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NAME

       sorcsd.f -

SYNOPSIS

   Functions/Subroutines
       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)
           SORCSD

Function/Subroutine Documentation

   recursive subroutine sorcsd (characterJOBU1, characterJOBU2, characterJOBV1T, characterJOBV2T,
       characterTRANS, characterSIGNS, integerM, integerP, integerQ, real, dimension( ldx11, *
       )X11, integerLDX11, real, dimension( ldx12, * )X12, integerLDX12, real, dimension( ldx21,
       * )X21, integerLDX21, real, dimension( ldx22,                         * )X22,
       integerLDX22, real, dimension( * )THETA, real, dimension( ldu1, * )U1, integerLDU1, real,
       dimension( ldu2, * )U2, integerLDU2, real, dimension( ldv1t, * )V1T, integerLDV1T, real,
       dimension( ldv2t, * )V2T, integerLDV2T, real, dimension( * )WORK, integerLWORK, integer,
       dimension( * )IWORK, integerINFO)
       SORCSD

       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).

       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.

           JOBV2T

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

           TRANS

                     TRANS is 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

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

           M

                     M is INTEGER
                     The number of rows and columns in X.

           P

                     P is INTEGER
                     The number of rows in X11 and X12. 0 <= P <= M.

           Q

                     Q is INTEGER
                     The number of columns in X11 and X21. 0 <= Q <= M.

           X11

                     X11 is REAL 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).

           X12

                     X12 is REAL array, dimension (LDX12,M-Q)
                     On entry, part of the orthogonal matrix whose CSD is desired.

           LDX12

                     LDX12 is INTEGER
                     The leading dimension of X12. LDX12 >= MAX(1,P).

           X21

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

           LDX21

                     LDX21 is INTEGER
                     The leading dimension of X11. LDX21 >= MAX(1,M-P).

           X22

                     X22 is REAL array, dimension (LDX22,M-Q)
                     On entry, part of the orthogonal matrix whose CSD is desired.

           LDX22

                     LDX22 is INTEGER
                     The leading dimension of X11. LDX22 >= MAX(1,M-P).

           THETA

                     THETA is 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

                     U1 is REAL 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 REAL 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 REAL 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).

           V2T

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

           LDV2T

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

           WORK

                     WORK is 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

                     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:  SBBCSD 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:
           November 2013

       Definition at line 297 of file sorcsd.f.

Author

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