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minor: improve docs formatting
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@cako
cako committed Jan 15, 2023
1 parent b8fb93a commit caff340
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Showing 2 changed files with 19 additions and 19 deletions.
14 changes: 7 additions & 7 deletions pylops/signalprocessing/nonstatconvolve1d.py
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Original file line number Diff line number Diff line change
Expand Up @@ -23,12 +23,12 @@ class NonStationaryConvolve1D(LinearOperator):
dims : :obj:`list` or :obj:`int`
Number of samples for each dimension
hs : :obj:`numpy.ndarray`
Bank of 1d compact filters of size :math:`n_{filts} \times n_h`.
Bank of 1d compact filters of size :math:`n_\text{filts} \times n_h`.
Filters must have odd number of samples and are assumed to be
centered in the middle of the filter support.
ih : :obj:`tuple`
Indices of the locations of the filters ``hs`` in the model (and data). Note
that the filters must be regularly sampled, i.e. :math:`dh=diff(ih)=const`
that the filters must be regularly sampled, i.e. :math:`dh=\text{diff}(ih)=\text{const.}`
axis : :obj:`int`, optional
Axis along which convolution is applied
dtype : :obj:`str`, optional
Expand Down Expand Up @@ -64,18 +64,18 @@ class NonStationaryConvolve1D(LinearOperator):
\begin{bmatrix}
\hat{h}_{0,0} & h_{1,0} & \hat{h}_{2,0} & h_{3,0} & \hat{h}_{4,0} \\
\hat{h}_{0,1} & h_{1,1} & \hat{h}_{2,1} & h_{3,1} & \hat{h}_{4,1} \\
... & ... & ... & ... & ... \\
\vdots & \vdots & \vdots & \vdots & \vdots \\
\hat{h}_{0,4} & h_{1,4} & \hat{h}_{2,4} & h_{3,4} & \hat{h}_{4,4} \\
\end{bmatrix}
\begin{bmatrix}
x_0 \\ x_1 \\ ... \\ x_4
x_0 \\ x_1 \\ \vdots \\ x_4
\end{bmatrix}
where :math:`\mathbf{h}_1 = [h_{1,0}, h_{1,1}, ..., h_{1,N}]` and
:math:`\mathbf{h}_3 = [h_{3,0}, h_{3,1}, ..., h_{3,N}]` are the provided filter,
where :math:`\mathbf{h}_1 = [h_{1,0}, h_{1,1}, \ldots, h_{1,N}]` and
:math:`\mathbf{h}_3 = [h_{3,0}, h_{3,1}, \ldots, h_{3,N}]` are the provided filter,
:math:`\hat{\mathbf{h}}_0 = \mathbf{h}_1` and :math:`\hat{\mathbf{h}}_4 = \mathbf{h}_3` are the
filters outside the range of the provided filters (which are extrapolated to be the same as
the nearest provided filter) and :math:`\hat{\mathbf{h}}_2 = 0.5 * \mathbf{h}_1 + 0.5 * \mathbf{h}_3`
the nearest provided filter) and :math:`\hat{\mathbf{h}}_2 = 0.5 \mathbf{h}_1 + 0.5 \mathbf{h}_3`
is the filter within the range of the provided filters (which is linearly interpolated from the two nearest
provided filter on either side of its location).
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24 changes: 12 additions & 12 deletions pylops/signalprocessing/nonstatconvolve2d.py
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Original file line number Diff line number Diff line change
Expand Up @@ -40,15 +40,15 @@ class NonStationaryConvolve2D(LinearOperator):
Number of samples for each dimension
hs : :obj:`numpy.ndarray`
Bank of 2d compact filters of size
:math:`n_{filts,x} \times n_{filts,z} \times n_h \times n_{h,x} \times n_{h,z}`.
:math:`n_{\text{filts},x} \times n_{\text{filts},z} \times n_h \times n_{h,x} \times n_{h,z}`.
