *          On entry, the M-by-N matrix C.
00095 *          On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q
00096 *          or P*C or P**H*C or C*P or C*P**H.
00097 *
00098 *  LDC     (input) INTEGER
00099 *          The leading dimension of the array C. LDC >= max(1,M).
00100 *
00101 *  WORK    (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK))
00102 *          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
00103 *
00104 *  LWORK   (input) INTEGER
00105 *          The dimension of the array WORK.
00106 *          If SIDE = 'L', LWORK >= max(1,N);
00107 *          if SIDE = 'R', LWORK >= max(1,M);
00108 *          if N = 0 or M = 0, LWORK >= 1.
00109 *          For optimum performance LWORK >= max(1,N*NB) if SIDE = 'L',
00110 *          and LWORK >= max(1,M*NB) if SIDE = 'R', where NB is the
00111 *          optimal blocksize. (NB = 0 if M = 0 or N = 0.)
00112 *
00113 *          If LWORK = -1, then a workspace query is assumed; the routine
00114 *          only calculates the optimal size of the WORK array, returns
00115 *          this value as the first entry of the WORK array, and no error
00116 *          message related to LWORK is issued by XERBLA.
00117 *
00118 *  INFO    (output) INTEGER
00119 *          = 0:  successful exit
00120 *          < 0:  if INFO = -i, the i-th argument had an illegal value
00121 *
00122 *  =====================================================================
00123 *
00124 *     .. Local Scalars ..
00125       LOGICAL            APPLYQ, LEFT, LQUERY, NOTRAN
00126       CHARACTER          TRANST
00127       INTEGER            I1, I2, IINFO, LWKOPT, MI, NB, NI, NQ, NW
00128 *     ..
00129 *     .. External Functions ..
00130       LOGICAL            LSAME
00131       INTEGER            ILAENV
00132       EXTERNAL           LSAME, ILAENV
00133 *     ..
00134 *     .. External Subroutines ..
00135       EXTERNAL           XERBLA, ZUNMLQ, ZUNMQR
00136 *     ..
00137 *     .. Intrinsic Functions ..
00138       INTRINSIC          MAX, MIN
00139 *     ..
00140 *     .. Executable Statements ..
