def correlation_array(self):
"The correlation function from the input power, on the grid"
pa = empty((self.N, ) * self.dim)
pa[...] = self.power_array()
return self.V * np.real(
dft.ifft(pa, L=self.boxlength, a=self.fourier_a,
b=self.fourier_b)[0])
def gaussian_power_array(self):
"The power spectrum required for a Gaussian field to produce the input power on a lognormal field"
gca = empty((self.N, ) * self.dim)
gca[...] = self.gaussian_correlation_array()
gpa = np.abs(
dft.fft(gca, L=self.boxlength, a=self.fourier_a,
b=self.fourier_b))[0]
gpa[self.k() == 0] = 0
return gpa
def delta_x(self):
"The real-space over-density field, from the input power spectrum"
dk = empty((self.N, ) * self.dim, dtype='complex128')
dk[...] = self.delta_k()
dk[...] = np.sqrt(self.V) * dft.ifft(
dk, L=self.boxlength, a=self.fourier_a, b=self.fourier_b)[0]
dk = np.real(dk)
sg = np.var(dk)
return np.exp(dk - sg / 2) - 1
def delta_x(self):
"The realised field in real-space from the input power spectrum"
# Here we multiply by V because the (inverse) fourier-transform of the (dimensionless) power has
# units of 1/V and we require a unitless quantity for delta_x.
dk = empty((self.N, ) * self.dim, dtype='complex128')
dk[...] = self.delta_k()
dk[...] = self.V * dft.ifft(
dk, L=self.boxlength, a=self.fourier_a, b=self.fourier_b)[0]
dk = np.real(dk)
if self.ensure_physical:
np.clip(dk, -1, np.inf, dk)
return dk