├── data ├── LA_model.vtk ├── LA_model_a.vtk └── LA_model_smooth_basis.vtk ├── requirements.txt ├── math_tools.py ├── mesh_tools.py ├── README.md ├── FiberNetModels_3D.py ├── FiberNetModels_2D.py └── LICENSE /data/LA_model.vtk: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/fsahli/FiberNet/HEAD/data/LA_model.vtk -------------------------------------------------------------------------------- /data/LA_model_a.vtk: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/fsahli/FiberNet/HEAD/data/LA_model_a.vtk -------------------------------------------------------------------------------- /data/LA_model_smooth_basis.vtk: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/fsahli/FiberNet/HEAD/data/LA_model_smooth_basis.vtk -------------------------------------------------------------------------------- /requirements.txt: -------------------------------------------------------------------------------- 1 | tensorflow 2 | fim-python 3 | meshio 4 | matplotlib 5 | pyvista 6 | panel 7 | jupyter_bokeh 8 | pydoe 9 | -------------------------------------------------------------------------------- /math_tools.py: -------------------------------------------------------------------------------- 1 | #!/usr/bin/env python3.7 2 | # -*- coding: utf-8 -*- 3 | 4 | """ 5 | Collection of tools to optimize and group mathematical calculations 6 | 7 | Functions: matMulProdSum, 8 | eigenDecompProd, 9 | metricNormMatrix 10 | Author: Thomas Grandits 11 | Edited by: Carlos Ruiz 12 | """ 13 | 14 | import tensorflow as tf 15 | 16 | def matMulProdSum(A, B): 17 | """Computes A @ B in a broadcasted fashion 18 | """ 19 | return tf.einsum('...xy,...yz->...xz', A, B) 20 | 21 | def eigenDecompProd(A, B): 22 | """Computes the eigenreconstruction of a tensor A * B * A^T 23 | """ 24 | 25 | result = matMulProdSum(matMulProdSum(A, B), tf.transpose(A, perm=[0, 2, 1])) 26 | 27 | return result 28 | 29 | def metricNormMatrix(A, x1, x2=None, ret_sqrt=True): 30 | """Computes \sqrt{<, x2>} with or without the sqrt. If x2 is not set, x2 = x1 31 | """ 32 | if x2 is None: 33 | x2 = x1 34 | 35 | sqr_norm = tf.reduce_sum(tf.reduce_sum(A * x1[..., tf.newaxis], axis=-2) * x2, axis=-1) 36 | 37 | return (tf.sqrt(sqr_norm) if ret_sqrt else sqr_norm) 38 | -------------------------------------------------------------------------------- /mesh_tools.py: -------------------------------------------------------------------------------- 1 | #!/usr/bin/env python3.7 2 | # -*- coding: utf-8 -*- 3 | 4 | """ 5 | Collection of tools for working with meshes with the vtk library 6 | 7 | Functions: createLocalManifoldBasis, 8 | calculateSurfaceNormalsManifold, 9 | pointToCellData, cellToPointData 10 | Author: Thomas Grandits 11 | Edited by: Carlos Ruiz 12 | """ 13 | 14 | import numpy as np 15 | import pyvista as pv 16 | import vtk 17 | from functools import reduce 18 | import operator 19 | 20 | def prod(x): 21 | """Computes the product over all elements \Prod_{i=1}^n x_i 22 | """ 23 | return reduce(operator.mul, x, 1) 24 | 25 | 26 | def createLocalManifoldBasis(points, tris, base_vecs): 27 | """ 28 | Create a local basis on a triangle basis for manifolds 29 | The local basis is given the given base_vecs, the triangle 30 | normal and their orthogonal basis 31 | """ 32 | 33 | assert points.shape[-1] == 3, "Only 3D supported" 34 | assert tris.shape[-1] == 3, "Only triangles are supported" 35 | assert base_vecs.shape[0] == tris.shape[0] 36 | assert np.allclose(np.linalg.norm(base_vecs, axis=-1), 1.), "Basis vectors need to be normalized" 37 | 38 | points_elems = points[tris] 39 | P = np.empty_like(points_elems) 40 | surf_normals = calculateSurfaceNormalsManifold(points, tris) 41 | assert np.allclose(np.sum(base_vecs * surf_normals, axis=-1), 0., atol=2e-5), "Basis vectors and surface normals are not orthonormal" 42 | 43 | orth_vec = np.cross(surf_normals, base_vecs) 44 | orth_vec /= np.linalg.norm(orth_vec, axis=-1, keepdims=True) 45 | assert np.allclose(np.sum(orth_vec * surf_normals, axis=-1), 0., atol=1e-6), "Failed to create an orthonormal basis" 46 | assert np.allclose(np.sum(orth_vec * base_vecs, axis=-1), 0., atol=1e-6), "Failed to create an orthonormal basis" 47 | 48 | P[..., :, 0] = base_vecs 49 | P[..., :, 1] = orth_vec 50 | P[..., :, 2] = surf_normals 51 | 52 | return P 53 | 54 | def calculateSurfaceNormalsManifold(points, triangs): 55 | assert triangs.shape[-1] == 3, "Only triangles are supported" 56 | mesh = pv.UnstructuredGrid({vtk.VTK_TRIANGLE: triangs}, points) 57 | mesh_surf = mesh.extract_surface().compute_normals() 58 | assert mesh.n_points == mesh_surf.n_points, "Non manifold vertices detected" 59 | return mesh_surf.cell_data["Normals"][mesh_surf.cell_data["vtkOriginalCellIds"]] 60 | 61 | def pointToCellData(points, elems, point_data): 62 | assert elems.shape[-1] == 3, "Only triangles are supported" 63 | mesh = pv.UnstructuredGrid({vtk.VTK_TRIANGLE: elems}, points) 64 | orig_shape = point_data.shape[1:] 65 | mesh.point_data["data"] = point_data.reshape([-1, prod(orig_shape)]) 66 | return mesh.point_data_to_cell_data().cell_data["data"].reshape((-1,) + orig_shape) 67 | 68 | def cellToPointData(points, elems, cell_data): 69 | assert elems.shape[-1] == 3, "Only triangles are supported" 70 | mesh = pv.UnstructuredGrid({vtk.VTK_TRIANGLE: elems}, points) 71 | orig_shape = cell_data.shape[1:] 72 | mesh.cell_data["data"] = cell_data.reshape([-1, prod(orig_shape)]) 73 | return mesh.cell_data_to_point_data().point_data["data"].reshape((-1,) + orig_shape) 74 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # Physics-informed neural networks to learn cardiac fiber orientation from multiple electroanatomical maps 2 | 3 | Carlos Ruiz Herrera\*, Thomas Grandits\*, Gernot Plank, Paris Perdikaris, Francisco Sahli Costabal, Simone Pezzuto 4 | 5 | Project homepage: https://fsahli.github.io/research/fibernet.html 6 | arXiv: https://arxiv.org/abs/2201.12362 7 | 8 | 9 | 2D example [![Open Demo in Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/drive/1h5A9LNhvLoIUouFKkL3DZYvM2u3QLXo-?usp=sharing) 10 | 3D example [![Open Demo in Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/drive/1hBQG12tfEa2wRATjpmgUCREDtzc5RHaZ?usp=sharing) 11 | 12 | ![Schematic Figure](images/schematic.svg) 13 | 14 | This repository contains a demo implementation of our paper [`Physics-informed neural networks to learn cardiac fiber orientation from multiple electroanatomical maps`](#citation). 