Polynomial regression: Difference between revisions
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=={{header|Phix}}== |
=={{header|Phix}}== |
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{{trans|REXX}} |
{{trans|REXX}} |
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<lang Phix> |
<!--<lang Phix>--> |
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<span style="color: #008080;">constant</span> <span style="color: #000000;">x</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">4</span><span style="color: #0000FF;">,</span><span style="color: #000000;">5</span><span style="color: #0000FF;">,</span><span style="color: #000000;">6</span><span style="color: #0000FF;">,</span><span style="color: #000000;">7</span><span style="color: #0000FF;">,</span><span style="color: #000000;">8</span><span style="color: #0000FF;">,</span><span style="color: #000000;">9</span><span style="color: #0000FF;">,</span><span style="color: #000000;">10</span><span style="color: #0000FF;">},</span> |
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constant y = {1,6,17,34,57,86,121,162,209,262,321} |
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<span style="color: #000000;">y</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">6</span><span style="color: #0000FF;">,</span><span style="color: #000000;">17</span><span style="color: #0000FF;">,</span><span style="color: #000000;">34</span><span style="color: #0000FF;">,</span><span style="color: #000000;">57</span><span style="color: #0000FF;">,</span><span style="color: #000000;">86</span><span style="color: #0000FF;">,</span><span style="color: #000000;">121</span><span style="color: #0000FF;">,</span><span style="color: #000000;">162</span><span style="color: #0000FF;">,</span><span style="color: #000000;">209</span><span style="color: #0000FF;">,</span><span style="color: #000000;">262</span><span style="color: #0000FF;">,</span><span style="color: #000000;">321</span><span style="color: #0000FF;">},</span> |
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constant n = length(x) |
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<span style="color: #000000;">n</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">x</span><span style="color: #0000FF;">)</span> |
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function regression() |
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<span style="color: #008080;">function</span> <span style="color: #000000;">regression</span><span style="color: #0000FF;">()</span> |
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atom {xm, ym, x2m, x3m, x4m, xym, x2ym} @= 0 |
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<span style="color: #004080;">atom</span> <span style="color: #000000;">xm</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">ym</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">x2m</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">x3m</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">x4m</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">xym</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">x2ym</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span> |
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for i=1 to n do |
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<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">n</span> <span style="color: #008080;">do</span> |
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atom xi = x[i], |
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<span style="color: #004080;">atom</span> <span style="color: #000000;">xi</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">],</span> |
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yi = y[i] |
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<span style="color: #000000;">yi</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">y</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span> |
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xm += xi |
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<span style="color: #000000;">xm</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">xi</span> |
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ym += yi |
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<span style="color: #000000;">ym</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">yi</span> |
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x2m += power(xi,2) |
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<span style="color: #000000;">x2m</span> <span style="color: #0000FF;">+=</span> <span style="color: #7060A8;">power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">xi</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)</span> |
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x3m += power(xi,3) |
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<span style="color: #000000;">x3m</span> <span style="color: #0000FF;">+=</span> <span style="color: #7060A8;">power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">xi</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3</span><span style="color: #0000FF;">)</span> |
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x4m += power(xi,4) |
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<span style="color: #000000;">x4m</span> <span style="color: #0000FF;">+=</span> <span style="color: #7060A8;">power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">xi</span><span style="color: #0000FF;">,</span><span style="color: #000000;">4</span><span style="color: #0000FF;">)</span> |
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xym += xi*yi |
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<span style="color: #000000;">xym</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">xi</span><span style="color: #0000FF;">*</span><span style="color: #000000;">yi</span> |
