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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"><html><head><meta http-equiv="Content-Type" content="text/html;charset=iso-8859-1"><title>The Polynomials Templates Library: polyzero.h Source File</title><link href="doxygen.css" rel="stylesheet" type="text/css"><link href="tabs.css" rel="stylesheet" type="text/css"></head><body><!-- Generated by Doxygen 1.4.5 --><div class="tabs"> <ul> <li><a href="index.html"><span>Main Page</span></a></li> <li><a href="modules.html"><span>Modules</span></a></li> <li><a href="annotated.html"><span>Classes</span></a></li> <li id="current"><a href="files.html"><span>Files</span></a></li> </ul></div><div class="tabs"> <ul> <li><a href="files.html"><span>File List</span></a></li> <li><a href="globals.html"><span>File Members</span></a></li> </ul></div><h1>polyzero.h</h1><a href="a00097.html">Go to the documentation of this file.</a><div class="fragment"><pre class="fragment"><a name="l00001"></a>00001 <span class="preprocessor">#ifndef POLYZERO_H</span><a name="l00002"></a>00002 <span class="preprocessor"></span><span class="preprocessor">#define POLYZERO_H</span><a name="l00003"></a>00003 <span class="preprocessor"></span><a name="l00037"></a>00037 <span class="preprocessor">#include "<a class="code" href="a00096.html">polynomial.h</a>"</span><a name="l00038"></a>00038 <a name="l00072"></a>00072 <span class="keyword">template</span> <<span class="keyword">class</span> T, <span class="keyword">class</span> U, <span class="keyword">class</span> V><a name="l00073"></a><a class="code" href="a00102.html#g7528de40f73b280a95202bc5b8947424">00073</a> <span class="keywordtype">bool</span> <a class="code" href="a00102.html#g7528de40f73b280a95202bc5b8947424">newtonZero</a>(<span class="keyword">const</span> Polynomial<T>& p, U& z, U& pz, V& mpz, <span class="keywordtype">bool</span> adaptive = <span class="keyword">false</span>) {<a name="l00074"></a>00074 <span class="keyword">const</span> <span class="keywordtype">int</span> MAX_RATIO = 6;<a name="l00075"></a>00075 U ppz, z1, z2, dz, y, y1, y2;<a name="l00076"></a>00076 V my, my1, my2;<a name="l00077"></a>00077 <span class="keywordtype">int</span> i, j = 0, m = p.<a class="code" href="a00090.html#b433e0edb11b32a205a9d07b89aefa8f">degree</a>();<a name="l00078"></a>00078 <a name="l00079"></a>00079 <span class="keywordflow">if</span> (m < 1)<a name="l00080"></a>00080 <span class="keywordflow">return</span> <span class="keyword">false</span>;<a name="l00081"></a>00081 <a name="l00082"></a>00082 <span class="keywordflow">if</span> (adaptive) {<a name="l00083"></a>00083 z1 = z;<a name="l00084"></a>00084 <span class="keywordflow">do</span> {<a name="l00085"></a>00085 ++j;<a name="l00086"></a>00086 y = <a class="code" href="a00100.html#gc143079d7e07a2b902831ec539e45fc6">evalAndDerive</a>(p, z1, ppz);<a name="l00087"></a>00087 my = abs(pz);<a name="l00088"></a>00088 <span class="keywordflow">if</span> (ppz == U(0))<a name="l00089"></a>00089 <span class="keywordflow">break</span>;<a name="l00090"></a>00090 z = z1;<a name="l00091"></a>00091 pz = y;<a name="l00092"></a>00092 mpz = my;<a name="l00093"></a>00093 dz = pz / ppz;<a name="l00094"></a>00094 <a name="l00095"></a>00095 z1 = z - dz;<a name="l00096"></a>00096 ++j;<a name="l00097"></a>00097 y1 = <a class="code" href="a00100.html#gc5161c8ecd75b0108d0ea60c92d30d21">eval</a>(p, z1);<a name="l00098"></a>00098 my1 = abs(y1);<a name="l00099"></a>00099 <a name="l00100"></a>00100 z2 = z1 - dz;<a name="l00101"></a>00101 ++j;<a name="l00102"></a>00102 y2 = <a class="code" href="a00100.html#gc5161c8ecd75b0108d0ea60c92d30d21">eval</a>(p, z2);<a name="l00103"></a>00103 my2 = abs(y2);<a name="l00104"></a>00104 <a name="l00105"></a>00105 