Last active
February 28, 2023 16:18
-
-
Save jclosure/f667500319819a91296f97397f097786 to your computer and use it in GitHub Desktop.
Back propagation for gradient descent
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
{ | |
"cells": [ | |
{ | |
"cell_type": "code", | |
"execution_count": 3, | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"import random\n", | |
"import numpy as np\n", | |
"import matplotlib.pyplot as plt\n", | |
"%matplotlib inline" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 6, | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"def f(x):\n", | |
" return 3*x**2 - 4*x + 5" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 7, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"20.0" | |
] | |
}, | |
"execution_count": 7, | |
"metadata": {}, | |
"output_type": "execute_result" | |
} | |
], | |
"source": [ | |
"f(3.0)" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 8, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"array([-5. , -4.75, -4.5 , -4.25, -4. , -3.75, -3.5 , -3.25, -3. ,\n", | |
" -2.75, -2.5 , -2.25, -2. , -1.75, -1.5 , -1.25, -1. , -0.75,\n", | |
" -0.5 , -0.25, 0. , 0.25, 0.5 , 0.75, 1. , 1.25, 1.5 ,\n", | |
" 1.75, 2. , 2.25, 2.5 , 2.75, 3. , 3.25, 3.5 , 3.75,\n", | |
" 4. , 4.25, 4.5 , 4.75])" | |
] | |
}, | |
"execution_count": 8, | |
"metadata": {}, | |
"output_type": "execute_result" | |
} | |
], | |
"source": [ | |
"xs = np.arange(-5, 5, 0.25)\n", | |
"xs" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 11, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"array([100. , 91.6875, 83.75 , 76.1875, 69. , 62.1875,\n", | |
" 55.75 , 49.6875, 44. , 38.6875, 33.75 , 29.1875,\n", | |
" 25. , 21.1875, 17.75 , 14.6875, 12. , 9.6875,\n", | |
" 7.75 , 6.1875, 5. , 4.1875, 3.75 , 3.6875,\n", | |
" 4. , 4.6875, 5.75 , 7.1875, 9. , 11.1875,\n", | |
" 13.75 , 16.6875, 20. , 23.6875, 27.75 , 32.1875,\n", | |
" 37. , 42.1875, 47.75 , 53.6875])" | |
] | |
}, | |
"execution_count": 11, | |
"metadata": {}, | |
"output_type": "execute_result" | |
} | |
], | |
"source": [ | |
"ys = f(xs)\n", | |
"ys" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 12, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"[<matplotlib.lines.Line2D at 0x11186f8e0>]" | |
] | |
}, | |
"execution_count": 12, | |
"metadata": {}, | |
"output_type": "execute_result" | |
}, | |
{ | |
"data": { | |
"image/png": "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", | |
"text/plain": [ | |
"<Figure size 640x480 with 1 Axes>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"plt.plot(xs, ys)" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 13, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"name": "stdout", | |
"output_type": "stream", | |
"text": [ | |
"20.0\n", | |
"20.014003000000002\n" | |
] | |
} | |
], | |
"source": [ | |
"# nudge x up by h (as h approaches 0, etc.)\n", | |
"h = .001\n", | |
"x = 3.0\n", | |
"print(f(x))\n", | |
"print(f(x + h)) # we expect an increase" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 19, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"14.00000009255109" | |
] | |
}, | |
"execution_count": 19, | |
"metadata": {}, | |
"output_type": "execute_result" | |
} | |
], | |
"source": [ | |
"# how much did the function respond?\n", | |