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x2ym += power(xi,2)*yi |
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<span style="color: #000000;">x2ym</span> <span style="color: #0000FF;">+=</span> <span style="color: #7060A8;">power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">xi</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)*</span><span style="color: #000000;">yi</span> |
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end for |
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span> |
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xm /= n |
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<span style="color: #000000;">xm</span> <span style="color: #0000FF;">/=</span> <span style="color: #000000;">n</span> |
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ym /= n |
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<span style="color: #000000;">ym</span> <span style="color: #0000FF;">/=</span> <span style="color: #000000;">n</span> |
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x2m /= n |
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<span style="color: #000000;">x2m</span> <span style="color: #0000FF;">/=</span> <span style="color: #000000;">n</span> |
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x3m /= n |
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<span style="color: #000000;">x3m</span> <span style="color: #0000FF;">/=</span> <span style="color: #000000;">n</span> |
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x4m /= n |
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<span style="color: #000000;">x4m</span> <span style="color: #0000FF;">/=</span> <span style="color: #000000;">n</span> |
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xym /= n |
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<span style="color: #000000;">xym</span> <span style="color: #0000FF;">/=</span> <span style="color: #000000;">n</span> |
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x2ym /= n |
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<span style="color: #000000;">x2ym</span> <span style="color: #0000FF;">/=</span> <span style="color: #000000;">n</span> |
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atom Sxx = x2m-power(xm,2), |
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<span style="color: #004080;">atom</span> <span style="color: #000000;">Sxx</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">x2m</span><span style="color: #0000FF;">-</span><span style="color: #7060A8;">power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">xm</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">),</span> |
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Sxy = xym-xm*ym, |
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<span style="color: #000000;">Sxy</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">xym</span><span style="color: #0000FF;">-</span><span style="color: #000000;">xm</span><span style="color: #0000FF;">*</span><span style="color: #000000;">ym</span><span style="color: #0000FF;">,</span> |
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Sxx2 = x3m-xm*x2m, |
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<span style="color: #000000;">Sxx2</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">x3m</span><span style="color: #0000FF;">-</span><span style="color: #000000;">xm</span><span style="color: #0000FF;">*</span><span style="color: #000000;">x2m</span><span style="color: #0000FF;">,</span> |
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Sx2x2 = x4m-power(x2m,2), |
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<span style="color: #000000;">Sx2x2</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">x4m</span><span style="color: #0000FF;">-</span><span style="color: #7060A8;">power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">x2m</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">),</span> |
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Sx2y = x2ym-x2m*ym, |
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<span style="color: #000000;">Sx2y</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">x2ym</span><span style="color: #0000FF;">-</span><span style="color: #000000;">x2m</span><span style="color: #0000FF;">*</span><span style="color: #000000;">ym</span><span style="color: #0000FF;">,</span> |
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B = (Sxy*Sx2x2-Sx2y*Sxx2)/(Sxx*Sx2x2-power(Sxx2,2)), |
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<span style="color: #000000;">B</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">Sxy</span><span style="color: #0000FF;">*</span><span style="color: #000000;">Sx2x2</span><span style="color: #0000FF;">-</span><span style="color: #000000;">Sx2y</span><span style="color: #0000FF;">*</span><span style="color: #000000;">Sxx2</span><span style="color: #0000FF;">)/(</span><span style="color: #000000;">Sxx</span><span style="color: #0000FF;">*</span><span style="color: #000000;">Sx2x2</span><span style="color: #0000FF;">-</span><span style="color: #7060A8;">power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">Sxx2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)),</span> |
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C = (Sx2y*Sxx-Sxy*Sxx2)/(Sxx*Sx2x2-power(Sxx2,2)), |
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<span style="color: #000000;">C</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">Sx2y</span><span style="color: #0000FF;">*</span><span style="color: #000000;">Sxx</span><span style="color: #0000FF;">-</span><span style="color: #000000;">Sxy</span><span style="color: #0000FF;">*</span><span style="color: #000000;">Sxx2</span><span style="color: #0000FF;">)/(</span><span style="color: #000000;">Sxx</span><span style="color: #0000FF;">*</span><span style="color: #000000;">Sx2x2</span><span style="color: #0000FF;">-</span><span style="color: #7060A8;">power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">Sxx2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)),</span> |
