Chebyshev coefficients: Difference between revisions
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=={{header|Phix}}== |
=={{header|Phix}}== |
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{{trans|Go}} |
{{trans|Go}} |
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<!--<lang Phix>(phixonline)--> |
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<lang Phix>function Cheb(atom cmin, cmax, integer ncoeff, nnodes) |
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<span style="color: #008080;">function</span> <span style="color: #000000;">Cheb</span><span style="color: #0000FF;">(</span><span style="color: #004080;">atom</span> <span style="color: #000000;">cmin</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">cmax</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">integer</span> <span style="color: #000000;">ncoeff</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">nnodes</span><span style="color: #0000FF;">)</span> |
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sequence c = repeat(0,ncoeff), |
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<span style="color: #004080;">sequence</span> <span style="color: #000000;">c</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">ncoeff</span><span style="color: #0000FF;">),</span> |
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f = repeat(0,nnodes), |
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<span style="color: #000000;">f</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">nnodes</span><span style="color: #0000FF;">),</span> |
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p = repeat(0,nnodes) |
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<span style="color: #000000;">p</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">nnodes</span><span style="color: #0000FF;">)</span> |
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atom z = (cmax + cmin) / 2, |
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<span style="color: #004080;">atom</span> <span style="color: #000000;">z</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">cmax</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">cmin</span><span style="color: #0000FF;">)</span> <span style="color: #0000FF;">/</span> <span style="color: #000000;">2</span><span style="color: #0000FF;">,</span> |
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r = (cmax - cmin) / 2 |
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<span style="color: #000000;">r</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">cmax</span> <span style="color: #0000FF;">-</span> <span style="color: #000000;">cmin</span><span style="color: #0000FF;">)</span> <span style="color: #0000FF;">/</span> <span style="color: #000000;">2</span> |
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for k=1 to nnodes do |
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<span style="color: #008080;">for</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">nnodes</span> <span style="color: #008080;">do</span> |
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p[k] = PI * ((k-1) + 0.5) / nnodes |
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<span style="color: #000000;">p</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #004600;">PI</span> <span style="color: #0000FF;">*</span> <span style="color: #0000FF;">((</span><span style="color: #000000;">k</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">0.5</span><span style="color: #0000FF;">)</span> <span style="color: #0000FF;">/</span> <span style="color: #000000;">nnodes</span> |
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f[k] = cos(z + cos(p[k]) * r) |
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<span style="color: #000000;">f</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">cos</span><span style="color: #0000FF;">(</span><span style="color: #000000;">z</span> <span style="color: #0000FF;">+</span> <span style="color: #7060A8;">cos</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">])</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">r</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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atom n2 = 2 / nnodes |
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<span style="color: #004080;">atom</span> <span style="color: #000000;">n2</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">2</span> <span style="color: #0000FF;">/</span> <span style="color: #000000;">nnodes</span> |
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for j=1 to nnodes do |
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<span style="color: #008080;">for</span> <span style="color: #000000;">j</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">nnodes</span> <span style="color: #008080;">do</span> |
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atom s := 0 |
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<span style="color: #004080;">atom</span> <span style="color: #000000;">s</span> <span style="color: #0000FF;">:=</span> <span style="color: #000000;">0</span> |
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for k=1 to nnodes do |
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<span style="color: #008080;">for</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">nnodes</span> <span style="color: #008080;">do</span> |
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s += f[k] * cos((j-1)*p[k]) |
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<span style="color: #000000;">s</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">f</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">*</span> <span style="color: #7060A8;">cos</span><span style="color: #0000FF;">((</span><span style="color: #000000;">j</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)*</span><span style="color: #000000;">p</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</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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c[j] = s * n2 |
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<span style="color: #000000;">c</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">s</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">n2</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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return c |
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<span style="color: #008080;">return</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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function evaluate(sequence c, atom cmin, cmax, x) |
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<span style="color: #008080;">function</span> <span style="color: #000000;">evaluate</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">c</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">atom</span> <span style="color: #000000;">cmin</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">cmax</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">)</span> |
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atom x1 = (2*x - cmax - cmin) / (cmax - cmin), |