00141 *
00142 *     Test the input arguments
00143 *
00144       INFO = 0
00145       APPLYQ = LSAME( VECT, 'Q' )
00146       LEFT = LSAME( SIDE, 'L' )
00147       NOTRAN = LSAME( TRANS, 'N' )
00148       LQUERY = ( LWORK.EQ.-1 )
00149 *
00150 *     NQ is the order of Q or P and NW is the minimum dimension of WORK
00151 *
00152       IF( LEFT ) THEN
00153          NQ = M
00154          NW = N
00155       ELSE
00156          NQ = N
00157          NW = M
00158       END IF
00159       IF( M.EQ.0 .OR. N.EQ.0 ) THEN
00160          NW = 0
00161       END IF
00162       IF( .NOT.APPLYQ .AND. .NOT.LSAME( VECT, 'P' ) ) THEN
00163          INFO = -1
00164       ELSE IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN
00165          INFO = -2
00166       ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'C' ) ) THEN
00167          INFO = -3
00168       ELSE IF( M.LT.0 ) THEN
00169          INFO = -4
00170       ELSE IF( N.LT.0 ) THEN
00171          INFO = -5
00172       ELSE IF( K.LT.0 ) THEN
00173          INFO = -6
00174       ELSE IF( ( APPLYQ .AND. LDA.LT.MAX( 1, NQ ) ) .OR.
00175      $         ( .NOT.APPLYQ .AND. LDA.LT.MAX( 1, MIN( NQ, K ) ) ) )
00176      $          THEN
00177          INFO = -8
00178       ELSE IF( LDC.LT.MAX( 1, M ) ) THEN
00179          INFO = -11
00180       ELSE IF( LWORK.LT.MAX( 1, NW ) .AND. .NOT.LQUERY ) THEN
00181          INFO = -13
00182       END IF
00183 *
00184       IF( INFO.EQ.0 ) THEN
00185          IF( NW.GT.0 ) THEN
00186             IF( APPLYQ ) THEN
00187                IF( LEFT ) THEN
00188                   NB = ILAENV( 1, 'ZUNMQR', SIDE // TRANS, M-1, N, M-1,
00189      $                 -1 )
00190                ELSE
00191                   NB = ILAENV( 1, 'ZUNMQR', SIDE // TRANS, M, N-1, N-1,
00192      $                 -1 )
00193                END IF
00194             ELSE
00195                IF( LEFT ) THEN
00196                   NB = ILAENV( 1, 'ZUNMLQ', SIDE // TRANS, M-1, N, M-1,
00197      $                 -1 )
00198                ELSE
00199                   NB = ILAENV( 1, 'ZUNMLQ', SIDE // TRANS, M, N-1, N-1,
00200      $                 -1 )
00201                END IF
00202             END IF
00203             LWKOPT = MAX( 1, NW*NB )
00204          ELSE
00205             LWKOPT = 1
00206          END IF
00207          WORK( 1 ) = LWKOPT
00208       END IF
00209 *
00210       IF( INFO.NE.0 ) THEN
00211          CALL XERBLA( 'ZUNMBR', -INFO )
00212          RETURN
00213       ELSE IF( LQUERY ) THEN
00214          RETURN
00215       END IF
00216 *
00217 *     Quick return if possible
00218 *
00219       IF( M.EQ.0 .OR. N.EQ.0 )
00220      $   RETURN
00221 *
00222       IF( APPLYQ ) THEN
00223 *
00224 *        Apply Q
00225 *
00226          IF( NQ.GE.K ) THEN
00227 *
00228 *           Q was determined by a call to ZGEBRD with nq >= k
00229 *
00230             CALL ZUNMQR( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
00231      $                   WORK, LWORK, IINFO )
00232          ELSE IF( NQ.GT.1 ) THEN
00233 *
00234 *           Q was determined by a call to ZGEBRD with nq < k
00235 *
00236             IF( LEFT ) THEN
00237                MI = M - 1
00238                NI = N
00239                I1 = 2
00240                I2 = 1
00241             ELSE
00242                MI = M
00243                NI = N - 1
00244                I1 = 1
00245                I2 = 2
00246             END IF
00247             CALL ZUNMQR( SIDE, TRANS, MI, NI, NQ-1, A( 2, 1 ), LDA, TAU,
00248      $                   C( I1, I2 ), LDC, WORK, LWORK, IINFO )
00249          END IF
00250       ELSE
00251 *
00252 *        Apply P
00253 *
00254          IF( NOTRAN ) THEN
00255             TRANST = 'C'
00256          ELSE
00257             TRANST = 'N'
00258          END IF
00259          IF( NQ.GT.K ) THEN
00260 *
00261 *           P was determined by a call to ZGEBRD with nq > k
00262 *
00263             CALL ZUNMLQ( SIDE, TRANST, M, N, K, A, LDA, TAU, C, LDC,
00264      $                   WORK, LWORK, IINFO )
00265          ELSE IF( NQ.GT.1 ) THEN
00266 *
00267 *           P was determined by a call to ZGEBRD with nq <= k
00268 *
00269             IF( LEFT ) THEN
00270                MI = M - 1
00271                NI = N
00272                I1 = 2
00273                I2 = 1
00274             ELSE
00275                MI = M
00276                NI = N - 1
00277                I1 = 1
00278                I2 = 2
00279             END IF
00280             CALL ZUNMLQ( SIDE, TRANST, MI, NI, NQ-1, A( 1, 2 ), LDA,
00281      $                   TAU, C( I1, I2 ), LDC, WORK, LWORK, IINFO )
00282          END IF
00283       END IF
00284       WORK( 1 ) = LWKOPT
00285       RETURN
00286 *
00287 *     End of ZUNMBR
00288 *
00289       END
 All Files Functions