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Bernstein basis polynomials: Difference between revisions

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Bernstein basis polynomials (view source)

Revision as of 06:32, 27 May 2023

34,151 bytes added ,  11 months ago
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bern [1, 1.0, 1] --> bern [1, 1.0, 1.0, 1]
bern [1, 2.0, 6] --> bern [1, 1.666666667, 3.333333333, 6]
</pre>
 
=={{header|Phix}}==
{{trans|Python}}
<!--<syntaxhighlight lang="phix">(phixonline)-->
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">monomial_to_bernstein_degree2</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">monomial_coefficients</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">atom</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">a0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">a1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">a2</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">monomial_coefficients</span>
<span style="color: #008080;">return</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">a0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">a0</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;">2</span><span style="color: #0000FF;">)</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">a1</span><span style="color: #0000FF;">),</span> <span style="color: #000000;">a0</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">a1</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">a2</span><span style="color: #0000FF;">}</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">evaluate_bernstein_degree2</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">bernstein_coefficients</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">atom</span> <span style="color: #000000;">t</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">atom</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">b0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">b1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">b2</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">bernstein_coefficients</span>
<span style="color: #000080;font-style:italic;">-- de Casteljau’s algorithm.</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span> <span style="color: #0000FF;">-</span> <span style="color: #000000;">t</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">b01</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;">b0</span><span style="color: #0000FF;">)</span> <span style="color: #0000FF;">+</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">t</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">b1</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">b12</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;">b1</span><span style="color: #0000FF;">)</span> <span style="color: #0000FF;">+</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">t</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">b2</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">b012</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;">b01</span><span style="color: #0000FF;">)</span> <span style="color: #0000FF;">+</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">t</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">b12</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">b012</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">monomial_to_bernstein_degree3</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">monomial_coefficients</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">atom</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">a0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">a1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">a2</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">a3</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">monomial_coefficients</span>
<span style="color: #008080;">return</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">a0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">a0</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;">3</span><span style="color: #0000FF;">)</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">a1</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">a0</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;">3</span><span style="color: #0000FF;">)</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">a1</span><span style="color: #0000FF;">)</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;">3</span><span style="color: #0000FF;">)</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">a2</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">a0</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">a1</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">a2</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">a3</span><span style="color: #0000FF;">}</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">evaluate_bernstein_degree3</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">bernstein_coefficients</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">atom</span> <span style="color: #000000;">t</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">atom</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">b0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">b1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">b2</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">b3</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">bernstein_coefficients</span>
<span style="color: #000080;font-style:italic;">// de Casteljau’s algorithm.</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span> <span style="color: #0000FF;">-</span> <span style="color: #000000;">t</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">b01</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;">b0</span><span style="color: #0000FF;">)</span> <span style="color: #0000FF;">+</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">t</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">b1</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">b12</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;">b1</span><span style="color: #0000FF;">)</span> <span style="color: #0000FF;">+</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">t</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">b2</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">b23</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;">b2</span><span style="color: #0000FF;">)</span> <span style="color: #0000FF;">+</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">t</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">b3</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">b012</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;">b01</span><span style="color: #0000FF;">)</span> <span style="color: #0000FF;">+</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">t</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">b12</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">b123</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;">b12</span><span style="color: #0000FF;">)</span> <span style="color: #0000FF;">+</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">t</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">b23</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">b0123</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;">b012</span><span style="color: #0000FF;">)</span> <span style="color: #0000FF;">+</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">t</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">b123</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">b0123</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">bernstein_degree2_to_degree3</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">bernstein_coefficients</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">atom</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">b0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">b1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">b2</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">bernstein_coefficients</span>