Filters must have odd number of samples and are assumed to be
centered in the middle of the filter support.
ihx : :obj:`tuple`
Indices of the x locations of the filters ``hs`` in the model (and data). Note
that the filters must be regularly sampled, i.e. :math:`dh_x=diff(ihx)=const`
that the filters must be regularly sampled, i.e. :math:`dh_x=\text{diff}(ihx)=\text{const.}`
ihz : :obj:`tuple`
Indices of the z locations of the filters ``hs`` in the model (and data). Note
that the filters must be regularly sampled, i.e. :math:`dh_z=diff(ihz)=const`
that the filters must be regularly sampled, i.e. :math:`dh_z=\text{diff}(ihz)=\text{const.}`
engine : :obj:`str`, optional
Engine used for spread computation (``numpy``, ``numba``, or ``cuda``)
num_threads_per_blocks : :obj:`tuple`, optional
Expand All @@ -71,7 +71,7 @@ class NonStationaryConvolve2D(LinearOperator):
ValueError
If filters ``hs`` have even size
ValueError
If ``ihx`` or `ihz`` is not regularly sampled
If ``ihx`` or ``ihz`` is not regularly sampled
NotImplementedError
If ``engine`` is neither ``numpy``, ``fftw``, nor ``scipy``.
Expand All @@ -87,22 +87,22 @@ class NonStationaryConvolve2D(LinearOperator):
.. math::
\mathbf{y} =
\begin{bmatrix}
\hat{h}_{(0,0),(0,0)} & ... & h_{(1,1),(0,0)} & ... & \hat{h}_{(2,2),(0,0)} & ... \\
\hat{h}_{(0,0),(0,1)} & ... & h_{(1,1),(0,1)} & ... & \hat{h}_{(2,2),(0,0)} & ... \\
... & ... & & ... & ... & ... \\
\hat{h}_{(0,0),(4,3)} & ... & h_{(1,1),(4,3)} & ... & \hat{h}_{(2,2),(0,0)} & ... \\
\hat{h}_{(0,0),(0,0)} & \cdots & h_{(1,1),(0,0)} & \cdots & \hat{h}_{(2,2),(0,0)} & \cdots \\
\hat{h}_{(0,0),(0,1)} & \cdots & h_{(1,1),(0,1)} & \cdots & \hat{h}_{(2,2),(0,0)} & \cdots \\
\vdots & \ddots & & \ddots & \vdots & \vdots \\
\hat{h}_{(0,0),(4,3)} & \cdots & h_{(1,1),(4,3)} & \cdots & \hat{h}_{(2,2),(0,0)} & \cdots \\
\end{bmatrix}
\begin{bmatrix}
x_{0,0} \\ ... \\ x_{0,N} \\ x_{1,0} \\ ... \\
x_{1,N} \\ x_{M,0} \\ ... \\ x_{M,N}
x_{0,0} \\ \vdots \\ x_{0,N} \\ x_{1,0} \\ \vdots \\
x_{1,N} \\ x_{M,0} \\ \vdots \\ x_{M,N}
\end{bmatrix}
where :math:`\mathbf{h}_{(1,1)} = [h_{(1,1),(0,0)}, h_{(1,1),(0,1)}, ..., h_{(1,1),(4,3)}]`
where :math:`\mathbf{h}_{(1,1)} = [h_{(1,1),(0,0)}, h_{(1,1),(0,1)}, \ldots, h_{(1,1),(4,3)}]`
(and :math:`\mathbf{h}_{(1,1)}`, :math:`\mathbf{h}_{(1,3)}`, :math:`\mathbf{h}_{(3,1)}`,
:math:`\mathbf{h}_{(3,3)}`) are the provided filter, :math:`\hat{\mathbf{h}}_{(0,0)} =
\mathbf{h}_{(1,1)}` and similar are the filters outside the range of the provided filters
(which are extrapolated to be the same as the nearest provided filter) and
:math:`\hat{\mathbf{h}}_{(2,2)} = BiLinear(\mathbf{h}_{(1,1)}, \mathbf{h}_{(3,1)},
:math:`\hat{\mathbf{h}}_{(2,2)} = \text{bilinear}(\mathbf{h}_{(1,1)}, \mathbf{h}_{(3,1)},
\mathbf{h}_{(1,3)},\mathbf{h}_{(3,3)})` is the filter within the range of the provided filters
(which is bilinearly interpolated from the four nearest provided filter on either side
of its location).
Expand Down

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