TESTING/EIG/scsdts.f(3)

NAME
TESTING/EIG/scsdts.f

SYNOPSIS

  Functions/Subroutines
subroutine scsdts (m, p, q, x, xf, ldx, u1, ldu1, u2, ldu2, v1t, ldv1t, v2t, ldv2t, theta, iwork, work, lwork, rwork, result)
SCSDTS

Function/Subroutine Documentation

  subroutine scsdts (integer m, integer p, integer q, real, dimension( ldx, * ) x, real, dimension( ldx, * ) xf, integer ldx, real, dimension( ldu1, * ) u1, integer ldu1, real, dimension( ldu2, * ) u2, integer ldu2, real, dimension( ldv1t, * ) v1t, integer ldv1t, real, dimension( ldv2t, * ) v2t, integer ldv2t, real, dimension( * ) theta, integer, dimension( * ) iwork, real, dimension( lwork ) work, integer lwork, real, dimension( * ) rwork, real, dimension( 15 ) result)

SCSDTS

Purpose:

    !>
    !> SCSDTS tests SORCSD, which, given an M-by-M partitioned orthogonal
    !> matrix X,
    !>              Q  M-Q
    !>       X = [ X11 X12 ] P   ,
    !>           [ X21 X22 ] M-P
    !>
    !> computes the CSD
    !>
    !>       [ U1    ]**T * [ X11 X12 ] * [ V1    ]
    !>       [    U2 ]      [ X21 X22 ]   [    V2 ]
    !>
    !>                             [  I  0  0 |  0  0  0 ]
    !>                             [  0  C  0 |  0 -S  0 ]
    !>                             [  0  0  0 |  0  0 -I ]
    !>                           = [---------------------] = [ D11 D12 ] .
    !>                             [  0  0  0 |  I  0  0 ]   [ D21 D22 ]
    !>                             [  0  S  0 |  0  C  0 ]
    !>                             [  0  0  I |  0  0  0 ]
    !>
    !> and also SORCSD2BY1, which, given
    !>          Q
    !>       [ X11 ] P   ,
    !>       [ X21 ] M-P
    !>
    !> computes the 2-by-1 CSD
    !>
    !>                                     [  I  0  0 ]
    !>                                     [  0  C  0 ]
    !>                                     [  0  0  0 ]
    !>       [ U1    ]**T * [ X11 ] * V1 = [----------] = [ D11 ] ,
    !>       [    U2 ]      [ X21 ]        [  0  0  0 ]   [ D21 ]
    !>                                     [  0  S  0 ]
    !>                                     [  0  0  I ]
    !>

Parameters
    M

    !>          M is INTEGER
    !>          The number of rows of the matrix X.  M >= 0.
    !>

    P

    !>          P is INTEGER
    !>          The number of rows of the matrix X11.  P >= 0.
    !>

    Q

    !>          Q is INTEGER
    !>          The number of columns of the matrix X11.  Q >= 0.
    !>

    X

    !>          X is REAL array, dimension (LDX,M)
    !>          The M-by-M matrix X.
    !>

    XF

    !>          XF is REAL array, dimension (LDX,M)
    !>          Details of the CSD of X, as returned by SORCSD;
    !>          see SORCSD for further details.
    !>

    LDX

    !>          LDX is INTEGER
    !>          The leading dimension of the arrays X and XF.
    !>          LDX >= max( 1,M ).
    !>

    U1

    !>          U1 is REAL array, dimension(LDU1,P)
    !>          The P-by-P orthogonal matrix U1.
    !>

    LDU1

    !>          LDU1 is INTEGER
    !>          The leading dimension of the array U1. LDU >= max(1,P).
    !>

    U2

    !>          U2 is REAL array, dimension(LDU2,M-P)
    !>          The (M-P)-by-(M-P) orthogonal matrix U2.
    !>

    LDU2

    !>          LDU2 is INTEGER
    !>          The leading dimension of the array U2. LDU >= max(1,M-P).
    !>

    V1T

    !>          V1T is REAL array, dimension(LDV1T,Q)
    !>          The Q-by-Q orthogonal matrix V1T.
    !>

    LDV1T

    !>          LDV1T is INTEGER
    !>          The leading dimension of the array V1T. LDV1T >=
    !>          max(1,Q).
    !>

    V2T

    !>          V2T is REAL array, dimension(LDV2T,M-Q)
    !>          The (M-Q)-by-(M-Q) orthogonal matrix V2T.
    !>

    LDV2T

    !>          LDV2T is INTEGER
    !>          The leading dimension of the array V2T. LDV2T >=
    !>          max(1,M-Q).
    !>

    THETA

    !>          THETA is REAL array, dimension MIN(P,M-P,Q,M-Q)
    !>          The CS values of X; the essentially diagonal matrices C and
    !>          S are constructed from THETA; see subroutine SORCSD for
    !>          details.
    !>

    IWORK

    !>          IWORK is INTEGER array, dimension (M)
    !>

    WORK

    !>          WORK is REAL array, dimension (LWORK)
    !>

    LWORK

    !>          LWORK is INTEGER
    !>          The dimension of the array WORK
    !>

    RWORK

    !>          RWORK is REAL array
    !>

    RESULT

    !>          RESULT is REAL array, dimension (15)
    !>          The test ratios:
    !>          First, the 2-by-2 CSD:
    !>          RESULT(1) = norm( U1'*X11*V1 - D11 ) / ( MAX(1,P,Q)*EPS2 )
    !>          RESULT(2) = norm( U1'*X12*V2 - D12 ) / ( MAX(1,P,M-Q)*EPS2 )
    !>          RESULT(3) = norm( U2'*X21*V1 - D21 ) / ( MAX(1,M-P,Q)*EPS2 )
    !>          RESULT(4) = norm( U2'*X22*V2 - D22 ) / ( MAX(1,M-P,M-Q)*EPS2 )
    !>          RESULT(5) = norm( I - U1'*U1 ) / ( MAX(1,P)*ULP )
    !>          RESULT(6) = norm( I - U2'*U2 ) / ( MAX(1,M-P)*ULP )
    !>          RESULT(7) = norm( I - V1T'*V1T ) / ( MAX(1,Q)*ULP )
    !>          RESULT(8) = norm( I - V2T'*V2T ) / ( MAX(1,M-Q)*ULP )
    !>          RESULT(9) = 0        if THETA is in increasing order and
    !>                               all angles are in [0,pi/2]
    !>                    = ULPINV   otherwise.
    !>          Then, the 2-by-1 CSD:
    !>          RESULT(10) = norm( U1'*X11*V1 - D11 ) / ( MAX(1,P,Q)*EPS2 )
    !>          RESULT(11) = norm( U2'*X21*V1 - D21 ) / ( MAX(1,M-P,Q)*EPS2 )
    !>          RESULT(12) = norm( I - U1'*U1 ) / ( MAX(1,P)*ULP )
    !>          RESULT(13) = norm( I - U2'*U2 ) / ( MAX(1,M-P)*ULP )
    !>          RESULT(14) = norm( I - V1T'*V1T ) / ( MAX(1,Q)*ULP )
    !>          RESULT(15) = 0        if THETA is in increasing order and
    !>                                all angles are in [0,pi/2]
    !>                     = ULPINV   otherwise.
    !>          ( EPS2 = MAX( norm( I - X'*X ) / M, ULP ). )
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 226 of file scsdts.f.

Author

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