Pharmacological activation of cGMP signaling promotes astrocyte remodeling and enrichment of perivascular GLUT1 in the murine retina.

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[1] § Methods › Single cell astrocyte and vessel analysis ↔ skfmm/__init__.py, lines 1–52 · score 0.52 · fast marching, scikit, boundary, Python, zero, distance

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Python · 902 lines · 33 KB · BSD-3-Clause · 1 match

# -*- mode: doctest -*-
"""scikit-fmm is a Python extension module which implements the fast
marching method.
https://github.com/scikit-fmm/scikit-fmm
The fast marching method is used to model the evolution of boundaries
and interfaces in a variety of application areas. More specifically,
the fast marching method is a numerical technique for finding
approximate solutions to boundary value problems of the Eikonal
equation:
F(x) | grad T(x) | = 1.
Typically, such a problem describes the evolution of a closed curve as
a function of time T with speed F(x)>0 in the normal direction at a
point x on the curve. The speed function is specified, and the time at
which the contour crosses a point x is obtained by solving the
equation.
skfmm.distance(phi, dx=1.0, self_test=False, order=2, narrow=0.0,
periodic=False)
Return the signed distance from the zero contour of the array phi.
skfmm.travel_time(phi, speed, dx=1.0, self_test=False, order=2,
narrow=0.0, periodic=False)
Return the travel from the zero contour of the array phi given the
scalar velocity field speed.
skfmm.extension_velocities(phi, speed, dx=1.0, self_test=False,
order=2, ext_mask=None, narrow=0.0, periodic=False)
Extend the velocities defined at the zero contour of phi, in the
normal direction, to the rest of the domain. Extend the velocities
such that grad f_ext dot grad d = 0 where where f_ext is the
extension velocity and d is the signed distance function.
:Copyright: Copyright 2025 The scikit-fmm team.
:License: BSD-style license. See LICENSE.txt in the source directory.
"""
__version__ = "2025.06.23"
__docformat__ = 'restructuredtext'
__all__ = ['distance', 'travel_time', 'extension_velocities', 'heap']
from .pfmm import distance, travel_time, extension_velocities
from .heap import heap
def testing():
r"""
These tests are gathered from FiPy_, PyLSMLIB_ and original
Scikit-fmm_ tests.
.. _FiPy: http://www.ctcms.nist.gov/fipy/
.. _PyLSMLIB: https://github.com/ktchu/LSMLIB/tree/master/pylsmlib
.. _Scikit-fmm: http://packages.python.org/scikit-fmm/
.. _LSMLIB: http://ktchu.serendipityresearch.org/software/lsmlib/index.html
**1D Test**
>>> import numpy as np
>>> print(np.allclose(distance((-1., -1., -1., -1., 1., 1., 1., 1.), dx=.5),
... (-1.75, -1.25, -.75, -0.25, 0.25, 0.75, 1.25, 1.75)))
True
Small dimensions.
>>> dx = 1e-10
>>> print(np.allclose(distance((-1., -1., -1., -1., 1., 1., 1., 1.), dx=dx),
... np.arange(8) * dx - 3.5 * dx))
True
**Bug Fix**
Test case for a bug in the upwind finite difference scheme for
negative phi. When computing finite differences we want to
preferentially use information from the frozen neighbors that
are closest to the zero contour in each dimension. This means
that we must compare absolute distances when checking neighbors
in the negative phi direction.
The error can result in incorrect values of the updated signed
distance function for regions close to the minimum contour of
the level set function, i.e. in the middle of holes.
To test we use a square matrix for the initial phi field that is
equal to -1 on the main diagonal and on the three diagonals above
and below this. The matrix is set to 1 everywhere else. The bug
results in errors in positions (1,1), (2,2), (3,3), (6,6), (7,7)
and (8,8) along the main diagonal.
This error occurs for first- and second-order updates. For
simplicity, we choose to only test the first-order update.
>>> phi = np.ones((10, 10))
>>> i,j = np.indices(phi.shape)
>>> phi[i==j-3] = -1
>>> phi[i==j-2] = -1
>>> phi[i==j-1] = -1
>>> phi[i==j] = -1
>>> phi[i==j+1] = -1
>>> phi[i==j+2] = -1
>>> phi[i==j+3] = -1
>>> phi = distance(phi, order=1)
>>> print(np.allclose(phi[1, 1], -2.70464, atol=1e-4))
True
>>> print(np.allclose(phi[2, 2], -2.50873, atol=1e-4))
True
>>> print(np.allclose(phi[3, 3], -2.47487, atol=1e-4))
True
>>> print(np.allclose(phi[6, 6], -2.47487, atol=1e-4))
True
>>> print(np.allclose(phi[7, 7], -2.50873, atol=1e-4))
True
>>> print(np.allclose(phi[8, 8], -2.70464, atol=1e-4))
True
**Bug Fix**
A 2D test case to test trial values for a pathological case.
>>> dx = 1.
>>> dy = 2.
>>> vbl = -dx * dy / np.sqrt(dx**2 + dy**2) / 2.
>>> vbr = dx / 2
>>> vml = dy / 2.
>>> crossProd = dx * dy
>>> dsq = dx**2 + dy**2
