{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Dynet tutorial: Visualizing the Mandelbrot fractal\n", "\n", "Here's a simple dynet program to get familiarized with some of the operations available by visualizing a fractal: the Mandelbrot set.\n", "\n", "The Mandelbrot set is defined as the set of complex numbers $c$ for which the sequence defined as \n", "\n", "\\begin{split}\n", "z_0&=0\\\\\n", "z_{n+1}&=z_{n}^2+c\\\\\n", "\\end{split}\n", "\n", "is bounded. You can read more about it in the [wikipedia entry](https://en.wikipedia.org/wiki/Mandelbrot_set)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First a few imports. I'm using one of the latest versions of dynet, but any release >2.0.3 should do the trick" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import dynet as dy\n", "# Plotting\n", "%matplotlib inline\n", "import matplotlib\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us declare all possible values of c we're testing for. We don't really need to bother with any $c$ such that $\\vert c\\vert>2$ because most of them will diverge at some points.\n", "\n", "Dynet doesn't have built-in complex numbers so we're going to represent those as 2d vectors " ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "# Resolution for the visualization\n", "N = 500\n", "# x and y coordinates\n", "x = np.linspace(-2.0, 1.0, N)\n", "y = np.linspace(-1.5, 1.5, N)\n", "# c values as a two lists of coordinates\n", "c_vals = np.stack(np.meshgrid(x, y), axis=0).reshape(2,-1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next thing we need to do is to code a `square` operation for complex numbers (as 2d vectors). Dynet will handle batching automatically so we don't need to explicitly consider the case when the input is batched and can treat it as a single vector" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "def square(complex_number):\n", " \"\"\"Square of a complex number (represented as a vector)\"\"\"\n", " # Retrieve real and imaginary part\n", " # z = a + bi\n", " a = complex_number[0] # This will pick the 1st sub-tensor along the 1st dimension\n", " b = complex_number[1]\n", " # z^2 = (a + bi)^2 = (a^2 - b^2) + (2ab)i\n", " a_2 = dy.square(a) - dy.square(b) # We can use the dy.square function for real numbers\n", " b_2 = 2*dy.cmult(a, b) # We use dy.cmult for component-wise multiplication of reals\n", " # Return the result as a vector by concatenating\n", " return dy.concatenate([a_2, b_2])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here comes the main loop. We're not doing any gradient descent here so there's not backward pass. Each iteration goes:\n", "1. Call `dy.renew_cg()` to garbage-collect the computation graph\n", "2. Add inputs to the computation graph with `dy.inputTensor`\n", "3. Write all our operations (builds the computation graph)\n", "4. Run the forward pass by calling `.npvalue()` on the output (all the computation is done here)\n", "5. Rinse and repeat" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/pmichel31415/.local/lib/python2.7/site-packages/ipykernel_launcher.py:27: RuntimeWarning: invalid value encountered in greater\n" ] } ], "source": [ "# Number of iterations. Increasing this number will make the border of the fractal more accurate\n", "# At our resolution, 25 is good enough\n", "n_iterations=25\n", "# Initial values z_0=0\n", "z_vals = np.zeros(c_vals.shape)\n", "# Keep track of whether each c value leads to divergence.\n", "# The default value is set to 2 * n_iterations so that points that never diverge have the highest value by a margin \n", "diverged = np.zeros(c_vals.shape[-1]) + 2*n_iterations\n", "# Now we start the iterative process of computing z_n\n", "for iteration in range(n_iterations):\n", " # Don't forget to renew the computation graph\n", " dy.renew_cg()\n", " # Input the current value of z_n in the computation graph.\n", " # Notice the `batched=True` argument so that z is an expression of dimension 2 and batch size N*N\n", " # z.dim() will return ((2,), N*N)\n", " z = dy.inputTensor(z_vals, batched=True)\n", " # Input c in the computation graph, batched as well\n", " c = dy.inputTensor(c_vals, batched=True)\n", " # Do the update\n", " z = square(z) + c\n", " # compute z's module (l2 norm of the vector)\n", " z_mod = dy.l2_norm(z)\n", " # Retrieve the module value (runs the forward pass).\n", " # This returns an array of shape (1, N*N): the batch size is the last dimension\n", " z_mod_vals = z_mod.npvalue().flatten()\n", " # Check for divergence (if |z|>2 then the sequence diverges for sure)\n", " diverged[z_mod_vals > 2]=iteration\n", " # Update z_vals by retrieving the update from the computation graph\n", " # This will not rerun the forward pass as z was already computed for z_mod\n", " z_vals = z.npvalue()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot the result!" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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Wtx1ms1XSfzjuZAhQkobLuMqRTL9Tb+IiMmfEMAvFas6oIYK/++U2ACCd2sc/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\nEEJcoFgihBBCCHHh/wcK0Xt/NnCFkAAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(10,10))\n", "plt.imshow(diverged.reshape((N,N)), cmap='plasma')\n", "_ = plt.axis('off')" ] } ], "metadata": { "kernelspec": { "display_name": "Python 2", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.6" } }, "nbformat": 4, "nbformat_minor": 2 }