Annotation of rpl/lapack/lapack/ztplqt.f, revision 1.1

1.1     ! bertrand    1: *> \brief \b ZTPLQT
        !             2: *
        !             3: *  =========== DOCUMENTATION ===========
        !             4: *
        !             5: * Online html documentation available at
        !             6: *            http://www.netlib.org/lapack/explore-html/
        !             7: *
        !             8: *> \htmlonly
        !             9: *> Download DTPQRT + dependencies
        !            10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dtplqt.f">
        !            11: *> [TGZ]</a>
        !            12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dtplqt.f">
        !            13: *> [ZIP]</a>
        !            14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dtplqt.f">
        !            15: *> [TXT]</a>
        !            16: *> \endhtmlonly
        !            17: *
        !            18: *  Definition:
        !            19: *  ===========
        !            20: *
        !            21: *       SUBROUTINE ZTPLQT( M, N, L, MB, A, LDA, B, LDB, T, LDT, WORK,
        !            22: *                          INFO )
        !            23: *
        !            24: *       .. Scalar Arguments ..
        !            25: *       INTEGER         INFO, LDA, LDB, LDT, N, M, L, MB
        !            26: *       ..
        !            27: *       .. Array Arguments ..
        !            28: *       COMPLEX*16      A( LDA, * ), B( LDB, * ), T( LDT, * ), WORK( * )
        !            29: *       ..
        !            30: *
        !            31: *
        !            32: *> \par Purpose:
        !            33: *  =============
        !            34: *>
        !            35: *> \verbatim
        !            36: *>
        !            37: *> DTPLQT computes a blocked LQ factorization of a complex
        !            38: *> "triangular-pentagonal" matrix C, which is composed of a
        !            39: *> triangular block A and pentagonal block B, using the compact
        !            40: *> WY representation for Q.
        !            41: *> \endverbatim
        !            42: *
        !            43: *  Arguments:
        !            44: *  ==========
        !            45: *
        !            46: *> \param[in] M
        !            47: *> \verbatim
        !            48: *>          M is INTEGER
        !            49: *>          The number of rows of the matrix B, and the order of the
        !            50: *>          triangular matrix A.
        !            51: *>          M >= 0.
        !            52: *> \endverbatim
        !            53: *>
        !            54: *> \param[in] N
        !            55: *> \verbatim
        !            56: *>          N is INTEGER
        !            57: *>          The number of columns of the matrix B.
        !            58: *>          N >= 0.
        !            59: *> \endverbatim
        !            60: *>
        !            61: *> \param[in] L
        !            62: *> \verbatim
        !            63: *>          L is INTEGER
        !            64: *>          The number of rows of the lower trapezoidal part of B.
        !            65: *>          MIN(M,N) >= L >= 0.  See Further Details.
        !            66: *> \endverbatim
        !            67: *>
        !            68: *> \param[in] MB
        !            69: *> \verbatim
        !            70: *>          MB is INTEGER
        !            71: *>          The block size to be used in the blocked QR.  M >= MB >= 1.
        !            72: *> \endverbatim
        !            73: *>
        !            74: *> \param[in,out] A
        !            75: *> \verbatim
        !            76: *>          A is COMPLEX*16 array, dimension (LDA,N)
        !            77: *>          On entry, the lower triangular N-by-N matrix A.
        !            78: *>          On exit, the elements on and below the diagonal of the array
        !            79: *>          contain the lower triangular matrix L.
        !            80: *> \endverbatim
        !            81: *>
        !            82: *> \param[in] LDA
        !            83: *> \verbatim
        !            84: *>          LDA is INTEGER
        !            85: *>          The leading dimension of the array A.  LDA >= max(1,N).
        !            86: *> \endverbatim
        !            87: *>
        !            88: *> \param[in,out] B
        !            89: *> \verbatim
        !            90: *>          B is COMPLEX*16 array, dimension (LDB,N)
        !            91: *>          On entry, the pentagonal M-by-N matrix B.  The first N-L columns
        !            92: *>          are rectangular, and the last L columns are lower trapezoidal.
        !            93: *>          On exit, B contains the pentagonal matrix V.  See Further Details.