<span style="color: #008080;">return</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">b0</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;">3</span><span style="color: #0000FF;">)</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">b0</span><span style="color: #0000FF;">)</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;">3</span><span style="color: #0000FF;">)</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">b1</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;">3</span><span style="color: #0000FF;">)</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">b1</span><span style="color: #0000FF;">)</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;">3</span><span style="color: #0000FF;">)</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">b2</span><span style="color: #0000FF;">),</span> <span style="color: #000000;">b2</span><span style="color: #0000FF;">}</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">evaluate_monomial_degree2</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">monomial_coefficients</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">atom</span> <span style="color: #000000;">t</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">atom</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">a0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">a1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">a2</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">monomial_coefficients</span>
<span style="color: #000080;font-style:italic;">/* Horner’s rule. */</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">a0</span> <span style="color: #0000FF;">+</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">t</span> <span style="color: #0000FF;">*</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">a1</span> <span style="color: #0000FF;">+</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">t</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">a2</span><span style="color: #0000FF;">)))</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">evaluate_monomial_degree3</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">monomial_coefficients</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">atom</span> <span style="color: #000000;">t</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">atom</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">a0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">a1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">a2</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">a3</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">monomial_coefficients</span>
<span style="color: #000080;font-style:italic;">--/* Horner’s rule. --*/</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">a0</span> <span style="color: #0000FF;">+</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">t</span> <span style="color: #0000FF;">*</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">a1</span> <span style="color: #0000FF;">+</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">t</span> <span style="color: #0000FF;">*</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">a2</span> <span style="color: #0000FF;">+</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">t</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">a3</span><span style="color: #0000FF;">)))))</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">constant</span> <span style="color: #000000;">pmono2</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;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">},</span> <span style="color: #000080;font-style:italic;">-- p(x) = 1</span>
<span style="color: #000000;">qmono2</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;">2</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">3</span><span style="color: #0000FF;">},</span> <span style="color: #000080;font-style:italic;">-- q(x) = 1 + 2x + 3x²</span>
<span style="color: #000000;">pbern2</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">monomial_to_bernstein_degree2</span><span style="color: #0000FF;">(</span><span style="color: #000000;">pmono2</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">qbern2</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">monomial_to_bernstein_degree2</span><span style="color: #0000FF;">(</span><span style="color: #000000;">qmono2</span><span style="color: #0000FF;">)</span>
<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;">"Subprogram (1) examples:\n"</span><span style="color: #0000FF;">)</span>
<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;">" mono %v --&gt; bern %v\n"</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">pmono2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">pbern2</span><span style="color: #0000FF;">})</span>
<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;">" mono %v --&gt; bern %v\n"</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">qmono2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">qbern2</span><span style="color: #0000FF;">})</span>
<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;">"Subprogram (2) examples:\n"</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">x</span> <span style="color: #008080;">in</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">0.25</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">7.50</span><span style="color: #0000FF;">}</span> <span style="color: #008080;">do</span>
<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;">" p(%g) = %g (mono %g)\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">x</span><span style="color: #0000FF;">,</span><span style="color: #000000;">evaluate_bernstein_degree2</span><span style="color: #0000FF;">(</span><span style="color: #000000;">pbern2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">x</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">evaluate_monomial_degree2</span><span style="color: #0000FF;">(</span><span style="color: #000000;">pmono2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">x</span><span style="color: #0000FF;">),})</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">x</span> <span style="color: #008080;">in</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">0.25</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">7.50</span><span style="color: #0000FF;">}</span> <span style="color: #008080;">do</span>
