LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
cungbr.f
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00001 *> \brief \b CUNGBR
00002 *
00003 *  =========== DOCUMENTATION ===========
00004 *
00005 * Online html documentation available at 
00006 *            http://www.netlib.org/lapack/explore-html/ 
00007 *
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00009 *> Download CUNGBR + dependencies 
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00011 *> [TGZ]</a> 
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00013 *> [ZIP]</a> 
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00015 *> [TXT]</a>
00016 *> \endhtmlonly 
00017 *
00018 *  Definition:
00019 *  ===========
00020 *
00021 *       SUBROUTINE CUNGBR( VECT, M, N, K, A, LDA, TAU, WORK, LWORK, INFO )
00022 * 
00023 *       .. Scalar Arguments ..
00024 *       CHARACTER          VECT
00025 *       INTEGER            INFO, K, LDA, LWORK, M, N
00026 *       ..
00027 *       .. Array Arguments ..
00028 *       COMPLEX            A( LDA, * ), TAU( * ), WORK( * )
00029 *       ..
00030 *  
00031 *
00032 *> \par Purpose:
00033 *  =============
00034 *>
00035 *> \verbatim
00036 *>
00037 *> CUNGBR generates one of the complex unitary matrices Q or P**H
00038 *> determined by CGEBRD when reducing a complex matrix A to bidiagonal
00039 *> form: A = Q * B * P**H.  Q and P**H are defined as products of
00040 *> elementary reflectors H(i) or G(i) respectively.
00041 *>
00042 *> If VECT = 'Q', A is assumed to have been an M-by-K matrix, and Q
00043 *> is of order M:
00044 *> if m >= k, Q = H(1) H(2) . . . H(k) and CUNGBR returns the first n
00045 *> columns of Q, where m >= n >= k;
00046 *> if m < k, Q = H(1) H(2) . . . H(m-1) and CUNGBR returns Q as an
00047 *> M-by-M matrix.
00048 *>
00049 *> If VECT = 'P', A is assumed to have been a K-by-N matrix, and P**H
00050 *> is of order N:
00051 *> if k < n, P**H = G(k) . . . G(2) G(1) and CUNGBR returns the first m
00052 *> rows of P**H, where n >= m >= k;
00053 *> if k >= n, P**H = G(n-1) . . . G(2) G(1) and CUNGBR returns P**H as
00054 *> an N-by-N matrix.
00055 *> \endverbatim
00056 *
00057 *  Arguments:
00058 *  ==========
00059 *
00060 *> \param[in] VECT
00061 *> \verbatim
00062 *>          VECT is CHARACTER*1
00063 *>          Specifies whether the matrix Q or the matrix P**H is
00064 *>          required, as defined in the transformation applied by CGEBRD:
00065 *>          = 'Q':  generate Q;
00066 *>          = 'P':  generate P**H.
00067 *> \endverbatim
00068 *>
00069 *> \param[in] M
00070 *> \verbatim
00071 *>          M is INTEGER
00072 *>          The number of rows of the matrix Q or P**H to be returned.
00073 *>          M >= 0.
00074 *> \endverbatim
00075 *>
00076 *> \param[in] N
00077 *> \verbatim
00078 *>          N is INTEGER
00079 *>          The number of columns of the matrix Q or P**H to be returned.
00080 *>          N >= 0.
00081 *>          If VECT = 'Q', M >= N >= min(M,K);
00082 *>          if VECT = 'P', N >= M >= min(N,K).
00083 *> \endverbatim
00084 *>
00085 *> \param[in] K
00086 *> \verbatim
00087 *>          K is INTEGER
00088 *>          If VECT = 'Q', the number of columns in the original M-by-K
00089 *>          matrix reduced by CGEBRD.
00090 *>          If VECT = 'P', the number of rows in the original K-by-N
00091 *>          matrix reduced by CGEBRD.
00092 *>          K >= 0.
00093 *> \endverbatim
00094 *>
00095 *> \param[in,out] A
00096 *> \verbatim
00097 *>          A is COMPLEX array, dimension (LDA,N)
00098 *>          On entry, the vectors which define the elementary reflectors,
00099 *>          as returned by CGEBRD.
00100 *>          On exit, the M-by-N matrix Q or P**H.
00101 *> \endverbatim
00102 *>
00103 *> \param[in] LDA
00104 *> \verbatim
00105 *>          LDA is INTEGER
00106 *>          The leading dimension of the array A. LDA >= M.