"h = .00000001 # the smaller we get the closer we converge to 0, is reflected in the slope\n", | |
"x = 3.0\n", | |
"\n", | |
"# take diff and normalize to get slope\n", | |
"(f(x + h) - f(x)) / h" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 27, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"name": "stdout", | |
"output_type": "stream", | |
"text": [ | |
"d1 4.0\n", | |
"d2 4.0001\n", | |
"slope 0.9999999999976694\n" | |
] | |
} | |
], | |
"source": [ | |
"# rate at which differential will increase with respect to nudging a, b, or c\n", | |
"h = 0.0001\n", | |
"\n", | |
"a = 2.0\n", | |
"b = -3.0\n", | |
"c = 10.0\n", | |
"\n", | |
"# differentiate\n", | |
"\n", | |
"d1 = a*b + c\n", | |
"\n", | |
"# nudge\n", | |
"# a += h\n", | |
"# b += h\n", | |
"c += h\n", | |
"\n", | |
"d2 = a*b + c\n", | |
"\n", | |
"print('d1', d1)\n", | |
"print('d2', d2)\n", | |
"print('slope', (d2 - d1)/h)" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 29, | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"# note above that \n", | |
"# the differential with respect to a is b\n", | |
"# and the differential with respect to b is a\n", | |
"# c does not affect a or b, but simply scales the fn by h (which is added above)" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 80, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"Value(data=4.0)" | |
] | |
}, | |
"execution_count": 80, | |
"metadata": {}, | |
"output_type": "execute_result" | |
} | |
], | |
"source": [ | |
"import math \n", | |
"\n", | |
"class Value:\n", | |
"\n", | |
" def __init__(self, data, _children=(), _op='', label=''):\n", | |
" self.data = data\n", | |
" self._prev = set(_children)\n", | |
" self._op = _op\n", | |
" self.label = label\n", | |
" self.grad = 0.0\n", | |
" self._backward = lambda: None\n", | |
"\n", | |
" def __repr__(self) -> str:\n", | |
" return f\"Value(data={self.data})\"\n", | |
"\n", | |
" def __add__(self, other):\n", | |
" out = Value(self.data + other.data, (self, other), '+')\n", | |
" \n", | |
" # chain rule for +\n", | |
" def _backward():\n", | |
" self.grad += 1.0 * out.grad\n", | |
" other.grad += 1.0 * out.grad\n", | |
" \n", | |
" out._backward = _backward\n", | |
"\n", | |
" return out\n", | |
"\n", | |
" def __mul__(self, other):\n", | |
" out = Value(self.data * other.data, (self, other), '*')\n", | |
"\n", | |
" # chain rule for *\n", | |
" def _backward():\n", | |
" self.grad += other.data * out.grad\n", | |
" other.grad += self.data * out.grad\n", | |
"\n", | |
" out._backward = _backward\n", | |
"\n", | |
" return out\n", | |
"\n", | |
" def tanh(self):\n", | |
" x = self.data\n", | |
" t = (math.exp(2*x) - 1)/(math.exp(2*x))\n", | |
" out = Value(t, (self, ), label='tanh')\n", | |
"\n", | |
" # chain rule for tanh\n", | |
" def _backward():\n", | |
" self.grad += (1 - t**2) * out.grad\n", | |
"\n", | |
" out._backward = _backward\n", | |
"\n", | |
" return out\n", | |
"\n", | |
"\n", | |
" def backward(self):\n", | |
"\n", | |
" # topological order all of the children in the graph\n", | |
" topo = []\n", | |
" visited = set()\n", | |
" def build_topo(v):\n", | |
" if v not in visited:\n", | |
" visited.add(v)\n", | |
" for child in v._prev:\n", | |
" build_topo(child)\n", | |
