Use matplotlib tri interpolators (#104)

* Use matplotlib tri interpolators instead of scipy.interpolate. This is much faster because the matplotlib versions can use the existing triangulation.

docs/notebooks/field-sources.ipynb

@@ -87,8 +87,8 @@
  {
  "data": {
  "text/html": [
- "<table><tr><th>Software</th><th>Version</th></tr><tr><td>SuperScreen</td><td>0.9.1</td></tr><tr><td>Numpy</td><td>1.23.3</td></tr><tr><td>Numba</td><td>0.57.0</td></tr><tr><td>SciPy</td><td>1.9.1</td></tr><tr><td>matplotlib</td><td>3.6.0</td></tr><tr><td>IPython</td><td>8.5.0</td></tr><tr><td>Python</td><td>3.9.13 | packaged by conda-forge | (main, May 27 2022, 17:01:00) \n",
- "[Clang 13.0.1 ]</td></tr><tr><td>OS</td><td>posix [darwin]</td></tr><tr><td>Number of CPUs</td><td>Physical: 10, Logical: 10</td></tr><tr><td>BLAS Info</td><td>OPENBLAS</td></tr><tr><td colspan='2'>Wed May 17 10:59:46 2023 PDT</td></tr></table>"
+ "<table><tr><th>Software</th><th>Version</th></tr><tr><td>SuperScreen</td><td>0.10.0</td></tr><tr><td>Numpy</td><td>1.23.3</td></tr><tr><td>Numba</td><td>0.57.0</td></tr><tr><td>SciPy</td><td>1.9.1</td></tr><tr><td>matplotlib</td><td>3.6.0</td></tr><tr><td>IPython</td><td>8.5.0</td></tr><tr><td>Python</td><td>3.9.13 | packaged by conda-forge | (main, May 27 2022, 17:01:00) \n",
+ "[Clang 13.0.1 ]</td></tr><tr><td>OS</td><td>posix [darwin]</td></tr><tr><td>Number of CPUs</td><td>Physical: 10, Logical: 10</td></tr><tr><td>BLAS Info</td><td>OPENBLAS</td></tr><tr><td colspan='2'>Thu Aug 03 13:18:33 2023 PDT</td></tr></table>"
  ],
  "text/plain": [
  "<IPython.core.display.HTML object>"
@@ -142,9 +142,9 @@
  "name": "stdout",
  "output_type": "stream",
  "text": [
- "x = 0.5517062950352116\n",
- "y = 0.708038021214086\n",
- "z = 0.6209502532087992\n",
+ "x = 0.45250693865850633\n",
+ "y = 0.26481336104450504\n",
+ "z = 0.4510648754100197\n",
  "field(x, y, z) = 5.0\n"
  ]
  }

docs/notebooks/logo.ipynb

@@ -59,8 +59,8 @@
  {
  "data": {
  "text/html": [
- "<table><tr><th>Software</th><th>Version</th></tr><tr><td>SuperScreen</td><td>0.9.1</td></tr><tr><td>Numpy</td><td>1.23.3</td></tr><tr><td>Numba</td><td>0.57.0</td></tr><tr><td>SciPy</td><td>1.9.1</td></tr><tr><td>matplotlib</td><td>3.6.0</td></tr><tr><td>IPython</td><td>8.5.0</td></tr><tr><td>Python</td><td>3.9.13 | packaged by conda-forge | (main, May 27 2022, 17:01:00) \n",
- "[Clang 13.0.1 ]</td></tr><tr><td>OS</td><td>posix [darwin]</td></tr><tr><td>Number of CPUs</td><td>Physical: 10, Logical: 10</td></tr><tr><td>BLAS Info</td><td>OPENBLAS</td></tr><tr><td colspan='2'>Wed May 17 11:00:35 2023 PDT</td></tr></table>"
+ "<table><tr><th>Software</th><th>Version</th></tr><tr><td>SuperScreen</td><td>0.10.0</td></tr><tr><td>Numpy</td><td>1.23.3</td></tr><tr><td>Numba</td><td>0.57.0</td></tr><tr><td>SciPy</td><td>1.9.1</td></tr><tr><td>matplotlib</td><td>3.6.0</td></tr><tr><td>IPython</td><td>8.5.0</td></tr><tr><td>Python</td><td>3.9.13 | packaged by conda-forge | (main, May 27 2022, 17:01:00) \n",
+ "[Clang 13.0.1 ]</td></tr><tr><td>OS</td><td>posix [darwin]</td></tr><tr><td>Number of CPUs</td><td>Physical: 10, Logical: 10</td></tr><tr><td>BLAS Info</td><td>OPENBLAS</td></tr><tr><td colspan='2'>Thu Aug 03 13:18:57 2023 PDT</td></tr></table>"
  ],
  "text/plain": [
  "<IPython.core.display.HTML object>"

