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|
{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"import Numeric.LinearAlgebra"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"import IHaskell.Display"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
":ext FlexibleInstances\n",
"\n",
"dec = 3\n",
"\n",
"instance IHaskellDisplay (Matrix C) where\n",
" display m = return $ Display [html (\"<p>$$\"++(latexFormat \"bmatrix\" . dispcf dec) m++\"$$</p>\")]\n",
"\n",
"instance IHaskellDisplay (Matrix R) where\n",
" display m = return $ Display [html (\"<p>$$\"++ (latexFormat \"bmatrix\" . dispf dec) m++\"$$</p>\")]"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"import Graphics.SVG\n",
"data RawSVG = RawSVG String\n",
"instance IHaskellDisplay RawSVG where\n",
" display (RawSVG s) = return $ Display [html $ \"<div style=\\\"width:600px\\\">\"++ s ++ \"</div>\"]\n",
"\n",
"lplot = RawSVG . hPlot"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# least squares polynomial model"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"expand :: Int -> Vector R -> Matrix R\n",
"expand n x = fromColumns $ map (x^) [0 .. n]\n",
"\n",
"polynomialModel :: Vector R -> Vector R -> Int -> (Vector R -> Vector R)\n",
"polynomialModel x y n = f\n",
" where\n",
" f z = expand n z #> ws\n",
" ws = expand n x <\\> y"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"[x,y] <- toColumns <$> loadMatrix \"data.txt\""
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"[0.9,2.1,3.1,4.0,4.9,6.1,7.0,7.9,9.1,10.2]"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
"[1.1,3.9,9.2,51.8,25.3,35.7,49.4,3.6,81.5,99.5]"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"x\n",
"y"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"<style>/*\n",
"Custom IHaskell CSS.\n",
"*/\n",
"\n",
"/* Styles used for the Hoogle display in the pager */\n",
".hoogle-doc {\n",
" display: block;\n",
" padding-bottom: 1.3em;\n",
" padding-left: 0.4em;\n",
"}\n",
".hoogle-code {\n",
" display: block;\n",
" font-family: monospace;\n",
" white-space: pre;\n",
"}\n",
".hoogle-text {\n",
" display: block;\n",
"}\n",
".hoogle-name {\n",
" color: green;\n",
" font-weight: bold;\n",
"}\n",
".hoogle-head {\n",
" font-weight: bold;\n",
"}\n",
".hoogle-sub {\n",
" display: block;\n",
" margin-left: 0.4em;\n",
"}\n",
".hoogle-package {\n",
" font-weight: bold;\n",
" font-style: italic;\n",
"}\n",
".hoogle-module {\n",
" font-weight: bold;\n",
"}\n",
".hoogle-class {\n",
" font-weight: bold;\n",
"}\n",
"\n",
"/* Styles used for basic displays */\n",
".get-type {\n",
" color: green;\n",
" font-weight: bold;\n",
" font-family: monospace;\n",
" display: block;\n",
" white-space: pre-wrap;\n",
"}\n",
"\n",
".show-type {\n",
" color: green;\n",
" font-weight: bold;\n",
" font-family: monospace;\n",
" margin-left: 1em;\n",
"}\n",
"\n",
".mono {\n",
" font-family: monospace;\n",
" display: block;\n",
"}\n",
"\n",
".err-msg {\n",
" color: red;\n",
" font-style: italic;\n",
" font-family: monospace;\n",
" white-space: pre;\n",
" display: block;\n",
"}\n",
"\n",
"#unshowable {\n",
" color: red;\n",
" font-weight: bold;\n",
"}\n",
"\n",
".err-msg.in.collapse {\n",
" padding-top: 0.7em;\n",
"}\n",
"\n",
"/* Code that will get highlighted before it is highlighted */\n",
".highlight-code {\n",
" white-space: pre;\n",
" font-family: monospace;\n",
"}\n",
"\n",
"/* Hlint styles */\n",
".suggestion-warning { \n",
" font-weight: bold;\n",
" color: rgb(200, 130, 0);\n",
"}\n",
".suggestion-error { \n",
" font-weight: bold;\n",
" color: red;\n",
"}\n",
".suggestion-name {\n",
" font-weight: bold;\n",
"}\n",
"</style><p>$$\\begin{bmatrix}\n",
"1.000 & 0.900 & 0.810\n",
"\\\\\n",
"1.000 & 2.100 & 4.410\n",
"\\\\\n",
"1.000 & 3.100 & 9.610\n",
"\\\\\n",
"1.000 & 4.000 & 16.000\n",
"\\\\\n",
"1.000 & 4.900 & 24.010\n",
"\\\\\n",
"1.000 & 6.100 & 37.210\n",
"\\\\\n",
"1.000 & 7.000 & 49.000\n",
"\\\\\n",
"1.000 & 7.900 & 62.410\n",
"\\\\\n",
"1.000 & 9.100 & 82.810\n",
"\\\\\n",
"1.000 & 10.200 & 104.040\n",
"\\end{bmatrix}$$</p>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"expand 2 x"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"pol = polynomialModel x y\n",
"view = [x, y, pol 1 x, pol 2 x, pol 3 x]"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
" x y p 1 p 2 p 3"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
" 0.90 1.10 -3.41 7.70 -6.99\n",
" 2.10 3.90 6.83 9.80 15.97\n",
" 3.10 9.20 15.36 13.39 25.09\n",
" 4.00 51.80 23.04 18.05 28.22\n",
" 4.90 25.30 30.72 24.05 28.86\n",
" 6.10 35.70 40.96 34.16 29.68\n",
" 7.00 49.40 48.64 43.31 33.17\n",
" 7.90 3.60 56.32 53.82 41.60\n",
" 9.10 81.50 66.57 69.92 64.39\n",
"10.20 99.50 75.95 86.80 101.01"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import Text.Printf\n",
"\n",
"putStrLn \" x y p 1 p 2 p 3\"\n",
"putStrLn $ format \" \" (printf \"%.2f\") $ fromColumns view"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"t = linspace 100 (minElement x, maxElement x)"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"collapsed": false
},
"outputs": [
{
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" display: block;\n",
" padding-bottom: 1.3em;\n",
" padding-left: 0.4em;\n",
"}\n",
".hoogle-code {\n",
" display: block;\n",
" font-family: monospace;\n",
" white-space: pre;\n",
"}\n",
".hoogle-text {\n",
" display: block;\n",
"}\n",
".hoogle-name {\n",
" color: green;\n",
" font-weight: bold;\n",
"}\n",
".hoogle-head {\n",
" font-weight: bold;\n",
"}\n",
".hoogle-sub {\n",
" display: block;\n",
" margin-left: 0.4em;\n",
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".hoogle-package {\n",
" font-weight: bold;\n",
" font-style: italic;\n",
"}\n",
".hoogle-module {\n",
" font-weight: bold;\n",
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".hoogle-class {\n",
" font-weight: bold;\n",
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"\n",
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".get-type {\n",
" color: green;\n",
" font-weight: bold;\n",
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".show-type {\n",
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" margin-left: 1em;\n",
"}\n",
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" font-family: monospace;\n",
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"source": [
"lplot\n",
" [ plotMark x y \"none\" 1 circles \"red\" 3 \"data\"\n",
" , plot t (pol 1 t) \"blue\" 1 \"degree 1\"\n",
" , plot t (pol 2 t) \"green\" 1 \"degree 2\"\n",
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" ] "
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