NAME

       zunbdb4.f -

SYNOPSIS

   Functions/Subroutines
       subroutine zunbdb4 (M, P, Q, X11, LDX11, X21, LDX21, THETA, PHI, TAUP1, TAUP2, TAUQ1,
           PHANTOM, WORK, LWORK, INFO)
           ZUNBDB4

Function/Subroutine Documentation

   subroutine zunbdb4 (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(*)PHANTOM, complex*16, dimension(*)WORK, integerLWORK, integerINFO)
       ZUNBDB4

Purpose:

        ZUNBDB4 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-Q must be no larger than P,
        M-P, or Q. Routines ZUNBDB1, ZUNBDB2, and ZUNBDB3 handle cases in
        which M-Q 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 (M-Q)-by-(M-Q) 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 <= M.

           Q

                     Q is INTEGER
                      The number of columns in X11 and X21. 0 <= Q <= M and
                      M-Q <= min(P,M-P,Q).

           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.

           PHANTOM

                     PHANTOM is COMPLEX*16 array, dimension (M)
                      The routine computes an M-by-1 column vector Y that is
                      orthogonal to the columns of [ X11; X21 ]. PHANTOM(1:P) and
                      PHANTOM(P+1:M) contain Householder vectors for Y(1:P) and
                      Y(P+1:M), respectively.

           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 212 of file zunbdb4.f.

Author

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