Data update
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2011 changed files with 35081 additions and 3229 deletions
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@ -1,62 +1,60 @@
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(phixonline)-->
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<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
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<span style="color: #008080;">function</span> <span style="color: #000000;">aitken</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">f</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">atom</span> <span style="color: #000000;">p0</span><span style="color: #0000FF;">)</span>
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<span style="color: #004080;">atom</span> <span style="color: #000000;">p1</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">f</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p0</span><span style="color: #0000FF;">),</span>
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<span style="color: #000000;">p2</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">f</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p1</span><span style="color: #0000FF;">),</span>
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<span style="color: #000000;">p1m0</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">p1</span> <span style="color: #0000FF;">-</span> <span style="color: #000000;">p0</span>
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<span style="color: #008080;">return</span> <span style="color: #000000;">p0</span> <span style="color: #0000FF;">-</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">p1m0</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">p1m0</span><span style="color: #0000FF;">)</span> <span style="color: #0000FF;">/</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">p2</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;">p1</span><span style="color: #0000FF;">)</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">p0</span><span style="color: #0000FF;">)</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
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with javascript_semantics
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function aitken(integer f, atom p0)
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atom p1 = f(p0),
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p2 = f(p1),
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p1m0 = p1 - p0
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return p0 - (p1m0 * p1m0) / (p2 - (2 * p1) + p0)
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end function
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<span style="color: #008080;">function</span> <span style="color: #000000;">steffensenAitken</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">f</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">maxiter</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">atom</span> <span style="color: #000000;">pinit</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">tol</span><span style="color: #0000FF;">)</span>
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<span style="color: #004080;">atom</span> <span style="color: #000000;">p0</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">pinit</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">p</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">aitken</span><span style="color: #0000FF;">(</span><span style="color: #000000;">f</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">p0</span><span style="color: #0000FF;">)</span>
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<span style="color: #004080;">integer</span> <span style="color: #000000;">iter</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span>
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<span style="color: #008080;">while</span> <span style="color: #7060A8;">abs</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">-</span><span style="color: #000000;">p0</span><span style="color: #0000FF;">)></span><span style="color: #000000;">tol</span> <span style="color: #008080;">and</span> <span style="color: #000000;">iter</span><span style="color: #0000FF;"><</span><span style="color: #000000;">maxiter</span> <span style="color: #008080;">do</span>
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<span style="color: #000000;">p0</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">p</span>
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<span style="color: #000000;">p</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">aitken</span><span style="color: #0000FF;">(</span><span style="color: #000000;">f</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">p0</span><span style="color: #0000FF;">)</span>
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<span style="color: #000000;">iter</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
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<span style="color: #008080;">return</span> <span style="color: #7060A8;">iff</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">abs</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">-</span><span style="color: #000000;">p0</span><span style="color: #0000FF;">)></span><span style="color: #000000;">tol</span><span style="color: #0000FF;">?</span><span style="color: #008000;">"none"</span><span style="color: #0000FF;">:</span><span style="color: #000000;">p</span><span style="color: #0000FF;">)</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
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function steffensenAitken(integer f, maxiter, atom pinit, tol)
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atom p0 = pinit, p = aitken(f, p0)
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integer iter = 1
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while abs(p-p0)>tol and iter<maxiter do
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p0 = p
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p = aitken(f, p0)
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iter += 1
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end while
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return iff(abs(p-p0)>tol?"none":p)
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end function
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<span style="color: #008080;">function</span> <span style="color: #000000;">deCasteljau</span><span style="color: #0000FF;">(</span><span style="color: #004080;">atom</span> <span style="color: #000000;">c0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">c1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">c2</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">t</span><span style="color: #0000FF;">)</span>
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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;">1</span> <span style="color: #0000FF;">-</span> <span style="color: #000000;">t</span><span style="color: #0000FF;">,</span>
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<span style="color: #000000;">c01</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;">c0</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;">c1</span><span style="color: #0000FF;">),</span>
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<span style="color: #000000;">c12</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;">c1</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;">c2</span><span style="color: #0000FF;">),</span>
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<span style="color: #000000;">c012</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;">c01</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;">c12</span><span style="color: #0000FF;">)</span>
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<span style="color: #008080;">return</span> <span style="color: #000000;">c012</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
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function deCasteljau(atom c0, c1, c2, t)
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atom s = 1 - t,
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c01 = (s * c0) + (t * c1),
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c12 = (s * c1) + (t * c2),
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c012 = (s * c01) + (t * c12)
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return c012
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end function