" topo.append(v)\n", | |
" build_topo(self)\n", | |
"\n", | |
" # go one variable at a time and apply the chain rule to get its gradient\n", | |
" self.grad = 1\n", | |
" for v in reversed(topo):\n", | |
" v._backward()\n", | |
"\n", | |
"a = Value(2.0, label='a')\n", | |
"b = Value(-3.0, label='b')\n", | |
"c = Value(10.0, label='c')\n", | |
"\n", | |
"d = a * b + c\n", | |
"d" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 73, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"(Value(data=4.0), {Value(data=-6.0), Value(data=10.0)}, '+')" | |
] | |
}, | |
"execution_count": 73, | |
"metadata": {}, | |
"output_type": "execute_result" | |
} | |
], | |
"source": [ | |
"d, d._prev, d._op" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 74, | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"# just borrowing these for viz\n", | |
"\n", | |
"# brew install graphviz\n", | |
"# pip install graphviz\n", | |
"from graphviz import Digraph\n", | |
"\n", | |
"def trace(root):\n", | |
" nodes, edges = set(), set()\n", | |
" def build(v):\n", | |
" if v not in nodes:\n", | |
" nodes.add(v)\n", | |
" for child in v._prev:\n", | |
" edges.add((child, v))\n", | |
" build(child)\n", | |
" build(root)\n", | |
" return nodes, edges\n", | |
"\n", | |
"def draw_dot(root, format='svg', rankdir='LR'):\n", | |
" \"\"\"\n", | |
" format: png | svg | ...\n", | |
" rankdir: TB (top to bottom graph) | LR (left to right)\n", | |
" \"\"\"\n", | |
" assert rankdir in ['LR', 'TB']\n", | |
" nodes, edges = trace(root)\n", | |
" dot = Digraph(format=format, graph_attr={'rankdir': rankdir}) #, node_attr={'rankdir': 'TB'})\n", | |
" \n", | |
" for n in nodes:\n", | |
" dot.node(name=str(id(n)), label = \"{ %s | data %.4f | grad %.4f }\" % (n.label, n.data, n.grad), shape='record')\n", | |
" if n._op:\n", | |
" dot.node(name=str(id(n)) + n._op, label=n._op)\n", | |
" dot.edge(str(id(n)) + n._op, str(id(n)))\n", | |
" \n", | |
" for n1, n2 in edges:\n", | |
" dot.edge(str(id(n1)), str(id(n2)) + n2._op)\n", | |
" \n", | |
" return dot" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 75, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/svg+xml": "<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n<!-- Generated by graphviz version 7.1.0 (20230121.1956)\n -->\n<!-- Pages: 1 -->\n<svg width=\"824pt\" height=\"127pt\"\n viewBox=\"0.00 0.00 824.00 127.00\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n<g id=\"graph0\" class=\"graph\" transform=\"scale(1 1) rotate(0) translate(4 123)\">\n<polygon fill=\"white\" stroke=\"none\" points=\"-4,4 -4,-123 820,-123 820,4 -4,4\"/>\n<!-- 4594135200 -->\n<g id=\"node1\" class=\"node\">\n<title>4594135200</title>\n<polygon fill=\"none\" stroke=\"black\" points=\"318.5,-27.5 318.5,-63.5 505.5,-63.5 505.5,-27.5 318.5,-27.5\"/>\n<text text-anchor=\"middle\" x=\"328.5\" y=\"-41.8\" font-family=\"Times,serif\" font-size=\"14.00\"> </text>\n<polyline fill=\"none\" stroke=\"black\" points=\"338.5,-27.5 338.5,-63.5\"/>\n<text text-anchor=\"middle\" x=\"381\" y=\"-41.8\" font-family=\"Times,serif\" font-size=\"14.00\">data -6.0000</text>\n<polyline fill=\"none\" stroke=\"black\" points=\"423.5,-27.5 423.5,-63.5\"/>\n<text text-anchor=\"middle\" x=\"464.5\" y=\"-41.8\" font-family=\"Times,serif\" font-size=\"14.00\">grad 0.0000</text>\n</g>\n<!