cuncsd2by1.f(3)

NAME
cuncsd2by1.f -

SYNOPSIS

  Functions/Subroutines
subroutine cuncsd2by1 (JOBU1, JOBU2, JOBV1T, M, P, Q, X11, LDX11, X21, LDX21, THETA, U1, LDU1, U2, LDU2, V1T, LDV1T, WORK, LWORK, RWORK, LRWORK, IWORK, INFO)
CUNCSD2BY1

Function/Subroutine Documentation

  subroutine cuncsd2by1 (characterJOBU1, characterJOBU2, characterJOBV1T, integerM, integerP, integerQ, complex, dimension(ldx11,*)X11, integerLDX11, complex, dimension(ldx21,*)X21, integerLDX21, real, dimension(*)THETA, complex, dimension(ldu1,*)U1, integerLDU1, complex, dimension(ldu2,*)U2, integerLDU2, complex, dimension(ldv1t,*)V1T, integerLDV1T, complex, dimension(*)WORK, integerLWORK, real, dimension(*)RWORK, integerLRWORK, integer, dimension(*)IWORK, integerINFO)

CUNCSD2BY1 .SH "Purpose:"

 CUNCSD2BY1 computes the CS decomposition of an M-by-Q matrix X with
 orthonormal columns that has been partitioned into a 2-by-1 block
 structure:
                                [  I  0  0 ]
                                [  0  C  0 ]
          [ X11 ]   [ U1 |    ] [  0  0  0 ]
      X = [-----] = [---------] [----------] V1**T .
          [ X21 ]   [    | U2 ] [  0  0  0 ]
                                [  0  S  0 ]
                                [  0  0  I ]

 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)..fi

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.

    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).

    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 X21. LDX21 >= MAX(1,M-P).

    THETA

              THETA is COMPLEX 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 (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 (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 (Q)
               If JOBV1T = 'Y', V1T contains the Q-by-Q matrix unitary
               matrix V1**T.

    LDV1T

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

    WORK

              WORK is COMPLEX 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.

    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.
     aram[out] 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 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:
    July 2012

Definition at line 260 of file cuncsd2by1.f.

Author

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