        !            94: *> \endverbatim
        !            95: *>
        !            96: *> \param[in] LDB
        !            97: *> \verbatim
        !            98: *>          LDB is INTEGER
        !            99: *>          The leading dimension of the array B.  LDB >= max(1,M).
        !           100: *> \endverbatim
        !           101: *>
        !           102: *> \param[out] T
        !           103: *> \verbatim
        !           104: *>          T is COMPLEX*16 array, dimension (LDT,N)
        !           105: *>          The lower triangular block reflectors stored in compact form
        !           106: *>          as a sequence of upper triangular blocks.  See Further Details.
        !           107: *> \endverbatim
        !           108: *>
        !           109: *> \param[in] LDT
        !           110: *> \verbatim
        !           111: *>          LDT is INTEGER
        !           112: *>          The leading dimension of the array T.  LDT >= MB.
        !           113: *> \endverbatim
        !           114: *>
        !           115: *> \param[out] WORK
        !           116: *> \verbatim
        !           117: *>          WORK is COMPLEX*16 array, dimension (MB*M)
        !           118: *> \endverbatim
        !           119: *>
        !           120: *> \param[out] INFO
        !           121: *> \verbatim
        !           122: *>          INFO is INTEGER
        !           123: *>          = 0:  successful exit
        !           124: *>          < 0:  if INFO = -i, the i-th argument had an illegal value
        !           125: *> \endverbatim
        !           126: *
        !           127: *  Authors:
        !           128: *  ========
        !           129: *
        !           130: *> \author Univ. of Tennessee
        !           131: *> \author Univ. of California Berkeley
        !           132: *> \author Univ. of Colorado Denver
        !           133: *> \author NAG Ltd.
        !           134: *
        !           135: *> \date December 2016
        !           136: *
        !           137: *> \ingroup doubleOTHERcomputational
        !           138: *
        !           139: *> \par Further Details:
        !           140: *  =====================
        !           141: *>
        !           142: *> \verbatim
        !           143: *>
        !           144: *>  The input matrix C is a M-by-(M+N) matrix
        !           145: *>
        !           146: *>               C = [ A ] [ B ]
        !           147: *>
        !           148: *>
        !           149: *>  where A is an lower triangular N-by-N matrix, and B is M-by-N pentagonal
        !           150: *>  matrix consisting of a M-by-(N-L) rectangular matrix B1 on left of a M-by-L
        !           151: *>  upper trapezoidal matrix B2:
        !           152: *>          [ B ] = [ B1 ] [ B2 ]
        !           153: *>                   [ B1 ]  <- M-by-(N-L) rectangular
        !           154: *>                   [ B2 ]  <-     M-by-L upper trapezoidal.
        !           155: *>
        !           156: *>  The lower trapezoidal matrix B2 consists of the first L columns of a
        !           157: *>  N-by-N lower triangular matrix, where 0 <= L <= MIN(M,N).  If L=0,
        !           158: *>  B is rectangular M-by-N; if M=L=N, B is lower triangular.
        !           159: *>
        !           160: *>  The matrix W stores the elementary reflectors H(i) in the i-th row
        !           161: *>  above the diagonal (of A) in the M-by-(M+N) input matrix C
        !           162: *>            [ C ] = [ A ] [ B ]
        !           163: *>                   [ A ]  <- lower triangular N-by-N
        !           164: *>                   [ B ]  <- M-by-N pentagonal
        !           165: *>
        !           166: *>  so that W can be represented as
        !           167: *>            [ W ] = [ I ] [ V ]
        !           168: *>                   [ I ]  <- identity, N-by-N
        !           169: *>                   [ V ]  <- M-by-N, same form as B.
        !           170: *>
        !           171: *>  Thus, all of information needed for W is contained on exit in B, which
        !           172: *>  we call V above.  Note that V has the same form as B; that is,
        !           173: *>            [ V ] = [ V1 ] [ V2 ]
        !           174: *>                   [ V1 ] <- M-by-(N-L) rectangular
        !           175: *>                   [ V2 ] <-     M-by-L lower trapezoidal.
        !           176: *>
        !           177: *>  The rows of V represent the vectors which define the H(i)'s.