-- 4594137504+ -->\n<g id=\"node7\" class=\"node\">\n<title>4594137504+</title>\n<ellipse fill=\"none\" stroke=\"black\" cx=\"571\" cy=\"-72.5\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"571\" y=\"-68.8\" font-family=\"Times,serif\" font-size=\"14.00\">+</text>\n</g>\n<!-- 4594135200->4594137504+ -->\n<g id=\"edge3\" class=\"edge\">\n<title>4594135200->4594137504+</title>\n<path fill=\"none\" stroke=\"black\" d=\"M505.24,-61.36C515.15,-63.07 524.76,-64.72 533.41,-66.21\"/>\n<polygon fill=\"black\" stroke=\"black\" points=\"532.61,-69.62 543.05,-67.87 533.79,-62.72 532.61,-69.62\"/>\n</g>\n<!-- 4594135200* -->\n<g id=\"node2\" class=\"node\">\n<title>4594135200*</title>\n<ellipse fill=\"none\" stroke=\"black\" cx=\"253\" cy=\"-45.5\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"253\" y=\"-41.8\" font-family=\"Times,serif\" font-size=\"14.00\">*</text>\n</g>\n<!-- 4594135200*->4594135200 -->\n<g id=\"edge1\" class=\"edge\">\n<title>4594135200*->4594135200</title>\n<path fill=\"none\" stroke=\"black\" d=\"M280.28,-45.5C288.21,-45.5 297.43,-45.5 307.25,-45.5\"/>\n<polygon fill=\"black\" stroke=\"black\" points=\"307.04,-49 317.04,-45.5 307.04,-42 307.04,-49\"/>\n</g>\n<!-- 4594236672 -->\n<g id=\"node3\" class=\"node\">\n<title>4594236672</title>\n<polygon fill=\"none\" stroke=\"black\" points=\"2.5,-55.5 2.5,-91.5 187.5,-91.5 187.5,-55.5 2.5,-55.5\"/>\n<text text-anchor=\"middle\" x=\"14\" y=\"-69.8\" font-family=\"Times,serif\" font-size=\"14.00\">a</text>\n<polyline fill=\"none\" stroke=\"black\" points=\"25.5,-55.5 25.5,-91.5\"/>\n<text text-anchor=\"middle\" x=\"65.5\" y=\"-69.8\" font-family=\"Times,serif\" font-size=\"14.00\">data 2.0000</text>\n<polyline fill=\"none\" stroke=\"black\" points=\"105.5,-55.5 105.5,-91.5\"/>\n<text text-anchor=\"middle\" x=\"146.5\" y=\"-69.8\" font-family=\"Times,serif\" font-size=\"14.00\">grad 0.0000</text>\n</g>\n<!-- 4594236672->4594135200* -->\n<g id=\"edge5\" class=\"edge\">\n<title>4594236672->4594135200*</title>\n<path fill=\"none\" stroke=\"black\" d=\"M187.2,-57.13C197.1,-55.35 206.71,-53.63 215.36,-52.08\"/>\n<polygon fill=\"black\" stroke=\"black\" points=\"215.79,-55.55 225.02,-50.34 214.56,-48.66 215.79,-55.55\"/>\n</g>\n<!-- 4594234656 -->\n<g id=\"node4\" class=\"node\">\n<title>4594234656</title>\n<polygon fill=\"none\" stroke=\"black\" points=\"0,-0.5 0,-36.5 190,-36.5 190,-0.5 0,-0.5\"/>\n<text text-anchor=\"middle\" x=\"11.5\" y=\"-14.8\" font-family=\"Times,serif\" font-size=\"14.00\">b</text>\n<polyline fill=\"none\" stroke=\"black\" points=\"23,-0.5 23,-36.5\"/>\n<text text-anchor=\"middle\" x=\"65.5\" y=\"-14.8\" font-family=\"Times,serif\" font-size=\"14.00\">data -3.0000</text>\n<polyline fill=\"none\" stroke=\"black\" points=\"108,-0.5 108,-36.5\"/>\n<text text-anchor=\"middle\" x=\"149\" y=\"-14.8\" font-family=\"Times,serif\" font-size=\"14.00\">grad 0.0000</text>\n</g>\n<!-- 4594234656->4594135200* -->\n<g id=\"edge4\" class=\"edge\">\n<title>4594234656->4594135200*</title>\n<path fill=\"none\" stroke=\"black\" d=\"M189.9,-34.75C198.81,-36.29 207.43,-37.79 215.28,-39.14\"/>\n<polygon fill=\"black\" stroke=\"black\" points=\"214.57,-42.57 225.02,-40.83 215.76,-35.68 214.57,-42.57\"/>\n</g>\n<!