>>> top = vbr * dx**2 + vml * dy**2
>>> sqrt = crossProd**2 *(dsq - (vbr - vml)**2)
>>> sqrt = np.sqrt(max(sqrt, 0))
>>> vmr = (top + sqrt) / dsq
>>> print(np.allclose(distance(((-1., 1., -1.), (1., 1., 1.)), dx=(dx, dy), order=1),
... ((vbl, vml, vbl), (vbr, vmr, vbr))))
True
**Test Extension Field Calculation**
>>> tmp = 1 / np.sqrt(2)
>>> phi = np.array([[-1., 1.], [1., 1.]])
>>> phi, ext = extension_velocities(phi,
... [[-1, .5], [2., -1.]],
... ext_mask=phi < 0,
... dx=1., order=1)
>>> print(np.allclose(phi, ((-tmp / 2, 0.5), (0.5, 0.5 + tmp))))
True
>>> print(np.allclose(ext, [[1.25, .5], [2., 1.25]]))
True
>>> phi = np.array(((-1., 1., 1.), (1., 1., 1.), (1., 1., 1.)))
>>> phi, ext = extension_velocities(phi,
... ((-1., 2., -1.),
... (.5, -1., -1.),
... (-1., -1., -1.)),
... ext_mask=phi < 0,
... order=1)
>>> v1 = 0.5 + tmp
>>> v2 = 1.5
>>> tmp1 = (v1 + v2) / 2 + np.sqrt(2. - (v1 - v2)**2) / 2
>>> tmp2 = tmp1 + 1 / np.sqrt(2)
>>> print(np.allclose(phi, ((-tmp / 2, 0.5, 1.5),
... (0.5, 0.5 + tmp, tmp1),
... (1.5, tmp1, tmp2))))
True
>>> print(np.allclose(ext, ((1.25, 2., 2.),
... (.5, 1.25, 1.5456),
... (.5, 0.9544, 1.25)),
... rtol = 1e-4))
True
**Bug Fix**
Test case for a bug that occurs when initializing the distance
variable at the interface. Currently it is assumed that adjacent
cells that are opposite sign neighbors have perpendicular normal
vectors. In fact the two closest cells could have opposite
normals.
>>> print(np.allclose(distance((-1., 1., -1.)), (-0.5, 0.5, -0.5)))
True
Testing second order. This example failed with Scikit-fmm_.
>>> phi = ((-1., -1., 1., 1.),
... (-1., -1., 1., 1.),
... (1., 1., 1., 1.),
... (1., 1., 1., 1.))
>>> answer = ((-1.30473785, -0.5, 0.5, 1.49923009),
... (-0.5, -0.35355339, 0.5, 1.45118446),
... (0.5, 0.5, 0.97140452, 1.76215286),
... (1.49923009, 1.45118446, 1.76215286, 2.33721352))
>>> print(np.allclose(distance(phi),
... answer,
... rtol=1e-9))
True
**A test for a bug in both LSMLIB and Scikit-fmm**
The following test gives different results depending on whether
LSMLIB_ or Scikit-fmm_ is used. This issue occurs when calculating
second order accurate distance functions. When a value becomes
"known" after previously being a "trial" value it updates its
neighbors' values. In a second order scheme the neighbors one step
away also need to be updated (if the cell between the new "known"
cell and the cell required for second order accuracy also happens
to be "known"), but are not updated in either package. By luck
(due to trial values having the same value), the values calculated
in Scikit-fmm_ for the following example are correct although an
example that didn't work for Scikit-fmm_ could also be
constructed.
>>> phi = distance([[-1, -1, -1, -1],
... [ 1, 1, -1, -1],
... [ 1, 1, -1, -1],
... [ 1, 1, -1, -1]], order=2)
>>> phi = distance(phi, order=2)
The following values come form Scikit-fmm_.
>>> answer = [[-0.5, -0.58578644, -1.08578644, -1.85136395],
... [ 0.5, 0.29289322, -0.58578644, -1.54389939],
... [ 1.30473785, 0.5, -0.5, -1.5 ],
... [ 1.49547948, 0.5, -0.5, -1.5 ]]
The 3rd and 7th element are different for LSMLIB_. This is because
the 15th element is not "known" when the "trial" value for the 7th
element is calculated. Scikit-fmm_ calculates the values in a
slightly different order so gets a seemingly better answer, but
this is just chance.
>>> print(np.allclose(phi, answer, rtol=1e-9))
True
The following tests for the same issue but is a better test case
guaranteed to fail.
>>> phi = np.array([[-1, 1, 1, 1, 1, -1],
... [-1, -1, -1, -1, -1, -1],
... [-1, -1, -1, -1, -1, -1]])
>>> phi = distance(phi)
>>> print(phi[2, 2] == phi[2, 3])
True
>>> phi = distance(phi)
>>> print(phi[2, 2] == phi[2, 3])
True
**Circle Example**
Solve the level set equation in two dimensions for a circle.
The 2D level set equation can be written,
.. math::
|\nabla \phi| = 1
and the boundary condition for a circle is given by, :math:`\phi = 0` at
:math:`(x - L / 2)^2 + (y - L / 2)^2 = (L / 4)^2`.
The solution to this problem will be demonstrated in the following
script. Firstly, setup the parameters.
>>> def mesh(nx=1, ny=1, dx=1., dy=1.):
... y, x = np.mgrid[0:nx,0:ny]
... x = x * dx + dx / 2
... y = y * dy + dy / 2
... return x, y
>>> dx = 1.
>>> N = 11
>>> L = N * dx
>>> x, y = mesh(nx=N, ny=N, dx=dx, dy=dx)
>>> phi = -np.ones(N * N, 'd')
>>> phi[(x.flatten() - L / 2.)**2 + (y.flatten() - L / 2.)**2 < (L / 4.)**2] = 1.
>>> phi = np.reshape(phi, (N, N))
>>> phi = distance(phi, dx=dx, order=1).flatten()
>>> dX = dx / 2.
>>> m1 = dX * dX / np.sqrt(dX**2 + dX**2)
>>> def evalCell(phix, phiy, dx):
... aa = dx**2 + dx**2
... bb = -2 * ( phix * dx**2 + phiy * dx**2)