docs/notebooks/scanning-squid.ipynb

@@ -97,8 +97,8 @@
  {
  "data": {
  "text/html": [
- "<table><tr><th>Software</th><th>Version</th></tr><tr><td>SuperScreen</td><td>0.9.2</td></tr><tr><td>Numpy</td><td>1.23.3</td></tr><tr><td>Numba</td><td>0.57.0</td></tr><tr><td>SciPy</td><td>1.9.1</td></tr><tr><td>matplotlib</td><td>3.6.0</td></tr><tr><td>IPython</td><td>8.5.0</td></tr><tr><td>Python</td><td>3.9.13 | packaged by conda-forge | (main, May 27 2022, 17:01:00) \n",
- "[Clang 13.0.1 ]</td></tr><tr><td>OS</td><td>posix [darwin]</td></tr><tr><td>Number of CPUs</td><td>Physical: 10, Logical: 10</td></tr><tr><td>BLAS Info</td><td>OPENBLAS</td></tr><tr><td colspan='2'>Thu May 18 14:28:01 2023 PDT</td></tr></table>"
+ "<table><tr><th>Software</th><th>Version</th></tr><tr><td>SuperScreen</td><td>0.10.0</td></tr><tr><td>Numpy</td><td>1.23.3</td></tr><tr><td>Numba</td><td>0.57.0</td></tr><tr><td>SciPy</td><td>1.9.1</td></tr><tr><td>matplotlib</td><td>3.6.0</td></tr><tr><td>IPython</td><td>8.5.0</td></tr><tr><td>Python</td><td>3.9.13 | packaged by conda-forge | (main, May 27 2022, 17:01:00) \n",
+ "[Clang 13.0.1 ]</td></tr><tr><td>OS</td><td>posix [darwin]</td></tr><tr><td>Number of CPUs</td><td>Physical: 10, Logical: 10</td></tr><tr><td>BLAS Info</td><td>OPENBLAS</td></tr><tr><td colspan='2'>Thu Aug 03 13:20:42 2023 PDT</td></tr></table>"
  ],
  "text/plain": [
  "<IPython.core.display.HTML object>"
@@ -160,10 +160,10 @@
  "name": "stderr",
  "output_type": "stream",
  "text": [
- "Solver iterations: 100%|███████████████████████████████████████████████████████████████████████████████████████████████| 5/5 [00:02<00:00, 2.32it/s]\n",
- "Solver iterations: 100%|███████████████████████████████████████████████████████████████████████████████████████████████| 5/5 [00:01<00:00, 2.74it/s]\n",
- "Solver iterations: 100%|███████████████████████████████████████████████████████████████████████████████████████████████| 5/5 [00:04<00:00, 1.19it/s]\n",
- "Solver iterations: 100%|███████████████████████████████████████████████████████████████████████████████████████████████| 5/5 [00:03<00:00, 1.29it/s]\n"
+ "Solver iterations: 100%|███████████████████████████████████████████████████████████████████████████████████████████████| 5/5 [00:02<00:00, 2.41it/s]\n",
+ "Solver iterations: 100%|███████████████████████████████████████████████████████████████████████████████████████████████| 5/5 [00:01<00:00, 2.59it/s]\n",
+ "Solver iterations: 100%|███████████████████████████████████████████████████████████████████████████████████████████████| 5/5 [00:03<00:00, 1.28it/s]\n",
+ "Solver iterations: 100%|███████████████████████████████████████████████████████████████████████████████████████████████| 5/5 [00:03<00:00, 1.42it/s]\n"
  ]
  }
  ],

