NAME

       dorcsd2by1.f -

SYNOPSIS

   Functions/Subroutines
       subroutine dorcsd2by1 (JOBU1, JOBU2, JOBV1T, M, P, Q, X11, LDX11, X21, LDX21, THETA, U1,
           LDU1, U2, LDU2, V1T, LDV1T, WORK, LWORK, IWORK, INFO)
           DORCSD2BY1

Function/Subroutine Documentation

   subroutine dorcsd2by1 (character JOBU1, character JOBU2, character JOBV1T, 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(ldu1,*) U1, integer LDU1, double precision, dimension(ldu2,*) U2,
       integer LDU2, double precision, dimension(ldv1t,*) V1T, integer LDV1T, double precision,
       dimension(*) WORK, integer LWORK, integer, dimension(*) IWORK, integer INFO)
       DORCSD2BY1

Purpose:

        Purpose:
        ========

        DORCSD2BY1 computes the CS decomposition of an M-by-Q matrix X with
        orthonormal columns that has been partitioned into a 2-by-1 block
        structure:

                                       [  I  0  0 ]
                                       [  0  C  0 ]
                 [ X11 ]   [ U1 |    ] [  0  0  0 ]
             X = [-----] = [---------] [----------] V1**T .
                 [ X21 ]   [    | U2 ] [  0  0  0 ]
                                       [  0  S  0 ]
                                       [  0  0  I ]

        X11 is P-by-Q. The orthogonal matrices U1, U2, and V1 are P-by-P,
        (M-P)-by-(M-P), and Q-by-Q, respectively. C and S are R-by-R
        nonnegative diagonal matrices satisfying C^2 + S^2 = I, in which
        R = MIN(P,M-P,Q,M-Q)..fi

       Parameters:
           JOBU1

                     JOBU1 is CHARACTER
                     = 'Y':      U1 is computed;
                     otherwise:  U1 is not computed.

           JOBU2

                     JOBU2 is CHARACTER
                     = 'Y':      U2 is computed;
                     otherwise:  U2 is not computed.

           JOBV1T

                     JOBV1T is CHARACTER
                     = 'Y':      V1T is computed;
                     otherwise:  V1T is not computed.

           M

                     M is INTEGER
                     The number of rows in X.

           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.

           X11

                     X11 is DOUBLE PRECISION array, dimension (LDX11,Q)
                     On entry, part of the orthogonal matrix whose CSD is desired.

           LDX11

                     LDX11 is INTEGER
                     The leading dimension of X11. LDX11 >= MAX(1,P).

           X21

                     X21 is DOUBLE PRECISION array, dimension (LDX21,Q)
                     On entry, part of the orthogonal matrix whose CSD is desired.

           LDX21

                     LDX21 is INTEGER
                     The leading dimension of X21. LDX21 >= MAX(1,M-P).

           THETA

                     THETA is DOUBLE PRECISION array, dimension (R), in which R =
                     MIN(P,M-P,Q,M-Q).
                     C = DIAG( COS(THETA(1)), ... , COS(THETA(R)) ) and
                     S = DIAG( SIN(THETA(1)), ... , SIN(THETA(R)) ).

           U1

                     U1 is DOUBLE PRECISION array, dimension (P)
                     If JOBU1 = 'Y', U1 contains the P-by-P orthogonal matrix U1.

           LDU1

                     LDU1 is INTEGER
                     The leading dimension of U1. If JOBU1 = 'Y', LDU1 >=
                     MAX(1,P).

           U2

                     U2 is DOUBLE PRECISION array, dimension (M-P)
                     If JOBU2 = 'Y', U2 contains the (M-P)-by-(M-P) orthogonal
                     matrix U2.

           LDU2

                     LDU2 is INTEGER
                     The leading dimension of U2. If JOBU2 = 'Y', LDU2 >=
                     MAX(1,M-P).

           V1T

                     V1T is DOUBLE PRECISION array, dimension (Q)
                     If JOBV1T = 'Y', V1T contains the Q-by-Q matrix orthogonal
                     matrix V1**T.

           LDV1T

                     LDV1T is INTEGER
                     The leading dimension of V1T. If JOBV1T = 'Y', LDV1T >=
                     MAX(1,Q).

           WORK

                     WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
                     On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
                     If INFO > 0 on exit, WORK(2:R) contains the values PHI(1),
                     ..., PHI(R-1) that, together with THETA(1), ..., THETA(R),
                     define the matrix in intermediate bidiagonal-block form
                     remaining after nonconvergence. INFO specifies the number
                     of nonzero PHI's.

           LWORK

                     LWORK is INTEGER
                     The dimension of the array WORK.

                     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.

           IWORK

                     IWORK is INTEGER array, dimension (M-MIN(P,M-P,Q,M-Q))

           INFO

                     INFO is INTEGER
                     = 0:  successful exit.
                     < 0:  if INFO = -i, the i-th argument had an illegal value.
                     > 0:  DBBCSD did not converge. See the description of WORK
                           above for details.

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

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           July 2012

Author

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