Exemple #1
0
def test_integrals():

    for N in (10, 11, 12, 13):

        g = Grid_1D.periodic(N, 0, 2 * pi)
        pnts = concatenate([g.verts, [g.xmax]])
        for f in (sin, cos):
            reference = deci.slow_integration(g.edges[0], g.edges[1], f)
            eq(deci.integrate_boole1(pnts, f), reference)
            eq(integrate_spectral_coarse(pnts, f), reference)
            eq(integrate_spectral(pnts, f), reference)

        g = Grid_1D.chebyshev(N, -1, +1)
        for f in ((lambda x: x), (lambda x: x**3), (lambda x: exp(x))):
            reference = deci.slow_integration(g.edges[0], g.edges[1], f)
            eq(deci.integrate_boole1(g.verts, f), reference)
            eq(integrate_chebyshev(g.verts, f), reference)

        g = Grid_1D.chebyshev(N, -1, +1)
        for f in ((lambda x: x), (lambda x: x**3), (lambda x: exp(x))):
            reference = deci.slow_integration(g.edges_dual[0], g.edges_dual[1],
                                              f)
            x = concatenate(([-1], g.verts_dual, [+1]))
            eq(deci.integrate_boole1(x, f), reference)
            eq(integrate_chebyshev_dual(x, f), reference)
Exemple #2
0
def test_integrals():
    
    for N in (10, 11, 12, 13):

        g = Grid_1D.periodic(N, 0, 2*pi)
        pnts = concatenate([g.verts, [g.xmax]])
        for f in (sin,
                  cos):
            reference = deci.slow_integration(g.edges[0], g.edges[1], f)
            eq( deci.integrate_boole1(pnts, f), reference )
            eq( integrate_spectral_coarse(pnts, f), reference )
            eq( integrate_spectral(pnts, f), reference )

        g = Grid_1D.chebyshev(N, -1, +1)
        for f in ((lambda x: x),
                  (lambda x: x**3),
                  (lambda x: exp(x))):
            reference = deci.slow_integration(g.edges[0], g.edges[1], f)
            eq( deci.integrate_boole1(g.verts, f), reference )
            eq( integrate_chebyshev(g.verts, f), reference )

        g = Grid_1D.chebyshev(N, -1, +1)
        for f in ((lambda x: x),
                  (lambda x: x**3),
                  (lambda x: exp(x))):
            reference = deci.slow_integration(g.edges_dual[0], g.edges_dual[1], f)
            x = concatenate(([-1], g.verts_dual, [+1]))
            eq( deci.integrate_boole1(x, f), reference )
            eq( integrate_chebyshev_dual(x, f), reference )
Exemple #3
0
def projection(cells):

    P={(0, True)  : lambda f: f(cells[0, True]), 
       (0, False) : lambda f: f(cells[0, False]),

       (1, True)  : lambda f: slow_integration(cells[1, True][0],
                                               cells[1, True][1], f),
       (1, False) : lambda f: slow_integration(cells[1, False][0],
                                               cells[1, False][1], f),} 
    return P