SRC/cunbdb1.f(3)           Library Functions Manual           SRC/cunbdb1.f(3)

NAME
       SRC/cunbdb1.f

SYNOPSIS
   Functions/Subroutines
       subroutine cunbdb1 (m, p, q, x11, ldx11, x21, ldx21, theta, phi, taup1,
           taup2, tauq1, work, lwork, info)
           CUNBDB1

Function/Subroutine Documentation
   subroutine cunbdb1 (integer m, integer p, integer q, complex,
       dimension(ldx11,*) x11, integer ldx11, complex, dimension(ldx21,*) x21,
       integer ldx21, real, dimension(*) theta, real, dimension(*) phi,
       complex, dimension(*) taup1, complex, dimension(*) taup2, complex,
       dimension(*) tauq1, complex, dimension(*) work, integer lwork, integer
       info)
       CUNBDB1

       Purpose:


           !>
           !> CUNBDB1 simultaneously bidiagonalizes the blocks of a tall and skinny
           !> matrix X with orthonormal columns:
           !>
           !>                            [ B11 ]
           !>      [ X11 ]   [ P1 |    ] [  0  ]
           !>      [-----] = [---------] [-----] Q1**T .
           !>      [ X21 ]   [    | P2 ] [ B21 ]
           !>                            [  0  ]
           !>
           !> X11 is P-by-Q, and X21 is (M-P)-by-Q. Q must be no larger than P,
           !> M-P, or M-Q. Routines CUNBDB2, CUNBDB3, and CUNBDB4 handle cases in
           !> which 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 Q-by-Q 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.
           !>

           Q

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

           X11

           !>          X11 is COMPLEX 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 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 REAL array, dimension (Q)
           !>           The entries of the bidiagonal blocks B11, B21 are defined by
           !>           THETA and PHI. See Further Details.
           !>

           PHI

           !>          PHI is REAL 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 array, dimension (P)
           !>           The scalar factors of the elementary reflectors that define
           !>           P1.
           !>

           TAUP2

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

           TAUQ1

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

           WORK

           !>          WORK is COMPLEX 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.

       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 CUNCSD for details.
           !>
           !>  P1, P2, and Q1 are represented as products of elementary reflectors.
           !>  See CUNCSD2BY1 for details on generating P1, P2, and Q1 using CUNGQR
           !>  and CUNGLQ.
           !>

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

       Definition at line 200 of file cunbdb1.f.

Author
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LAPACK                          Version 3.12.0                SRC/cunbdb1.f(3)