15 | It contains a few 2D and 3D examples showcasing how FiberNet works and can optimize fiber orientations from multiple electroanatomical maps. 16 | For more technical information on the approach, please have a look at the [project page](https://fsahli.github.io/research/fibernet.html) or the [arxiv paper](https://arxiv.org/abs/2201.12362). 17 | 18 | # Installation 19 | 20 | All examples are provided in the form of [jupyter-notebooks](https://jupyter.org). 21 | To run, makes sure you have python3 installed and then run 22 | ```bash 23 | pip install -r requirements.txt 24 | ``` 25 | from your command line. 26 | The notebooks can then be easily accessed by starting the jupyter-server via the command 27 | ```bash 28 | jupyter-notebook 29 | ``` 30 | 31 | # Provided Examples 32 | 33 | - [2D_example](2D_example.ipynb) 34 | 35 | Reconstructs the fiber orientation and velocity of two piecewise constant regions on a square 36 | 37 | - [2D_example_aniso](2D_example_aniso.ipynb) 38 | 39 | Same as above, but considers different levels of anisotropy between the two regions 40 | 41 | - [3D_example](3D_example.ipynb) 42 | 43 | Reconstructs the fiber orientation of a rule-based in-silico left atrial model for randomly paced pacing and measurement locations 44 | 45 | - [3D_example_CS](3D_example_CS.ipynb) 46 | 47 | Same as above, but considers only the approximate Bachmann bundle and coronary sinus locations as pacing loactions 48 | 49 | # Citation 50 | 51 | ```bibtex 52 | @article{ruiz_herrera_physics_informed_2022, 53 | title = {Physics-informed neural networks to learn cardiac fiber orientation from multiple electroanatomical maps}, 54 | issn = {1435-5663}, 55 | url = {https://doi.org/10.1007/s00366-022-01709-3}, 56 | doi = {10.1007/s00366-022-01709-3}, 57 | language = {en}, 58 | urldate = {2022-07-22}, 59 | journal = {Engineering with Computers}, 60 | author = {Ruiz Herrera, Carlos and Grandits, Thomas and Plank, Gernot and Perdikaris, Paris and Sahli Costabal, Francisco and Pezzuto, Simone}, 61 | month = jul, 62 | year = {2022}, 63 | keywords = {Anisotropic conduction velocity, Cardiac electrophysiology, Cardiac fibers, Deep learning, Eikonal equation, Physics-informed neural networks}, 64 | } 65 | ``` 66 | -------------------------------------------------------------------------------- /FiberNetModels_3D.py: -------------------------------------------------------------------------------- 1 | #!/usr/bin/env python3.7 2 | # -*- coding: utf-8 -*- 3 | """ 4 | Implementation of the FiberNet model to a 3D case 5 | Author: Carlos Ruiz Herrera, Thomas Grandits, Paris Perdikaris, Francisco Sahli Costabal, Simone Pezzuto 6 | """ 7 | 8 | import time 9 | import numpy as np 10 | import pyvista as pv 11 | import vtk 12 | import tensorflow as tf 13 | from fimpy.solver import FIMPY 14 | from scipy.spatial import cKDTree 15 | from mesh_tools import calculateSurfaceNormalsManifold, createLocalManifoldBasis, cellToPointData 16 | from math_tools import eigenDecompProd, matMulProdSum, metricNormMatrix 17 | from tqdm.auto import trange 18 | 19 | # Set up tensorflow in graph mode 20 | tf.compat.v1.disable_eager_execution() 21 | 22 | # PINN class construction 23 | 24 | class MultiAnisoEikonalPINN_3D: 25 | # Initialize the class 26 | def __init__(self, X, triangs, parallel, X_e, T_e, ind, 27 | layers, CVlayers, smooth_basis_file, 28 | CVmax=1.0, lambda_df=1., lambda_pde=1e-4, 29 | lambda_tve=1e-2, lambda_tva=1e-9, 30 | jobs=4): 31 | 32 | # Basic variables 33 | points = X # Just to distinguish geometric and NN calculations 34 | normals = calculateSurfaceNormalsManifold(points, triangs) 35 | 36 | # Creation of smooth basis mesh 37 | smooth_basis_mesh = pv.UnstructuredGrid(smooth_basis_file) 38 | smooth_basis = smooth_basis_mesh.cell_data["vf_smooth"] 39 | if not np.allclose(np.sum(smooth_basis * normals, axis=-1, keepdims=True),0.,atol=1e-4): 40 | smooth_basis = smooth_basis - normals * np.sum(smooth_basis * normals, axis=-1, keepdims=True) 41 | smooth_basis /= np.linalg.norm(smooth_basis, axis=-1, keepdims=True) 42 | 43 | # Check measurement points are subset of the collocation points 44 | self.kdtree_X = cKDTree(points) 45 | assert(np.allclose(self.kdtree_X.query(X_e)[0], 0.)) 46 | 47 | # Check data and normalize time values 48 | assert X_e.shape[0]==T_e.shape[0] 49 | # assert X_e.shape[-1]==parallel and T_e.shape[-1]==parallel 50 | assert X_e.shape[1]==3 and len(T_e.shape)==2 51 | T_top = np.array([]) 52 | T_base = np.zeros(parallel) 53 | x_range = (X.max(0)-X.min(0)).flatten() 54 | for i in range(parallel): 55 | t_range = T_e[ind[i]:ind[i+1],...].max(0)-T_e[ind[i]:ind[i+1],...].min(0) 56 | assert all(np.logical_and(1. < x_range, x_range < 1.e3)) # Check that spatial measurement units are mm 57 | assert all(np.logical_and(1. < t_range, t_range < 1.e3)) # Check time measurements are in ms and from a single cycle 58 | if T_e[ind[i]:ind[i+1],...].min(0).flatten() > 10. or T_e[ind[i]:ind[i+1],...].min(0).flatten() < 0.: 59 | T_base[i] = T_e.min(0) 60 | T_e[ind[i]:ind[i+1],...] -= T_base[i] 61 | T_top = np.append(T_top, T_e[ind[i]:ind[i+1],...].max(0)) 62 | T_e[ind[i]:ind[i+1],...] /= T_top[i] 63 | 64 | # Creation of Manifold Basis for vertices 65 | P = createLocalManifoldBasis(X, triangs, smooth_basis) 66 | self.P_p = cellToPointData(points, triangs, 67 | P.reshape([-1, 9])).reshape([-1, 3, 