... cc = dx**2 * phix**2 + dx**2 * phiy**2 - dx**2 * dx**2
... sqr = np.sqrt(bb**2 - 4. * aa * cc)
... return ((-bb - sqr) / 2. / aa, (-bb + sqr) / 2. / aa)
>>> v1 = evalCell(-dX, -m1, dx)[0]
>>> v2 = evalCell(-m1, -dX, dx)[0]
>>> v3 = evalCell(m1, m1, dx)[1]
>>> v4 = evalCell(v3, dX, dx)[1]
>>> v5 = evalCell(dX, v3, dx)[1]
>>> MASK = -1000.
>>> trialValues = np.array((
... MASK, MASK, MASK, MASK, MASK, MASK, MASK, MASK, MASK, MASK, MASK,
... MASK, MASK, MASK, MASK,-3*dX,-3*dX,-3*dX, MASK, MASK, MASK, MASK,
... MASK, MASK, MASK, v1, -dX, -dX, -dX, v1, MASK, MASK, MASK,
... MASK, MASK, v2, -m1, m1, dX, m1, -m1, v2, MASK, MASK,
... MASK, -dX*3, -dX, m1, v3, v4, v3, m1, -dX,-dX*3, MASK,
... MASK, -dX*3, -dX, dX, v5, MASK, v5, dX, -dX,-dX*3, MASK,
... MASK, -dX*3, -dX, m1, v3, v4, v3, m1, -dX,-dX*3, MASK,
... MASK, MASK, v2, -m1, m1, dX, m1, -m1, v2, MASK, MASK,
... MASK, MASK, MASK, v1, -dX, -dX, -dX, v1, MASK, MASK, MASK,
... MASK, MASK, MASK, MASK,-3*dX,-3*dX,-3*dX, MASK, MASK, MASK, MASK,
... MASK, MASK, MASK, MASK, MASK, MASK, MASK, MASK, MASK, MASK, MASK), 'd')
>>> phi[trialValues == MASK] = MASK
>>> print(np.allclose(phi, trialValues))
True
**Square Example**
Here we solve the level set equation in two dimensions for a square. The equation is
given by:
.. math::
|\nabla \phi| &= 1 \\
\phi &= 0 \qquad \text{at} \qquad \begin{cases}
x = \left( L / 3, 2 L / 3 \right)
& \text{for $L / 3 \le y \le 2 L / 3$} \\
y = \left( L / 3, 2 L / 3 \right)
& \text{for $L / 3 \le x \le 2 L / 3$}
\end{cases}
>>> dx = 0.5
>>> dy = 2.
>>> nx = 5
>>> ny = 5
>>> Lx = nx * dx
>>> Ly = ny * dy
>>> x, y = mesh(nx=nx, ny=ny, dx=dx, dy=dy)
>>> x = x.flatten()
>>> y = y.flatten()
>>> phi = -np.ones(nx * ny, 'd')
>>> phi[((Lx / 3. < x) & (x < 2. * Lx / 3.)) & ((Ly / 3. < y) & (y < 2. * Ly / 3))] = 1.
>>> phi = np.reshape(phi, (nx, ny))
>>> phi = distance(phi, dx=(dy, dx), order=1).flatten()
>>> def evalCell(phix, phiy, dx, dy):
... aa = dy**2 + dx**2
... bb = -2 * ( phix * dy**2 + phiy * dx**2)
... cc = dy**2 * phix**2 + dx**2 * phiy**2 - dx**2 * dy**2
... sqr = np.sqrt(bb**2 - 4. * aa * cc)
... return ((-bb - sqr) / 2. / aa, (-bb + sqr) / 2. / aa)
>>> val = evalCell(-dy / 2., -dx / 2., dx, dy)[0]
>>> v1 = evalCell(val, -3. * dx / 2., dx, dy)[0]
>>> v2 = evalCell(-3. * dy / 2., val, dx, dy)[0]
>>> v3 = evalCell(v2, v1, dx, dy)[0]
>>> v4 = dx * dy / np.sqrt(dx**2 + dy**2) / 2
>>> arr = np.array((
... v3 , v2 , -3. * dy / 2. , v2 , v3,
... v1 , val , -dy / 2. , val , v1 ,
... -3. * dx / 2., -dx / 2., v4 , -dx / 2., -3. * dx / 2.,
... v1 , val , -dy / 2. , val , v1 ,
... v3 , v2 , -3. * dy / 2. , v2 , v3 ))
>>> print(np.allclose(arr, phi))
True
**Assertion Errors**
>>> distance([[-1, 1],[1, 1]], dx=(1, 2, 3))
Traceback (most recent call last):
...
ValueError: dx must be of length len(phi.shape)
>>> extension_velocities([[-1, 1],[1, 1]], speed=[1, 1])
Traceback (most recent call last):
...
ValueError: phi and speed must have the same shape
**Test for 1D equality between `distance` and `travel_time`**
>>> phi = np.arange(-5, 5) + 0.499
>>> d = distance(phi)
>>> t = travel_time(phi, speed=np.ones_like(phi))
>>> np.testing.assert_allclose(t, np.abs(d))
**Tests taken from FiPy**
>>> phi = np.array(((-1, -1, 1, 1),
... (-1, -1, 1, 1),
... (1, 1, 1, 1),
... (1, 1, 1, 1)))
>>> o1 = distance(phi, order=1, self_test=True)
>>> dw_o1 = [[-1.20710678, -0.5, 0.5, 1.5],
... [-0.5, -0.35355339, 0.5, 1.5],
... [ 0.5, 0.5, 1.20710678, 2.04532893],
... [ 1.5, 1.5, 2.04532893, 2.75243571]]
>>> np.testing.assert_allclose(o1, dw_o1)
>>> phi = np.array(((-1, -1, 1, 1),
... (-1, -1, 1, 1),
... (1, 1, 1, 1),
... (1, 1, 1, 1)))
>>> o1 = travel_time(phi, np.ones_like(phi), order=1, self_test=True)
>>> dw_o1 = [[-1.20710678, -0.5, 0.5, 1.5],
... [-0.5, -0.35355339, 0.5, 1.5],
... [ 0.5, 0.5, 1.20710678, 2.04532893],
... [ 1.5, 1.5, 2.04532893, 2.75243571]]
>>> np.testing.assert_allclose(o1, np.abs(dw_o1))
>>> phi = np.array(((-1, -1, 1, 1),
... (-1, -1, 1, 1),
... (1, 1, 1, 1),
... (1, 1, 1, 1)))
>>> o2 = distance(phi, self_test=True)
>>> dw_o2 = [[-1.30473785, -0.5, 0.5, 1.49923009],
... [-0.5, -0.35355339, 0.5, 1.45118446],
... [ 0.5, 0.5, 0.97140452, 1.76215286],
... [ 1.49923009, 1.45118446, 1.76215286, 2.33721352]]
>>> np.testing.assert_allclose(o2, dw_o2)
>>> phi = np.array(((-1, -1, 1, 1),
... (-1, -1, 1, 1),
... (1, 1, 1, 1),
... (1, 1, 1, 1)))
>>> o2 = travel_time(phi, np.ones_like(phi), self_test=True)
>>> dw_o2 = [[-1.30473785, -0.5, 0.5, 1.49923009],
... [-0.5, -0.35355339, 0.5, 1.45118446],
... [ 0.5, 0.5, 0.97140452, 1.76215286],
... [ 1.49923009, 1.45118446, 1.76215286, 2.33721352]]
