TESTING/EIG/ccsdts.f(3)

NAME
TESTING/EIG/ccsdts.f

SYNOPSIS

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

Function/Subroutine Documentation

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

CCSDTS

Purpose:

     CCSDTS tests CUNCSD, which, given an M-by-M partitioned unitary
     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 COMPLEX array, dimension (LDX,M)
              The M-by-M matrix X.

    XF

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

    LDX

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

    U1

              U1 is COMPLEX array, dimension(LDU1,P)
              The P-by-P unitary matrix U1.

    LDU1

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

    U2

              U2 is COMPLEX array, dimension(LDU2,M-P)
              The (M-P)-by-(M-P) unitary matrix U2.

    LDU2

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

    V1T

              V1T is COMPLEX array, dimension(LDV1T,Q)
              The Q-by-Q unitary matrix V1T.

    LDV1T

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

    V2T

              V2T is COMPLEX array, dimension(LDV2T,M-Q)
              The (M-Q)-by-(M-Q) unitary 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 CUNCSD for
              details.

    IWORK

              IWORK is INTEGER array, dimension (M)

    WORK

              WORK is COMPLEX 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 ccsdts.f.

Author

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