-- 4594234704 -->\n<g id=\"node5\" class=\"node\">\n<title>4594234704</title>\n<polygon fill=\"none\" stroke=\"black\" points=\"316,-82.5 316,-118.5 508,-118.5 508,-82.5 316,-82.5\"/>\n<text text-anchor=\"middle\" x=\"327.5\" y=\"-96.8\" font-family=\"Times,serif\" font-size=\"14.00\">c</text>\n<polyline fill=\"none\" stroke=\"black\" points=\"339,-82.5 339,-118.5\"/>\n<text text-anchor=\"middle\" x=\"382.5\" y=\"-96.8\" font-family=\"Times,serif\" font-size=\"14.00\">data 10.0000</text>\n<polyline fill=\"none\" stroke=\"black\" points=\"426,-82.5 426,-118.5\"/>\n<text text-anchor=\"middle\" x=\"467\" y=\"-96.8\" font-family=\"Times,serif\" font-size=\"14.00\">grad 0.0000</text>\n</g>\n<!-- 4594234704->4594137504+ -->\n<g id=\"edge6\" class=\"edge\">\n<title>4594234704->4594137504+</title>\n<path fill=\"none\" stroke=\"black\" d=\"M507.95,-83.57C516.87,-81.98 525.49,-80.44 533.33,-79.04\"/>\n<polygon fill=\"black\" stroke=\"black\" points=\"533.84,-82.5 543.07,-77.3 532.61,-75.61 533.84,-82.5\"/>\n</g>\n<!-- 4594137504 -->\n<g id=\"node6\" class=\"node\">\n<title>4594137504</title>\n<polygon fill=\"none\" stroke=\"black\" points=\"634,-54.5 634,-90.5 816,-90.5 816,-54.5 634,-54.5\"/>\n<text text-anchor=\"middle\" x=\"644\" y=\"-68.8\" font-family=\"Times,serif\" font-size=\"14.00\"> </text>\n<polyline fill=\"none\" stroke=\"black\" points=\"654,-54.5 654,-90.5\"/>\n<text text-anchor=\"middle\" x=\"694\" y=\"-68.8\" font-family=\"Times,serif\" font-size=\"14.00\">data 4.0000</text>\n<polyline fill=\"none\" stroke=\"black\" points=\"734,-54.5 734,-90.5\"/>\n<text text-anchor=\"middle\" x=\"775\" y=\"-68.8\" font-family=\"Times,serif\" font-size=\"14.00\">grad 0.0000</text>\n</g>\n<!-- 4594137504+->4594137504 -->\n<g id=\"edge2\" class=\"edge\">\n<title>4594137504+->4594137504</title>\n<path fill=\"none\" stroke=\"black\" d=\"M598.48,-72.5C605.71,-72.5 614.01,-72.5 622.82,-72.5\"/>\n<polygon fill=\"black\" stroke=\"black\" points=\"622.69,-76 632.69,-72.5 622.69,-69 622.69,-76\"/>\n</g>\n</g>\n</svg>\n", | |
"text/plain": [ | |
"<graphviz.graphs.Digraph at 0x111d4c730>" | |
] | |
}, | |
"execution_count": 75, | |
"metadata": {}, | |
"output_type": "execute_result" | |
} | |
], | |
"source": [ | |
"draw_dot(d)" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 81, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"Value(data=-8.0)" | |
] | |
}, | |
"execution_count": 81, | |
"metadata": {}, | |
"output_type": "execute_result" | |
} | |
], | |
"source": [ | |
"a = Value(2.0, label='a')\n", | |
"b = Value(-3.0, label='b')\n", | |
"c = Value(10.0, label='c')\n", | |
"e = a * b; e.label = 'e'\n", | |
"d = e + c; d.label = 'd'\n", | |
"\n", | |
"f = Value(-2.0, label='f')\n", | |
"L = d * f; L.label = 'L'\n", | |
"\n", | |
"L.grad = 1.0\n", | |
"\n", | |
"L.backward()\n", | |
