TESTING/EIG/dcsdts.f(3)    Library Functions Manual    TESTING/EIG/dcsdts.f(3)

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

                     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.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

LAPACK                          Version 3.12.0         TESTING/EIG/dcsdts.f(3)