sorcsd.f(3)

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 2011

Definition at line 297 of file sorcsd.f'.

Author

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