        !           178: *>
        !           179: *>  The number of blocks is B = ceiling(M/MB), where each
        !           180: *>  block is of order MB except for the last block, which is of order
        !           181: *>  IB = M - (M-1)*MB.  For each of the B blocks, a upper triangular block
        !           182: *>  reflector factor is computed: T1, T2, ..., TB.  The MB-by-MB (and IB-by-IB
        !           183: *>  for the last block) T's are stored in the MB-by-N matrix T as
        !           184: *>
        !           185: *>               T = [T1 T2 ... TB].
        !           186: *> \endverbatim
        !           187: *>
        !           188: *  =====================================================================
        !           189:       SUBROUTINE ZTPLQT( M, N, L, MB, A, LDA, B, LDB, T, LDT, WORK,
        !           190:      $                   INFO )
        !           191: *
        !           192: *  -- LAPACK computational routine (version 3.7.0) --
        !           193: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
        !           194: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
        !           195: *     December 2016
        !           196: *
        !           197: *     .. Scalar Arguments ..
        !           198:       INTEGER     INFO, LDA, LDB, LDT, N, M, L, MB
        !           199: *     ..
        !           200: *     .. Array Arguments ..
        !           201:       COMPLEX*16  A( LDA, * ), B( LDB, * ), T( LDT, * ), WORK( * )
        !           202: *     ..
        !           203: *
        !           204: * =====================================================================
        !           205: *
        !           206: *     ..
        !           207: *     .. Local Scalars ..
        !           208:       INTEGER    I, IB, LB, NB, IINFO
        !           209: *     ..
        !           210: *     .. External Subroutines ..
        !           211:       EXTERNAL   ZTPLQT2, ZTPRFB, XERBLA
        !           212: *     ..
        !           213: *     .. Executable Statements ..
        !           214: *
        !           215: *     Test the input arguments
        !           216: *
        !           217:       INFO = 0
        !           218:       IF( M.LT.0 ) THEN
        !           219:          INFO = -1
        !           220:       ELSE IF( N.LT.0 ) THEN
        !           221:          INFO = -2
        !           222:       ELSE IF( L.LT.0 .OR. (L.GT.MIN(M,N) .AND. MIN(M,N).GE.0)) THEN
        !           223:          INFO = -3
        !           224:       ELSE IF( MB.LT.1 .OR. (MB.GT.M .AND. M.GT.0)) THEN
        !           225:          INFO = -4
        !           226:       ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
        !           227:          INFO = -6
        !           228:       ELSE IF( LDB.LT.MAX( 1, M ) ) THEN
        !           229:          INFO = -8
        !           230:       ELSE IF( LDT.LT.MB ) THEN
        !           231:          INFO = -10
        !           232:       END IF
        !           233:       IF( INFO.NE.0 ) THEN
        !           234:          CALL XERBLA( 'ZTPLQT', -INFO )
        !           235:          RETURN
        !           236:       END IF
        !           237: *
        !           238: *     Quick return if possible
        !           239: *
        !           240:       IF( M.EQ.0 .OR. N.EQ.0 ) RETURN
        !           241: *
        !           242:       DO I = 1, M, MB
        !           243: *
        !           244: *     Compute the QR factorization of the current block
        !           245: *
        !           246:          IB = MIN( M-I+1, MB )
        !           247:          NB = MIN( N-L+I+IB-1, N )
        !           248:          IF( I.GE.L ) THEN
        !           249:             LB = 0
        !           250:          ELSE
        !           251:             LB = NB-N+L-I+1
        !           252:          END IF
        !           253: *
        !           254:          CALL ZTPLQT2( IB, NB, LB, A(I,I), LDA, B( I, 1 ), LDB,
        !           255:      $                 T(1, I ), LDT, IINFO )
        !           256: *
        !           257: *     Update by applying H**T to B(I+IB:M,:) from the right
        !           258: *
        !           259:          IF( I+IB.LE.M ) THEN
        !           260:             CALL ZTPRFB( 'R', 'N', 'F', 'R', M-I-IB+1, NB, IB, LB,
        !           261:      $                    B( I, 1 ), LDB, T( 1, I ), LDT,
        !           262:      $                    A( I+IB, I ), LDA, B( I+IB, 1 ), LDB,
        !           263:      $                    WORK, M-I-IB+1)
        !           264:          END IF
        !           265:       END DO
        !           266:       RETURN
        !           267: *
        !           268: *     End of ZTPLQT
        !           269: *
        !           270:       END

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