"L" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 82, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/svg+xml": "<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n<!-- Generated by graphviz version 7.1.0 (20230121.1956)\n -->\n<!-- Pages: 1 -->\n<svg width=\"1157pt\" height=\"154pt\"\n viewBox=\"0.00 0.00 1157.00 154.00\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n<g id=\"graph0\" class=\"graph\" transform=\"scale(1 1) rotate(0) translate(4 150)\">\n<polygon fill=\"white\" stroke=\"none\" points=\"-4,4 -4,-150 1153,-150 1153,4 -4,4\"/>\n<!-- 4594124448 -->\n<g id=\"node1\" class=\"node\">\n<title>4594124448</title>\n<polygon fill=\"none\" stroke=\"black\" points=\"321,-27.5 321,-63.5 515,-63.5 515,-27.5 321,-27.5\"/>\n<text text-anchor=\"middle\" x=\"332.5\" y=\"-41.8\" font-family=\"Times,serif\" font-size=\"14.00\">e</text>\n<polyline fill=\"none\" stroke=\"black\" points=\"344,-27.5 344,-63.5\"/>\n<text text-anchor=\"middle\" x=\"386.5\" y=\"-41.8\" font-family=\"Times,serif\" font-size=\"14.00\">data -6.0000</text>\n<polyline fill=\"none\" stroke=\"black\" points=\"429,-27.5 429,-63.5\"/>\n<text text-anchor=\"middle\" x=\"472\" y=\"-41.8\" font-family=\"Times,serif\" font-size=\"14.00\">grad -2.0000</text>\n</g>\n<!-- 4594126128+ -->\n<g id=\"node7\" class=\"node\">\n<title>4594126128+</title>\n<ellipse fill=\"none\" stroke=\"black\" cx=\"579\" cy=\"-72.5\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"579\" y=\"-68.8\" font-family=\"Times,serif\" font-size=\"14.00\">+</text>\n</g>\n<!-- 4594124448->4594126128+ -->\n<g id=\"edge7\" class=\"edge\">\n<title>4594124448->4594126128+</title>\n<path fill=\"none\" stroke=\"black\" d=\"M514.7,-61.75C523.98,-63.33 532.95,-64.85 541.08,-66.23\"/>\n<polygon fill=\"black\" stroke=\"black\" points=\"540.39,-69.66 550.84,-67.89 541.56,-62.76 540.39,-69.66\"/>\n</g>\n<!-- 4594124448* -->\n<g id=\"node2\" class=\"node\">\n<title>4594124448*</title>\n<ellipse fill=\"none\" stroke=\"black\" cx=\"257\" cy=\"-45.5\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"257\" y=\"-41.8\" font-family=\"Times,serif\" font-size=\"14.00\">*</text>\n</g>\n<!-- 4594124448*->4594124448 -->\n<g id=\"edge1\" class=\"edge\">\n<title>4594124448*->4594124448</title>\n<path fill=\"none\" stroke=\"black\" d=\"M284.26,-45.5C291.86,-45.5 300.67,-45.5 310.07,-45.5\"/>\n<polygon fill=\"black\" stroke=\"black\" points=\"309.81,-49 319.81,-45.5 309.81,-42 309.81,-49\"/>\n</g>\n<!-- 4594123488 -->\n<g id=\"node3\" class=\"node\">\n<title>4594123488</title>\n<polygon fill=\"none\" stroke=\"black\" points=\"0,-55.5 0,-91.5 194,-91.5 194,-55.5 0,-55.5\"/>\n<text text-anchor=\"middle\" x=\"11.5\" y=\"-69.8\" font-family=\"Times,serif\" font-size=\"14.00\">b</text>\n<polyline fill=\"none\" stroke=\"black\" points=\"23,-55.5 23,-91.5\"/>\n<text text-anchor=\"middle\" x=\"65.5\" y=\"-69.8\" font-family=\"Times,serif\" font-size=\"14.00\">data -3.0000</text>\n<polyline fill=\"none\" stroke=\"black\" points=\"108,-55.5 108,-91.5\"/>\n<text text-anchor=\"middle\" x=\"151\" y=\"-69.8\" font-family=\"Times,serif\" font-size=\"14.00\">grad -4.0000</text>\n</g>\n<!-- 4594123488->4594124448* -->\n<g id=\"edge8\" class=\"edge\">\n<title>4594123488->4594124448*</title>\n<path fill=\"none\" stroke=\"black\" d=\"M193.55,-56.57C202.53,-54.98 211.21,-53.44 219.1,-52.04\"/>\n<polygon fill=\"black\" stroke=\"black\" points=\"219.67,-55.49 228.9,-50.3 218.45,-48.6 219.67,-55.49\"/>\n</g>\n<!