00107 *> \endverbatim
00108 *>
00109 *> \param[in] TAU
00110 *> \verbatim
00111 *>          TAU is COMPLEX array, dimension
00112 *>                                (min(M,K)) if VECT = 'Q'
00113 *>                                (min(N,K)) if VECT = 'P'
00114 *>          TAU(i) must contain the scalar factor of the elementary
00115 *>          reflector H(i) or G(i), which determines Q or P**H, as
00116 *>          returned by CGEBRD in its array argument TAUQ or TAUP.
00117 *> \endverbatim
00118 *>
00119 *> \param[out] WORK
00120 *> \verbatim
00121 *>          WORK is COMPLEX array, dimension (MAX(1,LWORK))
00122 *>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
00123 *> \endverbatim
00124 *>
00125 *> \param[in] LWORK
00126 *> \verbatim
00127 *>          LWORK is INTEGER
00128 *>          The dimension of the array WORK. LWORK >= max(1,min(M,N)).
00129 *>          For optimum performance LWORK >= min(M,N)*NB, where NB
00130 *>          is the optimal blocksize.
00131 *>
00132 *>          If LWORK = -1, then a workspace query is assumed; the routine
00133 *>          only calculates the optimal size of the WORK array, returns
00134 *>          this value as the first entry of the WORK array, and no error
00135 *>          message related to LWORK is issued by XERBLA.
00136 *> \endverbatim
00137 *>
00138 *> \param[out] INFO
00139 *> \verbatim
00140 *>          INFO is INTEGER
00141 *>          = 0:  successful exit
00142 *>          < 0:  if INFO = -i, the i-th argument had an illegal value
00143 *> \endverbatim
00144 *
00145 *  Authors:
00146 *  ========
00147 *
00148 *> \author Univ. of Tennessee 
00149 *> \author Univ. of California Berkeley 
00150 *> \author Univ. of Colorado Denver 
00151 *> \author NAG Ltd. 
00152 *
00153 *> \date April 2012
00154 *
00155 *> \ingroup complexGBcomputational
00156 *
00157 *  =====================================================================
00158       SUBROUTINE CUNGBR( VECT, M, N, K, A, LDA, TAU, WORK, LWORK, INFO )
00159 *
00160 *  -- LAPACK computational routine (version 3.4.1) --
00161 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00162 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00163 *     April 2012
00164 *
00165 *     .. Scalar Arguments ..
00166       CHARACTER          VECT
00167       INTEGER            INFO, K, LDA, LWORK, M, N
00168 *     ..
00169 *     .. Array Arguments ..
00170       COMPLEX            A( LDA, * ), TAU( * ), WORK( * )
00171 *     ..
00172 *
00173 *  =====================================================================
00174 *
00175 *     .. Parameters ..
00176       COMPLEX            ZERO, ONE
00177       PARAMETER          ( ZERO = ( 0.0E+0, 0.0E+0 ),
00178      $                   ONE = ( 1.0E+0, 0.0E+0 ) )
00179 *     ..
00180 *     .. Local Scalars ..
00181       LOGICAL            LQUERY, WANTQ
00182       INTEGER            I, IINFO, J, LWKOPT, MN
00183 *     ..
00184 *     .. External Functions ..
00185       LOGICAL            LSAME
00186       INTEGER            ILAENV
00187       EXTERNAL           ILAENV, LSAME
00188 *     ..
00189 *     .. External Subroutines ..
00190       EXTERNAL           CUNGLQ, CUNGQR, XERBLA
00191 *     ..
00192 *     .. Intrinsic Functions ..
00193       INTRINSIC          MAX, MIN
00194 *     ..
00195 *     .. Executable Statements ..
00196 *
00197 *     Test the input arguments
00198 *
00199       INFO = 0
00200       WANTQ = LSAME( VECT, 'Q' )
00201       MN = MIN( M, N )
00202       LQUERY = ( LWORK.EQ.-1 )
00203       IF( .NOT.WANTQ .AND. .NOT.LSAME( VECT, 'P' ) ) THEN
00204          INFO = -1
00205       ELSE IF( M.LT.0 ) THEN
00206          INFO = -2
00207       ELSE IF( N.LT.0 .OR. ( WANTQ .AND. ( N.GT.M .OR. N.LT.MIN( M,
00208      $         K ) ) ) .OR. ( .NOT.WANTQ .AND. ( M.GT.N .OR. M.LT.
