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authorAlberto Ruiz <aruiz@um.es>2015-10-02 10:39:21 +0200
committerAlberto Ruiz <aruiz@um.es>2015-10-02 10:39:21 +0200
commitf92699af9aa47eda9bd2c8a983487a706da75089 (patch)
tree9503511471883e078af7a6b390fe79763c334747 /examples
parent8ffe7887b459dc6be401b2d8c29187faeeae3f20 (diff)
pinv
Diffstat (limited to 'examples')
-rw-r--r--examples/pinv.hs13
-rw-r--r--examples/pinv.ipynb722
2 files changed, 728 insertions, 7 deletions
diff --git a/examples/pinv.hs b/examples/pinv.hs
index 7de50b8..6f093b4 100644
--- a/examples/pinv.hs
+++ b/examples/pinv.hs
@@ -1,20 +1,19 @@
1import Numeric.LinearAlgebra 1import Numeric.LinearAlgebra
2import Graphics.Plot
3import Text.Printf(printf) 2import Text.Printf(printf)
4 3
5expand :: Int -> Vector Double -> Matrix Double 4expand :: Int -> Vector R -> Matrix R
6expand n x = fromColumns $ map (x^) [0 .. n] 5expand n x = fromColumns $ map (x^) [0 .. n]
7 6
8polynomialModel :: Vector Double -> Vector Double -> Int 7polynomialModel :: Vector R -> Vector R -> Int
9 -> (Vector Double -> Vector Double) 8 -> (Vector R -> Vector R)
10polynomialModel x y n = f where 9polynomialModel x y n = f where
11 f z = expand n z <> ws 10 f z = expand n z #> ws
12 ws = expand n x <\> y 11 ws = expand n x <\> y
13 12
14main = do 13main = do
15 [x,y] <- (toColumns . readMatrix) `fmap` readFile "data.txt" 14 [x,y] <- toColumns <$> loadMatrix "data.txt"
16 let pol = polynomialModel x y 15 let pol = polynomialModel x y
17 let view = [x, y, pol 1 x, pol 2 x, pol 3 x] 16 let view = [x, y, pol 1 x, pol 2 x, pol 3 x]
18 putStrLn $ " x y p 1 p 2 p 3" 17 putStrLn $ " x y p 1 p 2 p 3"
19 putStrLn $ format " " (printf "%.2f") $ fromColumns view 18 putStrLn $ format " " (printf "%.2f") $ fromColumns view
20 mplot view 19
diff --git a/examples/pinv.ipynb b/examples/pinv.ipynb
new file mode 100644
index 0000000..532b8d0
--- /dev/null
+++ b/examples/pinv.ipynb
@@ -0,0 +1,722 @@
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 {
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100 "collapsed": false
101 },
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115 "[1.1,3.9,9.2,51.8,25.3,35.7,49.4,3.6,81.5,99.5]"
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122 "source": [
123 "x\n",
124 "y"
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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",
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233 "</style><p>$$\\begin{bmatrix}\n",
234 "1.000 & 0.900 & 0.810\n",
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239 "\\\\\n",
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260 "source": [
261 "expand 2 x"
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264 {
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267 "metadata": {
268 "collapsed": true
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271 "source": [
272 "pol = polynomialModel x y\n",
273 "view = [x, y, pol 1 x, pol 2 x, pol 3 x]"
274 ]
275 },
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278 "execution_count": 10,
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286 " x y p 1 p 2 p 3"
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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",
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305 ]
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307 "metadata": {},
308 "output_type": "display_data"
309 }
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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
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324 "outputs": [],
325 "source": [
326 "t = linspace 100 (minElement x, maxElement x)"
327 ]
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generated by cgit v1.2.3 (git 2.39.1) at 2024-05-19 10:48:21 +0000