589 lines
59 KiB
Plaintext
589 lines
59 KiB
Plaintext
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{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Week 3 - Fitting a curve"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 1,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"Plots.GRBackend()"
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]
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},
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"execution_count": 1,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"# You may need this setup\n",
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"using Plots\n",
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"gr() # Activate the GR backend for use with Plots"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"metadata": {},
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"outputs": [],
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"source": [
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"using DelimitedFiles"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Import the supplied data representing 15 pairs to x- and y-values. "
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]
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"metadata": {},
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"outputs": [],
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"source": [
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"data_tofit = readdlm(\"Week3_PR_Data.dat\", '\\t');"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 4,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"[0.1268004831284406, -1.6416953879765301]\n",
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"[0.5013092807380928, -0.9776975375269383]\n",
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"[1.5280121125586477, 0.5277112203195138]\n",
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"[1.7001225303407743, 1.711524991194374]\n",
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"[1.9924936253216172, 1.8910000148140624]\n",
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"[2.706075824201991, -0.46342779446395]\n",
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"[2.9949319274309043, -0.4435666186385725]\n",
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"[3.4918528112833935, -1.275179133203867]\n",
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"[3.501191722475427, -0.6904995966451337]\n",
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"[4.459924502120439, -5.51613079927097]\n",
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"[4.936965850879389, -6.001703074115855]\n",
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"[5.023289852369695, -8.364169009651015]\n",
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"[5.042336980089736, -7.924477516763416]\n",
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"[5.507392850419521, -10.774823709545498]\n",
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"[5.568665171088307, -10.917187797703853]\n"
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]
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}
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],
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"source": [
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"for i = 1:size(data_tofit)[1]\n",
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" println(data_tofit[i,:])\n",
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"end"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 5,
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"metadata": {},
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"outputs": [],
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"source": [
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"x, y = data_tofit[:,1], data_tofit[:,2];"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Then we do a scatterplot, this gives us the points the line must go through."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 6,
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"metadata": {},
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"outputs": [
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{
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},
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"execution_count": 6,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"# Plot the x and y data points using a scatter plot of the x and y array variables\n",
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"plot(x,y,line=:scatter,legend=:false)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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||
|
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"For the line, we need a function, which we now define. Note that the parameters a, b, c need not be passed to the function: we will keep resetting them to try to improve the fit."
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]
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},
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{
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"parabfit (generic function with 1 method)"
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]
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},
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"execution_count": 7,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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|
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"source": [
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||
|
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"# Create a function called parabfit, with x as the argument, returning a*x^2 + b*x + c\n",
|
||
|
|
"function parabfit(x)\n",
|
||
|
|
" return a*x^2 + b*x + c\n",
|
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|
|
"end"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
|
||
|
|
"Let's check that we do get a reasonable parabola. Choose your own interval [xmin, xmax] and parameters a, b, c. If it looks too much like a straight line, chance your choices until it does."
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]
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},
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{
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"cell_type": "code",
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"metadata": {},
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" 2290.04,87.9763 \n",
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" \"/>\n",
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"<path clip-path=\"url(#clip7500)\" d=\"\n",
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" \"/>\n",
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]
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},
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"execution_count": 8,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
|
||
|
|
"# Create variables a, b and c, assigning each the value 1\n",
|
||
|
|
"a = 1\n",
|
||
|
|
"b = 1\n",
|
||
|
|
"c = 1\n",
|
||
|
|
"\n",
|
||
|
|
"f = Array{Float64}(undef,length(-5:0.5:5))\n",
|
||
|
|
"\n",
|
||
|
|
"# Plot the function parabfit, for x values between -5 and 5 \n",
|
||
|
|
"i = 1\n",
|
||
|
|
"for j = -5:0.5:5\n",
|
||
|
|
" f[i] = parabfit(j) \n",
|
||
|
|
" i = i + 1\n",
|
||
|
|
"end\n",
|
||
|
|
"\n",
|
||
|
|
"plot(-5:0.5:5,f)"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"metadata": {},
|
||
|
|
"source": [
|
||
|
|
"Now we choose a, b, c and plot the curve together with the points. \n",
|
||
|
|
"\n",
|
||
|
|
"Note that by looking at where the data points lie, we can deduce some of the properties for a, b, c, as follows.\n",
|
||
|
|
"\n",
|
||
|
|
"The plot must have a y-intersection that is close to 0, so c is close to 0. Also, the parabola is open downwards, so a must be negative. Finally, it has its maximum at a positive x, so b must be positive. \n",
|
||
|
|
"\n",
|
||
|
|
"Use plot() to start with the scatter plot and plot!() to add the curve for parabfit. (There are other ways to do this ...)"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
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|
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"<circle clip-path=\"url(#clip7902)\" cx=\"1250.76\" cy=\"275.634\" r=\"14\" fill=\"#009af9\" fill-rule=\"evenodd\" fill-opacity=\"1\" stroke=\"#000000\" stroke-opacity=\"1\" stroke-width=\"3.2\"/>\n",
|
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"<circle clip-path=\"url(#clip7902)\" cx=\"2120.04\" cy=\"1106.09\" r=\"14\" fill=\"#009af9\" fill-rule=\"evenodd\" fill-opacity=\"1\" stroke=\"#000000\" stroke-opacity=\"1\" stroke-width=\"3.2\"/>\n",
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|
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" 1944.49,883.039 2117.48,1144.28 2290.48,1445.72 \n",
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|
|
" \"/>\n",
|
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|
|
"</svg>\n"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"execution_count": 9,
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "execute_result"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"# More plot!() tries.\n",
|
||
|
|
"rangez = 0:0.5:6\n",
|
||
|
|
"a,b,c = -1,4,-3\n",
|
||
|
|
"\n",
|
||
|
|
"f = Array{Float64}(undef,length(rangez))\n",
|
||
|
|
"\n",
|
||
|
|
"# Plot the function parabfit, for x values between -5 and 5 \n",
|
||
|
|
"i = 1\n",
|
||
|
|
"for j = rangez\n",
|
||
|
|
" f[i] = parabfit(j) \n",
|
||
|
|
" i = i + 1\n",
|
||
|
|
"end\n",
|
||
|
|
"plot(x,y,line=:scatter,legend=:false)\n",
|
||
|
|
"plot!(rangez,f)"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": null,
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [],
|
||
|
|
"source": []
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"metadata": {
|
||
|
|
"kernelspec": {
|
||
|
|
"display_name": "Julia 1.2.0",
|
||
|
|
"language": "julia",
|
||
|
|
"name": "julia-1.2"
|
||
|
|
},
|
||
|
|
"language_info": {
|
||
|
|
"file_extension": ".jl",
|
||
|
|
"mimetype": "application/julia",
|
||
|
|
"name": "julia",
|
||
|
|
"version": "1.2.0"
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"nbformat": 4,
|
||
|
|
"nbformat_minor": 4
|
||
|
|
}
|