superscreen/device/mesh.py

@@ -6,6 +6,7 @@
 import matplotlib.pyplot as plt
 import numpy as np
 import scipy.sparse as sp
+from matplotlib.tri import Triangulation
 
 from ..distance import q_matrix
 from ..fem import gradient_vertices, laplace_operator
@@ -51,9 +52,19 @@ def __init__(
  self.triangle_areas = np.asarray(triangle_areas)
  self.edge_mesh = edge_mesh
  self.operators: Optional[MeshOperators] = None
+ self._triangulation: Optional[Triangulation] = None
  if build_operators:
  self.operators = MeshOperators.from_mesh(self)
 
+ @property
+ def triangulation(self) -> Triangulation:
+ """Matplotlib triangulation of the mesh."""
+ if self._triangulation is None:
+ self._triangulation = Triangulation(
+ self.sites[:, 0], self.sites[:, 1], self.elements
+ )
+ return self._triangulation
+
  def stats(self) -> Dict[str, Union[int, float]]:
  """Returns a dictionary of information about the mesh."""
  edge_lengths = self.edge_mesh.edge_lengths

superscreen/solution.py

@@ -18,9 +18,9 @@
 
 import h5py
 import matplotlib.pyplot as plt
+import matplotlib.tri as mtri
 import numpy as np
 import pint
-from scipy import interpolate
 
 from .about import version_dict
 from .device import Device, Polygon
@@ -33,7 +33,7 @@
 
 logger = logging.getLogger("solution")
 
-InterpolatorType = Literal["nearest", "linear", "cubic"]
+InterpolatorType = Literal["linear", "cubic"]
 
 
 class Fluxoid(NamedTuple):
@@ -271,9 +271,8 @@ def version_info(self) -> Dict[str, str]:
  @staticmethod
  def _select_interpolator(method: InterpolatorType) -> type:
  return {
- "nearest": interpolate.NearestNDInterpolator,
- "linear": interpolate.LinearNDInterpolator,
- "cubic": interpolate.CloughTocher2DInterpolator,
+ "linear": mtri.LinearTriInterpolator,
+ "cubic": mtri.CubicTriInterpolator,
  }[method]
 
  def interp_current_density(
@@ -284,20 +283,14 @@ def interp_current_density(
  method: InterpolatorType = "linear",
  units: Optional[str] = None,
  with_units: bool = False,
- **kwargs,
  ) -> np.ndarray:
  """Interpolates the current density ``J = [dg/dy, -dg/dx]`` within a film.
 