3]).astype(np.float32) 68 | 69 | # Assign class parameters 70 | self.X = X 71 | self.p_NN = parallel 72 | self.Tmax = T_top 73 | self.Tmin = T_base 74 | self.lb = X.min(0) 75 | self.ub = X.max(0) 76 | self.normals = normals 77 | self.T_e = T_e 78 | self.X_e = X_e 79 | self.ind = ind 80 | self.layers = layers 81 | self.CVlayers = CVlayers 82 | self.points = points 83 | self.triangs = triangs 84 | 85 | # Initialize NN 86 | weights = [] 87 | biases = [] 88 | for i in np.arange(self.p_NN): 89 | w, b = self.initialize_NN(layers) 90 | weights.append(w) 91 | biases.append(b) 92 | self.weights = weights 93 | self.biases = biases 94 | self.CVweights, self.CVbiases = self.initialize_NN(CVlayers) 95 | 96 | # Assign tf constants 97 | self.C = tf.constant(CVmax, dtype=tf.float32) 98 | self.alpha_e = tf.constant(lambda_tve, dtype=tf.float32) 99 | self.alpha = tf.constant(lambda_tva, dtype=tf.float32) 100 | self.lambda_DF = tf.constant(lambda_df, dtype=tf.float32) 101 | self.lambda_PDE = tf.constant(lambda_pde, dtype=tf.float32) 102 | 103 | # tf placeholders and graph 104 | config = tf.compat.v1.ConfigProto(allow_soft_placement=True, 105 | intra_op_parallelism_threads=jobs, 106 | inter_op_parallelism_threads=jobs, 107 | device_count={'CPU': jobs}) 108 | config.gpu_options.allow_growth = True 109 | self.sess = tf.compat.v1.Session(config=config) 110 | 111 | self.X_tf = tf.compat.v1.placeholder(tf.float32, shape=[None, self.X.shape[1]]) 112 | self.P_p_tf = tf.compat.v1.placeholder(tf.float32, shape=[None, self.P_p.shape[1], self.P_p.shape[2]]) 113 | self.T_e_tf = tf.compat.v1.placeholder(tf.float32, shape=[None, self.T_e.shape[1]]) 114 | self.X_e_tf = tf.compat.v1.placeholder(tf.float32, shape=[None, self.X_e.shape[1]]) 115 | self.ind_tf = tf.compat.v1.placeholder(tf.int32, shape=[None]) 116 | 117 | self.T_pred, self.CV_pred, self.f_T_pred, self.eV_TV_func, self.aV_TV_func = self.net_eikonal(self.X_tf, 118 | self.P_p_tf) 119 | self.T_e_pred = self.net_data(self.X_e_tf, self.ind_tf) 120 | self.pde_loss = self.lambda_PDE * tf.reduce_mean(tf.square(self.f_T_pred)) 121 | self.tv_loss = self.alpha_e * tf.reduce_mean(self.eV_TV_func) + self.alpha * tf.reduce_mean(self.aV_TV_func) 122 | self.data_fidelity_loss = self.lambda_DF * tf.reduce_mean(tf.square(self.T_e_tf - self.T_e_pred)) 123 | 124 | self.loss = self.data_fidelity_loss + self.pde_loss + self.tv_loss 125 | 126 | # Define optimizer (ADAM) 127 | self.optimizer_Adam = tf.compat.v1.train.AdamOptimizer() 128 | self.train_op_Adam = self.optimizer_Adam.minimize(self.loss) 129 | 130 | # Initialize Tensorflow variables 131 | init = tf.compat.v1.global_variables_initializer() 132 | self.sess.run(init) 133 | 134 | # Initialize network weights and biases using Xavier initialization 135 | def initialize_NN(self, layers): 136 | # Xavier initialization 137 | def xavier_init(size): 138 | in_dim = size[0] 139 | out_dim = size[1] 140 | xavier_stddev = 1. / np.sqrt((in_dim + out_dim) / 2.) 141 | return tf.Variable(tf.random.normal([in_dim, out_dim], dtype=tf.float32) * xavier_stddev, dtype=tf.float32) 142 | 143 | weights = [] 144 | biases = [] 145 | num_layers = len(layers) 146 | for l in range(0, num_layers - 1): 147 | W = xavier_init(size=[layers[l], layers[l + 1]]) 148 | b = tf.Variable(tf.zeros([1, layers[l + 1]], dtype=tf.float32), dtype=tf.float32) 149 | weights.append(W) 150 | biases.append(b) 151 | return weights, biases 152 | 153 | # Construct neural network (Forward Propagation) 154 | def neural_net(self, X, weights, biases): 155 | num_layers = len(weights) + 1 156 | 157 | H = 2.0 * (X - self.lb) / (self.ub - self.lb) - 1.0 158 | for l in range(0, num_layers - 2): 159 | W = weights[l] 160 | b = biases[l] 161 | H = tf.tanh(tf.add(tf.matmul(H, W), b)) 162 | W = weights[-1] 163 | b = biases[-1] 164 | Y = tf.add(tf.matmul(H, W), b) 165 | return Y 166 | 167 | # TV-Huber regularization function 168 | def TVHuber(self, nabla_x, huber_norm_eps): 169 | nabla_x_norm_squared = tf.reduce_sum(nabla_x**2, axis=-1, keepdims=True) 170 | nabla_x_norm = tf.sqrt(nabla_x_norm_squared) 171 | nabla_x_reg_term = tf.where(nabla_x_norm <= huber_norm_eps, 172 | 0.5/huber_norm_eps * nabla_x_norm_squared, 173 | (tf.sqrt(tf.maximum(nabla_x_norm_squared, huber_norm_eps**2)) 174 | - 0.5 * huber_norm_eps)) 175 | 176 | return nabla_x_reg_term, nabla_x_norm_squared, nabla_x_norm 177 | 178 | # Application of Multimap Anistropic Eikonal equation and Huber Regularizations 179 | def net_eikonal(self, X, P_p_loc, eps=1.e-9): 180 | C = self.C 181 | T = [] 182 | T_x = [] 183 | for i in np.arange(self.p_NN): 184 | T.append(self.neural_net(X, self.weights[i], self.biases[i])) 185 | T_x.append(tf.gradients(T[i], X)[0]) 186 | T = tf.concat(T,-1) 187 | CV = self.neural_net(X, self.CVweights, self.CVbiases) 188 | eV = C * (tf.sigmoid(CV[:,:2])) 189 | aV = tf.tanh(CV[:,2]) 190 | self.CV = CV 191 | self.evals = eV 192 | 193 | T_x = tf.concat(T_x,-1) 194 | aV_x = tf.gradients(aV, X)[0] 195 | eV_x = tf.concat([tf.gradients(eV[:,0], X)[0],tf.gradients(eV[:,1], X)[0]],axis=-1) 196 | self.CV_x = [eV_x, aV_x] 197 | 198 | eV_flat = tf.cast(tf.reshape(eV, [-1]), dtype=tf.float64) 199 | aV_flat = tf.cast(tf.reshape(aV, [-1]), dtype=tf.float64) 200 | zero_e = tf.zeros_like(eV_flat[0::2]) 201 | aVr = tf.sqrt(tf.maximum(1-aV_flat**2,eps)) 202 | eVM_mat = tf.reshape(tf.stack([eV_flat[0::2], zero_e, zero_e, eV_flat[1::2]], axis=-1), [-1, 2, 2]) 203 | aVM_mat = tf.reshape(tf.stack([aV_flat, -1.