dorbdb3.f(3)

NAME
dorbdb3.f

SYNOPSIS

  Functions/Subroutines
subroutine dorbdb3 (M, P, Q, X11, LDX11, X21, LDX21, THETA, PHI, TAUP1, TAUP2, TAUQ1, WORK, LWORK, INFO)
DORBDB3

Function/Subroutine Documentation

  subroutine dorbdb3 (integer M, integer P, integer Q, double precision, dimension(ldx11,*) X11, integer LDX11, double precision, dimension(ldx21,*) X21, integer LDX21, double precision, dimension(*) THETA, double precision, dimension(*) PHI, double precision, dimension(*) TAUP1, double precision, dimension(*) TAUP2, double precision, dimension(*) TAUQ1, double precision, dimension(*) WORK, integer LWORK, integer INFO)

DORBDB3

Purpose:

     DORBDB3 simultaneously bidiagonalizes the blocks of a tall and skinny
     matrix X with orthonomal columns:
                                [ B11 ]
          [ X11 ]   [ P1 |    ] [  0  ]
          [-----] = [---------] [-----] Q1**T .
          [ X21 ]   [    | P2 ] [ B21 ]
                                [  0  ]
     X11 is P-by-Q, and X21 is (M-P)-by-Q. M-P must be no larger than P,
     Q, or M-Q. Routines DORBDB1, DORBDB2, and DORBDB4 handle cases in
     which M-P is not the minimum dimension.
     The orthogonal matrices P1, P2, and Q1 are P-by-P, (M-P)-by-(M-P),
     and (M-Q)-by-(M-Q), respectively. They are represented implicitly by
     Householder vectors.
     B11 and B12 are (M-P)-by-(M-P) bidiagonal matrices represented
     implicitly by angles THETA, PHI.

Parameters:
    M

              M is INTEGER
               The number of rows X11 plus the number of rows in X21.

    P

              P is INTEGER
               The number of rows in X11. 0 <= P <= M. M-P <= min(P,Q,M-Q).

    Q

              Q is INTEGER
               The number of columns in X11 and X21. 0 <= Q <= M.

    X11

              X11 is DOUBLE PRECISION array, dimension (LDX11,Q)
               On entry, the top block of the matrix X to be reduced. On
               exit, the columns of tril(X11) specify reflectors for P1 and
               the rows of triu(X11,1) specify reflectors for Q1.

    LDX11

              LDX11 is INTEGER
               The leading dimension of X11. LDX11 >= P.

    X21

              X21 is DOUBLE PRECISION array, dimension (LDX21,Q)
               On entry, the bottom block of the matrix X to be reduced. On
               exit, the columns of tril(X21) specify reflectors for P2.

    LDX21

              LDX21 is INTEGER
               The leading dimension of X21. LDX21 >= M-P.

    THETA

              THETA is DOUBLE PRECISION array, dimension (Q)
               The entries of the bidiagonal blocks B11, B21 are defined by
               THETA and PHI. See Further Details.

    PHI

              PHI is DOUBLE PRECISION array, dimension (Q-1)
               The entries of the bidiagonal blocks B11, B21 are defined by
               THETA and PHI. See Further Details.

    TAUP1

              TAUP1 is DOUBLE PRECISION array, dimension (P)
               The scalar factors of the elementary reflectors that define
               P1.

    TAUP2

              TAUP2 is DOUBLE PRECISION array, dimension (M-P)
               The scalar factors of the elementary reflectors that define
               P2.

    TAUQ1

              TAUQ1 is DOUBLE PRECISION array, dimension (Q)
               The scalar factors of the elementary reflectors that define
               Q1.

    WORK

              WORK is DOUBLE PRECISION array, dimension (LWORK)

    LWORK

              LWORK is INTEGER
               The dimension of the array WORK. LWORK >= M-Q.
               If LWORK = -1, then a workspace query is assumed; the routine
               only calculates the optimal size of the WORK array, returns
               this value as the first entry of the WORK array, and no error
               message related to LWORK is issued by XERBLA.

    INFO

              INFO is INTEGER
               = 0:  successful exit.
               < 0:  if INFO = -i, the i-th argument had an illegal value.

Author:
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Date:
    July 2012

Further Details:

      The upper-bidiagonal blocks B11, B21 are represented implicitly by
      angles THETA(1), ..., THETA(Q) and PHI(1), ..., PHI(Q-1). Every entry
      in each bidiagonal band is a product of a sine or cosine of a THETA
      with a sine or cosine of a PHI. See [1] or DORCSD for details.
      P1, P2, and Q1 are represented as products of elementary reflectors.
      See DORCSD2BY1 for details on generating P1, P2, and Q1 using DORGQR
      and DORGLQ.

References:
    [1] Brian D. Sutton. Computing the complete CS decomposition. Numer. Algorithms, 50(1):33-65, 2009.

Definition at line 203 of file dorbdb3.f.

Author

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