- Additional keyword arguments are passed to the relevant interpolator:
- :class:`scipy.interpolate.NearestNDInterpolator`,
- :class:`scipy.interpolate.LinearNDInterpolator`, or
- :class:`scipy.interpolate.CloughTocher2DInterpolator`.
-
  Args:
  positions: Shape ``(m, 2)`` array of x, y coordinates at which to evaluate
  the current density.
  film: The name of the film in which to interpolate current density.
- method: Interpolation method to use ("nearest", "linear" or "cubic").
+ method: Interpolation method to use ("linear" or "cubic").
  units: The desired units for the current density. Defaults to
  ``self.current_units / self.device.length_units``.
  with_units: Whether to return arrays of pint.Quantities with units attached.
@@ -310,12 +303,13 @@ def interp_current_density(
  if units is None:
  units = default_units
  positions = np.atleast_2d(positions)
- interpolator = self._select_interpolator(method)
- xy = device.meshes[film].sites
+ xv, yv = positions.T
+ interp_type = self._select_interpolator(method)
+ mesh = device.meshes[film]
  J = self.film_solutions[film].current_density
- Jx_interp = interpolator(xy, J[:, 0], **kwargs)
- Jy_interp = interpolator(xy, J[:, 1], **kwargs)
- J = np.stack([Jx_interp(positions), Jy_interp(positions)], axis=1)
+ Jx_interp = interp_type(mesh.triangulation, J[:, 0])
+ Jy_interp = interp_type(mesh.triangulation, J[:, 1])
+ J = np.array([Jx_interp(xv, yv).data, Jy_interp(xv, yv).data]).T
  in_film = device.films[film].contains_points(positions)
  J[~in_film] = 0
  J[~np.isfinite(J).all(axis=1)] = 0
@@ -339,7 +333,7 @@ def current_through_path(
  path_coords: An ``(n, 2)`` array of ``(x, y)`` coordinates defining
  the path.
  film: The name of the film in which to interpolate current density.
- interp_method: Interpolation method to use ("nearest", "linear" or "cubic").
+ interp_method: Interpolation method to use ("linear" or "cubic").
  units: The current units to return.
  with_units: Whether to return a :class:`pint.Quantity` with units attached.
 
@@ -378,22 +372,16 @@ def interp_field(
  method: InterpolatorType = "linear",
  units: Optional[str] = None,
  with_units: bool = False,
- **kwargs,
  ):
  """Interpolates the z-component of the field within a film.
 
- Additional keyword arguments are passed to the relevant interpolator:
- :class:`scipy.interpolate.NearestNDInterpolator`,
- :class:`scipy.interpolate.LinearNDInterpolator`, or
- :class:`scipy.interpolate.CloughTocher2DInterpolator`.
-
  Args:
  positions: Shape ``(m, 2)`` array of x, y coordinates at which to evaluate
  the fields.
  film: The name of the film in which to interpolate the field.
  dataset: The dataset to interpolate. One of 'field', 'self_field',
  'applied_field', or 'field_from_other_films'.
- method: Interpolation method to use: 'nearest', 'linear', or 'cubic'.
+ method: Interpolation method to use: 'linear' or 'cubic'.
  units: The desired units for the current density. Defaults to
  ``self.field_units``.
  with_units: Whether to return arrays of pint.Quantities with units attached.
@@ -403,7 +391,7 @@ def interp_field(
  """
  from .solver import convert_field
 
- interpolator = self._select_interpolator(method)
+ interp_type = self._select_interpolator(method)
  device = self.device
  if units is None:
  units = self.field_units
@@ -413,7 +401,7 @@ def interp_field(
  "applied_field",
  "field_from_other_films",
  )
- points = self.device.meshes[film].sites
+ mesh = self.device.meshes[film]
  if dataset not in valid_datasets:
  raise ValueError(
  f"Invalid dataset: {dataset!r}. Expected one of {valid_datasets!r}"
@@ -427,11 +415,11 @@ def interp_field(
  else:
  field = self.film_solutions[film].field_from_other_films
  if field is None:
- field = np.zeros(len(points))
+ field = np.zeros(len(mesh.sites))
  positions = np.atleast_2d(positions)
- Hz_interp = interpolator(points, field, **kwargs)
+ Hz_interp = interp_type(mesh.triangulation, field)
  Hz = convert_field(
- Hz_interp(positions),
+ Hz_interp(positions[:, 0], positions[:, 1]).data,
  units,
  old_units=self.field_units,
  ureg=device.ureg,

