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NumCosmo Reference Manual | ![]() |
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Top | Description | Object Hierarchy |
Gaussian window functionGaussian window function — Provides a NcWindow of Gaussian type filter. |
Synopsis
#define NC_WINDOW_VOLUME_GAUSSIAN struct NcWindowGaussian; struct NcWindowGaussianClass; NcWindow * nc_window_gaussian_new ();
Description
This object implements the NcWindow class for a Gaussian window function.
This function returns the gaussian window function in the real space, \begin{equation} W_G(r, R) = (2 \pi R^2)^{-3/2}\exp \left( \frac{-r^2}{2 R^2} \right). \end{equation} The mass enclosed within the volume selected by this window function is $M_G(R) = (2\pi)^{3/2}\overline{\rho}(z) R^3$, where $\overline{\rho}(z)$ is the mean density of the universe at redshift $z$.
This function returns the gaussian window function in the Fourier space, \begin{equation} W_G(k, R) = \exp \left( \frac{-k^2 R^2}{2} \right). \end{equation}
This function returns the derivative with respect to R of the gaussian window function in the real space, \begin{equation} \frac{dW_G(k, R)}{dR} = -k^2 R \exp \left( \frac{-k^2 R^2}{2} \right). \end{equation}
Details
NC_WINDOW_VOLUME_GAUSSIAN
#define NC_WINDOW_VOLUME_GAUSSIAN (sqrt(2.0 * M_PI)*sqrt(2.0 * M_PI)*sqrt(2.0 * M_PI)) /* (2.0 \Pi)^(3/2) */
nc_window_gaussian_new ()
NcWindow * nc_window_gaussian_new ();
This function returns a NcWindow with a NcWindowGaussian implementation.
Returns : |
A new NcWindow. |