cratepy.clustering.citoperations.set_discrete_freqs

set_discrete_freqs(n_dim, rve_dims, n_voxels_dims)

Perform frequency discretization of the spatial domain.

Perform frequency discretization by setting the spatial discrete frequencies (rad/m) for each dimension.

2D case:

\[\boldsymbol{\zeta}_{s_{1}, s_{2}} = \left( \dfrac{2\pi}{(l_{\mathrm{RVE}})_{1}} s_{1}, \, \dfrac{2\pi}{(l_{\mathrm{RVE}})_{2}} s_{2} \right) \, ,\]

\[s_{i}=0, 1, \dots, n_{i}-1 \, , \quad i=1,2 \, .\]

where \(\boldsymbol{\zeta}_{s_{1}, s_{2}} \equiv \boldsymbol{\zeta}(s_{1}, s_{2})\) denotes a sampling angular frequency, \((l_{\mathrm{RVE}})_{i}\) is the RVE size in the \(i\) th dimension, and \(n_{i}\) is the number of voxels in the \(i\) th dimension.

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3D case:

\[\boldsymbol{\zeta}_{s_{1}, s_{2}, s_{3}} = \left( \dfrac{2\pi}{(l_{\mathrm{RVE}})_{1}} s_{1}, \, \dfrac{2\pi}{(l_{\mathrm{RVE}})_{2}} s_{2}, \, \dfrac{2\pi}{(l_{\mathrm{RVE}})_{3}} s_{3} \right) \, ,\]

\[s_{i}=0, 1, \dots, n_{i}-1 \, , \quad i=1,2,3 \, .\]

where \(\boldsymbol{\zeta}_{s_{1}, s_{2}, s_{3}} \equiv \boldsymbol{\zeta}(s_{1}, s_{2}, s_{3})\) denotes a sampling angular frequency, \((l_{\mathrm{RVE}})_{i}\) is the RVE size in the \(i\) th dimension, and \(n_{i}\) is the number of voxels in the \(i\) th dimension.

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Parameters:

• n_dim (int) – Problem number of spatial dimensions.

• rve_dims (list) – RVE size in each dimension.

• n_voxels_dims (list[int]) – Number of voxels in each dimension of the regular grid (spatial discretization of the RVE).

Returns:

freq_dims – List containing the sample frequencies (numpy.ndarray (1d) of shape (n_voxels_dim,)) for each dimension.

Return type:

list[numpy.ndarray (1d)]