-- 4594125600 -->\n<g id=\"node4\" class=\"node\">\n<title>4594125600</title>\n<polygon fill=\"none\" stroke=\"black\" points=\"957,-81.5 957,-117.5 1149,-117.5 1149,-81.5 957,-81.5\"/>\n<text text-anchor=\"middle\" x=\"969.5\" y=\"-95.8\" font-family=\"Times,serif\" font-size=\"14.00\">L</text>\n<polyline fill=\"none\" stroke=\"black\" points=\"982,-81.5 982,-117.5\"/>\n<text text-anchor=\"middle\" x=\"1024.5\" y=\"-95.8\" font-family=\"Times,serif\" font-size=\"14.00\">data -8.0000</text>\n<polyline fill=\"none\" stroke=\"black\" points=\"1067,-81.5 1067,-117.5\"/>\n<text text-anchor=\"middle\" x=\"1108\" y=\"-95.8\" font-family=\"Times,serif\" font-size=\"14.00\">grad 1.0000</text>\n</g>\n<!-- 4594125600* -->\n<g id=\"node5\" class=\"node\">\n<title>4594125600*</title>\n<ellipse fill=\"none\" stroke=\"black\" cx=\"894\" cy=\"-99.5\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"894\" y=\"-95.8\" font-family=\"Times,serif\" font-size=\"14.00\">*</text>\n</g>\n<!-- 4594125600*->4594125600 -->\n<g id=\"edge2\" class=\"edge\">\n<title>4594125600*->4594125600</title>\n<path fill=\"none\" stroke=\"black\" d=\"M921.28,-99.5C928.52,-99.5 936.85,-99.5 945.72,-99.5\"/>\n<polygon fill=\"black\" stroke=\"black\" points=\"945.69,-103 955.69,-99.5 945.69,-96 945.69,-103\"/>\n</g>\n<!-- 4594126128 -->\n<g id=\"node6\" class=\"node\">\n<title>4594126128</title>\n<polygon fill=\"none\" stroke=\"black\" points=\"642,-54.5 642,-90.5 831,-90.5 831,-54.5 642,-54.5\"/>\n<text text-anchor=\"middle\" x=\"653.5\" y=\"-68.8\" font-family=\"Times,serif\" font-size=\"14.00\">d</text>\n<polyline fill=\"none\" stroke=\"black\" points=\"665,-54.5 665,-90.5\"/>\n<text text-anchor=\"middle\" x=\"705\" y=\"-68.8\" font-family=\"Times,serif\" font-size=\"14.00\">data 4.0000</text>\n<polyline fill=\"none\" stroke=\"black\" points=\"745,-54.5 745,-90.5\"/>\n<text text-anchor=\"middle\" x=\"788\" y=\"-68.8\" font-family=\"Times,serif\" font-size=\"14.00\">grad -2.0000</text>\n</g>\n<!-- 4594126128->4594125600* -->\n<g id=\"edge5\" class=\"edge\">\n<title>4594126128->4594125600*</title>\n<path fill=\"none\" stroke=\"black\" d=\"M830.65,-88.67C839.58,-90.22 848.23,-91.73 856.11,-93.09\"/>\n<polygon fill=\"black\" stroke=\"black\" points=\"855.45,-96.53 865.9,-94.79 856.64,-89.63 855.45,-96.53\"/>\n</g>\n<!-- 4594126128+->4594126128 -->\n<g id=\"edge3\" class=\"edge\">\n<title>4594126128+->4594126128</title>\n<path fill=\"none\" stroke=\"black\" d=\"M606.38,-72.5C613.63,-72.5 621.96,-72.5 630.82,-72.5\"/>\n<polygon fill=\"black\" stroke=\"black\" points=\"630.77,-76 640.77,-72.5 630.77,-69 630.77,-76\"/>\n</g>\n<!-- 4594126656 -->\n<g id=\"node8\" class=\"node\">\n<title>4594126656</title>\n<polygon fill=\"none\" stroke=\"black\" points=\"642.5,-109.5 642.5,-145.5 830.5,-145.5 830.5,-109.5 642.5,-109.5\"/>\n<text text-anchor=\"middle\" x=\"653\" y=\"-123.8\" font-family=\"Times,serif\" font-size=\"14.00\">f</text>\n<polyline fill=\"none\" stroke=\"black\" points=\"663.5,-109.5 663.5,-145.5\"/>\n<text text-anchor=\"middle\" x=\"706\" y=\"-123.8\" font-family=\"Times,serif\" font-size=\"14.00\">data -2.0000</text>\n<polyline fill=\"none\" stroke=\"black\" points=\"748.5,-109.5 748.5,-145.5\"/>\n<text text-anchor=\"middle\" x=\"789.5\" y=\"-123.8\" font-family=\"Times,serif\" font-size=\"14.00\">grad 4.0000</text>\n</g>\n<!