updated eigvalue solvers

doc/Programs/EigenvaluesDeepLearning/ODEEigenvalueSolverTF.py

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+# # Finding eigenvalues of matrices with neural networks. 
+# Script for finding the eigenvectors corresponding to the largest eigenvalue of a matrix with a neural network.
+
+import tensorflow.compat.v1 as tf
+tf.disable_v2_behavior()
+tf.reset_default_graph()
+# tf.set_random_seed(343)
+
+# import tensorflow as tf
+import numpy as np
+from matplotlib import cm
+from matplotlib import pyplot as plt
+from mpl_toolkits.mplot3d import axes3d
+#from lib import compute_dx_dt
+
+matrix_size = 6
+
+A = np.random.random_sample(size=(matrix_size,matrix_size))
+A = (A.T + A)/2.0
+start_matrix = A
+
+eigen_vals, eigen_vecs =  np.linalg.eig(A)
+
+A = tf.convert_to_tensor(A)
+print("A = ", A)
+
+x_0 = tf.convert_to_tensor(np.random.random_sample(size = (1,matrix_size)))
+print("x0 = ", x_0)
+
+## The construction phase
+
+num_iter = 10000
+num_hidden_neurons = [50]
+num_hidden_layers = np.size(num_hidden_neurons)
+
+
+with tf.variable_scope('dnn'):
+
+    previous_layer = x_0
+
+    for l in range(num_hidden_layers):
+        current_layer = tf.layers.dense(previous_layer, num_hidden_neurons[l],activation=tf.nn.sigmoid)
+        previous_layer = current_layer
+
+    dnn_output = tf.layers.dense(previous_layer, matrix_size)
+
+with tf.name_scope('loss'):
+    print("dnn_output = ", dnn_output)
+    
+    x_trial = tf.transpose(dnn_output)
+    print("x_trial = ", x_trial)
+    
+    temp1 = (tf.tensordot(tf.transpose(x_trial), x_trial, axes=1)*A)
+    temp2 = (1- tf.tensordot(tf.transpose(x_trial), tf.tensordot(A, x_trial, axes=1), axes=1))*np.eye(matrix_size)
+    func = tf.tensordot((temp1-temp2), x_trial, axes=1)
+    
+    print(temp1)
+    print(temp2)
+    print(func)
+    
+    func = tf.transpose(func)
+    x_trial = tf.transpose(x_trial)
+    
+    loss = tf.losses.mean_squared_error(func, x_trial)
+
+learning_rate = 0.001
+
+with tf.name_scope('train'):
+    optimizer = tf.train.GradientDescentOptimizer(learning_rate)
+    traning_op = optimizer.minimize(loss)
+
+init = tf.global_variables_initializer()
+
+g_dnn = None
+
+losses = []
+
+with tf.Session() as sess:
+    init.run()
+    for i in range(num_iter):
+        sess.run(traning_op)
+
+        if i % 100 == 0:
+            l = loss.eval()
+            print("Step:", i, "/",num_iter, "loss: ", l)
+            losses.append(l)
+
+    x_dnn = x_trial.eval()
+x_dnn = x_dnn.T
+
+
+# ## Plotting loss over time
+
+plt.plot(losses[:5])
+plt.xlabel("Iteration")
+plt.ylabel("Loss")
+
+print("Eigenvector NN = \n", (x_dnn/(x_dnn**2).sum()**0.5), "\n")
+
+eigen_val_nn = x_dnn.T @ (start_matrix @ x_dnn) / (x_dnn.T @ x_dnn)
+
+print("Eigenvalue NN = \n", eigen_val_nn, "\n \n")
+print("Eigenvector analytic = \n", eigen_vecs)
+print("\n")
+print("Eigenvalues analytic = \n",eigen_vals)
+