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1{
2 "cells": [
3 {
4 "cell_type": "code",
5 "execution_count": 1,
6 "metadata": {
7 "collapsed": true
8 },
9 "outputs": [],
10 "source": [
11 "import Numeric.LinearAlgebra"
12 ]
13 },
14 {
15 "cell_type": "code",
16 "execution_count": 2,
17 "metadata": {
18 "collapsed": true
19 },
20 "outputs": [],
21 "source": [
22 "import IHaskell.Display"
23 ]
24 },
25 {
26 "cell_type": "code",
27 "execution_count": 3,
28 "metadata": {
29 "collapsed": false
30 },
31 "outputs": [],
32 "source": [
33 ":ext FlexibleInstances\n",
34 "\n",
35 "dec = 3\n",
36 "\n",
37 "instance IHaskellDisplay (Matrix C) where\n",
38 " display m = return $ Display [html (\"<p>$$\"++(latexFormat \"bmatrix\" . dispcf dec) m++\"$$</p>\")]\n",
39 "\n",
40 "instance IHaskellDisplay (Matrix R) where\n",
41 " display m = return $ Display [html (\"<p>$$\"++ (latexFormat \"bmatrix\" . dispf dec) m++\"$$</p>\")]"
42 ]
43 },
44 {
45 "cell_type": "code",
46 "execution_count": 4,
47 "metadata": {
48 "collapsed": true
49 },
50 "outputs": [],
51 "source": [
52 "import Graphics.SVG\n",
53 "data RawSVG = RawSVG String\n",
54 "instance IHaskellDisplay RawSVG where\n",
55 " display (RawSVG s) = return $ Display [html $ \"<div style=\\\"width:600px\\\">\"++ s ++ \"</div>\"]\n",
56 "\n",
57 "lplot = RawSVG . hPlot"
58 ]
59 },
60 {
61 "cell_type": "markdown",
62 "metadata": {},
63 "source": [
64 "# least squares polynomial model"
65 ]
66 },
67 {
68 "cell_type": "code",
69 "execution_count": 5,
70 "metadata": {
71 "collapsed": false
72 },
73 "outputs": [],
74 "source": [
75 "expand :: Int -> Vector R -> Matrix R\n",
76 "expand n x = fromColumns $ map (x^) [0 .. n]\n",
77 "\n",
78 "polynomialModel :: Vector R -> Vector R -> Int -> (Vector R -> Vector R)\n",
79 "polynomialModel x y n = f\n",
80 " where\n",
81 " f z = expand n z #> ws\n",
82 " ws = expand n x <\\> y"
83 ]
84 },
85 {
86 "cell_type": "code",
87 "execution_count": 6,
88 "metadata": {
89 "collapsed": true
90 },
91 "outputs": [],
92 "source": [
93 "[x,y] <- toColumns <$> loadMatrix \"data.txt\""
94 ]
95 },
96 {
97 "cell_type": "code",
98 "execution_count": 7,
99 "metadata": {
100 "collapsed": false
101 },
102 "outputs": [
103 {
104 "data": {
105 "text/plain": [
106 "[0.9,2.1,3.1,4.0,4.9,6.1,7.0,7.9,9.1,10.2]"
107 ]
108 },
109 "metadata": {},
110 "output_type": "display_data"
111 },
112 {
113 "data": {
114 "text/plain": [
115 "[1.1,3.9,9.2,51.8,25.3,35.7,49.4,3.6,81.5,99.5]"
116 ]
117 },
118 "metadata": {},
119 "output_type": "display_data"
120 }
121 ],
122 "source": [
123 "x\n",
124 "y"
125 ]
126 },
127 {
128 "cell_type": "code",
129 "execution_count": 8,
130 "metadata": {
131 "collapsed": false
132 },
133 "outputs": [
134 {
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138 "Custom IHaskell CSS.\n",
139 "*/\n",
140 "\n",
141 "/* Styles used for the Hoogle display in the pager */\n",
142 ".hoogle-doc {\n",
143 " display: block;\n",
144 " padding-bottom: 1.3em;\n",
145 " padding-left: 0.4em;\n",
146 "}\n",
147 ".hoogle-code {\n",
148 " display: block;\n",
149 " font-family: monospace;\n",
150 " white-space: pre;\n",
151 "}\n",
152 ".hoogle-text {\n",
153 " display: block;\n",
154 "}\n",
155 ".hoogle-name {\n",
156 " color: green;\n",
157 " font-weight: bold;\n",
158 "}\n",
159 ".hoogle-head {\n",
160 " font-weight: bold;\n",
161 "}\n",
162 ".hoogle-sub {\n",
163 " display: block;\n",
164 " margin-left: 0.4em;\n",
165 "}\n",
166 ".hoogle-package {\n",
167 " font-weight: bold;\n",
168 " font-style: italic;\n",
169 "}\n",
170 ".hoogle-module {\n",
171 " font-weight: bold;\n",
172 "}\n",
