Exemple #1
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def raw_phi0(x, Z0):
    """Calculate \phi_0(x) for some array of x."""
    n_x = n(x)
    # taylor expand n(z) about x to see that these are the correct
    # parameters to fill in the singularity near x:
    y0, m, k = -dndx(x), -d2ndx2(x)/2.0, -d3ndx3(x)/6.0
    def integrand(z):
        return (n(z) - n_x) / (x - z) if abs(x - z) > 1e-4 else \
            y0 + m * (z - x) + k * (z - x) ** 2
    return integrate.quad(integrand, -Z0, Z0)[0]
Exemple #2
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def phi(xs, Z):
    """Evaluate phi(x) on a numpy list.
    
    This uses invibro.phi.phi0_cache to interpolate values."""
    Z0, x_bound = phi0_cache['Z0'], phi0_cache['xs'][0]
    c1 = pi ** 2 /6; c2 = 7 * pi ** 4 / 60.0
    neg = lambda x: log((Z - x) / (Z + x))
    interp = lambda x: phi0_cache['interp'](x) + log((Z + x) / (Z0 + x))
    large = lambda x: log(1 + Z / x) + c1 / x ** 2 + c2 / x ** 4
    return (
        piecewise(xs, [xs < 0], [neg, 0.0]) +
        piecewise(abs(xs), [abs(xs) < x_bound], [interp, large]) +
        complex(0, -0.5) * n(xs)
    )
Exemple #3
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 def integrand(z):
     return (n(z) - n_x) / (x - z) if abs(x - z) > 1e-4 else \
         y0 + m * (z - x) + k * (z - x) ** 2