<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;">" q(%g) = %g (mono %g)\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">x</span><span style="color: #0000FF;">,</span><span style="color: #000000;">evaluate_bernstein_degree2</span><span style="color: #0000FF;">(</span><span style="color: #000000;">qbern2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">x</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">evaluate_monomial_degree2</span><span style="color: #0000FF;">(</span><span style="color: #000000;">qmono2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">x</span><span style="color: #0000FF;">)})</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">constant</span> <span style="color: #000000;">pmono3</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;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">},</span> <span style="color: #000080;font-style:italic;">-- p(x) = 1</span>
<span style="color: #000000;">qmono3</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;">2</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">3</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">},</span> <span style="color: #000080;font-style:italic;">-- q(x) = 1 + 2x + 3x²</span>
<span style="color: #000000;">rmono3</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;">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: #000080;font-style:italic;">-- r(x) = 1 + 2x + 3x² + 4x³</span>
<span style="color: #000000;">pbern3</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">monomial_to_bernstein_degree3</span><span style="color: #0000FF;">(</span><span style="color: #000000;">pmono3</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">qbern3</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">monomial_to_bernstein_degree3</span><span style="color: #0000FF;">(</span><span style="color: #000000;">qmono3</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">rbern3</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">monomial_to_bernstein_degree3</span><span style="color: #0000FF;">(</span><span style="color: #000000;">rmono3</span><span style="color: #0000FF;">)</span>
<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;">"Subprogram (3) examples:\n"</span><span style="color: #0000FF;">)</span>
<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;">" mono %v --&gt; bern %v\n"</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">pmono3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">pbern3</span><span style="color: #0000FF;">})</span>
<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;">" mono %v --&gt; bern %v\n"</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">qmono3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">qbern3</span><span style="color: #0000FF;">})</span>
<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;">" mono %v --&gt; bern %v\n"</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">rmono3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">rbern3</span><span style="color: #0000FF;">})</span>
<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;">"Subprogram (4) examples:\n"</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">x</span> <span style="color: #008080;">in</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">0.25</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">7.50</span><span style="color: #0000FF;">}</span> <span style="color: #008080;">do</span>
<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;">" p(%g) = %g (mono %g)\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">x</span><span style="color: #0000FF;">,</span><span style="color: #000000;">evaluate_bernstein_degree3</span><span style="color: #0000FF;">(</span><span style="color: #000000;">pbern3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">x</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">evaluate_monomial_degree3</span><span style="color: #0000FF;">(</span><span style="color: #000000;">pmono3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">x</span><span style="color: #0000FF;">)})</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">x</span> <span style="color: #008080;">in</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">0.25</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">7.50</span><span style="color: #0000FF;">}</span> <span style="color: #008080;">do</span>
<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;">" q(%g) = %g (mono %g)\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">x</span><span style="color: #0000FF;">,</span><span style="color: #000000;">evaluate_bernstein_degree3</span><span style="color: #0000FF;">(</span><span style="color: #000000;">qbern3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">x</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">evaluate_monomial_degree3</span><span style="color: #0000FF;">(</span><span style="color: #000000;">qmono3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">x</span><span style="color: #0000FF;">)})</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">x</span> <span style="color: #008080;">in</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">0.25</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">7.50</span><span style="color: #0000FF;">}</span> <span style="color: #008080;">do</span>
<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;">" r(%g) = %g (mono %g)\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">x</span><span style="color: #0000FF;">,</span><span style="color: #000000;">evaluate_bernstein_degree3</span><span style="color: #0000FF;">(</span><span style="color: #000000;">rbern3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">x</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">evaluate_monomial_degree3</span><span style="color: #0000FF;">(</span><span style="color: #000000;">rmono3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">x</span><span style="color: #0000FF;">)})</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<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;">"Subprogram (5) examples:\n"</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">constant</span> <span style="color: #000000;">pbern3a</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">bernstein_degree2_to_degree3</span><span style="color: #0000FF;">(</span><span style="color: #000000;">pbern2</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">qbern3a</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">bernstein_degree2_to_degree3</span><span style="color: #0000FF;">(</span><span style="color: #000000;">qbern2</span><span style="color: #0000FF;">)</span>
<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;">" bern %v --&gt; bern %v\n"</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">pbern2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">pbern3a</span><span style="color: #0000FF;">})</span>
<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;">" bern %v --&gt; bern %v\n"</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">qbern2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">qbern3a</span><span style="color: #0000FF;">})</span>
<!--</syntaxhighlight>-->
{{out}}
<pre>
Subprogram (1) examples:
mono {1,0,0} --> bern {1,1,1}
mono {1,2,3} --> bern {1,2,6}
Subprogram (2) examples:
p(0.25) = 1 (mono 1)
p(7.5) = 1 (mono 1)
q(0.25) = 1.6875 (mono 1.6875)
q(7.5) = 184.75 (mono 184.75)
Subprogram (3) examples:
mono {1,0,0,0} --> bern {1,1,1,1}
mono {1,2,3,0} --> bern {1,1.666666667,3.333333333,6}
mono {1,2,3,4} --> bern {1,1.666666667,3.333333333,10}
Subprogram (4) examples:
p(0.25) = 1 (mono 1)
p(7.5) = 1 (mono 1)
q(0.25) = 1.6875 (mono 1.6875)
q(7.5) = 184.75 (mono 184.75)
r(0.25) = 1.75 (mono 1.75)
r(7.5) = 1872.25 (mono 1872.25)
Subprogram (5) examples:
bern {1,1,1} --> bern {1,1,1,1}
bern {1,2,6} --> bern {1,1.666666667,3.333333333,6}
</pre>
 
Petelomax
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