00209      $         MIN( N, K ) ) ) ) THEN
00210          INFO = -3
00211       ELSE IF( K.LT.0 ) THEN
00212          INFO = -4
00213       ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
00214          INFO = -6
00215       ELSE IF( LWORK.LT.MAX( 1, MN ) .AND. .NOT.LQUERY ) THEN
00216          INFO = -9
00217       END IF
00218 *
00219       IF( INFO.EQ.0 ) THEN
00220          WORK( 1 ) = 1
00221          IF( WANTQ ) THEN
00222             IF( M.GE.K ) THEN
00223                CALL CUNGQR( M, N, K, A, LDA, TAU, WORK, -1, IINFO )
00224             ELSE
00225                IF( M.GT.1 ) THEN
00226                   CALL CUNGQR( M-1, M-1, M-1, A( 2, 2 ), LDA, TAU, WORK,
00227      $                         -1, IINFO )
00228                END IF
00229             END IF
00230          ELSE
00231             IF( K.LT.N ) THEN
00232                CALL CUNGLQ( M, N, K, A, LDA, TAU, WORK, -1, IINFO )
00233             ELSE
00234                IF( N.GT.1 ) THEN
00235                   CALL CUNGLQ( N-1, N-1, N-1, A( 2, 2 ), LDA, TAU, WORK,
00236      $                         -1, IINFO )
00237                END IF
00238             END IF
00239          END IF
00240          LWKOPT = WORK( 1 )
00241          LWKOPT = MAX (LWKOPT, MN)
00242       END IF
00243 *
00244       IF( INFO.NE.0 ) THEN
00245          CALL XERBLA( 'CUNGBR', -INFO )
00246          RETURN
00247       ELSE IF( LQUERY ) THEN
00248          WORK( 1 ) = LWKOPT
00249          RETURN
00250       END IF
00251 *
00252 *     Quick return if possible
00253 *
00254       IF( M.EQ.0 .OR. N.EQ.0 ) THEN
00255          WORK( 1 ) = 1
00256          RETURN
00257       END IF
00258 *
00259       IF( WANTQ ) THEN
00260 *
00261 *        Form Q, determined by a call to CGEBRD to reduce an m-by-k
00262 *        matrix
00263 *
00264          IF( M.GE.K ) THEN
00265 *
00266 *           If m >= k, assume m >= n >= k
00267 *
00268             CALL CUNGQR( M, N, K, A, LDA, TAU, WORK, LWORK, IINFO )
00269 *
00270          ELSE
00271 *
00272 *           If m < k, assume m = n
00273 *
00274 *           Shift the vectors which define the elementary reflectors one
00275 *           column to the right, and set the first row and column of Q
00276 *           to those of the unit matrix
00277 *
00278             DO 20 J = M, 2, -1
00279                A( 1, J ) = ZERO
00280                DO 10 I = J + 1, M
00281                   A( I, J ) = A( I, J-1 )
00282    10          CONTINUE
00283    20       CONTINUE
00284             A( 1, 1 ) = ONE
00285             DO 30 I = 2, M
00286                A( I, 1 ) = ZERO
00287    30       CONTINUE
00288             IF( M.GT.1 ) THEN
00289 *
00290 *              Form Q(2:m,2:m)
00291 *
00292                CALL CUNGQR( M-1, M-1, M-1, A( 2, 2 ), LDA, TAU, WORK,
00293      $                      LWORK, IINFO )
00294             END IF
00295          END IF
00296       ELSE
00297 *
00298 *        Form P**H, determined by a call to CGEBRD to reduce a k-by-n
00299 *        matrix
00300 *
00301          IF( K.LT.N ) THEN
00302 *
00303 *           If k < n, assume k <= m <= n
00304 *
00305             CALL CUNGLQ( M, N, K, A, LDA, TAU, WORK, LWORK, IINFO )
00306 *
00307          ELSE
00308 *
00309 *           If k >= n, assume m = n
00310 *
00311 *           Shift the vectors which define the elementary reflectors one
00312 *           row downward, and set the first row and column of P**H to
00313 *           those of the unit matrix
00314 *
00315             A( 1, 1 ) = ONE
00316             DO 40 I = 2, N
00317                A( I, 1 ) = ZERO
00318    40       CONTINUE
00319             DO 60 J = 2, N
00320                DO 50 I = J - 1, 2, -1
00321                   A( I, J ) = A( I-1, J )
00322    50          CONTINUE
00323                A( 1, J ) = ZERO
00324    60       CONTINUE
00325             IF( N.GT.1 ) THEN
00326 *
00327 *              Form P**H(2:n,2:n)
00328 *
00329                CALL CUNGLQ( N-1, N-1, N-1, A( 2, 2 ), LDA, TAU, WORK,
00330      $                      LWORK, IINFO )
00331             END IF
00332          END IF
00333       END IF
00334       WORK( 1 ) = LWKOPT
00335       RETURN
00336 *
00337 *     End of CUNGBR
00338 *
00339       END
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