>>> np.testing.assert_allclose(o2, np.abs(dw_o2))
>>> distance([-1,1], order=0)
Traceback (most recent call last):
...
ValueError: order must be 1 or 2
>>> distance([-1,1], order=3)
Traceback (most recent call last):
...
ValueError: order must be 1 or 2
**Extension velocity tests**
Test 1d extension constant.
>>> phi = [-1,-1,-1,1,1,1]
>>> speed = [1,1,1,1,1,1]
>>> d, f_ext = extension_velocities(phi, speed, self_test=True)
>>> np.testing.assert_allclose(speed, f_ext)
Test the 1D extension block.
>>> phi = np.ones(10)
>>> phi[0] =- 1
>>> speed = np.ones(10)
>>> speed[0:3] = 5
>>> d, f_ext = extension_velocities(phi, speed, self_test=True)
>>> np.testing.assert_allclose(f_ext, 5)
Test that a uniform speed value is preserved.
>>> N = 50
>>> X, Y = np.meshgrid(np.linspace(-1, 1, N), np.linspace(-1, 1, N))
>>> r = 0.25
>>> dx = 2.0 / (N - 1)
>>> phi = (X) ** 2 + (Y) ** 2 - r ** 2
>>> speed = np.ones_like(phi)
>>> d, f_ext = extension_velocities(phi, speed, dx, self_test=True)
>>> np.testing.assert_allclose(f_ext, 1.0)
Constant value march-out test
>>> speed[abs(Y)<0.3] = 10.0
>>> d, f_ext = extension_velocities(phi, speed, dx, self_test=True)
>>> np.testing.assert_allclose(f_ext, 10.0)
Test distance from extension
>>> speed = np.ones_like(phi)
>>> d, f_ext = extension_velocities(phi, speed, dx, self_test=True)
>>> d2 = distance(phi, dx, self_test=True)
>>> np.testing.assert_allclose(d, d2)
Test for extension velocity bug
>>> N = 150
>>> X, Y = np.meshgrid(np.linspace(-1, 1, N), np.linspace(-1, 1, N))
>>> r = 0.5
>>> dx = 2.0 / (N - 1)
>>> phi = (X) ** 2 + (Y) ** 2 - r ** 2
>>> speed = np.ones_like(phi)
>>> speed[X>0.25] = 3.0
>>> d2, f_ext = extension_velocities(phi, speed, dx)
>>> assert (f_ext <= 3.0000001).all()
>>> assert (f_ext >= 1).all()
>>> np.testing.assert_almost_equal(f_ext[137, 95], 1, 3)
>>> np.testing.assert_almost_equal(f_ext[103, 78], 1, 2)
>>> np.testing.assert_almost_equal(f_ext[72, 100], 3, 3)
>>> np.testing.assert_almost_equal(f_ext[72, 86], 3, 3)
>>> np.testing.assert_almost_equal(f_ext[110, 121], 3, 3)
Simple two point tests
>>> np.testing.assert_array_equal(distance([-1, 1]),
... [-0.5, 0.5])
>>> np.testing.assert_allclose(distance([-1, -1, -1, 1, 1, 1]),
... [-2.5, -1.5, -0.5, 0.5, 1.5, 2.5])
>>> np.testing.assert_allclose(distance([1, 1, 1, -1, -1, -1]),
... [2.5, 1.5, 0.5, -0.5, -1.5, -2.5])
Three point test case
>>> np.testing.assert_array_equal(distance([-1, 0, 1]), [-1, 0, 1])
>>> np.testing.assert_array_equal(distance([-1, 0, 1], dx=[2]), [-2, 0, 2])
>>> np.testing.assert_array_equal(distance([-1, 0, 1], dx=2), [-2, 0, 2])
>>> np.testing.assert_array_equal(distance([-1, 0, 1], dx=2.0), [-2, 0, 2])
>>> np.testing.assert_array_equal(travel_time([1, 0, -1], [1, 1, 1]),
... [1, 0, 1])
>>> np.testing.assert_array_equal(travel_time([-1, 0, 1], [1, 1, 1]),
... [1, 0, 1])
>>> np.testing.assert_array_equal(travel_time([1, 0, -1], [1, 1, 1], dx=2),
... [2, 0, 2])
>>> np.testing.assert_array_equal(travel_time([1, 0, -1], [1, 1, 1], dx=[2]),
... [2, 0, 2])
>>> np.testing.assert_array_equal(travel_time([1, 0, -1], [1, 1, 1], dx=2.0),
... [2, 0, 2])
Travel time tests 1
>>> np.testing.assert_allclose(travel_time([0, 1, 1, 1, 1], [2, 2, 2, 2, 2]),
... [0, 0.5, 1.0, 1.5, 2.0])
>>> np.testing.assert_array_equal(travel_time([1, 0, -1], [2, 2, 2]),
... [0.5, 0, 0.5])
Travel time tests 2
>>> phi = [1, 1, 1, -1, -1, -1]
>>> t = travel_time(phi, np.ones_like(phi))
>>> exact = [2.5, 1.5, 0.5, 0.5, 1.5, 2.5]
>>> np.testing.assert_allclose(t, exact)
Travel time tests 3
>>> phi = [-1, -1, -1, 1, 1, 1]
>>> t = travel_time(phi, np.ones_like(phi))
>>> exact = [2.5, 1.5, 0.5, 0.5, 1.5, 2.5]
>>> np.testing.assert_allclose(t, exact)
Corner case
>>> np.testing.assert_array_equal(distance([0, 0]), [0, 0])
>>> np.testing.assert_array_equal(travel_time([0, 0], [1, 1]), [0, 0])
Test zero
>>> distance([1, 0, 1, 1], 0)
Traceback (most recent call last):
...
ValueError: dx must be greater than zero
Test dx shape
>>> distance([0, 0, 1, 0, 0], [0, 0, 1, 0, 0])
Traceback (most recent call last):
...
ValueError: dx must be of length len(phi.shape)
Test for small speeds
Test catching speeds which are too small. Speeds less than the
machine epsilon are masked off to avoid an overflow.
>>> t = travel_time([-1, -1, 0, 1, 1], [1, 1, 1, 1, 0])
>>> assert isinstance(t, np.ma.MaskedArray)
>>> np.testing.assert_array_equal(t.data[:-1], [2, 1, 0, 1])
>>> np.testing.assert_array_equal(t.mask, [False, False, False, False, True])
>>> t2 = travel_time([-1, -1, 0, 1, 1], [1, 1, 1, 1, 1e-300])
>>> np.testing.assert_array_equal(t, t2)
Mask test
Test that when the mask cuts off the solution, the cut off points
are also masked.