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<span style="color: #008080;">function</span> <span style="color: #000000;">xConvexLeftParabola</span><span style="color: #0000FF;">(</span><span style="color: #004080;">atom</span> <span style="color: #000000;">t</span><span style="color: #0000FF;">)</span>
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<span style="color: #008080;">return</span> <span style="color: #000000;">deCasteljau</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;">8</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">t</span><span style="color: #0000FF;">)</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
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function xConvexLeftParabola(atom t)
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return deCasteljau(2, -8, 2, t)
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end function
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<span style="color: #008080;">function</span> <span style="color: #000000;">yConvexLeftParabola</span><span style="color: #0000FF;">(</span><span style="color: #004080;">atom</span> <span style="color: #000000;">t</span><span style="color: #0000FF;">)</span>
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<span style="color: #008080;">return</span> <span style="color: #000000;">deCasteljau</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;">t</span><span style="color: #0000FF;">)</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
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function yConvexLeftParabola(atom t)
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return deCasteljau(1, 2, 3, t)
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end function
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<span style="color: #008080;">function</span> <span style="color: #000000;">implicitEquation</span><span style="color: #0000FF;">(</span><span style="color: #004080;">atom</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">y</span><span style="color: #0000FF;">)</span>
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<span style="color: #008080;">return</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">5</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: #0000FF;">+</span> <span style="color: #000000;">y</span> <span style="color: #0000FF;">-</span> <span style="color: #000000;">5</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
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function implicitEquation(atom x, y)
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return (5 * x * x) + y - 5
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end function
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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;">t</span><span style="color: #0000FF;">)</span>
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<span style="color: #004080;">atom</span> <span style="color: #000000;">x</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">xConvexLeftParabola</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t</span><span style="color: #0000FF;">),</span>
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<span style="color: #000000;">y</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">yConvexLeftParabola</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t</span><span style="color: #0000FF;">)</span>
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<span style="color: #008080;">return</span> <span style="color: #000000;">implicitEquation</span><span style="color: #0000FF;">(</span><span style="color: #000000;">x</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">y</span><span style="color: #0000FF;">)</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">t</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
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function f(atom t)
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atom x = xConvexLeftParabola(t),
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y = yConvexLeftParabola(t)
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return implicitEquation(x, y) + t
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end function
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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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<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;">"t0 = %.1f : "</span><span style="color: #0000FF;">,</span><span style="color: #000000;">i</span><span style="color: #0000FF;">/</span><span style="color: #000000;">10</span><span style="color: #0000FF;">)</span>
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<span style="color: #004080;">object</span> <span style="color: #000000;">t</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">steffensenAitken</span><span style="color: #0000FF;">(</span><span style="color: #000000;">f</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1000</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">/</span><span style="color: #000000;">10</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0.00000001</span><span style="color: #0000FF;">)</span>
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<span style="color: #008080;">if</span> <span style="color: #004080;">string</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
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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;">"no answer\n"</span><span style="color: #0000FF;">)</span>
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<span style="color: #008080;">else</span>
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<span style="color: #004080;">atom</span> <span style="color: #000000;">x</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">xConvexLeftParabola</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t</span><span style="color: #0000FF;">),</span>
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<span style="color: #000000;">y</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">yConvexLeftParabola</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t</span><span style="color: #0000FF;">)</span>
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<span style="color: #008080;">if</span> <span style="color: #7060A8;">abs</span><span style="color: #0000FF;">(</span><span style="color: #000000;">implicitEquation</span><span style="color: #0000FF;">(</span><span style="color: #000000;">x</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">y</span><span style="color: #0000FF;">))</span> <span style="color: #0000FF;"><=</span> <span style="color: #000000;">0.000001</span> <span style="color: #008080;">then</span>
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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;">"intersection at (%.6f, %.6f)\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">x</span><span style="color: #0000FF;">,</span><span style="color: #000000;">y</span><span style="color: #0000FF;">})</span>
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<span style="color: #008080;">else</span>
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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;">"spurious solution\n"</span><span style="color: #0000FF;">)</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
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<!--
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for i=0 to 10 do
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printf(1,"t0 = %.1f : ",i/10)
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object t = steffensenAitken(f, 1000, i/10, 0.00000001)
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if string(t) then
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printf(1,"no answer\n")
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else
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atom x = xConvexLeftParabola(t),
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y = yConvexLeftParabola(t)
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if abs(implicitEquation(x, y)) <= 0.000001 then
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printf(1,"intersection at (%.6f, %.6f)\n",{x,y})
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else
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printf(1,"spurious solution\n")
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end if
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end if
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end for
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