*aVr,aVr, aV_flat], axis=-1), [-1, 2, 2]) 204 | 205 | D = eigenDecompProd(aVM_mat, eVM_mat) 206 | self.D = D 207 | 208 | P_p_local = tf.cast(P_p_loc, dtype=np.float64) 209 | 210 | zeros = tf.zeros_like(aVM_mat[..., 0, 0]) 211 | ones = tf.ones_like(aVM_mat[..., 0, 0]) 212 | aVM_3D = tf.reshape(tf.stack([aVM_mat[..., 0, 0], aVM_mat[..., 0, 1], zeros, 213 | aVM_mat[..., 1, 0], aVM_mat[..., 1, 1], zeros, 214 | zeros, zeros, ones], axis=-1), [-1, 3, 3]) 215 | evecs = matMulProdSum(P_p_local, aVM_3D) 216 | self.evecs = tf.cast(evecs, dtype=tf.float32) 217 | 218 | evals3D = tf.reshape(tf.stack([eVM_mat[..., 0, 0], zeros, zeros, 219 | zeros, eVM_mat[..., 1, 1], zeros, 220 | zeros, zeros, zeros], axis=-1), [-1, 3, 3]) 221 | 222 | 223 | D_canon_3D = eigenDecompProd(evecs, evals3D) 224 | D_canon_3D = tf.cast(D_canon_3D, dtype=tf.float32) 225 | self.D_canon_3D = D_canon_3D 226 | 227 | # Eikonal Residuals 228 | eik_loss = [] 229 | for i in np.arange(self.p_NN): 230 | eik_loss.append(self.Tmax[i]*metricNormMatrix(D_canon_3D, T_x[...,3*i:3*i+3], ret_sqrt=True) - 1) 231 | eik_loss = tf.transpose(tf.stack(eik_loss,0)) 232 | 233 | # Huber Regularization 234 | self.nabla_eV_reg_term = self.TVHuber(eV_x, 1e-3)[0] 235 | self.nabla_aV_reg_term = self.TVHuber(aV_x, 1e-3)[0] 236 | 237 | return (T, CV, eik_loss, self.nabla_eV_reg_term, self.nabla_aV_reg_term) 238 | 239 | def net_data(self, X_e, ind): 240 | T_e = [] 241 | for i in np.arange(self.p_NN): 242 | T_e.append(self.neural_net(X_e[ind[i]:ind[i+1],...], self.weights[i], self.biases[i])) 243 | T_e = tf.concat(T_e,0) 244 | 245 | return T_e 246 | 247 | def callback(self, loss): 248 | self.lossit.append(loss) 249 | # print('Loss: %.5e (loss)) 250 | 251 | def train_Adam_minibatch(self, nEpoch, size=50): 252 | 253 | self.lossit = [] 254 | 255 | start_time = time.time() 256 | idx_global = np.arange(self.X.shape[0]) 257 | np.random.shuffle(idx_global) 258 | splits = np.array_split(idx_global, idx_global.shape[0] // size) 259 | pbar = trange(nEpoch,desc='Training') 260 | for ep in pbar: 261 | for it, idx in enumerate(splits): 262 | tf_dict = {self.X_tf: self.X[idx], 263 | self.X_e_tf: self.X_e, 264 | self.T_e_tf: self.T_e, 265 | self.P_p_tf: self.P_p[idx], 266 | self.ind_tf: self.ind} 267 | self.sess.run(self.train_op_Adam, tf_dict) 268 | 269 | loss_value = self.sess.run(self.loss, tf_dict) 270 | loss_df, loss_pde = self.sess.run((self.data_fidelity_loss, self.pde_loss), tf_dict) 271 | elapsed = time.time() - start_time 272 | #pbar.set_postfix({'Loss': loss_value, 'DF': loss_df, 'PDE': loss_pde, 'Time': elapsed}) 273 | pbar.set_postfix_str('Loss: %.3e, DF: %.3e, PDE: %.3e, Time: %.2f' % 274 | (loss_value, loss_df, loss_pde, elapsed)) 275 | self.lossit.append([loss_value, loss_df, loss_pde]) 276 | start_time = time.time() 277 | pbar.close() 278 | 279 | return self.lossit 280 | 281 | def predict(self, X_star): 282 | 283 | indices = self.kdtree_X.query(X_star)[1] 284 | P_p_predict = self.P_p[indices] 285 | 286 | tf_dict = {self.X_tf: X_star, 287 | self.P_p_tf: P_p_predict} 288 | 289 | result = self.sess.run([self.Tmax*self.T_pred + self.Tmin, self.CV_pred, self.CV_x, self.D, self.D_canon_3D, 290 | self.evals, self.evecs, self.f_T_pred], tf_dict) 291 | 292 | return result 293 | 294 | def predict_errors(self): 295 | 296 | tf_dict = {self.X_tf: self.X, 297 | self.X_e_tf: self.X_e, 298 | self.T_e_tf: self.T_e, 299 | self.P_p_tf: self.P_p, 300 | self.ind_tf: self.ind} 301 | 302 | total_loss, df_loss, pde_loss, tv_loss = self.sess.run([self.loss, self.data_fidelity_loss, 303 | self.pde_loss, self.tv_loss], tf_dict) 304 | return total_loss, df_loss, pde_loss, tv_loss 305 | 306 | class SyntheticDataGenerator3D: 307 | """ 308 | Create a set of cardiac activation maps from a geometry file with fiber orientations 309 | 310 | Parameters: 311 | vtk_file: geometry file in .vtk format with a cell data field called "fibers" (a vector) 312 | maps: int or vector: if int, number of activation maps desired; if vector, ids of init sites 313 | ppm: int of the number of sample points per map 314 | noise: A factor in milliseconds by which a standard normal distribution of noise 315 | is applied to the activation maps 316 | x0: initial sites 317 | """ 318 | 319 | def __init__(self, vtk_file, maps=1, ppm=100, noise=0.): 320 | vf = pv.UnstructuredGrid(vtk_file) 321 | self.points = vf.points 322 | self.triangs = vf.cells_dict[vtk.VTK_TRIANGLE] 323 | self.l = vf.cell_data["fibers"] 324 | 325 | self.n = calculateSurfaceNormalsManifold(self.points, self.triangs) 326 | self.l = self.l - self.n * np.sum(self.l * self.n, axis=-1, keepdims=True) 327 | self.l /= np.linalg.norm(self.l, axis=-1, keepdims=True) 328 | self.t = np.cross(self.l, self.n, axis=-1) 329 | self.t /= np.linalg.norm(self.t, axis=-1, keepdims=True) 330 | D_init = (1. ** 2 * self.l[..., np.newaxis] * self.l[..., np.newaxis, :] 331 | + 1. ** 2 * self.t[..., np.newaxis] * self.t[..., np.newaxis, :] 332 | + 1. ** 2 * self.n[..., np.newaxis] * self.n[..., np.newaxis, :]) 333 | D_init = 0.5*(D_init + np.transpose(D_init, axes=(0, 2, 1))) 334 | 335 | fim = FIMPY.create_fim_solver(self.points, self.triangs, D_init, device='cpu', use_active_list=False) 336 | if not np.isscalar(maps): 337 | x0 = maps 338 | maps = len(maps) 339 | else: 340 | first_point = np.random.choice(self.points.shape[0]) 341 | x0 = [first_point] 342 | for i in range(maps): 343 | dist = fim.comp_fim(x0, [0.0]*(i + 1)) 344 | x0.append(np.argmax(dist)) 345 | 346 | x0_vals = np.zeros(maps) 347 | D_n = (.6 ** 2 * self.l[..., np.newaxis] * self.l[..., np.newaxis, :] 348 | + .4 ** 2 * self.t[..., np.newaxis] * self.t[..., np.newaxis, :] 349 | + 1e-2 * self.n[..., np.newaxis] * self.n[..., np.newaxis, :]) 350 | D_n = 0.5*(D_n + np.transpose(D_n, axes=(0, 2, 1))) 351 | self.evecs = np.linalg.eigh(D_n)[1] 352 | 353 | phis = [] 354 | mm = [] 355 | x_e = [] 356 | t_e = [] 357 | inds = [0] 358 | m_ind = np.random.choice(self.points.shape[0],[ppm,maps],replace=False) 359 | for i in range(maps): 360 | phi = fim.comp_fim(x0[i], x0_vals[i], D_n) 361 | phi = phi + noise * np.random.randn(phi.shape[0]) 362 | m_mask = np.zeros(self.points.shape[0], dtype=bool) 363 | m_mask[m_ind[:,i]] = True 364 | phis.append(phi) 365 | mm.append(m_mask) 366 | x_e.append(self.points[m_mask]) 367 | t_e.append(phi[m_mask][...,np.newaxis]) 368 | inds.append(len(phi[m_mask]) + inds[-1]) 369 | self.x_e = np.squeeze(np.vstack(x_e)) 370 | self.mm = np.stack(mm, axis=-1) 371 | self.t_e = np.vstack(t_e) 372 | self.phis = np.stack(phis, axis=-1) 373 | self.inds = np.stack(inds) 374 | 375 | def get_values(self): 376 | return self.phis, self.t_e, self.x_e, self.mm, self.evecs, self.inds 377 | -------------------------------------------------------------------------------- /FiberNetModels_2D.py: -------------------------------------------------------------------------------- 1 | #!