>>> ma = np.ma.MaskedArray([1, 1, 1, 0], [False, True, False, False])
>>> d = distance(ma)
>>> exact = np.ma.MaskedArray([0, 0, 1, 0], [True, True, False, False])
>>> np.testing.assert_array_equal(d.mask, exact.mask)
>>> np.testing.assert_array_equal(d, exact)
Circular level set
>>> N = 50
>>> X, Y = np.meshgrid(np.linspace(-1, 1, N), np.linspace(-1, 1, N))
>>> r = 0.5
>>> dx = 2.0 / (N - 1)
>>> phi = (X) ** 2 + (Y) ** 2 - r ** 2
>>> d = distance(phi, dx, self_test=True)
>>> exact = np.sqrt(X ** 2 + Y ** 2) - r
>>> np.testing.assert_allclose(d, exact, atol=dx)
Planar level set
>>> N = 50
>>> X, Y = np.meshgrid(np.linspace(-1, 1, N), np.linspace(-1, 1, N))
>>> dx = 2.0 / (N - 1)
>>> phi = np.ones_like(X)
>>> phi[0, :] = -1
>>> d = distance(phi, dx, self_test=True)
>>> exact = Y + 1 - dx / 2.0
>>> np.testing.assert_allclose(d, exact)
Masked input
>>> N = 50
>>> X, Y = np.meshgrid(np.linspace(-1, 1, N), np.linspace(-1, 1, N))
>>> dx = 2.0 / (N - 1)
>>> phi = np.ones_like(X)
>>> phi[0, 0] = -1
>>> mask = np.logical_and(abs(X) < 0.25, abs(Y) < 0.25)
>>> mphi = np.ma.MaskedArray(phi.copy(), mask)
>>> d0 = distance(phi, dx, self_test=True)
>>> d = distance(mphi, dx, self_test=True)
>>> d0[mask] = 0
>>> d[mask] = 0
>>> shadow = d0 - d
>>> bsh = abs(shadow) > 0.001
>>> diff = (bsh).sum()
>>> assert diff > 635 and diff < 645
Test Eikonal solution
>>> N = 50
>>> X, Y = np.meshgrid(np.linspace(-1, 1, N), np.linspace(-1, 1, N))
>>> r = 0.5
>>> dx = 2.0 / (N - 1)
>>> phi = (X) ** 2 + (Y) ** 2 - r ** 2
>>> speed = np.ones_like(phi) * 2
>>> t = travel_time(phi, speed, dx)
>>> exact = 0.5 * np.abs(np.sqrt(X ** 2 + Y ** 2) - 0.5)
>>> np.testing.assert_allclose(t, exact, atol=dx)
Test 1d
>>> N = 100
>>> X = np.linspace(-1.0, 1.0, N)
>>> dx = 2.0 / (N - 1)
>>> phi = np.zeros_like(X)
>>> phi[X < 0] = -1
>>> phi[X > 0] = 1
>>> d = distance(phi, dx, self_test=True)
>>> np.testing.assert_allclose(d, X)
Test 3d
>>> N = 15
>>> X = np.linspace(-1, 1, N)
>>> Y = np.linspace(-1, 1, N)
>>> Z = np.linspace(-1, 1, N)
>>> phi = np.ones((N, N, N))
>>> phi[0, 0, 0] = -1.0
>>> dx = 2.0 / (N - 1)
>>> d = distance(phi, dx, self_test=True)
>>> exact = np.sqrt((X + 1) ** 2 +
... (Y + 1)[:, np.newaxis] ** 2 +
... (Z + 1)[:, np.newaxis, np.newaxis] ** 2)
>>> np.testing.assert_allclose(d, exact, atol=dx)
Test default dx
>>> N = 50
>>> X, Y = np.meshgrid(np.linspace(-1, 1, N), np.linspace(-1, 1, N))
>>> r = 0.5
>>> phi = (X) ** 2 + (Y) ** 2 - r ** 2
>>> speed = np.ones_like(phi) * 2
>>> out = travel_time(phi, speed, self_test=True)
Test non-square grid and dx different in different directions
>>> N = 50
>>> NX, NY = N, 5 * N
>>> X, Y = np.meshgrid(np.linspace(-1, 1, NY), np.linspace(-1, 1, NX))
>>> r = 0.5
>>> phi = X ** 2 + Y ** 2 - r ** 2
>>> dx = [2.0 / (NX - 1), 2.0 / (NY - 1)]
>>> d = distance(phi, dx, self_test=True)
>>> exact = np.sqrt(X ** 2 + Y ** 2) - r
>>> np.testing.assert_allclose(d, exact, atol=1.3*max(dx))
No zero level set test
>>> distance([1, 1], self_test=False)
Traceback (most recent call last):
...
ValueError: the array phi contains no zero contour (no zero level set)
Shape mismatch test
>>> travel_time([-1, 1], [2])
Traceback (most recent call last):
...
ValueError: phi and speed must have the same shape
Speed wrong type test
>>> travel_time([0, 0, 1, 1], 2)
Traceback (most recent call last):
...
ValueError: speed must be a 1D to 12-D array of doubles
dx mismatch test
>>> travel_time([-1, 1], [2, 2], [2, 2, 2, 2])
Traceback (most recent call last):
...
ValueError: dx must be of length len(phi.shape)
Test c error handling
>>> distance([-1, 1], self_test=44)
Traceback (most recent call last):
...
ValueError: self_test must be 0 or 1
Check array type test
>>> distance(np.array(["a", "b"]))
Traceback (most recent call last):
...
ValueError: phi must be a 1 to 12-D array of doubles
>>> from skfmm import heap
>>> h = heap(10,True)
>>> h.push(0,0.2)
0
>>> h.push(1,0.3)
1
>>> h.push(2,0.1)
2
>>> h.update(1, 0.01)
>>> h.pop()
(1, 0.01)
>>> h.pop()
(2, 0.1)
>>> h.pop()
(0, 0.2)
>>> h.empty()
True
>>> h.pop()
Traceback (most recent call last):
...
RuntimeError: heap pop error: empty heap
<BLANKLINE>
Test narrow optional argument.
>>> phi = np.array([-1,-1,-1,1,1,1])
>>> d = distance(phi, narrow=1.0)
>>> d.data[2:-2]
array([-0.5, 0.5])
>>> assert (d.mask == [ True, True, False, False, True, True]).all()
>>> N = 50
>>> X, Y = np.meshgrid(np.linspace(-1, 1, N), np.linspace(-1, 1, N))
>>> r = 0.5
>>> dx = 2.0 / (N - 1)
>>> phi = (X) ** 2 + (Y) ** 2 - r ** 2
>>> exact = np.sqrt(X ** 2 + Y ** 2) - r
>>> d = distance(phi, dx)
>>> bandwidth=5*dx
>>> d2 = distance(phi, dx, narrow=bandwidth)
>>> np.testing.assert_allclose(d, exact, atol=dx)
