def demo():
"""demo shows how to interpolate on regular/irregular grids"""
# 1. create mesh
mesh_obj, _ = layer_circle(n_layer=8, n_fan=6)
pts = mesh_obj["node"]
tri = mesh_obj["element"]
# set anomaly
anomaly = [{"x": 0.5, "y": 0.5, "d": 0.2, "perm": 100.0}]
mesh_new = set_perm(mesh_obj, anomaly=anomaly)
# 2. interpolate using averaged neighbor triangle area
perm_node = sim2pts(pts, tri, mesh_new["perm"])
# 3. interpolate on grids (irregular or regular) using IDW, sigmod
xg, yg, mask = meshgrid(pts)
im = np.ones_like(mask)
# mapping from values on xy to values on xyi
xy = np.mean(pts[tri], axis=1)
xyi = np.vstack((xg.flatten(), yg.flatten())).T
# w_mat = weight_idw(xy, xyi)
w_mat = weight_sigmod(xy, xyi)
im = np.dot(w_mat.T, mesh_new["perm"])
# im = weight_linear_rbf(xy, xyi, mesh_new['perm'])
im[mask] = 0.0
# reshape to grid size
im = im.reshape(xg.shape)
# Inverse mapping
# w_mat_T_inv = np.linalg.pinv(w_mat.T)
w_mat_T_inv = w_mat
mesh_new_r = np.dot(w_mat_T_inv, im)
# plot mesh and interpolated mesh (tri2pts)
fig, axs = plt.subplots(1, 3)
ax1, ax2, ax3 = axs[0], axs[1], axs[2]
ax1.set_aspect('equal')
ax1.triplot(pts[:, 0], pts[:, 1], tri)
im1 = ax1.tripcolor(pts[:, 0], pts[:, 1], tri, mesh_new['perm'])
ax2.set_aspect('equal')
ax2.triplot(pts[:, 0], pts[:, 1], tri)
im2 = ax2.tripcolor(pts[:, 0], pts[:, 1], tri, perm_node, shading='flat')
# plot interpolated values
fig, ax = plt.subplots(figsize=fig_size)
ax.set_aspect("equal")
ax.triplot(pts[:, 0], pts[:, 1], tri, alpha=0.5)
im3 = ax.pcolor(xg, yg, im, edgecolors=None, linewidth=0, alpha=0.8)
fig.colorbar(im3, orientation="vertical")
plt.show()
def demo():
"""demo shows how to interpolate on regular/irregular grids"""
# 1. create mesh
mesh_obj, _ = layer_circle(n_layer=8, n_fan=6)
pts = mesh_obj['node']
tri = mesh_obj['element']
# set anomaly
anomaly = [{'x': 0.5, 'y': 0.5, 'd': 0.2, 'perm': 100.0}]
mesh_new = set_perm(mesh_obj, anomaly=anomaly)
# 2. interpolate using averaged neighbor triangle area
perm_node = sim2pts(pts, tri, mesh_new['perm'])
# plot mesh and interpolated mesh (tri2pts)
fig_size = (6, 4)
fig = plt.figure(figsize=fig_size)
ax = fig.add_subplot(111)
ax.set_aspect('equal')
ax.triplot(pts[:, 0], pts[:, 1], tri)
im1 = ax.tripcolor(pts[:, 0], pts[:, 1], tri, mesh_new['perm'])
fig.colorbar(im1, orientation='vertical')
fig = plt.figure(figsize=fig_size)
ax2 = fig.add_subplot(111)
ax2.set_aspect('equal')
ax2.triplot(pts[:, 0], pts[:, 1], tri)
im2 = ax2.tripcolor(pts[:, 0], pts[:, 1], tri, perm_node, shading='flat')
fig.colorbar(im2, orientation='vertical')
# 3. interpolate on grids (irregular or regular) using IDW, sigmod
xg, yg, mask = meshgrid(pts)
im = np.ones_like(mask)
# mapping from values on xy to values on xyi
xy = np.mean(pts[tri], axis=1)
xyi = np.vstack((xg.flatten(), yg.flatten())).T
# w_mat = weight_idw(xy, xyi)
w_mat = weight_sigmod(xy, xyi)
im = np.dot(w_mat.T, mesh_new['perm'])
# im = weight_linear_rbf(xy, xyi, mesh_new['perm'])
im[mask] = 0.
# reshape to grid size
im = im.reshape(xg.shape)
# plot interpolated values
fig, ax = plt.subplots(figsize=fig_size)
ax.set_aspect('equal')
ax.triplot(pts[:, 0], pts[:, 1], tri, alpha=0.5)
im3 = ax.pcolor(xg, yg, im, edgecolors=None, linewidth=0, alpha=0.8)
fig.colorbar(im3, orientation='vertical')
plt.show()
from __future__ import division, absolute_import, print_function
# numeric
import numpy as np
import scipy as sp
import matplotlib.pyplot as plt
import matplotlib.gridspec as gridspec
# pyEIT
import pyeit.mesh as mesh
from pyeit.eit.interp2d import tri_area, sim2pts
from pyeit.mesh import quality
from pyeit.eit.fem import Forward
from pyeit.eit.utils import eit_scan_lines
""" 0. build mesh """
mesh_obj, el_pos = mesh.layer_circle(n_layer=8, n_fan=6)
# mesh_obj, el_pos = mesh.create()
# extract node, element, alpha
pts = mesh_obj['node']
tri = mesh_obj['element']
x, y = pts[:, 0], pts[:, 1]
quality.stats(pts, tri)
def calc_sens(fwd, ex_mat):
"""
see Adler2017 on IEEE TBME, pp 5, figure 6,
Electrical Impedance Tomography: Tissue Properties to Image Measures
"""
# solving EIT problem