SRC/cuncsd.f(3)

NAME
SRC/cuncsd.f

SYNOPSIS

  Functions/Subroutines
recursive subroutine cuncsd (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, rwork, lrwork, iwork, info)
CUNCSD

Function/Subroutine Documentation

  recursive subroutine cuncsd (character jobu1, character jobu2, character jobv1t, character jobv2t, character trans, character signs, integer m, integer p, integer q, complex, dimension( ldx11, * ) x11, integer ldx11, complex, dimension( ldx12, * ) x12, integer ldx12, complex, dimension( ldx21, * ) x21, integer ldx21, complex, dimension( ldx22, * ) x22, integer ldx22, real, dimension( * ) theta, complex, dimension( ldu1, * ) u1, integer ldu1, complex, dimension( ldu2, * ) u2, integer ldu2, complex, dimension( ldv1t, * ) v1t, integer ldv1t, complex, dimension( ldv2t, * ) v2t, integer ldv2t, complex, dimension( * ) work, integer lwork, real, dimension( * ) rwork, integer lrwork, integer, dimension( * ) iwork, integer info)

CUNCSD

Purpose:

     CUNCSD computes the CS decomposition of an M-by-M partitioned
     unitary matrix X:
                                     [  I  0  0 |  0  0  0 ]
                                     [  0  C  0 |  0 -S  0 ]
         [ X11 | X12 ]   [ U1 |    ] [  0  0  0 |  0  0 -I ] [ V1 |    ]**H
     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 unitary 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 COMPLEX array, dimension (LDX11,Q)
              On entry, part of the unitary matrix whose CSD is desired.

    LDX11

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

    X12

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

    LDX12

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

    X21

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

    LDX21

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

    X22

              X22 is COMPLEX array, dimension (LDX22,M-Q)
              On entry, part of the unitary 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 COMPLEX array, dimension (LDU1,P)
              If JOBU1 = 'Y', U1 contains the P-by-P unitary matrix U1.

    LDU1

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

    U2

              U2 is COMPLEX array, dimension (LDU2,M-P)
              If JOBU2 = 'Y', U2 contains the (M-P)-by-(M-P) unitary
              matrix U2.

    LDU2

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

    V1T

              V1T is COMPLEX array, dimension (LDV1T,Q)
              If JOBV1T = 'Y', V1T contains the Q-by-Q matrix unitary
              matrix V1**H.

    LDV1T

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

    V2T

              V2T is COMPLEX array, dimension (LDV2T,M-Q)
              If JOBV2T = 'Y', V2T contains the (M-Q)-by-(M-Q) unitary
              matrix V2**H.

    LDV2T

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

    WORK

              WORK is COMPLEX array, dimension (MAX(1,LWORK))
              On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

    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.

    RWORK

              RWORK is REAL array, dimension MAX(1,LRWORK)
              On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK.
              If INFO > 0 on exit, RWORK(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.

    LRWORK

              LRWORK is INTEGER
              The dimension of the array RWORK.
              If LRWORK = -1, then a workspace query is assumed; the routine
              only calculates the optimal size of the RWORK array, returns
              this value as the first entry of the work array, and no error
              message related to LRWORK 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:  CBBCSD did not converge. See the description of RWORK
                    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.

Definition at line 314 of file cuncsd.f.

Author

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