Merge pull request #2142 from gaotingyi/draft/momo

Final merge branch Draft/momo

Author: AlbertZyy

.gitignore

@@ -75,3 +75,4 @@ tags
 .DS_Store
 *env
 tmp
+*.msh

Git使用规范与commit整理指南.md

@@ -0,0 +1,26 @@
+
+from fealpy.backend import bm
+from lafemeit.data import *
+
+from matplotlib import pyplot as plt
+
+
+num = 2
+clim = (-0.9, 0.9, -0.9, 0.9)
+XLIM = (-1, 1)
+YLIM = (-1, 1)
+
+# model = random_gaussian2d_model(num, clim, (2, 6), (0.5, 1))
+# model = random_unioned_circles_model(num)
+model = random_unioned_triangles_model(num, clim, rlim=(0.2, 0.5), kind="equ")
+print(model)
+
+X = bm.linspace(XLIM[0], XLIM[1], 100)
+Y = bm.linspace(YLIM[0], YLIM[1], 100)
+X, Y = bm.meshgrid(X, Y)
+points = bm.stack((X, Y), axis=-1)
+phi = model.coef(points)
+ai = plt.pcolormesh(X, Y, phi, cmap="jet")
+plt.colorbar(ai)
+
+plt.show()

app/lafem-eit/examples/random_conductivity_data.py

@@ -1,6 +1,4 @@
 
 from fealpy.backend import backend_manager as bm
 
-__version__ = "0.1.0"
-
-bm.set_backend('pytorch')
+__version__ = "0.2.0"

app/lafem-eit/lafemeit/__init__.py

@@ -0,0 +1,139 @@
+
+__all__ = [
+    'random_gaussian2d_model',
+    'random_unioned_circles_model',
+    'random_unioned_triangles_model',
+]
+
+from typing import Literal
+from collections import namedtuple
+
+from fealpy.backend import bm, TensorLike as Tensor
+
+from . import shapes as _S
+
+
+FunctionModel = namedtuple("FunctionModel", ["coef", "levelset", "shape"])
+
+
+def _gaussian(p: Tensor, centers: Tensor, inv_cov: Tensor, base: float = 10.):
+    # p (NC, NQ, GD)
+    # centers (NGuassian, GD)
+    # inv_cov (NGuassian, GD, GD)
+    struct = p.shape[:-1]
+    p = p.reshape(-1, p.shape[-1])
+    p0 = p[:, None, :] - centers[None, :, :] # (NC*NQ, NGuassian, GD)
+    ind = bm.exp(-0.5 * bm.einsum("ngi, gij, ngj -> ng", p0, inv_cov, p0))
+    ind = bm.sum(ind, axis=-1).reshape(struct) # (NC, NQ)
+    minim = bm.min(ind)
+    maxim = bm.max(ind)
+    ind = (ind - minim) / (maxim - minim)
+    return base**ind
+
+
+def random_gaussian2d_model(
+    num: int,
+    box: tuple[float, float, float, float],
+    major_lim: tuple[float, float],
+    ecc_lim: tuple[float, float] = (0.5, 1.0),
+    base: float = 10.
+):
+    """
+    Generate a random Gaussian conductivity model.
+
+    Parameters:
+        num (int): Number of Gaussian
+        box (tuple[xmin, xmax, ymin, ymax]): The box of Gaussian centers
+        major_lim (tuple[major_min, major_max]): The major axis covariance range
+        ecc_lim (tuple[ecc_min, ecc_max]): The eccentricity range
+        base (float): The ratio of the conductivity value that ranges [1.0, ratio]
+
+    Returns:
+        namedtuple
+        - coef (Callable): A function that takes points and returns the conductivity values.
+        - levelset (None): No levelset function.
+    """
+    gaussian = _S.random_gaussian_2d(
+        num, box, major_lim, ecc_lim
+    )
+
+    def gaussian_conductivity(points: Tensor, *args, **kwargs) -> Tensor:
+        return _gaussian(
+            points,
+            bm.from_numpy(gaussian.centers),
+            bm.from_numpy(gaussian.invcov),
+            base
+        )
+
+    gaussian_conductivity.__dict__['coordtype'] = 'cartesian'
+
+    return FunctionModel(gaussian_conductivity, None, gaussian)
+
+
+def random_unioned_circles_model(
+    num: int,
+    values: tuple[float, float] = (10.0, 1.0),
+):
+    """Generate a random unioned circles conductivity model.
+
+    Parameters:
+        num (int): Number of circles
+        values (tuple[float, float]): The conductivity values of the circles and the rest.
+
+    Returns:
+        namedtuple:
+        - coef (Callable): A function that takes points and returns the conductivity values.
+        - levelset (Callable): Level set function.
+    """
+    circles = _S.random_circles(num)
+    level_set_func = lambda p: _S.circle_union_levelset(p, circles)
+
+    def circle_conductivity(points: Tensor, *args, **kwargs) -> Tensor:
+        inclusion = level_set_func(points) < 0. # a bool tensor on quadrature points.
+        sigma = bm.empty(points.shape[:2], **bm.context(points)) # (Q, C)
+        sigma = bm.set_at(sigma, inclusion, values[0])
+        sigma = bm.set_at(sigma, ~inclusion, values[1])
+        return sigma
+
+    circle_conductivity.__dict__['coordtype'] = 'cartesian'
+
+    return FunctionModel(circle_conductivity, level_set_func, circles)
+
+
+def random_unioned_triangles_model(
+    num: int,
+    box: tuple[float, float, float, float] = [-1., 1., -1., 1.],
+    kind: Literal["", "equ"] = "",
+    rlim: tuple[float, float] = (0.5, 1.0),
+    values: tuple[float, float] = (10.0, 1.0),
+):
+    """Generate a random unioned triangles conductivity model.
+
+    Parameters:
+        num (int): Number of triangles
+        box (tuple[xmin, xmax, ymin, ymax]): The box of triangles
+        kind (str): The kind of triangles.
+        rlim (tuple[r_min, r_max]): The radius range, available when kind is "equ".
+        values (tuple[float, float]): The conductivity values of the triangles and the rest.
+
+    Returns:
+        namedtuple:
+        - coef (Callable): A function that takes points and returns the conductivity values.
+        - levelset (Callable): Level set function.
+    """
+    if kind == "equ":
+        tris = _S.random_equ_triangles(num, box[0:2], box[2:4], rlim)
+    else:
+        tris = _S.random_ccw_triangles(num, box[0:2], box[2:4])
+    level_set_func = lambda p: _S.triangle_union_levelset(p, tris)
+
+    def triangle_conductivity(points: Tensor, *args, **kwargs) -> Tensor:
+        inclusion = level_set_func(points) < 0. # a bool tensor on quadrature points.
+        sigma = bm.empty(points.shape[:2], **bm.context(points)) # (Q, C)
+        sigma = bm.set_at(sigma, inclusion, values[0])
+        sigma = bm.set_at(sigma, ~inclusion, values[1])
+        return sigma
+
+    triangle_conductivity.__dict__['coordtype'] = 'cartesian'
+
+    return FunctionModel(triangle_conductivity, level_set_func, tris)