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A = ym-B*xm-C*x2m |
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<span style="color: #000000;">A</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">ym</span><span style="color: #0000FF;">-</span><span style="color: #000000;">B</span><span style="color: #0000FF;">*</span><span style="color: #000000;">xm</span><span style="color: #0000FF;">-</span><span style="color: #000000;">C</span><span style="color: #0000FF;">*</span><span style="color: #000000;">x2m</span> |
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return {C,B,A} |
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<span style="color: #008080;">return</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">C</span><span style="color: #0000FF;">,</span><span style="color: #000000;">B</span><span style="color: #0000FF;">,</span><span style="color: #000000;">A</span><span style="color: #0000FF;">}</span> |
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end function |
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<span style="color: #008080;">end</span> <span style="color: #008080;">function</span> |
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atom {a,b,c} = regression() |
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<span style="color: #004080;">atom</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">a</span><span style="color: #0000FF;">,</span><span style="color: #000000;">b</span><span style="color: #0000FF;">,</span><span style="color: #000000;">c</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">regression</span><span style="color: #0000FF;">()</span> |
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function f(atom x) |
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<span style="color: #008080;">function</span> <span style="color: #000000;">f</span><span style="color: #0000FF;">(</span><span style="color: #004080;">atom</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">)</span> |
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return a*x*x+b*x+c |
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<span style="color: #008080;">return</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">*</span><span style="color: #000000;">x</span><span style="color: #0000FF;">*</span><span style="color: #000000;">x</span><span style="color: #0000FF;">+</span><span style="color: #000000;">b</span><span style="color: #0000FF;">*</span><span style="color: #000000;">x</span><span style="color: #0000FF;">+</span><span style="color: #000000;">c</span> |
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end function |
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<span style="color: #008080;">end</span> <span style="color: #008080;">function</span> |
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printf(1,"y=%gx^2+%gx+%g\n",{a,b,c}) |
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<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"y=%gx^2+%gx+%g\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">a</span><span style="color: #0000FF;">,</span><span style="color: #000000;">b</span><span style="color: #0000FF;">,</span><span style="color: #000000;">c</span><span style="color: #0000FF;">})</span> |
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printf(1,"\n x y f(x)\n") |
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<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"\n x y f(x)\n"</span><span style="color: #0000FF;">)</span> |
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for i=1 to n do |
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<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">n</span> <span style="color: #008080;">do</span> |
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printf(1," %2d %3d %3g\n",{x[i],y[i],f(x[i])}) |
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<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">" %2d %3d %3g\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">x</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">],</span><span style="color: #000000;">y</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">],</span><span style="color: #000000;">f</span><span style="color: #0000FF;">(</span><span style="color: #000000;">x</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">])})</span> |
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end for</lang> |
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span> |
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<!--</lang>--> |
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{{out}} |
{{out}} |
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<pre> |
<pre> |
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</pre> |
</pre> |
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===plot=== |
===plot=== |
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A simple plot, as per [[Polynomial_regression#Racket|Racket]]: |
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{{libheader|Phix/pGUI}} |
{{libheader|Phix/pGUI}} |
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<lang Phix> |
<!--<lang Phix>--> |
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<span style="color: #008080;">include</span> <span style="color: #000000;">pGUI</span><span style="color: #0000FF;">.</span><span style="color: #000000;">e</span> |
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constant x = {0,1,2,3,4,5,6,7,8,9,10} |