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<span style="color: #004080;">atom</span> <span style="color: #000000;">x1</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">2</span><span style="color: #0000FF;">*</span><span style="color: #000000;">x</span> <span style="color: #0000FF;">-</span> <span style="color: #000000;">cmax</span> <span style="color: #0000FF;">-</span> <span style="color: #000000;">cmin</span><span style="color: #0000FF;">)</span> <span style="color: #0000FF;">/</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">cmax</span> <span style="color: #0000FF;">-</span> <span style="color: #000000;">cmin</span><span style="color: #0000FF;">),</span> |
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x2 = 2*x1, |
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<span style="color: #000000;">x2</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">2</span><span style="color: #0000FF;">*</span><span style="color: #000000;">x1</span><span style="color: #0000FF;">,</span> |
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t = 0, s = 0 |
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<span style="color: #000000;">t</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span> |
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for j=length(c) to 2 by -1 do |
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<span style="color: #008080;">for</span> <span style="color: #000000;">j</span><span style="color: #0000FF;">=</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">c</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">to</span> <span style="color: #000000;">2</span> <span style="color: #008080;">by</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">1</span> <span style="color: #008080;">do</span> |
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{t, s} = {x2 * t - s + c[j], t} |
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<span style="color: #0000FF;">{</span><span style="color: #000000;">t</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">x2</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">t</span> <span style="color: #0000FF;">-</span> <span style="color: #000000;">s</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">c</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">],</span> <span style="color: #000000;">t</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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return x1 * t - s + c[1] / 2 |
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<span style="color: #008080;">return</span> <span style="color: #000000;">x1</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">t</span> <span style="color: #0000FF;">-</span> <span style="color: #000000;">s</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">c</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">/</span> <span style="color: #000000;">2</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 cmin = 0.0, cmax = 1.0 |
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<span style="color: #004080;">atom</span> <span style="color: #000000;">cmin</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0.0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">cmax</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1.0</span> |
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sequence c = Cheb(cmin, cmax, 10, 10) |
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<span style="color: #004080;">sequence</span> <span style="color: #000000;">c</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">Cheb</span><span style="color: #0000FF;">(</span><span style="color: #000000;">cmin</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">cmax</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">10</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">10</span><span style="color: #0000FF;">)</span> |
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printf(1, "Coefficients:\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;">"Coefficients:\n"</span><span style="color: #0000FF;">)</span> |
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pp(c,{pp_Nest,1,pp_FltFmt,"%18.15f"}) |
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<span style="color: #7060A8;">pp</span><span style="color: #0000FF;">(</span><span style="color: #000000;">c</span><span style="color: #0000FF;">,{</span><span style="color: #004600;">pp_Nest</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #004600;">pp_FltFmt</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%18.15f"</span><span style="color: #0000FF;">})</span> |
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printf(1,"\nx computed approximated computed-approx\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;">"\nx computed approximated computed-approx\n"</span><span style="color: #0000FF;">)</span> |
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constant n = 10 |
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<span style="color: #008080;">constant</span> <span style="color: #000000;">n</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">10</span> |
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for i=0 to 10 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;">0</span> <span style="color: #008080;">to</span> <span style="color: #000000;">10</span> <span style="color: #008080;">do</span> |
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atom x = (cmin * (n - i) + cmax * i) / n, |
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<span style="color: #004080;">atom</span> <span style="color: #000000;">x</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">cmin</span> <span style="color: #0000FF;">*</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">n</span> <span style="color: #0000FF;">-</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">)</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">cmax</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">)</span> <span style="color: #0000FF;">/</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">,</span> |
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calc = cos(x), |
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<span style="color: #000000;">calc</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">cos</span><span style="color: #0000FF;">(</span><span style="color: #000000;">x</span><span style="color: #0000FF;">),</span> |
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est = evaluate(c, cmin, cmax, x) |
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<span style="color: #000000;">est</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">evaluate</span><span style="color: #0000FF;">(</span><span style="color: #000000;">c</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">cmin</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">cmax</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">)</span> |
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printf(1,"%.1f %12.8f %12.8f %10.3e\n", {x, calc, est, calc-est}) |
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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;">"%.1f %12.8f %12.8f %10.3e\n"</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">x</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">calc</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">est</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">calc</span><span style="color: #0000FF;">-</span><span style="color: #000000;">est</span><span style="color: #0000FF;">})</span> |
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span> |
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{{out}} |
{{out}} |
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<pre> |
<pre> |
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