/usr/bin/env python3.7 2 | # -*- coding: utf-8 -*- 3 | """ 4 | Implementation of the FiberNet model to a 2D case 5 | Author: Carlos Ruiz Herrera, Thomas Grandits, Paris Perdikaris, Francisco Sahli Costabal, Simone Pezzuto 6 | """ 7 | 8 | import time 9 | import numpy as np 10 | import tensorflow as tf 11 | from pyDOE import lhs 12 | from fimpy.solver import FIMPY 13 | from scipy.spatial import cKDTree 14 | from collections import defaultdict 15 | from mesh_tools import cellToPointData, pointToCellData 16 | from math_tools import eigenDecompProd, matMulProdSum, metricNormMatrix 17 | from tqdm.auto import trange 18 | 19 | # Set up tensorflow in graph mode 20 | tf.compat.v1.disable_eager_execution() 21 | 22 | # PINN class construction 23 | 24 | class MultiAnisoEikonalPINN_2D: 25 | # Initialize the class 26 | def __init__(self, X, triangs, parallel, X_e, T_e, layers, CVlayers, Tmax, 27 | CVmax=1.0, lambda_df=1., lambda_pde=1e-4, 28 | lambda_tve=1e-2, lambda_tva=1e-9, 29 | jobs=4): 30 | 31 | # Basic variables 32 | points = X # Just to distinguish geometric and NN calculations 33 | # Creation of smooth basis mesh 34 | 35 | # Check measurement points are subset of the collocation points 36 | self.kdtree_X = cKDTree(points) 37 | 38 | # Creation of Manifold Basis for vertices 39 | p1 = np.concatenate([np.ones([triangs.shape[0],1]),np.zeros([triangs.shape[0],2])], axis=-1) 40 | p2 = np.concatenate([np.zeros([triangs.shape[0],1]),np.ones([triangs.shape[0],1]),np.zeros([triangs.shape[0],1])], axis=-1) 41 | p3 = np.concatenate([np.zeros([triangs.shape[0],2]),np.ones([triangs.shape[0],1])], axis=-1) 42 | P = np.concatenate([p1,p2,p3],axis=-1) #geom.createLocalManifoldBasis(X[triangs], smooth_basis) 43 | self.P_p = cellToPointData(points, triangs, P.reshape([-1, 9])).reshape([-1, 3, 3]).astype(np.float32) 44 | 45 | # Assign class parameters 46 | self.X = X 47 | self.p_NN = parallel 48 | self.Tmax = Tmax 49 | self.lb = X.min(0) 50 | self.ub = X.max(0)+[0.,0.,1.] 51 | self.T_e = T_e 52 | self.X_e = X_e 53 | self.layers = layers 54 | self.CVlayers = CVlayers 55 | self.points = points 56 | self.triangs = triangs 57 | 58 | # Initialize NN 59 | weights = [] 60 | biases = [] 61 | for i in np.arange(self.p_NN): 62 | w, b = self.initialize_NN(layers) 63 | weights.append(w) 64 | biases.append(b) 65 | self.weights = weights 66 | self.biases = biases 67 | self.CVweights, self.CVbiases = self.initialize_NN(CVlayers) 68 | 69 | # Assign tf constants 70 | self.C = tf.constant(CVmax, dtype=tf.float32) 71 | self.alpha_e = tf.constant(lambda_tve, dtype=tf.float32) 72 | self.alpha = tf.constant(lambda_tva, dtype=tf.float32) 73 | self.lambda_DF = tf.constant(lambda_df, dtype=tf.float32) 74 | self.lambda_PDE = tf.constant(lambda_pde, dtype=tf.float32) 75 | 76 | # tf placeholders and graph 77 | config = tf.compat.v1.ConfigProto(allow_soft_placement=True, 78 | intra_op_parallelism_threads=jobs, 79 | inter_op_parallelism_threads=jobs, 80 | device_count={'CPU': jobs}) 81 | config.gpu_options.allow_growth = True 82 | self.sess = tf.compat.v1.Session(config=config) 83 | 84 | self.X_tf = tf.compat.v1.placeholder(tf.float32, shape=[None, self.X.shape[1]]) 85 | self.P_p_tf = tf.compat.v1.placeholder(tf.float32, shape=[None, self.P_p.shape[1], self.P_p.shape[2]]) 86 | self.T_e_tf = tf.compat.v1.placeholder(tf.float32, shape=[None, self.T_e.shape[1]]) 87 | self.X_e_tf = tf.compat.v1.placeholder(tf.float32, shape=[None, self.X_e.shape[1], None]) 88 | 89 | self.T_pred, self.CV_pred, self.f_T_pred, self.eV_TV_func, self.aV_TV_func = self.net_eikonal(self.X_tf, 90 | self.P_p_tf) 91 | self.T_e_pred = self.net_data(self.X_e_tf) 92 | self.pde_loss = self.lambda_PDE * tf.reduce_mean(tf.square(self.f_T_pred)) 93 | self.tv_loss = self.alpha_e * tf.reduce_mean(self.eV_TV_func) + self.alpha * tf.reduce_mean(self.aV_TV_func) 94 | self.data_fidelity_loss = self.lambda_DF * tf.reduce_mean(tf.square(self.T_e_tf - self.T_e_pred)) 95 | 96 | self.loss = self.data_fidelity_loss + self.pde_loss + self.tv_loss 97 | 98 | # Define optimizer (ADAM) 99 | self.optimizer_Adam = tf.compat.v1.train.AdamOptimizer() 100 | self.train_op_Adam = self.optimizer_Adam.minimize(self.loss) 101 | 102 | # Initialize Tensorflow variables 103 | init = tf.compat.v1.global_variables_initializer() 104 | self.sess.run(init) 105 | 106 | # Initialize network weights and biases using Xavier initialization 107 | def initialize_NN(self, layers): 108 | # Xavier initialization 109 | def xavier_init(size): 110 | in_dim = size[0] 111 | out_dim = size[1] 112 | xavier_stddev = 1. / np.sqrt((in_dim + out_dim) / 2.) 113 | return tf.Variable(tf.random.normal([in_dim, out_dim], dtype=tf.float32) * xavier_stddev, dtype=tf.float32) 114 | 115 | weights = [] 116 | biases = [] 117 | num_layers = len(layers) 118 | for l in range(0, num_layers - 1): 119 | W = xavier_init(size=[layers[l], layers[l + 1]]) 120 | b = tf.Variable(tf.zeros([1, layers[l + 1]], dtype=tf.float32), dtype=tf.float32) 121 | weights.append(W) 122 | biases.append(b) 123 | return weights, biases 124 | 125 | # Construct neural network (Forward Propagation) 126 | def neural_net(self, X, weights, biases): 127 | num_layers = len(weights) + 1 128 | 129 | H = 2.0 * (X - self.lb) / (self.ub - self.lb) - 1.0 130 | for l in range(0, num_layers - 2): 131 | W = weights[l] 132 | b = biases[l] 133 | H = tf.tanh(tf.add(tf.matmul(H, W), b)) 134 | W = weights[-1] 135 | b = biases[-1] 136 | Y = tf.add(tf.matmul(H, W), b) 137 | return Y 138 | 139 | # TV-Huber regularization function 140 | def TVHuber(self, nabla_x, huber_norm_eps): 141 | nabla_x_norm_squared = tf.reduce_sum(nabla_x**2, axis=-1, keepdims=True) 142 | nabla_x_norm = tf.sqrt(nabla_x_norm_squared) 143 | nabla_x_reg_term = tf.where(nabla_x_norm <= huber_norm_eps, 144 | 0.5/huber_norm_eps * nabla_x_norm_squared, 145 | (tf.sqrt(tf.maximum(nabla_x_norm_squared, huber_norm_eps**2)) 146 | - 0.5 * huber_norm_eps)) 147 | 148 | return nabla_x_reg_term, nabla_x_norm_squared, nabla_x_norm 149 | 150 | # Application of Multimap Anistropic Eikonal equation and Huber Regularizations 151 | def net_eikonal(self, X, P_p_loc, eps=1.e-9): 152 | C = self.C 153 | T = [] 154 | T_x = [] 155 | for i in np.arange(self.p_NN): 156 | T.append(self.neural_net(X, self.weights[i], self.biases[i])) 157 | T_x.append(tf.gradients(T[i], X)[0]) 158 | T = tf.concat(T,-1) 159 | CV = self.neural_net(X, self.CVweights, self.CVbiases) 160 | eV = C * (tf.sigmoid(CV[:,:2])) 161 | aV = tf.tanh(CV[:,2]) 162 | self.CV = CV 163 | self.evals = eV 164 | 165 | T_x = tf.concat(T_x,-1) 166 | aV_x = tf.gradients(aV, X)[0] 167 | eV_x = tf.concat([tf.gradients(eV[:,0], X)[0],tf.gradients(eV[:,1], X)[0]],axis=-1) 168 | self.CV_x = [eV_x, aV_x] 169 | 170 | eV_flat = tf.cast(tf.reshape(eV, [-1]), dtype=tf.float64) 171 | aV_flat = tf.cast(tf.reshape(aV, [-1]), dtype=tf.float64) 172 | zero_e = tf.zeros_like(eV_flat[0::2]) 173 | aVr = tf.sqrt(tf.maximum(1-aV_flat**2,eps)) 174 | eVM_mat = tf.reshape(tf.stack([eV_flat[0::2], zero_e, zero_e, eV_flat[1::2]], axis=-1), [-1, 2, 2]) 175 | aVM_mat = tf.reshape(tf.stack([aV_flat, -1.*aVr,aVr, aV_flat], axis=-1), [-1, 2, 2]) 176 | 177 | D = eigenDecompProd(aVM_mat, eVM_mat) 178 | self.D = D 179 | 180 | P_p_local = tf.cast(P_p_loc, dtype=np.float64) 181 | 182 | zeros = tf.zeros_like(aVM_mat[..., 0, 0]) 183 | ones = tf.ones_like(aVM_mat[..., 0, 0]) 184 | aVM_3D = tf.reshape(tf.stack([aVM_mat[..., 0, 0], aVM_mat[..., 0, 1], zeros, 185 | aVM_mat[..., 1, 0], aVM_mat[..., 1, 1], zeros, 186 | zeros, zeros, ones], axis=-1), [-1, 3, 3]) 187 | evecs = matMulProdSum(P_p_local, aVM_3D) 188 | self.evecs = tf.cast(evecs, dtype=tf.float32) 189 | 190 | evals3D = tf.reshape(tf.stack([eVM_mat[..., 0, 0], zeros, zeros, 191 | zeros, eVM_mat[..., 1, 1], zeros, 192 | zeros, zeros, zeros], axis=-1), [-1, 3, 3]) 193 | 194 | 195 | D_canon_3D = eigenDecompProd(evecs, evals3D) 196 | D_canon_3D = tf.cast(D_canon_3D, dtype=tf.float32) 197 | self.D_canon_3D = D_canon_3D 198 | 199 | # Eikonal Residuals 200 | eik_loss = [] 201 | for i in np.arange(self.p_NN): 202 | eik_loss.append(self.Tmax[i]*metricNormMatrix(D_canon_3D, T_x[...,3*i:3*i+3], ret_sqrt=True) - 1) 203 | eik_loss = tf.transpose(tf.stack(eik_loss,0)) 204 | 205 | # Huber Regularization 206 | self.nabla_eV_reg_term = self.TVHuber(eV_x, 1e-3)[0] 207 | self.nabla_aV_reg_term = self.TVHuber(aV_x, 1e-3)[0] 208 | 209 | return (T, CV, eik_loss, self.nabla_eV_reg_term, self.nabla_aV_reg_term) 210 | 211 | def net_data(self, X_e): 212 | T_e = [] 213 | for i in np.arange(self.p_NN): 214 | T_e.append(self.neural_net(X_e[...,i], self.weights[i], self.biases[i])) 215 | T_e = tf.concat(T_e,-1) 216 | 217 | return T_e 218 | 219 | def callback(self, loss): 220 | self.lossit.append([loss]) 221 | # print('Loss: %.3e, DF: %.3e, PDE: %.3e' % (loss[0],loss[1],loss[2])) 222 | 223 | def train_Adam_minibatch(self, nEpoch, size=50): 224 | 225 | self.lossit = [] 226 | 227 | start_time = time.time() 228 | idx_global = np.arange(self.X.shape[0]) 229 | np.random.shuffle(idx_global) 230 | splits = np.array_split(idx_global, idx_global.shape[0] // size) 231 | pbar = trange(nEpoch,desc='Training') 232 | for ep in pbar: 233 | for it, idx in enumerate(splits): 234 | tf_dict = {self.X_tf: self.X[idx], 235 | self.X_e_tf: self.X_e, 236 | self.T_e_tf: self.T_e, 237 | self.P_p_tf: self.P_p[idx]} 238 | self.sess.run(self.train_op_Adam, tf_dict) 239 | 240 | loss_value = self.sess.run(self.loss, tf_dict) 241 | loss_df, loss_pde = self.sess.run((self.data_fidelity_loss, self.pde_loss), tf_dict) 242 | elapsed = time.time() - start_time 243 | pbar.set_postfix_str('Loss: %.3e, DF: %.3e, PDE: %.3e, Time: %.2f' % 244 | (loss_value, loss_df, loss_pde, elapsed)) 245 | self.lossit.append([loss_value, loss_df, loss_pde]) 246 | start_time = time.time() 247 | 248 | pbar.close() 249 | 250 | return self.lossit 251 | 252 | def predict(self, X_star): 253 | 254 | indices = self.kdtree_X.query(X_star)[1] 255 | P_p_predict = self.P_p[indices] 256 | 257 | tf_dict = {self.X_tf: X_star, 258 | self.P_p_tf: P_p_predict} 259 | 260 | result = self.sess.run([self.Tmax*self.T_pred, self.CV_pred, self.CV_x, self.D, self.D_canon_3D, 261 | self.evals, self.evecs, self.f_T_pred], tf_dict) ##T_normalization: T out original scale 262 | 263 | return result 264 | 265 | def predict_errors(self): 266 | 267 | tf_dict = {self.X_tf: self.X, 268 | self.X_e_tf: self.X_e, 269 | self.T_e_tf: self.T_e, 270 | self.P_p_tf: self.P_p} 271 | 272 | total_loss, pde_loss, tv_loss = self.sess.run([self.loss, self.pde_loss, self.tv_loss], tf_dict) 273 | return total_loss, pde_loss, tv_loss 274 | 275 | class SyntheticDataGenerator2D: 276 | """ 277 | Create a set of cardiac activation maps on 2D grid mesh 278 | 279 | Parameters: 280 | grid_points: int number of points on the side of the square grid (total points = grid_points x grid_points) 281 | sample_points: int total number of points to sample across all maps (each map has sample_points/maps_number) 282 | maps_number: int number of activation maps desired 283 | """ 284 | def __init__(self, grid_points=35, sample_points=245, maps_number=2, noise=0.) -> None: 285 | # Grid points must be more than sample points 286 | assert grid_points**2 > sample_points 287 | 288 | # Create mesh points 289 | x = y = np.linspace(-1,1,grid_points)[:,None] 290 | X_m, Y_m = np.meshgrid(x,y) 291 | self.X_m, self.Y_m = X_m, Y_m 292 | X = X_m.flatten()[:,None] 293 | Y = Y_m.flatten()[:,None] 294 | Z = np.zeros_like(X) 295 | self.points = np.concatenate([X,Y,Z],axis=-1) 296 | 297 | # Create conduction velocity values 298 | cv = self.get_simulated_CV(X,Y) 299 | self.cv = cv 300 | eigenvectors = cv[0:4] 301 | eigenvectors.reshape(X_m.shape[0],X_m.shape[1],4) 302 | 303 | # Create mesh triangles 304 | triangles_list = [] 305 | for i in np.arange(len(self.points)-grid_points): 306 | if i%grid_points!=grid_points-1: 307 | triangles_list.append([3,i,i+1,i+grid_points]) 308 | triangles_list.append([3,i+1,i+grid_points,i+grid_points+1]) 309 | triangles_array = np.array(triangles_list) 310 | self.triangles = triangles_array[:,1:] 311 | 312 | ## Create D tensor 313 | zed = np.zeros_like(cv[4]) 314 | normal_cv = np.ones_like(cv[4]) * 1.e-3 315 | D_init = np.stack([cv[4],cv[6],zed,cv[6],cv[5],zed,zed,zed,normal_cv], axis=-1).reshape([-1,3,3]) 316 | self.fiber_vecs = np.linalg.eigh(D_init)[1] 317 | D_init_cells = pointToCellData(self.points, self.triangles, D_init) 318 | 319 | # Select measurement points and initiation sites 320 | measurement_mask = np.zeros(self.points.shape[0], dtype=bool) 321 | kdtree_X = cKDTree(self.points) 322 | X_t = lhs(2, sample_points, 'c')*2-1 323 | X_train = np.concatenate([X_t,Z[:X_t.shape[0]]],axis=-1) 324 | sample_indices = kdtree_X.query(X_train)[1] 325 | sample_indices = self.remove_duplicates(sample_indices) 326 | sample_indices = sample_indices[:len(sample_indices)//maps_number*maps_number] #This might throw off exact number of sample points 327 | measurement_mask[sample_indices] = True 328 | print("Real number of sample points taken: ", len(sample_indices)) 329 | initiation_sites = lhs(2, 5, 'm')*2-1 330 | initiation_sites = np.concatenate([initiation_sites,Z[:initiation_sites.shape[0]]],axis=-1) 331 | initiation_sites = kdtree_X.query(initiation_sites)[1] 332 | 333 | # Get activation times from initiation sites and cv with FIM method 334 | split_sample_points = np.array_split(sample_indices, maps_number) 335 | fim = FIMPY.create_fim_solver(self.points, self.triangles, D_init_cells, device='cpu', use_active_list=False) 336 | X_dirichlet = [] 337 | phi_dirichlet = [] 338 | phi_max = [] 339 | phis = [] 340 | x0_vals = np.zeros(maps_number) 341 | for i, idx in enumerate(split_sample_points): 342 | phi = fim.comp_fim(initiation_sites[i], x0_vals[i]) 343 | phi += noise * np.random.randn(phi.shape[0]) 344 | phis.append(phi) 345 | m_mask = np.zeros(self.points.shape[0], dtype=bool) 346 | m_mask[idx] = True 347 | X_dirichlet.append(self.points[m_mask]) 348 | phi_dirichlet.append(phi[m_mask]) 349 | phi_max.append(phi_dirichlet[i].max()) 350 | phi_dirichlet[i] = phi_dirichlet[i]/phi_max[i] 351 | X_dirichlet = np.transpose(np.stack(X_dirichlet, axis=0),[1,2,0]) 352 | phi_dirichlet = np.transpose(np.stack(phi_dirichlet, axis=0)) 353 | phis = np.transpose(np.stack(phis, axis=0)) 354 | 355 | self.phi = phis 356 | self.phi_max = phi_max 357 | self.T_e = phi_dirichlet 358 | self.X_e = X_dirichlet 359 | 360 | def get_simulated_CV(self, X, Y): 361 | """ 362 | Returns values of 2d FiberNet paper simulated conduction velocities in different formats 363 | The values are: 364 | [eigenvector1_x_val, eigenvector1_y_val, eigenvector2_x_val, eigenvector1_y_val, 365 | matrix_format_val_00, matrix_format_val_11, matrix_format_val_10] 366 | """ 367 | mask = np.less_equal(np.sqrt((X+1)**2 + 2*(Y+1)**2),np.sqrt(2*(X-1)**2 + (Y-1)**2)) 368 | d1 = mask*1.0 + ~mask*0.5 369 | d2 = mask*0.5 + ~mask*1.0 370 | d12 = mask*0.0 + ~mask*0.0 371 | c = (d1+d2)/2 372 | r = np.sqrt((d1-c)**2+d12**2) 373 | a = np.arctan2(d12,(d1-c))/2 374 | e1 = c+r 375 | e2 = c-r 376 | e1x = e1*np.cos(a) 377 | e1y = e1*np.sin(a) 378 | e2x = -e2*np.sin(a) 379 | e2y = e2*np.cos(a) 380 | return np.array([e1x, e1y, e2x, e2y, d1, d2, d12]) 381 | 382 | def remove_duplicates(self, old_list): 383 | unwanted = [] 384 | tally = defaultdict(list) 385 | for i,item in enumerate(old_list): 386 | tally[item].append(i) 387 | duples = ((key,locs) for key,locs in tally.items() 388 | if len(locs)>1) 389 | for duplicates in sorted(duples): 390 | dupe = duplicates[1][1:] 391 | for name in dupe: 392 | unwanted.append(name) 393 | new_list = [i for j, i in enumerate(old_list) if j not in unwanted] 394 | return new_list 395 | 396 | def get_geometry(self): 397 | return self.points, self.triangles, self.X_m, self.Y_m 398 | 399 | def get_activation_maps(self): 400 | return self.phi, self.X_e, self.T_e, self.phi_max 401 | 402 | def get_fiber_vectors(self): 403 | return self.fiber_vecs, self.cv 404 | 405 | def D_printer(D): 406 | d1 = D[:,0,0] 407 | d2 = D[:,1,1] 408 | d12 = D[:,0,1] 409 | c = (d1+d2)/2 410 | r = np.sqrt((d1-c)**2+d12**2) 411 | a = np.arctan2(d12,(d1-c))/2 412 | e1 = c+r 413 | e2 = c-r 414 | e1x = e1*np.cos(a) 415 | e1y = e1*np.sin(a) 416 | e2x = -e2*np.sin(a) 417 | e2y = e2*np.cos(a) 418 | return np.array([e1x, e1y, e2x, e2y]) 419 | -------------------------------------------------------------------------------- /LICENSE: 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Remote Network Interaction; Use with the GNU General Public License. 541 | 542 | Notwithstanding any other provision of this License, if you modify the 543 | Program, your modified version must prominently offer all users 544 | interacting with it remotely through a computer network (if your version 545 | supports such interaction) an opportunity to receive the Corresponding 546 | Source of your version by providing access to the Corresponding Source 547 | from a network server at no charge, through some standard or customary 548 | means of facilitating copying of software. This Corresponding Source 549 | shall include the Corresponding Source for any work covered by version 3 550 | of the GNU General Public License that is incorporated pursuant to the 551 | following paragraph. 552 | 553 | Notwithstanding any other provision of this License, you have 554 | permission to link or combine any covered work with a work licensed 555 | under version 3 of the GNU General Public License into a single 556 | combined work, and to convey the resulting work. The terms of this 557 | License will continue to apply to the part which is the covered work, 558 | but the work with which it is combined will remain governed by version 559 | 3 of the GNU General Public License. 560 | 561 | 14. Revised Versions of this License. 562 | 563 | The Free Software Foundation may publish revised and/or new versions of 564 | the GNU Affero General Public License from time to time. Such new versions 565 | will be similar in spirit to the present version, but may differ in detail to 566 | address new problems or concerns. 567 | 568 | Each version is given a distinguishing version number. If the 569 | Program specifies that a certain numbered version of the GNU Affero General 570 | Public License "or any later version" applies to it, you have the 571 | option of following the terms and conditions either of that numbered 572 | version or of any later version published by the Free Software 573 | Foundation. If the Program does not specify a version number of the 574 | GNU Affero General Public License, you may choose any version ever published 575 | by the Free Software Foundation. 576 | 577 | If the Program specifies that a proxy can decide which future 578 | versions of the GNU Affero General Public License can be used, that proxy's 579 | public statement of acceptance of a version permanently authorizes you 580 | to choose that version for the Program. 581 | 582 | Later license versions may give you additional or different 583 | permissions. However, no additional obligations are imposed on any 584 | author or copyright holder as a result of your choosing to follow a 585 | later version. 586 | 587 | 15. Disclaimer of Warranty. 588 | 589 | THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY 590 | APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT 591 | HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY 592 | OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, 593 | THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR 594 | PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM 595 | IS WITH YOU. SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF 596 | ALL NECESSARY SERVICING, REPAIR OR CORRECTION. 597 | 598 | 16. Limitation of Liability. 599 | 600 | IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING 601 | WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS 602 | THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY 603 | GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE 604 | USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF 605 | DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD 606 | PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS), 607 | EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF 608 | SUCH DAMAGES. 609 | 610 | 17. Interpretation of Sections 15 and 16. 611 | 612 | If the disclaimer of warranty and limitation of liability provided 613 | above cannot be given local legal effect according to their terms, 614 | reviewing courts shall apply local law that most closely approximates 615 | an absolute waiver of all civil liability in connection with the 616 | Program, unless a warranty or assumption of liability accompanies a 617 | copy of the Program in return for a fee. 618 | 619 | END OF TERMS AND CONDITIONS 620 | 621 | How to Apply These Terms to Your New Programs 622 | 623 | If you develop a new program, and you want it to be of the greatest 624 | possible use to the public, the best way to achieve this is to make it 625 | free software which everyone can redistribute and change under these terms. 626 | 627 | To do so, attach the following notices to the program. It is safest 628 | to attach them to the start of each source file to most effectively 629 | state the exclusion of warranty; and each file should have at least 630 | the "copyright" line and a pointer to where the full notice is found. 631 | 632 | 633 | Copyright (C) 634 | 635 | This program is free software: you can redistribute it and/or modify 636 | it under the terms of the GNU Affero General Public License as published 637 | by the Free Software Foundation, either version 3 of the License, or 638 | (at your option) any later version. 639 | 640 | This program is distributed in the hope that it will be useful, 641 | but WITHOUT ANY WARRANTY; without even the implied warranty of 642 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 643 | GNU Affero General Public License for more details. 644 | 645 | You should have received a copy of the GNU Affero General Public License 646 | along with this program. If not, see . 647 | 648 | Also add information on how to contact you by electronic and paper mail. 649 | 650 | If your software can interact with users remotely through a computer 651 | network, you should also make sure that it provides a way for users to 652 | get its source. For example, if your program is a web application, its 653 | interface could display a "Source" link that leads users to an archive 654 | of the code. There are many ways you could offer source, and different 655 | solutions will be better for different programs; see section 13 for the 656 | specific requirements. 657 | 658 | You should also get your employer (if you work as a programmer) or school, 659 | if any, to sign a "copyright disclaimer" for the program, if necessary. 660 | For more information on this, and how to apply and follow the GNU AGPL, see 661 | . 662 | --------------------------------------------------------------------------------