SRC/sorcsd2by1.f(3)

NAME
SRC/sorcsd2by1.f

SYNOPSIS

  Functions/Subroutines
subroutine sorcsd2by1 (jobu1, jobu2, jobv1t, m, p, q, x11, ldx11, x21, ldx21, theta, u1, ldu1, u2, ldu2, v1t, ldv1t, work, lwork, iwork, info)
SORCSD2BY1

Function/Subroutine Documentation

  subroutine sorcsd2by1 (character jobu1, character jobu2, character jobv1t, integer m, integer p, integer q, real, dimension(ldx11,*) x11, integer ldx11, real, dimension(ldx21,*) x21, integer ldx21, real, dimension(*) theta, real, dimension(ldu1,*) u1, integer ldu1, real, dimension(ldu2,*) u2, integer ldu2, real, dimension(ldv1t,*) v1t, integer ldv1t, real, dimension(*) work, integer lwork, integer, dimension(*) iwork, integer info)

SORCSD2BY1

Purpose:

    !>
    !> SORCSD2BY1 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:
    !>
    !>                                [  I1 0  0 ]
    !>                                [  0  C  0 ]
    !>          [ X11 ]   [ U1 |    ] [  0  0  0 ]
    !>      X = [-----] = [---------] [----------] V1**T .
    !>          [ X21 ]   [    | U2 ] [  0  0  0 ]
    !>                                [  0  S  0 ]
    !>                                [  0  0  I2]
    !>
    !> X11 is P-by-Q. The orthogonal matrices U1, U2, and V1 are P-by-P,
    !> (M-P)-by-(M-P), and Q-by-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). I1 is a K1-by-K1 identity matrix and I2 is a
    !> K2-by-K2 identity matrix, where K1 = MAX(Q+P-M,0), K2 = MAX(Q-P,0).
    !>

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 in X.
    !>

    P

    !>          P is INTEGER
    !>          The number of rows in X11. 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).
    !>

    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 X21. LDX21 >= 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).
    !>

    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.

Definition at line 230 of file sorcsd2by1.f.

Author

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