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update docstrings #21

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Mar 17, 2023
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update docstrings #21

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56 changes: 20 additions & 36 deletions lapy/Conformal.py
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Original file line number Diff line number Diff line change
Expand Up @@ -276,13 +276,13 @@ def beltrami_coefficient(tria, mapping):
----------
tria : TriaMesh
(vertices, triangle) of genus-0 closed triangle mesh
TriaMesh should be planar mapping on complex plane
mapping : np.ndarray of shape (n,3)
coordinates of the spherical conformal parameterization

Returns
-------
mu: Union[complex, float]
[MISSING]
mu: np.ndarray of complex beltrami coefficient per triangle

Notes
-------
Expand Down Expand Up @@ -353,17 +353,16 @@ def linear_beltrami_solver(tria, mu, landmark, target):
----------
tria : TriaMesh
(vertices, triangle) of genus-0 closed triangle mesh
mu : Union[complex, float]
[MISSING]
landmark : np.ndarray of shape ()
[MISSING]
target : np.ndarray of shape ()
[MISSING]
TriaMesh should be planar mapping on complex plane
mu : np.array of complex beltrami coefficients
landmark : np.ndarray of fixed vertex indices
target : np.ndarray of shape (n,3)
2D landmark target coordinates (third coordinate is zero)

Returns
-------
mapping : np.ndarray of shape (n,3)
vertex coordinates of [MISSING]
vertex coordinates of new mapping

Notes
------
Expand Down Expand Up @@ -457,36 +456,20 @@ def linear_beltrami_solver(tria, mu, landmark, target):

def sparse_symmetric_solve(A, b, use_cholmod=True):
"""
[MISSING]
A sparse symmetric solver for ``A x = b``

Parameters
----------
A : [MISSING]
b : [MISSING]
A : sparse matrix of shape (n, n)
b : np.ndarray vector of length n
use_cholmod : bool, default=True
Which solver to use:
* True : Use Cholesky decomposition from scikit-sparse cholmod
* False: Use spsolve (LU decomposition)

Returns
-------
x: np.ndarray
[MISSING]

Notes
------
If you use this code in your own work, please cite the following paper:
[1] P. T. Choi, K. C. Lam, and L. M. Lui,
"FLASH: Fast Landmark Aligned Spherical Harmonic Parameterization
for Genus-0 Closed Brain Surfaces."
SIAM Journal on Imaging Sciences, vol. 8, no. 1, pp. 67-94, 2015.

Adopted by Martin Reuter from Matlab code at
https://github.com/garyptchoi/spherical-conformal-map
with this
Copyright (c) 2013-2020, Gary Pui-Tung Choi
https://math.mit.edu/~ptchoi
and has been distributed with the Apache 2 License
x: np.ndarray of length n, solution to ``A x = b``
"""

sksparse = import_optional_dependency("sksparse", raise_error=use_cholmod)
Expand All @@ -505,17 +488,17 @@ def sparse_symmetric_solve(A, b, use_cholmod=True):

def stereographic(u):
"""
Map sphere to complex plane
Map sphere to complex plane via stereographic projection

Parameters
----------
u : np.ndarray
u has three columns (x,y,z)
u : np.ndarray of shape (n,3)
u represents the three vertex coordinates

Returns
-------
v: np.ndarray
return z as array of complex numbers
v: np.ndarray of n complex numbers
stereographic map of u in complex plane

Notes
-------
Expand Down Expand Up @@ -544,17 +527,18 @@ def stereographic(u):

def inverse_stereographic(u):
"""
Computes mapping from complex plane to sphere
Map from complex plane to sphere via inverse stereographic projection

Parameters
----------
u : np.ndarray
can be complex array, or two columns (real,img)
for coordinates on complex plane

Returns
-------
v: np.ndarray of shape (n,3)
coordinates on sphere
coordinates on sphere in 3D

Notes
-------
Expand Down