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

NAME

       LAPACK-3 - computes the CS decomposition of an M-by-M partitioned orthogonal matrix X

SYNOPSIS

       RECURSIVE SUBROUTINE SORCSD(  JOBU1,  JOBU2,  JOBV1T,  JOBV2T, TRANS, SIGNS, M, P, Q, X11,
                            LDX11, X12, LDX12, X21, LDX21, X22, LDX22, THETA, U1, LDU1, U2, LDU2,
                            V1T, LDV1T, V2T, LDV2T, WORK, LWORK, IWORK, INFO )

           IMPLICIT         NONE

           CHARACTER        JOBU1, JOBU2, JOBV1T, JOBV2T, SIGNS, TRANS

           INTEGER          INFO, LDU1, LDU2, LDV1T, LDV2T, LDX11, LDX12, LDX21, LDX22, LWORK, M,
                            P, Q

           INTEGER          IWORK( * )

           REAL             THETA( * )

           REAL             U1( LDU1, * ), U2( LDU2, * ), V1T( LDV1T, * ), V2T( LDV2T, * ), WORK(
                            * ), X11( LDX11, * ), X12( LDX12, * ), X21( LDX21, * ), X22( LDX22, *
                            )

PURPOSE

       SORCSD computes the CS decomposition of an M-by-M partitioned orthogonal matrix X:
                                        [  I  0  0 |  0  0  0 ]
                                        [  0  C  0 |  0 -S  0 ]
            [ X11 | X12 ]   [ U1 |    ] [  0  0  0 |  0  0 -I ] [ V1 |    ]**T
        X = [-----------] = [---------] [---------------------] [---------]   .
            [ X21 | X22 ]   [    | U2 ] [  0  0  0 |  I  0  0 ] [    | V2 ]
                                        [  0  S  0 |  0  C  0 ]
                                        [  0  0  I |  0  0  0 ]
        X11 is P-by-Q. The orthogonal matrices U1, U2, V1, and V2 are P-by-P,
        (M-P)-by-(M-P), Q-by-Q, and (M-Q)-by-(M-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).

ARGUMENTS

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

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

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

        JOBV2T  (input) CHARACTER
                = 'Y':      V2T is computed;
                otherwise:  V2T is not computed.

        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 <= M.

        X       (input/workspace) REAL array, dimension (LDX,M)
                On entry, the orthogonal matrix whose CSD is desired.

        LDX     (input) INTEGER
                The leading dimension of X. LDX >= MAX(1,M).

        THETA   (output) REAL 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      (output) REAL array, dimension (P)
                If JOBU1 = 'Y', U1 contains the P-by-P orthogonal matrix U1.

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

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

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

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

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

        V2T     (output) REAL array, dimension (M-Q)
                If JOBV2T = 'Y', V2T contains the (M-Q)-by-(M-Q) orthogonal
                matrix V2**T.

        LDV2T   (input) INTEGER
                The leading dimension of V2T. If JOBV2T = 'Y', LDV2T >=
                MAX(1,M-Q).

        WORK    (workspace) REAL 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   (input) 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   (workspace) INTEGER array, dimension (M-MIN(P, M-P, Q, M-Q))

        INFO    (output) INTEGER
                = 0:  successful exit.
                < 0:  if INFO = -i, the i-th argument had an illegal value.
                > 0:  SBBCSD did not converge. See the description of WORK
                above for details.
                Reference
                =========
                [1] Brian D. Sutton. Computing the complete CS decomposition. Numer.
                Algorithms, 50(1):33-65, 2009.

 LAPACK routine (version 3.3.1)             April 2011                            SORCSD(3lapack)