Provided by: liblapack-doc_3.3.1-1_all bug

NAME

       LAPACK-3 - simultaneously bidiagonalize the blocks of an M-by-M partitioned unitary matrix
       X

SYNOPSIS

       SUBROUTINE CUNBDB( TRANS, SIGNS, M, P, Q, X11, LDX11, X12, LDX12, X21, LDX21, X22,  LDX22,
                          THETA, PHI, TAUP1, TAUP2, TAUQ1, TAUQ2, WORK, LWORK, INFO )

           IMPLICIT       NONE

           CHARACTER      SIGNS, TRANS

           INTEGER        INFO, LDX11, LDX12, LDX21, LDX22, LWORK, M, P, Q

           REAL           PHI( * ), THETA( * )

           COMPLEX        TAUP1(  * ), TAUP2( * ), TAUQ1( * ), TAUQ2( * ), WORK( * ), X11( LDX11,
                          * ), X12( LDX12, * ), X21( LDX21, * ), X22( LDX22, * )

PURPOSE

       CUNBDB simultaneously bidiagonalizes the blocks of an M-by-M partitioned unitary matrix X:
                                        [ B11 | B12 0  0 ]
            [ X11 | X12 ]   [ P1 |    ] [  0  |  0 -I  0 ] [ Q1 |    ]**H
        X = [-----------] = [---------] [----------------] [---------]   .
            [ X21 | X22 ]   [    | P2 ] [ B21 | B22 0  0 ] [    | Q2 ]
                                        [  0  |  0  0  I ]
        X11 is P-by-Q. Q must be no larger than P, M-P, or M-Q. (If this is
        not the case, then X must be transposed and/or permuted. This can be
        done in constant time using the TRANS and SIGNS options. See CUNCSD
        for details.)
        The unitary matrices P1, P2, Q1, and Q2 are P-by-P, (M-P)-by-
        (M-P), Q-by-Q, and (M-Q)-by-(M-Q), respectively. They are
        represented implicitly by Householder vectors.
        B11, B12, B21, and B22 are Q-by-Q bidiagonal matrices represented
        implicitly by angles THETA, PHI.

ARGUMENTS

        TRANS   (input) CHARACTER
                = 'T':      X, U1, U2, V1T, and V2T are stored in row-major
                order;
                otherwise:  X, U1, U2, V1T, and V2T are stored in column-
                major order.

        SIGNS   (input) CHARACTER
                = 'O':      The lower-left block is made nonpositive (the
                "other" convention);
                otherwise:  The upper-right block is made nonpositive (the
                "default" convention).

        M       (input) INTEGER
                The number of rows and columns in X.

        P       (input) INTEGER
                The number of rows in X11 and X12. 0 <= P <= M.

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

        X11     (input/output) COMPLEX array, dimension (LDX11,Q)
                On entry, the top-left block of the unitary matrix to be
                reduced. On exit, the form depends on TRANS:
                If TRANS = 'N', then
                the columns of tril(X11) specify reflectors for P1,
                the rows of triu(X11,1) specify reflectors for Q1;
                else TRANS = 'T', and
                the rows of triu(X11) specify reflectors for P1,
                the columns of tril(X11,-1) specify reflectors for Q1.

        LDX11   (input) INTEGER
                The leading dimension of X11. If TRANS = 'N', then LDX11 >=
                P; else LDX11 >= Q.

        X12     (input/output) CMPLX array, dimension (LDX12,M-Q)
                On entry, the top-right block of the unitary matrix to
                be reduced. On exit, the form depends on TRANS:
                If TRANS = 'N', then
                the rows of triu(X12) specify the first P reflectors for
                Q2;
                else TRANS = 'T', and
                the columns of tril(X12) specify the first P reflectors
                for Q2.

        LDX12   (input) INTEGER
                The leading dimension of X12. If TRANS = 'N', then LDX12 >=
                P; else LDX11 >= M-Q.

        X21     (input/output) COMPLEX array, dimension (LDX21,Q)
                On entry, the bottom-left block of the unitary matrix to
                be reduced. On exit, the form depends on TRANS:
                If TRANS = 'N', then
                the columns of tril(X21) specify reflectors for P2;
                else TRANS = 'T', and
                the rows of triu(X21) specify reflectors for P2.

        LDX21   (input) INTEGER
                The leading dimension of X21. If TRANS = 'N', then LDX21 >=
                M-P; else LDX21 >= Q.

        X22     (input/output) COMPLEX array, dimension (LDX22,M-Q)
                On entry, the bottom-right block of the unitary matrix to
                be reduced. On exit, the form depends on TRANS:
                If TRANS = 'N', then
                the rows of triu(X22(Q+1:M-P,P+1:M-Q)) specify the last
                M-P-Q reflectors for Q2,
                else TRANS = 'T', and
                the columns of tril(X22(P+1:M-Q,Q+1:M-P)) specify the last
                M-P-Q reflectors for P2.

        LDX22   (input) INTEGER
                The leading dimension of X22. If TRANS = 'N', then LDX22 >=
                M-P; else LDX22 >= M-Q.

        THETA   (output) REAL array, dimension (Q)
                The entries of the bidiagonal blocks B11, B12, B21, B22 can
                be computed from the angles THETA and PHI. See Further
                Details.

        PHI     (output) REAL array, dimension (Q-1)
                The entries of the bidiagonal blocks B11, B12, B21, B22 can
                be computed from the angles THETA and PHI. See Further
                Details.

        TAUP1   (output) COMPLEX array, dimension (P)
                The scalar factors of the elementary reflectors that define
                P1.

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

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

        TAUQ2   (output) COMPLEX array, dimension (M-Q)
                The scalar factors of the elementary reflectors that define
                Q2.

        WORK    (workspace) COMPLEX array, dimension (LWORK)

        LWORK   (input) 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    (output) INTEGER
                = 0:  successful exit.
                < 0:  if INFO = -i, the i-th argument had an illegal value.

FURTHER DETAILS

        The bidiagonal blocks B11, B12, B21, and B22 are represented
        implicitly by angles THETA(1), ..., THETA(Q) and PHI(1), ...,
        PHI(Q-1). B11 and B21 are upper bidiagonal, while B21 and B22 are
        lower bidiagonal. 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, Q1, and Q2 are represented as products of elementary
        reflectors. See CUNCSD for details on generating P1, P2, Q1, and Q2
        using CUNGQR and CUNGLQ.
        Reference
        =========
        [1] Brian D. Sutton. Computing the complete CS decomposition. Numer.
            Algorithms, 50(1):33-65, 2009.

 LAPACK routine ((version 3.3.0))           April 2011                            CUNBDB(3lapack)