173 ".hoogle-class {\n",
174 " font-weight: bold;\n",
175 "}\n",
176 "\n",
177 "/* Styles used for basic displays */\n",
178 ".get-type {\n",
179 " color: green;\n",
180 " font-weight: bold;\n",
181 " font-family: monospace;\n",
182 " display: block;\n",
183 " white-space: pre-wrap;\n",
184 "}\n",
185 "\n",
186 ".show-type {\n",
187 " color: green;\n",
188 " font-weight: bold;\n",
189 " font-family: monospace;\n",
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191 "}\n",
192 "\n",
193 ".mono {\n",
194 " font-family: monospace;\n",
195 " display: block;\n",
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197 "\n",
198 ".err-msg {\n",
199 " color: red;\n",
200 " font-style: italic;\n",
201 " font-family: monospace;\n",
202 " white-space: pre;\n",
203 " display: block;\n",
204 "}\n",
205 "\n",
206 "#unshowable {\n",
207 " color: red;\n",
208 " font-weight: bold;\n",
209 "}\n",
210 "\n",
211 ".err-msg.in.collapse {\n",
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214 "\n",
215 "/* Code that will get highlighted before it is highlighted */\n",
216 ".highlight-code {\n",
217 " white-space: pre;\n",
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219 "}\n",
220 "\n",
221 "/* Hlint styles */\n",
222 ".suggestion-warning { \n",
223 " font-weight: bold;\n",
224 " color: rgb(200, 130, 0);\n",
225 "}\n",
226 ".suggestion-error { \n",
227 " font-weight: bold;\n",
228 " color: red;\n",
229 "}\n",
230 ".suggestion-name {\n",
231 " font-weight: bold;\n",
232 "}\n",
233 "</style><p>$$\\begin{bmatrix}\n",
234 "1.000 & 0.900 & 0.810\n",
235 "\\\\\n",
236 "1.000 & 2.100 & 4.410\n",
237 "\\\\\n",
238 "1.000 & 3.100 & 9.610\n",
239 "\\\\\n",
240 "1.000 & 4.000 & 16.000\n",
241 "\\\\\n",
242 "1.000 & 4.900 & 24.010\n",
243 "\\\\\n",
244 "1.000 & 6.100 & 37.210\n",
245 "\\\\\n",
246 "1.000 & 7.000 & 49.000\n",
247 "\\\\\n",
248 "1.000 & 7.900 & 62.410\n",
249 "\\\\\n",
250 "1.000 & 9.100 & 82.810\n",
251 "\\\\\n",
252 "1.000 & 10.200 & 104.040\n",
253 "\\end{bmatrix}$$</p>"
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256 "metadata": {},
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260 "source": [
261 "expand 2 x"
262 ]
263 },
264 {
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266 "execution_count": 9,
267 "metadata": {
268 "collapsed": true
269 },
270 "outputs": [],
271 "source": [
272 "pol = polynomialModel x y\n",
273 "view = [x, y, pol 1 x, pol 2 x, pol 3 x]"
274 ]
275 },
276 {
277 "cell_type": "code",
278 "execution_count": 10,
279 "metadata": {
280 "collapsed": false
281 },
282 "outputs": [
283 {
284 "data": {
285 "text/plain": [
286 " x y p 1 p 2 p 3"
287 ]
288 },
289 "metadata": {},
290 "output_type": "display_data"
291 },
292 {
293 "data": {
294 "text/plain": [
295 " 0.90 1.10 -3.41 7.70 -6.99\n",
296 " 2.10 3.90 6.83 9.80 15.97\n",
297 " 3.10 9.20 15.36 13.39 25.09\n",
298 " 4.00 51.80 23.04 18.05 28.22\n",
299 " 4.90 25.30 30.72 24.05 28.86\n",
300 " 6.10 35.70 40.96 34.16 29.68\n",
301 " 7.00 49.40 48.64 43.31 33.17\n",
302 " 7.90 3.60 56.32 53.82 41.60\n",
303 " 9.10 81.50 66.57 69.92 64.39\n",
304 "10.20 99.50 75.95 86.80 101.01"
305 ]
306 },
307 "metadata": {},
308 "output_type": "display_data"
309 }
310 ],
311 "source": [
312 "import Text.Printf\n",
313 "\n",
314 "putStrLn \" x y p 1 p 2 p 3\"\n",
315 "putStrLn $ format \" \" (printf \"%.2f\") $ fromColumns view"
316 ]
317 },
318 {
319 "cell_type": "code",
320 "execution_count": 11,
321 "metadata": {
322 "collapsed": false
323 },
324 "outputs": [],
325 "source": [
326 "t = linspace 100 (minElement x, maxElement x)"
327 ]
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