Static Convolution

class Convolve(L)

Bases: object

Static graph convolution context using CHOLMOD.

Designed for high-performance GSP operations on graphs with constant topology. Manages CHOLMOD symbolic and numeric factorizations internally.

Parameters:

L (csc_matrix) – Sparse Graph Laplacian of shape (n_vertices, n_vertices).

See also

DyConvolve

For graphs with evolving topologies.

Examples

>>> from sgwt import Convolve, LAPLACIAN_TEXAS_DELAY
>>> import numpy as np
>>> L = LAPLACIAN_TEXAS_DELAY
>>> signal = np.random.randn(L.shape[0], 100)
>>> with Convolve(L) as conv:
...     lp = conv.lowpass(signal, scales=[0.1, 1.0, 10.0])
...     bp = conv.bandpass(signal, scales=[1.0])

bandpass(B, scales=[1], order=1)

Computes band-pass filtered wavelet coefficients at specified scales.

Applies the spectral wavelet kernel:

\[\Psi_s(\mathbf{L}) = \left( \frac{4\mathbf{L}/s}{(\mathbf{L} + \mathbf{I}/s)^2} \right)^n\]

where \(s\) is the scale and \(n\) is the filter order. This kernel satisfies the admissibility condition \(\Psi(0) = 0\).

Parameters:

• B (ndarray) – Input signal array. Can be 1D (n_vertices,) or 2D (n_vertices, n_timesteps).

• scales (float | list[float], default: [1]) – Scale or list of scales \(s\) to compute coefficients for. If a scalar is passed, returns a single array instead of a list.

• order (int, default: 1) – Filter order \(n\).

Returns:

Filtered signal(s). Returns a single array if scales is a scalar, otherwise a list of arrays for each scale.

Return type:

np.ndarray | list[np.ndarray]

convolve(B, K)

Performs graph convolution using a specified kernel.

Parameters:

• B (ndarray) – Input signal array. Can be 1D (n_vertices,) or 2D (n_vertices, n_timesteps).

• K (VFKernel | dict) – Kernel function (Vector Fitting model) to apply.

Returns:

Convolved signal. Shape depends on input: (n_vertices, nDim) for 1D input, (n_vertices, n_timesteps, nDim) for 2D input.

Return type:

ndarray

highpass(B, scales=[1])

Computes high-pass filtered coefficients at specified scales.

Applies the spectral filter:

\[\mu_s(\mathbf{L}) = \frac{s\mathbf{L}}{s\mathbf{L} + \mathbf{I}}\]

where \(s\) is the scale.

Parameters:

• B (ndarray) – Input signal array. Can be 1D (n_vertices,) or 2D (n_vertices, n_timesteps).

• scales (float | list[float], default: [1]) – Scale or list of scales \(s\) to compute coefficients for. If a scalar is passed, returns a single array instead of a list.

Returns:

Filtered signal(s). Returns a single array if scales is a scalar, otherwise a list of arrays for each scale.

Return type:

np.ndarray | list[np.ndarray]

lowpass(B, scales=[1], Bset=None, refactor=True, order=1)

Computes low-pass filtered scaling coefficients at specified scales.

Applies the spectral filter:

\[\phi_s(\mathbf{L}) = \left( \frac{\mathbf{I}}{s\mathbf{L} + \mathbf{I}} \right)^n\]

where \(s\) is the scale and \(n\) is the filter order.

Parameters:

• B (ndarray) – Input signal array. Can be 1D (n_vertices,) or 2D (n_vertices, n_timesteps).

• scales (float | list[float], default: [1]) – Scale or list of scales \(s\) to compute coefficients for. If a scalar is passed, returns a single array instead of a list.

• Bset (csc_matrix, optional) – Sparse indicator vector for localized coefficient computation.

• refactor (bool, default: True) – Whether to perform numeric factorization for each scale.

• order (int, default: 1) – Filter order \(n\).

Returns:

Filtered signal(s). Returns a single array if scales is a scalar, otherwise a list of arrays for each scale.

Return type:

np.ndarray | list[np.ndarray]