zunbdb2.f(3)

NAME
zunbdb2.f -

SYNOPSIS

  Functions/Subroutines

subroutine zunbdb2 (M, P, Q, X11, LDX11, X21, LDX21, THETA, PHI, TAUP1, TAUP2, TAUQ1, WORK, LWORK, INFO)
ZUNBDB2

Function/Subroutine Documentation

  subroutine zunbdb2 (integerM, integerP, integerQ, complex*16, dimension(ldx11,*)X11, integerLDX11, complex*16, dimension(ldx21,*)X21, integerLDX21, double precision, dimension(*)THETA, double precision, dimension(*)PHI, complex*16, dimension(*)TAUP1, complex*16, dimension(*)TAUP2, complex*16, dimension(*)TAUQ1, complex*16, dimension(*)WORK, integerLWORK, integerINFO)

ZUNBDB2

Purpose:

 ZUNBDB2 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. P must be no larger than M-P,
 Q, or M-Q. Routines ZUNBDB1, ZUNBDB3, and ZUNBDB4 handle cases in
 which P is not the minimum dimension.

 The unitary 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 P-by-P bidiagonal matrices represented implicitly by
 angles THETA, PHI..fi

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 <= min(M-P,Q,M-Q).

    Q

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

    X11

              X11 is COMPLEX*16 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 COMPLEX*16 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 COMPLEX*16 array, dimension (P)
               The scalar factors of the elementary reflectors that define
               P1.

    TAUP2

              TAUP2 is COMPLEX*16 array, dimension (M-P)
               The scalar factors of the elementary reflectors that define
               P2.

    TAUQ1

              TAUQ1 is COMPLEX*16 array, dimension (Q)
               The scalar factors of the elementary reflectors that define
               Q1.

    WORK

              WORK is COMPLEX*16 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 ZUNCSD for details.

      P1, P2, and Q1 are represented as products of elementary reflectors.
      See ZUNCSD2BY1 for details on generating P1, P2, and Q1 using ZUNGQR
      and ZUNGLQ.

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

Definition at line 201 of file zunbdb2.f.

Author

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