NAME

TESTING/EIG/dcsdts.f

SYNOPSIS

Functions/Subroutines

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

Function/Subroutine Documentation

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

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 is INTEGER


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



          P is INTEGER


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



          Q is INTEGER


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



          X is DOUBLE PRECISION array, dimension (LDX,M)


          The M-by-M matrix X.



          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 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 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.

Author

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