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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