>>> # make sure we get a normal array if there are no points outside the narrow band
>>> np.testing.assert_allclose(distance(phi, dx, narrow=1000*dx), exact, atol=dx)
>>> assert (d2<bandwidth).all()
>>> assert type(d2) is np.ma.masked_array
>>> speed = np.ones_like(phi)
>>> speed[X>0] = 1.8
>>> t = travel_time(phi, speed, dx)
>>> t2 = travel_time(phi, speed, dx, narrow=bandwidth)
>>> assert type(t2) is np.ma.masked_array
>>> assert (t2<bandwidth).all()
>>> speed = np.ones_like(phi)
>>> speed = X + Y
>>> ed, ev = extension_velocities(phi, speed, dx)
>>> ed2, ev2 = extension_velocities(phi, speed, dx, narrow=bandwidth)
>>> assert type(ed2) is np.ma.masked_array
>>> assert type(ev2) is np.ma.masked_array
>>> assert (ed2<bandwidth).all()
>>> assert ed2.shape == ed.shape == ev.shape == ev2.shape
>>> distance(phi, dx, narrow=-1)
Traceback (most recent call last):
...
ValueError: parameter "narrow" must be greater than or equal to zero.
>>> # make sure the narrow options works with an existing mask.
>>> mask = abs(X)<0.25
>>> d3 = distance(np.ma.masked_array(phi, mask), dx, narrow=bandwidth)
>>> assert (d3.mask[mask]==True).all()
>>> assert d3.mask.sum() > mask.sum()
Testing periodic argument
>>> X, Y = np.meshgrid(np.linspace(-2,2,200), np.linspace(-2,2,200))
>>> phi = -1*np.ones_like(X); phi[X**2+(Y-0.9)**2<0.5] = 1.0
>>> speed = np.ones_like(X); speed[(X-0.9)**2+Y**2<1.0] = 2.0
>>> np.allclose(distance(phi),distance(phi,periodic=False)) and np.allclose(distance(phi),distance(phi,periodic=(0,0)))
True
>>> np.allclose(travel_time(phi,speed),travel_time(phi,speed,periodic=False)) and np.allclose(travel_time(phi,speed),travel_time(phi,speed,periodic=(0,0)))
True
>>> phi = -1*np.ones_like(X); phi[X**2+Y**2<0.5] = 1.0
>>> speed = np.ones_like(X); speed[X**2+Y**2<1.0] = 2.0
>>> np.allclose(distance(phi),distance(phi,periodic=True)) and np.allclose(distance(phi),distance(phi,periodic=(1,1)))
True
>>> np.allclose(travel_time(phi,speed),travel_time(phi,speed,periodic=True)) and np.allclose(travel_time(phi,speed),travel_time(phi,speed,periodic=(1,1)))
True
>>> np.allclose(travel_time(phi,speed),travel_time(phi,speed,periodic=True)) and np.allclose(travel_time(phi,speed),travel_time(phi,speed,periodic=[1,1]))
True
>>> np.allclose(travel_time(phi,speed),travel_time(phi,speed,periodic=True)) and np.allclose(travel_time(phi,speed),travel_time(phi,speed,periodic=[True,True]))
True
>>> phi = -1*np.ones_like(X); phi[X**2+(Y-0.9)**2<0.5] = 1.0
>>> speed = np.ones_like(X); speed[(X-0.9)**2+Y**2<1.0] = 2.0
>>> np.allclose(distance(np.roll(phi,137,axis=0),periodic=True),np.roll(distance(phi,periodic=True),137,axis=0))
True
>>> np.allclose(travel_time(np.roll(phi,-77,axis=1),np.roll(speed,-77,axis=1),periodic=True),np.roll(travel_time(phi,speed,periodic=True),-77,axis=1))
True
>>> phi=[1,-1,1,1,1,1]
>>> speed=[4,1,2,2,2,2]
>>> np.allclose(extension_velocities(phi,speed)[1],(2.5,2.5,1.5,1.5,1.5,1.5))
True
>>> np.allclose(extension_velocities(phi,speed,periodic=True)[1],(2.5,2.5,1.5,1.5,1.5,2.5))
True
This is issue #18,
>>> phi = np.array([[ 1, 1, -1, -1, -1, -1, 1],
... [ 3, 1, -1, -1, -1, -1, 1],
... [ 3, 3, 1, 1, 1, 1, 3],
... [ 3, 3, 3, 3, 3, 3, 3],
... [ 3, 3, 3, 3, 3, 3, 3]])
>>> speed = np.array([[ 1. , 1. , 0.057, 0.128, 0.037, 0.039, 1. ],
... [ 1. , 1. , 0.199, 0.408, 0.997, 0.688, 1. ],
... [ 1. , 1. , 1. , 1. , 1. , 1. , 1. ],
... [ 1. , 1. , 1. , 1. , 1. , 1. , 1. ],
... [ 1. , 1. , 1. , 1. , 1. , 1. , 1. ]])
>>> assert not travel_time(phi,speed)[0][3] == 0
>>> phi = np.array([[1, -1, -1],
... [0, 0, -1],
... [0, 0, 1]])
>>> value = 0.01
>>> speed = np.array([[ 1, value, 0.1],
... [ 0, 0, 1. ],
... [ 0, 0, 1. ]])
>>> phi = np.ma.MaskedArray(phi, phi==0)
>>> tt = travel_time(phi,speed)
>>> tt.fill_value=0
>>> np.testing.assert_allclose(tt.data, ((0.5, 50, 7.5),
... (0, 0, 0.5),
... (0, 0, 0.5)))
This is from Pull Request #57:
>>> a = np.array([[[600, 399, 641], [607, 605, 796], [602, 641, 797], [602, 658, 814]], [[272, -1, 398], [208, 282, 539], [209, 285, 513], [208, 298, 519]], [[-19, 51, 307], [-191, 2, 403], [-171, 5, 325], [-172, 3, 318]]])
>>> d = distance(a)
>>> assert not (d==0).any()
A 2D version of this bug was also discovered
>>> a = np.array([[399, -1, 51, 10.0], [605, 282, 2, -3], [641, 285, 5, -100], [658, 298, 3, -3]])
>>> d = distance(a)
>>> assert not (d==0).any()
"""
def test(verbose=None):
r"""
Run all the doctests available.
"""
import doctest
import skfmm
fail0, test0 = doctest.testmod(skfmm, verbose=verbose)
fail1, test1 = doctest.testfile("heap.py", verbose=verbose)
print ("Summary: {} tests run {} failures".format(test0+test1,
fail0+fail1))
return fail0+fail1

__init__.py at commit 3618765, under BSD-3-Clause · at the source

Overview

Authors: Kristin L Clark¹, Shane Mecca¹, Elio Almaoui¹, Olivia L Bossardet², Joseph M Holden¹, David J Calkins¹, Lauren K Wareham¹

Institutions: Vanderbilt University Medical Center (United States); University of Miami (United States)

Journal: Frontiers in cellular neuroscience, volume 20, article 1870679

Dates: received 1 May 2026; accepted 12 June 2026; published online 2 July 2026

Type: Research article · Language: English

License: CC BY

Identifiers: DOI 10.3389/fncel.2026.1870679 · PMID 42459923 · PMCID PMC13372325 · OpenAlex W7166842734

Open access: gold, a free copy (OpenAlex)

Status: code verified

Categories: mouse (organism), cellular / molecular (subfield)

Methods: Statistics, Connectivity, fMRI & imaging

Keywords: astrocyte, GLUT1, neurovascular coupling, neurovascular unit, perivascular endfeet, retina, retinal ganglion cell

Topic: Retinal Development and Disorders (Molecular Biology, Biochemistry, Genetics and Molecular Biology), according to OpenAlex

Funding: NEI NIH HHS (R01 EY036002)

Citations: not cited yet (Europe PMC); 44 references in the paper

Abstract

Astrocytes regulate metabolic exchange between the vasculature and neurons in the central nervous system (CNS). In the retina of the eye, also a component of the CNS, astrocyte endfeet couple to vascular elements to mediate glucose uptake via the glucose transporter GLUT1 and shuttle metabolic resources to the axons of retinal ganglion cells (RGCs), which provide visual input to the brain. In addition to its own transcriptional regulation, GLUT1 is also modulated by signaling pathways that influence its subcellular localization at the astrocyte-vascular interface. For example, cyclic guanosine monophosphate (cGMP) signaling, a key regulator of vascular tone, is associated with changes in retinal astrocyte morphology and is implicated in age-related loss of RGCs, suggesting a potential role in astrocyte function within the neurovascular unit. Here, we tested this possibility directly by investigating the effects of 8-Br-cGMP on astrocyte morphology, vascular interactions, and GLUT1 localization in the retina. Using a transgenic mouse that allows resolution of individual astrocytes in great detail across the retina (the G-MORF mouse), we show that acute elevation of 8-Br-cGMP increases astrocyte coverage area without altering overall vascular structure. 8-Br-cGMP treatment was also associated with enhanced astrocyte-vascular association, reflected by increased endfoot coverage of blood vessels and altered scaling of astrocyte contact with vessel size. Treatment to increase cGMP signaling promoted redistribution of GLUT1 to astrocyte perivascular endfeet without changing overall levels of GLUT1. Together, these findings indicate that increased cGMP signaling induces coordinated structural and molecular remodeling of astrocytes at the vascular interface. These results provide important insight into how cyclic nucleotide signaling pathways may regulate astrocyte organization in the retina and suggests a potential role for cGMP in modulating astrocyte-vascular interactions within the neurovascular unit.