superscreen/sources/vortex.py

@@ -166,9 +166,9 @@ def pearl_vortex(
  hzk = np.fft.fftshift(hzk)
  hz = np.abs(np.fft.fftshift(np.fft.ifft2(hzk))) / (dx * dy)
  # Interpolate to x, y, z coordinates
- XY = np.stack([X.ravel(), Y.ravel()], axis=1)
+ XY = np.array([X.ravel(), Y.ravel()]).T
  interp = LinearNDInterpolator(XY, hz.ravel())
- return interp(np.stack([x, y], axis=1)).squeeze()
+ return interp(np.array([x, y]).T).squeeze()
 
 
 def PearlVortexField(

superscreen/test/test_solution.py

@@ -236,7 +236,7 @@ def test_fluxoid_simply_connected(
 @pytest.mark.parametrize(
  "film, method, positions",
  [
- ("disk", "nearest", [0, 0]),
+ ("disk", "linear", [0, 0]),
  ("ring", "linear", np.array([[1, 0], [0, 1]])),
  ("disk", "cubic", None),
  ],
@@ -340,7 +340,7 @@ def test_bz_from_vector_potential(
 
 @pytest.mark.parametrize("units", [None, "mT", "mA/um"])
 @pytest.mark.parametrize("with_units", [False, True])
-@pytest.mark.parametrize("method", ["nearest", "linear", "cubic"])
+@pytest.mark.parametrize("method", ["linear", "cubic"])
 def test_interp_field(solution2: sc.Solution, units, with_units, method):
  solution = solution2
  positions = np.random.random(size=(100, 2))

superscreen/test/test_visualization.py

@@ -92,11 +92,11 @@ def test_plot_streams(solution, films, units):
 ]
 thetas = np.linspace(0, 2 * np.pi, endpoint=False)
 cross_section_coord_params.append(
- [r * np.stack([np.cos(thetas), np.sin(thetas)], axis=1) for r in (0.5, 1.0, 1.5)]
+ [r * np.array([np.cos(thetas), np.sin(thetas)]).T for r in (0.5, 1.0, 1.5)]
 )
 
 
-@pytest.mark.parametrize("interp_method", ["nearest", "linear", "cubic"])
+@pytest.mark.parametrize("interp_method", ["linear", "cubic"])
 @pytest.mark.parametrize("cross_section_coords", cross_section_coord_params)
 def test_cross_section(solution, cross_section_coords, interp_method):
  if cross_section_coords is None:

superscreen/version.py

@@ -1,2 +1,2 @@
-__version_info__ = (0, 9, 2)
+__version_info__ = (0, 10, 0)
 __version__ = ".".join(map(str, __version_info__))

superscreen/visualization.py

@@ -219,24 +219,22 @@ def cross_section(
  cross_section_coords: A shape (m, 2) array of (x, y) coordinates specifying
  the cross-section path (or a list of such arrays for multiple
  cross sections).
- interp_method: The interpolation method to use: "nearest", "linear", "cubic".
+ interp_method: The interpolation method to use: "linear" or "cubic".
 
  Returns:
  A list of coordinate arrays, a list of curvilinear coordinate (path) arrays,
  and a list of cross section values.
  """
- valid_methods = ("nearest", "linear", "cubic")
+ valid_methods = ("linear", "cubic")
  if interp_method not in valid_methods:
  raise ValueError(
  f"Interpolation method must be one of {valid_methods} "
  f"(got {interp_method})."
  )
- if interp_method == "nearest":
- interpolator = interpolate.NearestNDInterpolator
- elif interp_method == "linear":
- interpolator = interpolate.LinearNDInterpolator
- else: # "cubic"
- interpolator = interpolate.CloughTocher2DInterpolator
+ interpolator = {
+ "linear": interpolate.LinearNDInterpolator,
+ "cubic": interpolate.CloughTocher2DInterpolator,
+ }[interp_method]
 
  if not (isinstance(cross_section_coords, Sequence)):
  cross_section_coords = [cross_section_coords]