dcsdts.f - Man Page

subroutine dcsdts (m, p, q, x, xf, ldx, u1, ldu1, u2, ldu2, v1t, ldv1t, v2t, ldv2t, theta, iwork, work, lwork, rwork, result)
DCSDTS

DCSDTS

Purpose:

 DCSDTS tests DORCSD, 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 DORCSD2BY1, 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 DOUBLE PRECISION array, dimension (LDX,M)
          The M-by-M matrix X.

XF

          XF is DOUBLE PRECISION array, dimension (LDX,M)
          Details of the CSD of X, as returned by DORCSD;
          see DORCSD for further details.

LDX

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

U1

          U1 is DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DORCSD for
          details.

IWORK

          IWORK is INTEGER array, dimension (M)

WORK

          WORK is DOUBLE PRECISION array, dimension (LWORK)

LWORK

          LWORK is INTEGER
          The dimension of the array WORK

RWORK

          RWORK is DOUBLE PRECISION array

RESULT

          RESULT is DOUBLE PRECISION 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 dcsdts.f.