Reproduced under the paper's license (CC BY), from the paper cited above.

Repository

Its files are read in the Code ↔ Paper reader above, with 1 match between paragraphs and lines of code.

scikit-fmm/scikit-fmm

License: BSD-3-Clause

State: the link answers, verified on 27 September 2026

Evidence: files inventoried

Commit: 3618765f26fe469163840dd0d9775848ec379c3e, 1 July 2026

Languages: Python (8), C++ (8), C/C++ (5), Shell (2)

Size: 55 files, 23 scripts

Software Heritage: archived

Found in: the text

Holds: README, license file, environment (pyproject.toml, doc/requirements.txt), continuous integration, documentation

Not found: CITATION.cff, tests

Tools: NumPy (5 files), Matplotlib (4 files)

Availability: 1 check, the latest on 27 September 2026: the link answers

27 September 2026: the link answers

25 files

doc/conf.py, Python, 269 lines
examples/2d_example.py, Python, 54 lines
examples/boundaryconditions_example.py, Python, 36 lines
examples/extension_velocities_example.py, Python, 31 lines
profile/prof.cpp, C++, 42 lines
profile/prof.sh, Shell, 33 lines
profile/profile.py, Python, 31 lines
skfmm/__init__.py, Python, 902 lines, 1 match
skfmm/base_marcher.cpp, C++, 225 lines
skfmm/base_marcher.h, C/C++, 105 lines
skfmm/distance_marcher.cpp, C++, 166 lines
skfmm/distance_marcher.h, C/C++, 23 lines
skfmm/extension_velocity_marcher.cpp, C++, 155 lines
skfmm/extension_velocity_marcher.h, C/C++, 27 lines
skfmm/fmm.cpp, C++, 337 lines
skfmm/heap.cpp, C++, 205 lines
skfmm/heap.h, C/C++, 60 lines
skfmm/heap.py, Python, 173 lines
skfmm/pfmm.py, Python, 245 lines
skfmm/pheap.cpp, C++, 5,075 lines
skfmm/travel_time_marcher.cpp, C++, 118 lines
skfmm/travel_time_marcher.h, C/C++, 37 lines
static_analysis.sh, Shell, 20 lines
LICENSE.txt, License, 31 lines
README.md, Text, 99 lines

At the source: github.com/scikit-fmm/scikit-fmm

Tracing map

Proposed by the machine: these links were found in the paper and verified at the source, without human review. The map will receive a Zenodo DOI once one of the paper's authors has validated it with their ORCID.

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1 repository of the authors' code, each at its verified commit, with its license and how the link was found in the paper;
23 scripts, each with its path and the digest of its content;
1 match between paragraphs of the paper and lines of the code (method lexical-v1);
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Data availability statement

The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.

Reproduced under the paper's license (CC BY), from the paper cited above.

Versions

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Version 1, 27 September 2026: the first record

Recorded: type, language, journal, volume, pages, dates, 7 authors, 7 keywords, 1 funder, 44 references.

Cite

This paper

Clark, K. L., Mecca, S., Almaoui, E., Bossardet, O. L., Holden, J. M., Calkins, D. J., & Wareham, L. K. (2026). Pharmacological activation of cGMP signaling promotes astrocyte remodeling and enrichment of perivascular GLUT1 in the murine retina. Frontiers in cellular neuroscience, 20, 1870679. https://doi.org/10.3389/fncel.2026.1870679

BibTeX

@article{clark2026pharmacological, author = {Clark, Kristin L and Mecca, Shane and Almaoui, Elio and Bossardet, Olivia L and Holden, Joseph M and Calkins, David J and Wareham, Lauren K}, title = {{Pharmacological activation of cGMP signaling promotes astrocyte remodeling and enrichment of perivascular GLUT1 in the murine retina}}, journal = {Frontiers in cellular neuroscience}, year = {2026}, month = jul, volume = {20}, pages = {1870679}, publisher = {Frontiers Media SA}, issn = {1662-5102}, doi = {10.3389/fncel.2026.1870679}, url = {https://doi.org/10.3389/fncel.2026.1870679}, pmid = {42459923}, pmcid = {PMC13372325} }

RIS

TY - JOUR AU - Clark, Kristin L AU - Mecca, Shane AU - Almaoui, Elio AU - Bossardet, Olivia L AU - Holden, Joseph M AU - Calkins, David J AU - Wareham, Lauren K TI - Pharmacological activation of cGMP signaling promotes astrocyte remodeling and enrichment of perivascular GLUT1 in the murine retina T2 - Frontiers in cellular neuroscience J2 - Front Cell Neurosci PY - 2026 DA - 2026/07/02 VL - 20 SP - 1870679 SN - 1662-5102 PB - Frontiers Media SA DO - 10.3389/fncel.2026.1870679 UR - https://doi.org/10.3389/fncel.2026.1870679 LA - en ER -

CSL-JSON

{ "id": "10.3389/fncel.2026.1870679", "type": "article-journal", "title": "Pharmacological activation of cGMP signaling promotes astrocyte remodeling and enrichment of perivascular GLUT1 in the murine retina", "container-title": "Frontiers in cellular neuroscience", "author": [ { "family": "Clark", "given": "Kristin L" }, { "family": "Mecca", "given": "Shane" }, { "family": "Almaoui", "given": "Elio" }, { "family": "Bossardet", "given": "Olivia L" }, { "family": "Holden", "given": "Joseph M" }, { "family": "Calkins", "given": "David J" }, { "family": "Wareham", "given": "Lauren K" } ], "container-title-short": "Front Cell Neurosci", "volume": "20", "page": "1870679", "DOI": "10.3389/fncel.2026.1870679", "PMID": "42459923", "PMCID": "PMC13372325", "ISSN": "1662-5102", "publisher": "Frontiers Media SA", "URL": "https://doi.org/10.3389/fncel.2026.1870679", "language": "en", "issued": { "date-parts": [ [ 2026, 7, 2 ] ] } }

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