-- 4594126656->4594125600* -->\n<g id=\"edge4\" class=\"edge\">\n<title>4594126656->4594125600*</title>\n<path fill=\"none\" stroke=\"black\" d=\"M830.2,-110.81C839.38,-109.16 848.27,-107.56 856.33,-106.1\"/>\n<polygon fill=\"black\" stroke=\"black\" points=\"856.77,-109.58 865.99,-104.36 855.53,-102.69 856.77,-109.58\"/>\n</g>\n<!-- 4594123680 -->\n<g id=\"node9\" class=\"node\">\n<title>4594123680</title>\n<polygon fill=\"none\" stroke=\"black\" points=\"320,-82.5 320,-118.5 516,-118.5 516,-82.5 320,-82.5\"/>\n<text text-anchor=\"middle\" x=\"331.5\" y=\"-96.8\" font-family=\"Times,serif\" font-size=\"14.00\">c</text>\n<polyline fill=\"none\" stroke=\"black\" points=\"343,-82.5 343,-118.5\"/>\n<text text-anchor=\"middle\" x=\"386.5\" y=\"-96.8\" font-family=\"Times,serif\" font-size=\"14.00\">data 10.0000</text>\n<polyline fill=\"none\" stroke=\"black\" points=\"430,-82.5 430,-118.5\"/>\n<text text-anchor=\"middle\" x=\"473\" y=\"-96.8\" font-family=\"Times,serif\" font-size=\"14.00\">grad -2.0000</text>\n</g>\n<!-- 4594123680->4594126128+ -->\n<g id=\"edge9\" class=\"edge\">\n<title>4594123680->4594126128+</title>\n<path fill=\"none\" stroke=\"black\" d=\"M515.62,-83.49C524.6,-81.9 533.27,-80.38 541.15,-78.99\"/>\n<polygon fill=\"black\" stroke=\"black\" points=\"541.71,-82.44 550.95,-77.26 540.5,-75.55 541.71,-82.44\"/>\n</g>\n<!-- 4594126800 -->\n<g id=\"node10\" class=\"node\">\n<title>4594126800</title>\n<polygon fill=\"none\" stroke=\"black\" points=\"4.5,-0.5 4.5,-36.5 189.5,-36.5 189.5,-0.5 4.5,-0.5\"/>\n<text text-anchor=\"middle\" x=\"16\" y=\"-14.8\" font-family=\"Times,serif\" font-size=\"14.00\">a</text>\n<polyline fill=\"none\" stroke=\"black\" points=\"27.5,-0.5 27.5,-36.5\"/>\n<text text-anchor=\"middle\" x=\"67.5\" y=\"-14.8\" font-family=\"Times,serif\" font-size=\"14.00\">data 2.0000</text>\n<polyline fill=\"none\" stroke=\"black\" points=\"107.5,-0.5 107.5,-36.5\"/>\n<text text-anchor=\"middle\" x=\"148.5\" y=\"-14.8\" font-family=\"Times,serif\" font-size=\"14.00\">grad 6.0000</text>\n</g>\n<!-- 4594126800->4594124448* -->\n<g id=\"edge6\" class=\"edge\">\n<title>4594126800->4594124448*</title>\n<path fill=\"none\" stroke=\"black\" d=\"M189.45,-34.13C199.89,-35.91 210.03,-37.64 219.12,-39.2\"/>\n<polygon fill=\"black\" stroke=\"black\" points=\"218.46,-42.64 228.91,-40.87 219.64,-35.74 218.46,-42.64\"/>\n</g>\n</g>\n</svg>\n", | |
"text/plain": [ | |
"<graphviz.graphs.Digraph at 0x111dbbe20>" | |
] | |
}, | |
"execution_count": 82, | |
"metadata": {}, | |
"output_type": "execute_result" | |
} | |
], | |
"source": [ | |
"draw_dot(L)" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": null, | |
"metadata": {}, | |
"outputs": [], | |
"source": [] | |
} | |
], | |
"metadata": { | |
"kernelspec": { | |
"display_name": "Python 3", | |
"language": "python", | |
"name": "python3" | |
}, | |
"language_info": { | |
"codemirror_mode": { | |
"name": "ipython", | |
"version": 3 | |
}, | |
"file_extension": ".py", | |
"mimetype": "text/x-python", | |
"name": "python", | |
"nbconvert_exporter": "python", | |
"pygments_lexer": "ipython3", | |
"version": "3.8.15" | |
}, | |
"orig_nbformat": 4, | |
"vscode": { | |
"interpreter": { | |
"hash": "b0e2ad85f7434abbcb65688a4a227052854c4563d73b2012845d81a87cc24790" | |
} | |
} | |
}, | |
"nbformat": 4, | |
"nbformat_minor": 2 | |
} |
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment