diff --git a/IsingModel/Ising2.py b/IsingModel/Ising2.py index 87276c6..c9691ca 100644 --- a/IsingModel/Ising2.py +++ b/IsingModel/Ising2.py @@ -29,7 +29,7 @@ def __init__(self, height, width): self.vertical_correlations = np.zeros([height - 1, width]) self.horizontal_correlations = np.zeros([height, width - 1]) self.mean_parameters = np.zeros([height, width]) - self.__canonical_parameters = np.zeros([height, width, 5]) + self._canonical_parameters = np.zeros([height, width, 5]) def random_init(self): self.linear_factors = 2 * np.random.rand(self.height, self.width) - 1 @@ -66,14 +66,14 @@ def energy(self, grid): enrg -= 1 / 2 * np.sum(self.horizontal_correlations * grid[:, 1:] * grid[:, :-1]) return enrg - def __set_canonical(self): - self.__canonical_parameters[:, :, 0] = self.linear_factors - self.__canonical_parameters[:-1, :, 1] = self.vertical_correlations # with lower neighbor - self.__canonical_parameters[1:, :, 2] = self.vertical_correlations # with upper neighbor - self.__canonical_parameters[:, :-1, 3] = self.horizontal_correlations # with right neighbor - self.__canonical_parameters[:, 1:, 4] = self.horizontal_correlations # with left neighbor + def _set_canonical(self): + self._canonical_parameters[:, :, 0] = self.linear_factors + self._canonical_parameters[:-1, :, 1] = self.vertical_correlations # with lower neighbor + self._canonical_parameters[1:, :, 2] = self.vertical_correlations # with upper neighbor + self._canonical_parameters[:, :-1, 3] = self.horizontal_correlations # with right neighbor + self._canonical_parameters[:, 1:, 4] = self.horizontal_correlations # with left neighbor - def __sum_neighbors(self, grid): + def _sum_neighbors(self, grid): """ return a new grid with the weighted sum of all neighbors on each point """ @@ -82,12 +82,12 @@ def __sum_neighbors(self, grid): + np.pad(grid[:, 1:] * self.horizontal_correlations, ((0, 0), (0, 1)), mode='constant') + np.pad(grid[:, :-1] * self.horizontal_correlations, ((0, 0), (1, 0)), mode='constant')) - def __gibbs_update(self, grid, mask): + def _gibbs_update(self, grid, mask): """ return a new grid where nodes that are not masked have been re sampled conditionally to their neighbors """ # how to specify type in python 3 annotation - probagrid = logistic(self.linear_factors + self.__sum_neighbors(grid)) + probagrid = logistic(self.linear_factors + self._sum_neighbors(grid)) return mask * grid + (1 - mask) * (2 * (np.random.rand(self.height, self.width) < probagrid) - 1) def gibbs_sampling(self, grid): @@ -103,9 +103,9 @@ def gibbs_sampling(self, grid): # mask half of the nodes in a checkerboard pattern mask = np.fromfunction(lambda x, y: (x + y) % 2, (self.height, self.width)) # update nodes that are not touching each other - grid = self.__gibbs_update(grid, mask) + grid = self._gibbs_update(grid, mask) # update the other half - grid = self.__gibbs_update(grid, 1 - mask) + grid = self._gibbs_update(grid, 1 - mask) energylist.append(self.energy(grid)) return grid, energylist[1:] @@ -120,9 +120,9 @@ def gibbs_video(self, grid, time_max=100): # mask half of the nodes in a checkerboard pattern mask = np.fromfunction(lambda x, y: (x + y) % 2, (self.height, self.width)) # update nodes that are not touching each other - grid = self.__gibbs_update(grid, mask) + grid = self._gibbs_update(grid, mask) # update the other half - grid = self.__gibbs_update(grid, 1 - mask) + grid = self._gibbs_update(grid, 1 - mask) video[t, :, :] = grid energylist.append(self.energy(grid)) return video, energylist[1:] @@ -144,27 +144,27 @@ def meanfields(self, initial_grid, max_iter=100): while abs(means_energy[-2] - means_energy[-1]) > epsilon and countiter < max_iter: countiter += 1 # update the means similarly to gibbs sampling - grid = 2 * logistic(self.linear_factors + self.__sum_neighbors(grid)) - 1 + grid = 2 * logistic(self.linear_factors + self._sum_neighbors(grid)) - 1 grid = self.observations + (1 - np.absolute(self.observations)) * grid means_energy.append(self.energy(grid)) self.mean_parameters = grid return means_energy[1:] @staticmethod - def __repeat_symmetric(grid): + def _repeat_symmetric(grid): tmp = np.expand_dims(grid, axis=-1) return np.concatenate((tmp, - tmp), axis=-1) - def __messages2means(self, messages): + def _messages2means(self, messages): self.mean_parameters = np.product(messages, axis=0) self.mean_parameters = self.mean_parameters[:, :, 0] / (np.sum(self.mean_parameters, axis=-1) + 1e-10) self.mean_parameters = 2 * self.mean_parameters - 1 - def loopybelief(self, max_iter=25, damping=0.5): + def loopybelief(self, max_iter=25, damping=0.5, update_order='cyclic'): """ update the mean_parameters field with the probability given by the sum product algorithm - :param max_iter: - :param damping: momentum coefficient + :param max_iter: maximum number of iteration, should depend on the damping + :param damping: momentum coefficient, from 0 to 1 :return: means_energy: the sequence of mean parameters energy """ messages = np.ones([5, self.height, self.width, 2]) @@ -178,34 +178,41 @@ def loopybelief(self, max_iter=25, damping=0.5): # 4 : log-potentials in each point # potentials are stored in an additional channel # if +1 is observed, set potential for -1 to 0 - messages[4, :, :, 1] = (1 - (self.observations == 1)) * (-1) * self.linear_factors / 2 + messages[4, :, :, 1] = (1 - (self.observations == 1)) * np.exp(- self.linear_factors / 2) # if -1 is observed, set potential for +1 to 0 - messages[4, :, :, 0] = (1 - (self.observations == -1)) * self.linear_factors / 2 + messages[4, :, :, 0] = (1 - (self.observations == -1)) * np.exp(self.linear_factors / 2) correlations = [self.vertical_correlations, self.horizontal_correlations, self.vertical_correlations, self.horizontal_correlations] - means_energy = [] # we stop when we reach max_iter iterations. # Murphy et al. found that in average, max_iter = 15 is sufficient - for _ in range(max_iter): - old_messages = messages.copy() - for k, (newmessages, oldmessages) in zip([0, 2, 1, 3], - [(messages[:, :-1, :], old_messages[:, 1:, :]), - (messages[:, 1:, :], old_messages[:, :-1, :]), - (messages[:, :, 1:], old_messages[:, :, :-1]), - (messages[:, :, :-1], old_messages[:, :, 1:])]): - # sum of messages coming to the source node, except the one coming from the destination node - newmessages[k] = oldmessages[(k - 1)] * oldmessages[k] * oldmessages[(k + 1) % 4] * oldmessages[4] - corr = self.__repeat_symmetric(correlations[k] / 2) - # x_i=+1 in newmessages[k, :, :, 0] - tmp = np.sum(newmessages[k] * np.exp(corr), axis=-1) - # x_i=-1 in newmessages[k, :, :, 1] - newmessages[k, :, :, 1] = np.sum(newmessages[k] * np.exp(- corr), axis=-1) - newmessages[k, :, :, 0] = tmp - # normalization of messages to 1 - newmessages[k] /= (np.expand_dims(np.sum(newmessages[k], axis=-1), axis=-1) + 1e-10) + video = np.empty([max_iter, self.height, self.width]) + means_energy = [] + old_messages = messages.copy() + list_new_old = [(messages[:, :-1, :], old_messages[:, 1:, :]), + (messages[:, :, 1:], old_messages[:, :, :-1]), + (messages[:, 1:, :], old_messages[:, :-1, :]), + (messages[:, :, :-1], old_messages[:, :, 1:])] + if update_order == 'cyclic': + list_update = np.array([0, 1, 2, 3] * (max_iter // 4)) + else: + list_update = np.random.randint(0, 4, max_iter) + for count_iter, k in enumerate(list_update): + newmessages, oldmessages = list_new_old[k] + # sum of messages coming to the source node, except the one coming from the destination node + newmessages[k] = oldmessages[(k - 1) % 4] * oldmessages[k] * oldmessages[(k + 1) % 4] * oldmessages[4] + corr = self._repeat_symmetric(correlations[k] / 2) + # x_i=+1 in newmessages[k, :, :, 0] + tmp = np.sum(newmessages[k] * np.exp(corr), axis=-1) + # x_i=-1 in newmessages[k, :, :, 1] + newmessages[k, :, :, 1] = np.sum(newmessages[k] * np.exp(- corr), axis=-1) + newmessages[k, :, :, 0] = tmp # damping - messages[:4] = damping * messages[:4] + (1 - damping) * old_messages[:4] - self.__messages2means(messages) + messages[k] = damping * messages[k] + (1 - damping) * old_messages[k] + # normalization of messages to 1 + newmessages[k] /= (np.expand_dims(np.sum(newmessages[k], axis=-1), axis=-1) + 1e-10) + old_messages[k] = messages[k].copy() + self._messages2means(messages) means_energy.append(self.energy(self.mean_parameters)) - return means_energy + video[count_iter] = self.mean_parameters + return video, means_energy diff --git a/Poster/Poster.pptx b/Poster/Poster.pptx new file mode 100644 index 0000000..404eb8a Binary files /dev/null and b/Poster/Poster.pptx differ diff --git a/Poster/ising_model.svg b/Poster/ising_model.svg new file mode 100644 index 0000000..299d5be --- /dev/null +++ b/Poster/ising_model.svg @@ -0,0 +1,794 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + image/svg+xml + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/Poster/rgising1.png b/Poster/rgising1.png new file mode 100644 index 0000000..f689c8d Binary files /dev/null and b/Poster/rgising1.png differ diff --git a/Poster/scratch.pptx b/Poster/scratch.pptx new file mode 100644 index 0000000..37d3719 Binary files /dev/null and b/Poster/scratch.pptx differ diff --git a/Rapport/scratch.pptx b/Rapport/scratch.pptx new file mode 100644 index 0000000..37d3719 Binary files /dev/null and b/Rapport/scratch.pptx differ diff --git a/Test_Ising2.ipynb b/Test_Ising2.ipynb index dd89057..8a4b378 100644 --- a/Test_Ising2.ipynb +++ b/Test_Ising2.ipynb @@ -12,7 +12,8 @@ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "%matplotlib inline\n", - "from IsingModel.Ising2 import IsingGrid" + "from IsingModel.Ising2 import IsingGrid\n", + "from IsingModel.util import *" ] }, { @@ -215,7 +216,7 @@ }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 7, "metadata": { "collapsed": true }, @@ 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duuSYYw7cjjpK5xMsFYENAAArR9vWdwUsk+OOSzZt6raDeeih5MEHkwcemN+2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\nAAAGzj57OAIbc9jAXMxLADD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IEREREZEwUKEchJgY+OMP2L073JmIiIiIyLGiQjkIMTHeby2/EBEREak4VCgHwV8o64E+\nERERkYpDhXIQoqO93yqURURERCoOFcpB8BfKWnohIiIiUnGoUA5CtWpQo4ZmlEVERMqzuXPn4vF4\n2Lx5c7hTKTGPx8NNN90Usv42bdqEx+PhmWeeyW1LTU3F4yl+Kfnss8/SokULqlSpQp06dUKRZshV\nCncCx4u6dVUoi4iIlGdmhpmFO43jhpkVu1Beu3YtI0eOpF+/ftx+++1ERkaGOLvQUKEcpNhYLb0Q\nERER8Rs3bhy33357sa59//33cc7x8MMPc+qpp4Y4s9DR0osgxcZqRllERETEz+PxUKVKlWJdu23b\nNgBq1aoVypRCToVykLT0QkREpGJ6/PHHad26NdWqVaNBgwbccMMNZGVlHRb30ksv0b59eyIjIznh\nhBMYNmwYP/30U56Yyy+/nKioKDZs2EDv3r2pWbMmDRo04J577skTd+qpp3LBBRccNsaBAweIjo7m\nuuuuCyr3efPm0bx5c6pXr0779u358MMPD4v56aefuOKKK6hfvz7VqlWjdevWzJkzp9C+j7RG+bnn\nnsv971C3bl2Sk5P58ccf89xbamoqACeccAIej4cJEyYEdT/HWpkolM2sipl9aWY5ZtY237l4M1tg\nZr+Z2VYzm2Jmnnwxbc1suZn9bmabzGxsAWN0M7N0M9tvZt+Z2Yii5KilFyIiIhVPamoqN9xwAyef\nfDJTp05l8ODBzJo1i969e5OdnZ0bN3fuXIYMGULlypWZNGkSo0aN4tVXX6VLly7sDni1r5mRk5ND\nnz59OPHEE7n//vtp374948ePzy0eAYYOHcqiRYvYtWtXnnzeeOMN9u7dy7BhwwrN/f333yclJYVh\nw4Zxzz33sHPnTvr27cuaNWtyY37++Wc6dOjAu+++y0033cT06dNp0qQJV155JdOnTz9q/wWt6Z44\ncSIjRoygWbNmTJs2jZSUFJYtW8bZZ5+d+9/h4Ycfzv0lYNasWTz33HNceOGFhd5PWDjnwv4BHgLe\nArKBtgHtHmA1sBhoA/QGfgbuDYiJAv4LPA20AC4GfgOuCohJAPYCU4BmwGjgENCzkLwSAZeenu7u\nvtu5+vWdiIhIhZaenu78/zaWN3PnznUej8dt2rTJOefcL7/84qpWrer69u2bJ+6xxx5zHo/HzZ07\n1znn3KFDh1xcXJxr166dO3DgQG7cggULnJm51NTU3LbLL7/ceTwed/PNN+fps3///q5atWpux44d\nzjnnvvvuO2dmbtasWXniBgwY4Bo1alTovZiZ83g87osvvsht27x5s6tevbobNGhQbtuVV17pGjRo\n4H799dc81ycnJ7vatWu7/fv3O+ec27hxozMz9/TTT+fGpKamOo/Hk3u8adMmV6lSJTdp0qQ8fX3z\nzTeucuXK7r777jvsWv/9Hkkwf9/8MUCiC3GNGvaH+cysL9ATGAT0y3e6N9AcOMc5tx1YbWbjgElm\nluqc+wMYClQGrvQdZ5rZ6cAYYLavn+uA9c65W3zHa82sM5ACvBNMnnXremeUnQM9ECsiIlK4fYf2\n8e32b0t9nOaxzYmsHPpdE5YuXcqhQ4e4+eab87RfffXV3HHHHSxYsIARI0bw+eef8/PPPzNhwoQ8\na3b79etH8+bNWbBgAePHj8/Tx+jRo/Mc33DDDSxcuJClS5dy8cUX06RJEzp06MDzzz/PqFGjAPj1\n1195++23ue2224LK/6yzzuJPf/pT7nF8fDznn38+b731Fs45zIxXX32VIUOGkJ2dzY6A/3Xeq1cv\nXnjhBTIyMujUqVNQ473yyis457jooovy9FWvXj2aNGnCe++9F3TuZUVYC2UziwOeAAYAvxcQ0hFY\n7SuS/RYDM4BWwCpfzHJfkRwYc4uZRTvnsnwxS/P1vRiYFmyusbFw6BDs2QNlfN25iIhImfDt9m9J\neiKp1MdJH5VO4omJIe9306ZNADRt2jRPe+XKlWnUqFHu+U2bNmFmh8UBNG/enBUrVuRp83g8NGrU\nKE9b06ZNcc6xcePG3Lbhw4dz4403smXLFuLj43nxxRf5448/GDp0aFD5n3baaYe1NW3alH379vHL\nL79gZuzatYsnnniCWbNmHRZrZvz8889BjQXw/fffk5OTU+C4ZlbsB//CKdwzynOAx51zX5jZKQWc\nrw9sy9e2LeDcKt/3+qPEZB2ln1pmVtU5d6CwRGNjvd/bt6tQFhERCUbz2Oakj0o/JuOUR5dccgkp\nKSk8//zz3HbbbTz//PO0b9+eJk2ahKT/nJwcwLseesSIgh/datu2bYHtR+rP4/Hw9ttvF/iQX82a\nNYuXaBiFvFA2s/uAW48S4vCuJe4D1AQm+y8NdSqh7KxuXe/3jh2Q75dAERERKUBk5chSmek9Vk45\nxTuHt3btWhISEnLbDx06xIYNG+jZs2dunHOOtWvX0q1btzx9rF27Nrcfv5ycHNavX59n5nXt2rUA\necapXbs25513Hs8//zyXXnopK1asKPQBu0Dr1q07rG3t2rW5u3I454iKiiI7O5vu3bsH3e+RNG7c\nGOccCQkJBc4qH49KY9eLB/CuKz7SpwWwATgH6AQcMLNDgP+n+bmZ+fck2QrE5es/LuDc0WJcEDG7\ng5lNTklJYezYAcAAbrxxAAMGDCAtLa2wy0REROQ4du6551K5cuXDitPZs2eze/du+vfvD0D79u2p\nV68eM2fO5NChQ7lxixYtIjMzMzcu0KOPPnrYcZUqVejRo0ee9mHDhvHNN98wduxYKlWqxJAhQ4LO\nf+XKlXzxxRe5x1u2bOGNN96gd+/euW/VGzRoEK+88grffPPNYddvL+K+uBdeeCEej4e77767wPM7\nd+4sUn8FSUtLY8CAAXk+KSkpJe73SEI+o+yc2wEUupGamd0I3BnQdBLedcMXA5/52lYCd5hZbMA6\n5V54l1OsCYi518winHPZATFrfeuT/TF986XQy9deqGnTptGiRSKRkTB6NASxI4uIiIgc52JjY7n9\n9tuZMGECffr0YcCAAXz77bfMmDGDM888k8suuwyASpUqMXnyZK644gq6du1KcnIyW7duZfr06TRq\n1OiwhwGrVq3K22+/zeWXX06HDh1YuHAhixYt4s4776Su/39h+5x33nnUrVuXl156iX79+hHrXwsa\nhNatW9OnTx9uvPFGqlSpwowZMzCzPNvQTZo0iffff58OHTpw9dVX07JlS3bu3El6ejrvvvtukYrl\nRo0ace+993LHHXewYcMGBg4cSFRUFOvXr+e1117jmmuuYcyYMUH3V5Dk5GSSk5PztGVkZJCUVDpr\n4cO2Rtk592PgsZn9hne5xHrnnH937iV4C+JnzexW4ETgHuBR55z/V7Z5wF3AU2Y2Ge82cjcBfw3o\nfiYw2nf+KaAHMJjDd9k4ourVITJSeymLiIhUJOPHj6devXo8+uijjBkzhjp16nDttdcyceJEIiIi\ncuNGjBhBjRo1mDRpErfddhs1atRg0KBBTJo06bC3z1WqVIm3336ba6+9lltuuYWoqChSU1MZN27c\nYeNXrlyZIUOGMGPGDIYPHx503mZGt27d6NixI6mpqWzZsoVWrVrxzDPP0Lp169y4evXq8dlnnzFh\nwgTmz5/PjBkzqFu3Lq1atWLKlCmH9VnQOIFuvfXW3D2U/S8RiY+Pz/1F43hjzrtfcNj5HuZbD5zu\nnPsqoD0e7y4X3fDujzwXuN05lxMQ0xp4DDgD2A5Md849kK//rnh3uWgJ/AhMcM49W0hOiUB6eno6\niYmJnHKKdzb53ntLerciIiLHJ//snf/fRimakSNH8sorr+R5CUlhxowZw1NPPcXWrVupVq1aKWZX\n9gTz9y1gRjnJOZcRyvHDvetFLufcJiCigPYtwOGLe/LGfA2cXUjMcqBE8/J6jbWIiIgcSwcOHOC5\n555j8ODBFa5ILgvKTKF8PNBrrEVERORY+OWXX3jnnXd4+eWX2blzJzfddFO4U6qQVCgXQWws/Pe/\n4c5CREREjmcFrfXNb82aNQwdOpS4uDgeeeSRIu1nLKGjQrkI6taF1avDnYWIiIgcr+bMmcOcOXMK\njTv77LNzXwgi4VMa+yiXW1p6ISIiIlJxqFAugthY78N8ZWSjEBEREREpRSqUi6BuXTh0CPbsCXcm\nIiIiIlLaVCgXgf9lOFp+ISIiIlL+qVAuAn+hrL2URURERMo/7XpRBP7Xr2tGWUREKrrMzMxwpyAV\nQLj/nqlQLgJ/oawZZRERqahiY2OJjIxk6NCh4U5FKojIyEhi/f9b/xhToVwEkZFQvboKZRERqbga\nNmxIZmYm2/WPoRwjsbGxNGzYMCxjq1AuIu2lLCIiFV3Dhg3DVriIHEt6mK+I/Hspi4iIiEj5pkK5\niOrWVaEsIiIiUhGEvVA2s/PM7BMz22dmO83s1Xzn481sgZn9ZmZbzWyKmXnyxbQ1s+Vm9ruZbTKz\nsQWM083M0s1sv5l9Z2YjipOvll6IiIiIVAxhLZTNbBDwDPAk0AY4C5gXcN4DLMS7lrojMAK4HJgQ\nEBMFLAY2AInAWCDVzK4KiEkA3gKWAe2Ah4HZZtazqDlr6YWIiIhIxRC2h/nMLAJ4CPibc25uwKlv\nA/7cG2gOnOOc2w6sNrNxwCQzS3XO/QEMBSoDV/qOM83sdGAMMNvXz3XAeufcLb7jtWbWGUgB3ilK\n3lp6ISIiIlIxhHNGORE4CcDMMszsJzNbaGatAmI6Aqt9RbLfYiAaaBUQs9xXJAfGNDOz6ICYpfnG\nXwx0KmrS/qUXzhX1ShERERE5noSzUG4EGDAe71KK84BfgffNLMYXUx/Ylu+6bQHnShpTy8yqFiXp\n2Fg4eBD27i3KVSIiIiJyvAl5oWxm95lZzlE+2WbWNGDse51zrznnvgBGAg64KBSphKCPw+jtfCIi\nIiIVQ2msUX4AmFNIzHp8yy6A3Jd4O+cOmtl6wL+L+VbgjHzXxgWc83/HFRDjgojZ7Zw7UEiupKSk\nEB3tXcWRleVtmzcvmTvvTC7sUhEREREJkbS0NNLS0vK0ZfmLs1IQ8kLZObcDKHQDNTNLBw4AzYCP\nfW2VgQRgky9sJXCHmcUGrFPuBWQBawJi7jWzCOdcdkDMWudcVkBM33wp9PK1F2ratGkkJiYCsGUL\nNGwISUnBXCkiIiIioZKcnExyct6JyoyMDJJKqTAL2xpl59weYCZwt5n19C3HmIF3JvglX9gSvAXx\ns769knsD9wCPOucO+WLmAQeBp8yspZkNAW4CHgwYbibQyMwmm1kzM7seGAxMLWreWnohIiIiUjGE\nbXs4n78Dh/DupVwd+BTo7p8Jds7lmFl/vAX0x8BvwFy8DwDii9ltZr2Ax4DPge1AqnPuyYCYjWZ2\nHjANbxH9I97t5PLvhFGoyEioXl0vHREREREp78JaKPuWStzi+xwpZgvQv5B+vgbOLiRmORCSefna\ntWHXrlD0JCIiIiJlVdhfYX08io5WoSwiIiJS3qlQLoaYGBXKIiIiIuWdCuViiI7+3zZxIiIiIlI+\nqVAuBs0oi4iIiJR/KpSLQTPKIiIiIuWfCuVi0IyyiIiISPmnQrkYVCiLiIiIlH8qlIvBv/TCuXBn\nIiIiIiKlRYVyMcTEQHY2/PZbuDMRERERkdKiQrkYoqO933qgT0RERKT8UqFcDDEx3m+tUxYREREp\nv1QoF4O/UNaMsoiIiEj5pUK5GPxLLzSjLCIiIlJ+qVAuBi29EBERESn/VCgXQ2QkRERo6YWIiIhI\neRbWQtnMmpjZa2b2i5llmdmHZtYtX0y8mS0ws9/MbKuZTTEzT76Ytma23Mx+N7NNZja2gLG6mVm6\nme03s+/MbETx89ZLR0RERETKu3DPKC8AIoBuQCKwCnjLzOoB+ArihUAloCMwArgcmODvwMyigMXA\nBl8fY4FUM7sqICYBeAtYBrQDHgZmm1nPYJLM/CXzsDb/S0dEREREpHwKW6FsZnWB04BJzrlvnHM/\nALcBkUBrX1hvoDlwmXNutXNuMTAOGG1mlXwxQ4HKwJXOuUzn3IvAdGBMwHDXAeudc7c459Y65x4D\nXgZSgsl18orJ5LicPG2aURYREREp38JWKDvndgDfAsPNLNJX+F4HbAPSfWEdgdXOue0Bly4GooFW\nATHLnXNj+5g6AAAgAElEQVR/5ItpZmbRATFL86WwGOgUTK6rt63mmVXP5GmLidGMsoiIiEh5Fu6l\nFz3xLpfYA/wO/BXo45zzl6D18RbOgbYFnCtpTC0zq1pYkr1P682tS29l1/7/TSFHR2tGWURERKQ8\nC3mhbGb3mVnOUT7ZZtbUF/443oL1z8AZwGt41yjHhSKVEPQBwM0dbmbfoX2Mf298bpuWXoiIiIiU\nb5UKDymyB4A5hcSsN7MeQD8gxjn3m6/9BjPrhfehvSnAVrwFdCB/Eb014Dt/YR0HuCBidjvnDhSS\nK/eNu4/47HimPz2dVQ+tolbVWhw6lExWVnJhl4qIiIhIiKSlpZGWlpanLasU18KGvFD2rT3eUVic\nmVXHW8zm5DuVw/9mulcCd5hZbMA65V5AFrAmIOZeM4twzmUHxKwNWMKxEuibb5xevvZCTZs2jdbt\nWtNuZjtyInN4/fLXmTDBWLUqmKtFREREJBSSk5NJTs47UZmRkUFSUlKpjBfONcorgV3AM759kJuY\n2f1AAt5t4wCW4C2In/XF9AbuAR51zh3yxcwDDgJPmVlLMxsC3AQ8GDDWTKCRmU02s2Zmdj0wGJga\nbLJVIqrwSN9H+HDzh6R9nabt4URERETKuXDvetEHqIl3f+N/A2cBA5xzq30xOUB/IBv4GHgGmAuM\nD+hnN97Z4QTgc+B+INU592RAzEbgPOBc4Eu828Jd6ZzLvxPGUZ3b6FwGtxzM35f8naq1drNvHxw6\nVPh1IiIiInL8KY01ykFzzmVw+JKI/DFb8BbLR4v5Gji7kJjlQInn5af2mkqzR5vxwcGpQCpZWRAb\nW9JeRURERKSsCff2cMed+Oh4rkq8ird3PgaVftfOFyIiIiLllArlYri5483sObQT2j2jQllERESk\nnFKhXAyNajeizymD4KwH+XVX/k07RERERKQ8UKFcTH89829Qdx1Lt7wZ7lREREREpBSoUC6m7k07\nwKbOzN/2YOHBIiIiInLcUaFcTJUqQbUv/sa6Ax/y6Y+fhjsdEREREQkxFcolUHfHX6jjmvDgSs0q\ni4iIiJQ3KpRLIKZWBO32jeGVzFfY8OuGcKcjIiIiIiGkQrkEYmLgxJ+HU7tabR765KFwpyMiIiIi\nIaRCuQSio+G3XZGMPmM0T37xJL/+/mu4UxIRERGREFGhXAIxMbBrF4w+czR/5PzBrPRZ4U5JRERE\nREJEhXIJxMRAVhbUq1GP4e2GM/3T6RzMPhjutEREREQkBFQol0B0NLmvsB7TaQz/3ftf5q2eF96k\nRERERCQkVCiXgH9GGaB5bHMGNh/IuPfGsefAnvAmJiIiIiIlpkK5BKKjvYVyTo73eFrvaez8fSd3\nvntneBMTERERkRIrtULZzO4wsxVm9puZ7TxCTLyZLfDFbDWzKWbmyRfT1syWm9nvZrbJzMYW0E83\nM0s3s/1m9p2ZjSgg5iIzy/T1s8rM+pb0HmNivEXy3r3e44SYBCZ2n8ijnz3Kyi0rS9q9iIiIiIRR\nac4oVwZeBGYUdNJXEC8EKgEdgRHA5cCEgJgoYDGwAUgExgKpZnZVQEwC8BawDGgHPAzMNrOeATFn\nAfOAfwJ/Al4HXjOzliW5weho77d/+QXAjWfeSPuT2nP1m1frwT4RERGR41ipFcrOubudcw8Dq48Q\n0htoDlzmnFvtnFsMjANGm1klX8xQvAX3lc65TOfci8B0YExAP9cB651ztzjn1jrnHgNeBlICYm4C\nFjnnpvpi7gIygBtKco8xMd5v/wN9ABGeCGYPmM3aHWuZ/NHkknQvIiIiImEUzjXKHYHVzrntAW2L\ngWigVUDMcufcH/limplZdEDM0nx9LwY6BRx3CiKmyPyFcuCMMkDbuLbcctYt3PvhvWT+klmSIURE\nREQkTMJZKNcHtuVr2xZwrqQxtcysaiEx9SkB/9KLwBllv3FnjyMhJoGr37yaHJdTkmFEREREJAyK\nVCib2X1mlnOUT7aZNS2tZANTOQZjFOpIM8oA1SpV44n+T7BiywqeSH/i2CYmIiIiIiVWqfCQPB4A\n5hQSsz7IvrYCZ+Rriws45/+OKyDGBRGz2zl3oJCYrQQhJSWFaP/0sU9ycjKXXJJM5coFzygDnJ1w\nNlcnXs0t79zCX5r+hQa1GgQznIiIiIgUIC0tjbS0tDxtWQXNWIZIkQpl59wOYEeIxl4J3GFmsQHr\nlHsBWcCagJh7zSzCOZcdELPWOZcVEJN/q7devvbAsXrgfRDQr2e+mCOaNm0aiYmJBZ6LiTlyoQww\npecU3vzuTW5cdCOvDnk1mOFEREREpADJyckkJyfnacvIyCApKalUxivNfZTjzawdcAoQYWbtfJ8a\nvpAleAviZ317JfcG7gEedc4d8sXMAw4CT5lZSzMbgncHiwcDhpoJNDKzyWbWzMyuBwYDUwNiHgb6\nmNkYX0wqkAQ8WtL7DHw7X4Hnq8XwYK8Hmf/tfO2tLCIiInIcKc2H+Sbg3YJtPFDT9+cMvAUqzrkc\noD+QDXwMPAPM9cXji9mNd3Y4AfgcuB9Idc49GRCzETgPOBf4Eu+2cFc655YGxKwELgVG+WIuBM53\nzvlnrostOvroM8oAl7S+hDb12vB/7/1fSYcTERERkWOkqGuUg+acGwmMLCRmC95i+WgxXwNnFxKz\nHF8BfpSYV4BXjhZTHIXNKAN4zMM959zDwBcG8u6Gd+l+avdQpyEiIiIiIRbO7eHKhWBmlAEGNBvA\nGSedwZ3v3olzrvQTExEREZESUaFcQsHMKAOYGfd2v5dPfvyEBesWlH5iIiIiIlIiKpRLKNgZZYCe\njXrS9ZSujHtvnF5CIiIiIlLGqVAuocK2hwtkZkzsPpEvt37JK2tCvlxaREREREJIhXIJBbv0wq9z\nw870Oa0Pd71/F9k52YVfICIiIiJhoUK5hKKjYf9+OHCg8Fi/e8+5l2+3f8tzXz1XeomJiIiISImo\nUC6hmBjvd1FmlZNOSuKC5hdw9wd3czD7YOkkJiIiIiIlokK5hKKjvd/BrlP2u+ece9i4ayNPffFU\n6JMSERERkRJToVxCxZlRBmhVrxWXtrmUCR9M4MfdP4Y+MREREREpERXKJVTcGWWA+3rcR5WIKvz5\nqT+zdvva0CYmIiIiIiWiQrmE/DPKxSmU46PjWXHFCmpWqUnnOZ35/KfPQ5uciIiIiBSbCuUSqlUL\nzIq+9MKvQa0GfDjyQ06rcxrnPH0Oy9YvC22CIiIiIlIsKpRLyOOBqKjizSj71aleh6XDltK5YWf6\nzevHy2teDl2CIiIiIlIsKpRDoKgvHSlIjSo1eP2S1xnUYhAXv3QxT6Q/EZrkRERERKRYKoU7gfIg\nOrpkM8p+VSKq8NyFz1G3el2ueesaqleqzrB2w0resYiIiIgUWanNKJvZHWa2wsx+M7OdBZxva2bz\nzGyzme0zs2/M7KYjxC03s9/NbJOZjS0gppuZpZvZfjP7zsxGFBBzkZll+vpZZWZ9Q3WvoZhR9vOY\nh+l9p3P5ny5n1FujyPhvRmg6FhEREZEiKc2lF5WBF4EZRzifBGwDLgNaAhOB+8zsen+AmUUBi4EN\nQCIwFkg1s6sCYhKAt4BlQDvgYWC2mfUMiDkLmAf8E/gT8Drwmpm1DMF9EhMTmhllPzNjxnkzaHVC\nKy584UK279seus5FREREJCilVig75+52zj0MrD7C+TnOuRTn3IfOuY3OuXnAHODCgLCheAvuK51z\nmc65F4HpwJiAmOuA9c65W5xza51zjwEvAykBMTcBi5xzU30xdwEZwA2huNdQLb0IVK1SNV4d8iq/\nHfqN5FeS+SPnj9AOICIiIiJHVdYe5osGApdpdASWO+cCq8TFQDMziw6IWZqvn8VAp4DjTkHEFFso\nl14EahjdkBcGv8C7G97lzmV3hn4AERERETmiMlMo+5ZHXAzMCmiuj3d5RqBtAeeOFlPLzKoWElOf\nECiNGWW/7qd2Z8q5U5jy8RRe+ual0hlERERERA5TpELZzO4zs5yjfLLNrGlRkzCz1sBrQKpzLpg3\nblhRxyhNpTWj7Dem0xguaX0JI18fydc/f116A4mIiIhIrqJuD/cA3nXER7O+KB36HqhbCsx0zt2X\n7/RWIC5fWxzgfOeOFrPbOXegkJitBCElJYXo6Og8bcnJySQnJwPeGeXduyEnx/sCklAzM2b/ZTad\nfu7EBS9cwGdXfUbt6rVDP5CIiIhIGZaWlkZaWlqetqxSnK0sUqHsnNsB7AjV4GbWCu9uFXN8D9jl\ntxK418winHPZvrZewFrnXFZATP6t3nr52gP76YH3QUC/nvlijmjatGkkJiYe8XxMDDgHe/Z4i+bS\nUKNKDeYPmc8Z/zyDPz/1Z+YPmU+z2GalM5iIiIhIGRQ4UemXkZFBUlJSqYxXmvsox5tZO+AUIMLM\n2vk+NXznWwPv4X2o7iEzi/N9YgO6mQccBJ4ys5ZmNgTvDhYPBsTMBBqZ2WQza+bbXm4wMDUg5mGg\nj5mN8cWk4t2e7tFQ3GtMjPe7tNYp+zWu05iPr/wYgDP+eQbzM+eX7oAiIiIiFVhpPsw3Ae8WbOOB\nmr4/Z+AtUAEGAXXxbgH3U8DnM38HzrndeGeHE4DPgfvxrmN+MiBmI3AecC7wJd5t4a50zi0NiFkJ\nXAqM8sVcCJzvnFsTihv1zyKXdqEM0Dy2OZ9e9Sm9T+vNhS9eyB3L7iA7J7vwC0VERESkSErtFdbO\nuZHAyKOcvxu4O4h+vgbOLiRmOf8rwI8U8wrwSmHjFYd/Rrk0H+gLFFU1ihcHv8gDHz/Abctu4/Of\nPmfeoHnERsYWfrGIiIiIBKXMbA93PDuWM8p+ZsbYP4/lnWHv8MXWL0h6IkmvuxYREREJIRXKIeAv\nlI/VjHKg7qd2J31UOvVq1KPLnC4sXLfw2CchIiIiUg6pUA6BatW8n2M5oxyoYXRDPrj8A85tdC4D\n0gYwO2N2eBIRERERKUdUKIdIab6dLxiRlSN59eJXGZU0iqvfvJrx743HORe+hERERESOc6X2MF9F\nU9pv5wtGhCeCx/o9RsPohty+7Ha27N7CrP6zqBxRObyJiYiIiByHVCiHSLhnlP3MjNs638bJtU7m\nitev4Kc9P/HSRS8RVTUq3KmJiIiIHFe09CJEysKMcqChbYey6LJFrPxxJR2f7Mj7G98Pd0oiIiIi\nxxUVyiFSVmaUA/Vo1IMVV6ygVtVanPP0OQx5eQibszaHOy0RERGR44IK5RApazPKfq3rtWbFFSt4\nZuAzLN+0nOaPNueeD+7h90O/hzs1ERERkTJNhXKIxMSUvRllP495GNZuGN/d8B03nnkj9yy/h5aP\nt+SVNa9oZwwRERGRI1ChHCJlcelFflFVo5jcczJfX/81LU9oyeCXBtN5Tmc+2vxRuFMTERERKXNU\nKIeIf+nF8TBB27RuUxZcuoAlQ5ew/4/9dJnThQFpA/j656/DnZqIiIhImaFCOUSio+HgQdi/P9yZ\nBK9n4578++p/kzYojW9++YZ2M9sx8vWReuBPREREBBXKIRMT4/0uiw/0HY3HPFzS+hIyR2cyvc90\nFq5bSJNHmjDk5SEs+G4Bh7IPhTtFERERkbBQoRwi0dHe77K+TvlIqkRUYfSZo/n+xu/5R/d/kPlL\nJv3T+tNgagNufvtm0n9K14N/IiIiUqGUWqFsZneY2Qoz+83