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<span style="color: #008080;">constant</span> <span style="color: #000000;">x</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">4</span><span style="color: #0000FF;">,</span><span style="color: #000000;">5</span><span style="color: #0000FF;">,</span><span style="color: #000000;">6</span><span style="color: #0000FF;">,</span><span style="color: #000000;">7</span><span style="color: #0000FF;">,</span><span style="color: #000000;">8</span><span style="color: #0000FF;">,</span><span style="color: #000000;">9</span><span style="color: #0000FF;">,</span><span style="color: #000000;">10</span><span style="color: #0000FF;">}</span> |
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constant y = {1,6,17,34,57,86,121,162,209,262,321} |
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<span style="color: #008080;">constant</span> <span style="color: #000000;">y</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">6</span><span style="color: #0000FF;">,</span><span style="color: #000000;">17</span><span style="color: #0000FF;">,</span><span style="color: #000000;">34</span><span style="color: #0000FF;">,</span><span style="color: #000000;">57</span><span style="color: #0000FF;">,</span><span style="color: #000000;">86</span><span style="color: #0000FF;">,</span><span style="color: #000000;">121</span><span style="color: #0000FF;">,</span><span style="color: #000000;">162</span><span style="color: #0000FF;">,</span><span style="color: #000000;">209</span><span style="color: #0000FF;">,</span><span style="color: #000000;">262</span><span style="color: #0000FF;">,</span><span style="color: #000000;">321</span><span style="color: #0000FF;">}</span> |
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IupOpen() |
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<span style="color: #7060A8;">IupOpen</span><span style="color: #0000FF;">()</span> |
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Ihandle plot = IupPlot("GRID=YES, MARGINLEFT=50, MARGINBOTTOM=40") |
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<span style="color: #004080;">Ihandle</span> <span style="color: #000000;">plot</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">IupPlot</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"GRID=YES, MARGINLEFT=50, MARGINBOTTOM=40"</span><span style="color: #0000FF;">)</span> |
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-- (just add ", AXS_YSCALE=LOG10" for a nice log scale) |
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<span style="color: #000080;font-style:italic;">-- (just add ", AXS_YSCALE=LOG10" for a nice log scale)</span> |
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IupPlotBegin(plot, 0) |
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<span style="color: #7060A8;">IupPlotBegin</span><span style="color: #0000FF;">(</span><span style="color: #000000;">plot</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">)</span> |
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for i=1 to length(x) do |
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<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">x</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span> |
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IupPlotAdd(plot, x[i], y[i]) |
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<span style="color: #7060A8;">IupPlotAdd</span><span style="color: #0000FF;">(</span><span style="color: #000000;">plot</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">],</span> <span style="color: #000000;">y</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">])</span> |
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end for |
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span> |
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{} = IupPlotEnd(plot) |
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<span style="color: #0000FF;">{}</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">IupPlotEnd</span><span style="color: #0000FF;">(</span><span style="color: #000000;">plot</span><span style="color: #0000FF;">)</span> |
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Ihandle dlg = IupDialog(plot) |
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<span style="color: #004080;">Ihandle</span> <span style="color: #000000;">dlg</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">IupDialog</span><span style="color: #0000FF;">(</span><span style="color: #000000;">plot</span><span style="color: #0000FF;">,</span><span style="color: #008000;">`TITLE="simple plot", RASTERSIZE=640x480`</span><span style="color: #0000FF;">)</span> |
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IupSetAttributes(dlg, "RASTERSIZE=%dx%d", {640, 480}) |
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<span style="color: #7060A8;">IupShow</span><span style="color: #0000FF;">(</span><span style="color: #000000;">dlg</span><span style="color: #0000FF;">)</span> |
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IupSetAttribute(dlg, "TITLE", "simple plot") |
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<span style="color: #008080;">if</span> <span style="color: #7060A8;">platform</span><span style="color: #0000FF;">()!=</span><span style="color: #004600;">JS</span> <span style="color: #008080;">then</span> |
|||
IupShow(dlg) |
|||
<span style="color: #7060A8;">IupMainLoop</span><span style="color: #0000FF;">()</span> |
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<span style="color: #7060A8;">IupClose</span><span style="color: #0000FF;">()</span> |
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IupMainLoop() |
|||
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span> |
|||
IupClose()</lang> |
|||
<!--</lang>--> |
|||
=={{header|PowerShell}}== |
=={{header|PowerShell}}== |