MdhYSW8fMfjSzbDOrle9cWzNbbma/\nm9kmMxtbwPXdzCzdzPab2XdmNqKAmIvMLNPXzyoz61vyu/yf43VGOb+oqlH87ay/8dV1X/HlNV8y\nrO0wXvjmBdr/sz2tZ7Rm4vKJfL/z+3CnKSIiIlLqSnNGuTLwIjAjiNgngS/zN5pZFLAY2AAkAmOB\nVDO7KiAmAXgLWAa0Ax4GZptZz4CYs4B5wD+BPwGvA6+ZWcti3FeB/IXy8TqjXJB29dvxYO8H2ZKy\nhUWXLeJP9f/EfR/dR5NHmpD0RBJTVkxh466N4U5TREREpFRUKq2OnXN3AxQ0uxvIzK4DooF7gPyz\nvEPxFtxXOuf+ADLN7HRgDDDbF3MdsN45d4vveK2ZdQZSgHd8bTcBi5xzU33Hd/kK6RuA64t5i3kc\n70svjqaSpxJ9TutDn9P6sO/QPhauW8i/vv4X498fz61Lb6VDgw70b9qfTid34swGZxJVNSrcKYuI\niIiUWKkVysHwzej+H3AmcFoBIR2B5b4i2W8xcIuZRTvnsnwxS/NdtxiYFnDcCXiwgJjzS5B+HjVr\ngsdz/C+9KExk5UgGtxzM4JaD2XNgD29+9yYvfvMiD3z8AFkHsvCYhzb12tDp5E50iu9Ej1N70KBW\ng3CnLSIiIlJkYSuUzawK3uUQf3fO/cfMCiqU6wPr87VtCziX5fveVkBMLTOr6pw7cJSY+iW4hTw8\nHqhVq3zOKB9JVNUoLm1zKZe2uZQcl0PmL5ms/HElK7es5INNHzAzfSZVIqowpuMY7uhyh2aaRURE\n5LhSpELZzO4Dbj1KiANaOOe+C6K7ScAa51yav/t830dNJYiYY87/0pGKyGMeWtVrRat6rbgq0buE\nfOfvO3nk00eYtGIST696mknnTmJo26F4TJutiIiISNlX1BnlB4A5hcTknwE+knOA1mZ2ke/YfJ9f\nzGyib43zViAu33VxeAvyrb7jI8Xs9s0mHy1mK0FISUkh2r8I2Sc5OZnk5OQ8bTExFWtGuTB1qtdh\nfLfxjDx9JGPfGcuI10bw+L8fZ3rf6ZzZ4MxwpyciIiLHmbS0NNLS0vK0ZZXiLKWV9t64vof5pjnn\n6uRrPxWoHtB0Jt7dLzrhfThvu5ldC9wLxDnnsn3X/QMY6Jxr6TueBPR1zrUL6HseEOOc6+c7/hdQ\n3Tl3fkDMCmCVc+6ID/OZWSKQnp6eTmJiYqH32r071KsH//pXoaEV0vJNy7lp0U2s2raKIa2G0C2h\nG+3i2tEmrg01q9QMd3oiIiJyHMrIyCApKQkgyTmXEcq+S22NspnFA3WAU4AIM/MXst87535zzm3I\nF38C3hnlb51zu33N84C7gKfMbDLQBu8OFn8NuHQmMNp3/imgBzAY6BcQ8zDwvpmNARYAyUAScHWo\n7hegWTNYsSKUPZYvXU/pSvqodJ784kke+ewRXl7zMtkuG8NoXKcx7eLa0f6k9txw5g0qnEVERCTs\nSvNhvgnA8IBjf4V/DrD8CNfkmd52zu02s17AY8DnwHYg1Tn3ZEDMRjM7D+8uFzcBP+LdTm5pQMxK\nM7sUmOj7rAPOd86tKcH9HaZtW3jySTh4EKpUCWXP5UeEJ4JRSaMYlTSKA38cYM0va1i1bRWrtq7i\nq5+/YsIHE1i4biELL1uoYllERETCqtSXXhzPirr0YsUK6NwZvvoK2rQp/fzKo5VbVtLruV4knZjE\ngksXUKNKjXCnJCIiImVYaS690PYDIdS6tff7q6/Cm8fxrFN8J96+7G0+/+lz/pL2F/Yd2hfulERE\nRKSCUqEcQtHRcMopKpRL6s8N/8yiyxbx2X8+4/x/nc/vh34Pd0oiIiJSAalQDrG2bVUoh0KXU7qw\n4NIFfLzlYwa+MJD9f+wPd0oiIiJSwahQDrG2bWH16nBnUT6cnXA2byW/xYebPuSCFy5QsSwiIiLH\nlArlEGvbFv7zH9ixI9yZlA/nnHoObya/yfsb36fLnC6s27Eu3CmJiIhIBaFCOcT8u11oVjl0ejTq\nwUcjP2LX/l0kPpHIM6ueQbu1iIiISGlToRxiTZpA1apapxxqSSclkTEqg0EtBjHitREMnT+U3Qd2\nF36hiIiISDGpUA6xSpWgVSsVyqUhqmoUcwfO5fkLn+fNtW/yp5l/4tMfPw13WiIiIlJOleab+Sos\nPdBXui5tcykdT+7Ipa9cSuc5nRnccjDN6jajUe1GNK7dmMZ1GhNXIw4zC3eqIiIichxToVwK2raF\nF1+E7GyIiAh3NuVTo9qN+HDkh0z6aBKLf1jM+xvfZ+verbnna1SuwZkNzuTOLnfS/dTuKppFRESk\nyFQol4I2bWDfPli/3rtmWUpH5YjKjDt7HOPOHgfAbwd/Y/2v6/nh1x/4fuf3vPDNC5z77Ll0PaUr\nE7pN4OyEs8OcsYiIiBxPtEa5FLRt6/3WOuVjq0aVGrSJa8PA5gP5+1l/57OrPuONS95gz4E9dHu6\nG92f7s5Hmz8Kd5oiIiJynFChXArq1YO4OBXK4WZm/KXZX0gflc78IfPZ+ftOuszpQo9nejBv9Tx+\nO/hbuFMUERGRMkyFcinRq6zLDjNjYPOBZFyTwcsXvcz+P/Zz2auXEfdAHENfHcqidYv4I+ePcKcp\nIiIiZYzWKJeStm3htdfCnYUE8piHQS0HMajlIDb8uoF5q+fx/OrneX7185wQeQJDWg2hX5N+dDml\nCzWr1Ax3uiIiIhJmpTajbGZ3mNkKM/vNzHYeJe5yM1tlZr+b2VYzeyTf+bZmttx3fpOZjS2gj25m\nlm5m+83sOzMbUUDMRWaW6etnlZn1Dc2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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -364,35 +353,42 @@ ], "source": [ "model = IsingGrid(100, 100)\n", - "model.constant_init(0,10,10)\n", + "model.constant_init(0,1,1)\n", "model.linear_factors = model.gibbs_sampling(model.random_grid(.55))[0]\n", - "plt.figure(figsize=(14,4))\n", + "plt.figure(figsize=(14,5))\n", "plt.subplot(131)\n", "plt.title('Potentials')\n", "plt.axis('off')\n", "plt.imshow(model.linear_factors, interpolation=\"nearest\", cmap=plt.get_cmap('winter'), vmin=-1, vmax=1)\n", "\n", - "elist = model.loopybelief()\n", + "_,LBPlist = model.loopybelief(damping=0.3)\n", "plt.subplot(132)\n", "plt.title('LBP')\n", "plt.axis('off')\n", "plt.imshow(model.mean_parameters, interpolation=\"nearest\", cmap=plt.get_cmap('winter'), vmin=-1, vmax=1)\n", "\n", + "MFlist = model.meanfields(np.zeros([model.height,model.width]))\n", "plt.subplot(133)\n", - "plt.plot(np.log10(np.absolute(np.array(elist-elist[-1]+1))))\n", + "plt.title('MF')\n", + "plt.axis('off')\n", + "plt.imshow(model.mean_parameters, interpolation=\"nearest\", cmap=plt.get_cmap('winter'), vmin=-1, vmax=1)\n", + "plt.show()\n", "\n", - "print(elist)\n", - "print(model.mean_parameters[0])" + "plt.figure(figsize=(8,3))\n", + "plt.plot(MFlist,label='meanfields')\n", + "plt.plot(LBPlist,label='loopy belief')\n", + "plt.legend()" ] }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [], "source": [ + "model = IsingGrid(100, 100)\n", "observation1 = np.zeros((model.height, model.width))\n", "observation2 = np.zeros((model.height, model.width))\n", "observation3 = np.zeros((model.height, model.width))\n", @@ -414,16 +410,16 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "data": { - "image/png": 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xXSyJZiB75Q+SPKCqHtlaOza5/yFJXpXko5ezrB25fZL3zO9srf3bEtayDh7a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\nunYaZAjC6ZMReMbUtcVkBkK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OGAgAAAAASewaegDMQXu55DfOnDx2c2f/nP2zHw9sV/f1\n2n49WxYMTKu7xMuSLrar77Vj2TCspu7/7WNqSuu4+gIsGDMDAQAAACAJYSAAAAAAJCEMBAAAAIAk\nSq3Df0u8r6of0CXXT+5ftm+8XfxYWAC19a3oe/dMHnvFeXMdCmO1xqZfV5+Zurag9AhkCO2+YRF6\nCC4oda2furYN3ZrTpv4AM1RjbdOaZmYgAAAAACQhDAQAAACAJISBAAAAAJCEnoFMave22NvpJ6iH\nIPNQO+0NLmv1BdRnaWHordRPXVsg7bqmRxOLoN1DUF1bGOpaP3XtBPX1D4xQn4AdpWcgAAAAALBO\nGAgAAAAASVgmzPFd0lkmfOFNk/vn7J/fWFhdN585uX/1Iyf3X3FesHgsp+qnrg2ouxTL0isWWXvJ\ncIRlwwNS1/qpazusb9mwugWcIMuEAQAAAIB1wkAAAAAASEIYCAAAAABJ6BnI1j3105P792n1DHzt\nR+Y7FpbbCy8Yb3+j0zPwXQ+b71jYFr2V+qlrc6RHIKuk3UNQ/8C5Utf6qWszpocgsIP0DAQAAAAA\n1gkDAQAAACAJYSAAAAAAJKFnINu3+67x9smdH+G3XzO5f/KR8fZph2Y3JoZzx+7x9l2dzxl++EWT\n+3e1WhgcOnl2Y2Jm9Fbqp67NWLu3kl5KrKp2/8AIPQRnTF3rp67NUV//wAh1D9iUnoEAAAAAwDph\nIAAAAAAkYZkw8/Hyj4+3T+r8uC+/br5jYWdcev7k/pHWTOQrz53vWJg7y6n6qWs7rLtkyhIpMrJs\neKbUtX7q2oD6lg2rh8AGLBMGAAAAANYJAwEAAAAgCWEgAAAAACShZyDzd8rh/uO3/JfjHzvjzp0d\nC5O+f7fjH7vXi/uve3DXzo6Fhaa3Uj91bQe0eyTpiQTHavcQ1D/whKlr/dS1BaKHILAJPQMBAAAA\ngHXCQAAAAABIwjJhFtvzb+w//oYPzWccq+qix/Ufv+rR8xkHS8dyqn7q2jZ0lz1Z6gRb114yHGHZ\n8Daoa/3UtQVlyTCwAcuEAQAAAIB1wkAAAAAASEIYCAAAAABJ6BkIwNT0Vuqnrm2BHoEwO3oITk1d\n66euLQk9BIHQMxAAAAAAaBEGAgAAAEASwkAAAAAASELPQACmprdSP3XtONq9jPQugvlp9xDUP3BD\n6lo/dW0J9fUPjFCHYYXpGQgAAAAArBMGAgAAAEASlgkDMDXLqfqpayPdJUqWJMHw2kuGIywbHlHX\n+qlrK6CvBm+2pBhYKpYJAwAAAADrhIEAAAAAkIQwEAAAAACS0DMQgKnprdQvbV3TIxCWjx6CEaGu\nbSZtXVtlegjCytIzEAAAAABYJwwEAAAAgCSEgQAAAACQhJ6BAExNb6V+qepau6+QHoGw/No9BBP1\nD1TX+qWqaxltVr/1EISlomcgAAAAALBOGAgAAAAASVgmDMDULKfqt9J1rbtUyNJgWF3tJcMRK71s\nWF3rt9J1jWP11XZLhmHhWSYMAAAAAKwTBgIAAABAEsJAAAAAAEhCz0AApqa3Ur+Vqmt6BAJHrXAP\nQXWt30rVNaanhyAsFT0DAQAAAIB1wkAAAAAASEIYCAAAAABJ6BkIwNT0Vuq39HWt3f9Hj0DgeNo9\nBJe8f6C61m/p6xo7Z7PfC/QQhMHpGQgAAAAArBMGAgAAAEASlgkDMDXLqfotXV3rLumxNBiYVnvJ\ncMTSLRtW1/otXV1jfvp+Z7BkGAZhmTAAAAAAsE4YCAAAAABJCAMBAAAAIAk9AwGYmt5K/Ra+rukR\nCMzakvUQVNf6LXxdY3HoIQiD0zMQAAAAAFgnDAQAAACAJISBAAAAAJCEnoEATE1vpX4LWdfafXr0\nCATmrd1DcAH7B6pr/RayrrH4Nvt9Qw9BmAk9AwEAAACAdcJAAAAAAEjCMmEApmY5Vb+FqGvdpTeW\nBgOLor1kOGIhlg2ra/0Woq6x/Pp+F7FkGHaMZcIAAAAAwDphIAAAAAAkIQwEAAAAgCT0DARganor\n9RukrukRCCyrBeghqK718/caM3H5dcc/dsn18xsHrBg9AwEAAACAdcJAAAAAAEhCGAgAAAAASegZ\nCMDU9FbqN7e61u4TqEcgsCraPQTn1D9QXevn7zVm7j3v7T/+5M/MZxywAvQMBAAAAADWCQMBAAAA\nIAnLhAGYmuVU/WZW19rLgiMsDQZWX3vJcMTMlg2ra/38vcbcHbr8+Md2HZnfOGAJWSYMAAAAAKwT\nBgIAAABAEsJAAAAAAEhi19ADAACOQ49AILvN3vdm1EMQGNjuSyf369ogw4BVZWYgAAAAACQhDAQA\nAACAJISBAAAAAJCEnoEAsEjafQL1CASY1Pe+qH8grI6zDk7un/2S8fatr57vWGAFmRkIAAAAAEkI\nAwEAAAAgiVJrHXoMUUoMPwgAtqzWKEOPYZFNVdfay4IjLA0G2K61PZP7UywbVtf6+XuNwV197fGP\nPX5nYroAABnYSURBVOem+Y0DlkCNtU1rmpmBAAAAAJCEMBAAAAAAkhAGAgAAAEASegYCMDW9lfr1\n1jU9AgHmY4oegupaP3+vsVDq2tAjgIWmZyAAAAAAsE4YCAAAAABJCAMBAAAAIAk9AwGYmt5K/Xrr\nmj43AMMoa8c9pK718/cagys9L8Ejl81vHLAE9AwEAAAAANYJAwEAAAAgiV1DDwAAVs7avsn9vfs2\nuhQA89Ru03DZns7B7j6wUGpr1eMdV0weO9CJNU49PPvxwJIzMxAAAAAAkhAGAgAAAEASwkAAAAAA\nSKLU6lviAQAAACADMwMBAAAAIAlhIAAAAAAkIQwEAAAAgCSEgQAAAACQhDAQAAAAAJIQBgIAAABA\nEsJAAAAAAEhCGAgAAAAASQgDAQAAACAJYSAAAAAAJCEMBAAAAIAkhIEAAAAAkIQwEAAAAACSEAYC\nAAAAQBLCQAAAAABIQhgIAAAAAEkIAwEAAAAgCWEgAAAAACQhDAQAAACAJISBAAAAAJCEMBAAAAAA\nkhAGAgAAAEASwkAAAAAASEIYCAAAAABJCAMBAAAAIAlhIAAAAAAkIQwEAAAAgCSEgQAAAACQhDAQ\nAAAAAJIQBgIAAABAEsJAAAAAAEhCGAgAAAAASQgDAQAAACAJYSAAAAAAJCEMBAAAAIAkhIEAAAAA\nkIQwEAAAAACSEAYCAAAAQBLCQAAAAABIQhgIAAAAAEkIAwEAAAAgCWEgAAAAACQhDAQAAACAJISB\nAAAAAJCEMBAAAAAAkhAGAgAAAEASwkAAAAAASEIYCAAAAABJCAMBAAAAIAlhIAAAAAAkIQwEAAAA\ngCSEgdBSSnl2KeVIKeURO3iba6WUI53zvlJK+Z1t3t7ppZS3lFJuHo31N3ZmpMfcz9ro9v/WLG4f\ngNlS0ybuR00DWHLq2sT9qGucEGEgU5vFm/CCqTO4ve5tHjmB+3l5RDwrIn4rIp4REb+7/aH12mjc\n21ZKubCUck0p5auj18+2CizATlLTtnV7qWtaKeVHSil7Syk3llK+W0q5pZRyXSnlZ3fi9gFOhLq2\nrdvLXtdOKaW8tZTy6VLKraWU/aWUT5VSLiql7NqJ+2Dx+MGyXTv9JpzNg6IpMttxfkT8Sa31ih0c\nzzy8OCLOiIj/HRH3HngsAG1q2onJVtOeEBEvioj3R8Tbo/l9+lkR8dFSyr+rtb5jwLEBRKhrJypb\nXTs1Ih4SEX8QEV+J5rH/44j4zYh4VDShJitGGAgDqLUeOoGr/3BEfGanxjJH59Zavx4RUUrZP/Rg\nANgZCWvaxyLivrXW7x49o5Ty2xHxqYi4PCKEgQBLLFtdq7V+L5rwr+3NpZTbI+J5pZRfr7V+e4Ch\nMUOWCTMzpZR7jaYbf7OUcmA01fhZG1zutFLK60opXyulHCylfK6U8oINLneklPKGUsrTRpc5UEq5\nqZTyM63L7Bld7gkbXP9po2OP3sLwTy+l/HYp5TullNtKKe8opZy9wW0+rpTy8VLK90spt5dSri2l\n/MQWnptj+lCUUs4qpby+9Tz8RSnlxaWUMjp+3qifxY9HxONHj+WuUsp9t/B4uvf/z0opN4zG/b1S\nyvtLKQ8+zsXvNVree9vo+Xh9KeXundv7udHtfW80rfxzpZQr25c5GgQCLCM1rfe5SVXTaq2fbQeB\no/PujIgPRsSPlFJOn/YxAMybutb73KSqaz2+Ovr3mOeW5WdmIDNRSjklIq6PiPtHxFXRTDd+UkS8\nvZRyVq31qtbFfz8izouIt0TEn0XEz0fEa0op96m1dgvNnoh4SkS8ISJ+EBHPjYgPlVIeVWv9f7XW\nfaWUr0fE0yPiA53rPj0i/rLWeuNmw4+IN0bE9yJibzTTxJ8bEfeNZtr30cf4zGiWB304miWwp0XE\nhRFxQynl4bXWr/Xcx8TU/VLKqRHx8Yg4JyLeFBFfj+bTmVdFs6T21yPis9FM0X796PjrRle/ZZPH\nM/ngSnlsNH+wfHH0+E6NiIsi4hOllEd0xl0i4pqI+HJEvCQifnp02bMj4t+Obu8novkZfioiLonm\n5/KAOPbTJYClpKapabG1mnZORNwxOgEsLHVNXYsN6lopZXdE3GN0n/8oIl4QzWvjL6d5DCyJWquT\n01SniHh2RNwVEY/oucyvji7zS63zTo6IP46I2yLi9NF5T4imJ8FLOte/JiIOR8T9WucdGd3mP2id\n96PR/NL9e63zrhydd2brvHtGxJ0RcckWHtuRiLgxIk5unf/C0X0/frR/ekR8NyKu7lz/XtEUpje1\nztsbEXd1LvfliPid1v7FEXF7RNy/c7lXjsb9dzvX/Z8n8PP7vxFxc0Sc1TrvYaPn+22dcR+JiPd1\nrv/G0XPxk52f9Q9NMYb97cfv5OTkNNRJTVPTTrS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xXSyJZiB75Q+SPKCqHtlaOza5/yFJXpXko5ezrB25fZL3zO9srf3bEtayDh7a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\nj/39I/O+x1YAgIlgZyAAAAAAFEIxEAAAAAAKoRgIAAAAAIWQGTgt5uX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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -431,7 +427,6 @@ } ], "source": [ - "model = IsingGrid(100, 100)\n", "model.constant_init(0,3,3)\n", "grid = np.zeros((model.height, model.width))\n", "#model.linear_factors = model.gibbs_sampling(model.random_grid(0.5))[0]/100\n", @@ -461,7 +456,7 @@ "plt.title('Mean field, obs1')\n", "plt.axis('off')\n", "plt.subplot(337)\n", - "mess_list1 = model.loopybelief(max_iter=max_iter_lb)\n", + "video1,mess_list1 = model.loopybelief(max_iter=max_iter_lb,update_order='cyclic')\n", "plt.imshow(model.mean_parameters, interpolation=\"nearest\", cmap=plt.get_cmap('winter'), vmin=-1, vmax=1)\n", "plt.title('Loopy belief, obs1')\n", "plt.axis('off')\n", @@ -473,7 +468,7 @@ "plt.title('Mean field, obs2')\n", "plt.axis('off')\n", "plt.subplot(338)\n", - "mess_list2 = model.loopybelief(max_iter=max_iter_lb)\n", + "_,mess_list2 = model.loopybelief(max_iter=max_iter_lb)\n", "plt.imshow(model.mean_parameters, interpolation=\"nearest\", cmap=plt.get_cmap('winter'), vmin=-1, vmax=1)\n", "plt.title('Loopy belief, obs2')\n", "plt.axis('off')\n", @@ -486,7 +481,7 @@ "plt.title('Mean field, obs3')\n", "plt.axis('off')\n", "plt.subplot(339)\n", - "mess_list3 = model.loopybelief(max_iter=max_iter_lb)\n", + "_,mess_list3 = model.loopybelief(max_iter=max_iter_lb)\n", "plt.imshow(model.mean_parameters, interpolation=\"nearest\", cmap=plt.get_cmap('winter'), vmin=-1, vmax=1)\n", "plt.title('Loopy belief, obs3')\n", "plt.axis('off')\n", @@ -496,7 +491,73 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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Xtc3Ozubf//43y5Yt46yzznLrfDNmzMBay5VXXlmhr6SkJNq2bcvChQvdjl2C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\n6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73dpheNWiy5udYuHkv8cfI8xmNpaLA/qMNh++O6pSXxp3xNje0M45zFMrjqTNp/9ya1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\n2xLgt8A0z/PWozztw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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure(figsize=(16,5))\n", + "plt.subplot(131)\n", + "plt.plot(mlist1,label='meanfield 1')\n", + "plt.plot(mess_list1,label='loopy belief 1')\n", + "plt.legend()\n", + "plt.subplot(132)\n", + "plt.plot(mlist2,label='meanfield 2')\n", + "plt.plot(mess_list2,label='loopy belief 2')\n", + "plt.legend()\n", + "plt.subplot(133)\n", + "plt.plot(mlist3,label='meanfield 3')\n", + "plt.plot(mess_list3,label='loopy belief 3')\n", + "plt.legend()" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "save_video('images/LBP2obs1',video1)" + ] + }, + { + "cell_type": "code", + "execution_count": 14, "metadata": { "collapsed": false, "scrolled": false @@ -505,10 +566,10 @@ { "data": { "text/plain": [ - "" + "" ] }, - "execution_count": 6, + "execution_count": 14, "metadata": {}, "output_type": "execute_result" }, @@ -516,7 +577,7 @@ "data": { "image/png": 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fmeGthoMFAAAAAN1Y9ELxAAAAADA1oRYAAAAA3RFqAQAAANAdoRYAAAAA3RFq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\nsI9+e1gE1q0/xm92nxv/rPcm+X+2OGed+uP/SPL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