i = 3;<a name="l00106"></a>00106 <span class="keywordflow">while</span>(my2 < my1 && i++ < MAX_RATIO) {<a name="l00107"></a>00107 z1 = z2;<a name="l00108"></a>00108 y1 = y2;<a name="l00109"></a>00109 my1 = my2;<a name="l00110"></a>00110 z2 = z2 - dz;<a name="l00111"></a>00111 ++j;<a name="l00112"></a>00112 y2 = <a class="code" href="a00100.html#gc5161c8ecd75b0108d0ea60c92d30d21">eval</a>(p, z2);<a name="l00113"></a>00113 my2 = abs(y2);<a name="l00114"></a>00114 }<a name="l00115"></a>00115 <span class="keywordflow">if</span> (_isnan(my1))<a name="l00116"></a>00116 <span class="keywordflow">break</span>;<a name="l00117"></a>00117 } <span class="keywordflow">while</span> (my1 < my);<a name="l00118"></a>00118 }<a name="l00119"></a>00119 <span class="keywordflow">else</span> {<a name="l00120"></a>00120 ++j;<a name="l00121"></a>00121 y = <a class="code" href="a00100.html#gc143079d7e07a2b902831ec539e45fc6">evalAndDerive</a>(p, z, ppz);<a name="l00122"></a>00122 my = abs(y);<a name="l00123"></a>00123 z1 = z;<a name="l00124"></a>00124 <span class="keywordflow">do</span> {<a name="l00125"></a>00125 z = z1;<a name="l00126"></a>00126 pz = y;<a name="l00127"></a>00127 mpz = my;<a name="l00128"></a>00128 <span class="keywordflow">if</span> (ppz == U(0))<a name="l00129"></a>00129 <span class="keywordflow">break</span>;<a name="l00130"></a>00130 z1 -= pz / ppz;<a name="l00131"></a>00131 <span class="keywordflow">if</span> (z1 == z)<a name="l00132"></a>00132 <span class="keywordflow">break</span>;<a name="l00133"></a>00133 ++j;<a name="l00134"></a>00134 y = <a class="code" href="a00100.html#gc143079d7e07a2b902831ec539e45fc6">evalAndDerive</a>(p, z1, ppz);<a name="l00135"></a>00135 my = abs(y);<a name="l00136"></a>00136 <span class="keywordflow">if</span> (_isnan(my))<a name="l00137"></a>00137 <span class="keywordflow">break</span>;<a name="l00138"></a>00138 } <span class="keywordflow">while</span>(my < mpz);<a name="l00139"></a>00139 }<a name="l00140"></a>00140 <span class="comment">//printf("j:%d, mpz:%le\n", j, mpz);</span><a name="l00141"></a>00141 <span class="keywordflow">return</span> <span class="keyword">true</span>;<a name="l00142"></a>00142 }<a name="l00143"></a>00143 <a name="l00167"></a>00167 template<class T><a name="l00168"></a><a class="code" href="a00102.html#g206394af98d861f1a81bea25ae6d84da">00168</a> <span class="keywordtype">int</span> <a class="code" href="a00102.html#g206394af98d861f1a81bea25ae6d84da">removeNullZeros</a>(Polynomial<T>& p) {<a name="l00169"></a>00169 <span class="keywordtype">int</span> i, m = p.degree();<a name="l00170"></a>00170 <span class="keywordflow">for</span> (i = 0; i < m && p[i] == T(0); ++i)<a name="l00171"></a>00171 ;<a name="l00172"></a>00172 p.shift(-i);<a name="l00173"></a>00173 <span class="keywordflow">return</span> i;<a name="l00174"></a>00174 }<a name="l00175"></a>00175 <a name="l00232"></a>00232 <span class="keyword">template</span><<span class="keyword">class</span> T><a name="l00233"></a><a class="code" href="a00099.html#g4c00b88d043d1f70cdcb4d2cec66b55e">00233</a> T <a class="code" href="a00099.html#g4c00b88d043d1f70cdcb4d2cec66b55e">cauchyLowerBound</a>(<span class="keyword">const</span> Polynomial<T>& p, <span class="keyword">const</span> T& upperBound = T(0)) {<a name="l00234"></a>00234 <span class="keyword">static</span> FloatSpecs<T> fpSpecs;<a name="l00235"></a>00235 T x, y, my;<a name="l00236"></a>00236 <span class="keywordflow">if</span> (upperBound <= 0) {<a name="l00237"></a>00237 x = <a class="code" href="a00099.html#ga911d353ac1900e9da22160a11d8b350">zerosGeometricMean</a>(p);<a name="l00238"></a>00238 <span class="keywordflow">if</span> (p[1] != 0)<a name="l00239"></a>00239 x = std::min(x, -p[0] / p[1]);<a name="l00240"></a>00240 }<a name="l00241"></a>00241 <span class="keywordflow">else</span><a name="l00242"></a>00242 x = upperBound;<a name="l00243"></a>00243 <a name="l00244"></a>00244 <a class="code" href="a00102.html#g7528de40f73b280a95202bc5b8947424">newtonZero</a>(p, x, y, my);<a name="l00245"></a>00245 <span class="keywordflow">return</span> x;<a name="l00246"></a>00246 }<a name="l00247"></a>00247 <a name="l00265"></a>00265 <span class="keyword">template</span><<span class="keyword">class</span> T><a name="l00266"></a><a class="code" href="a00099.html#g70251f7099324b613e81181a4f022f0e">00266</a> T <a class="code" href="a00099.html#g70251f7099324b613e81181a4f022f0e">cauchyUpperBound</a>(<span class="keyword">const</span> Polynomial<T>& p) {<a name="l00267"></a>00267 <span class="keywordtype">int</span> m = p.<a class="code" href="a00090.html#b433e0edb11b32a205a9d07b89aefa8f">degree</a>();<a name="l00268"></a>00268 T x = abs(p[0]);<a name="l00269"></a>00269 <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 1; i <= m; ++i)<a name="l00270"></a>00270 x = std::max(x, abs(p[i]));<a name="l00271"></a>00271 <span class="keywordflow">return</span> x + T(1);<a name="l00272"></a>00272 }<a name="l00273"></a>00273 <a name="l00292"></a>00292 <span class="keyword">template</span><<span class="keyword">class</span> T><a name="l00293"></a><a class="code" href="a00099.html#ga911d353ac1900e9da22160a11d8b350">00293</a> T <a class="code" href="a00099.html#ga911d353ac1900e9da22160a11d8b350">zerosGeometricMean</a>(<span class="keyword">const</span> Polynomial<T>& p) {<a name="l00294"></a>00294 <span class="keyword">const</span> T SMALL = T(1.e-3);<a name="l00295"></a>00295 T m = Float(p.<a class="code" href="a00090.html#b433e0edb11b32a205a9d07b89aefa8f">degree</a>());<a name="l00296"></a>00296 <span class="keywordflow">return</span> exp(log(abs(p[0]) - log(abs(p[p.degree()])))/m + SMALL);<a name="l00297"></a>00297 }<a name="l00298"></a>00298 <a name="l00305"></a>00305 <span class="keyword">template</span><<span class="keyword">class</span> T><a name="l00306"></a><a class="code" href="a00099.html#gff48f345e1c619a7fcfef4fec02674f8">00306</a> T <a class="code" href="a00099.html#ga911d353ac1900e9da22160a11d8b350">zerosGeometricMean</a>(<span class="keyword">const</span> <a class="code" href="a00090.html">Polynomial</a>< std::complex <T> >& p) {<a name="l00307"></a>00307 <span class="keyword">const</span> T SMALL = T(1.e-3);<a name="l00308"></a>00308 T m = Float(p.<a class="code" href="a00090.html#b433e0edb11b32a205a9d07b89aefa8f">degree</a>());<a name="l00309"></a>00309 <span class="keywordflow">return</span> exp(log(abs(p[0]) - log(abs(p[p.degree()])))/m + SMALL);<a name="l00310"></a>00310 }<a name="l00311"></a>00311 <a name="l00327"></a>00327 <span class="keyword">template</span><<span class="keyword">class</span> T><a name="l00328"></a><a class="code" href="a00102.html#g3536daa88b2578a96cd84d2680ac9d66">00328</a> <span class="keyword">inline</span> <span class="keywordtype">void</span> <a class="code" href="a00102.html#g3536daa88b2578a96cd84d2680ac9d66">sortZeros</a>(std::vector<std::complex<T> >& zeros) {<a name="l00329"></a>00329 <span class="keyword">class </span>local {<a name="l00330"></a>00330 <span class="keyword">public</span>:<a name="l00331"></a>00331 <span class="keyword">static</span> <span class="keyword">inline</span> <span class="keywordtype">bool</span> zeroSortPred(<span class="keyword">const</span> std::complex<T>& z1, <span class="keyword">const</span> std::complex<T>& z2) {<a name="l00332"></a>00332 <span class="keywordflow">return</span> z1.real() < z2.real();<a name="l00333"></a>00333 }<a name="l00334"></a>00334 };<a name="l00335"></a>00335 std::sort(zeros.begin(), zeros.end(), local::zeroSortPred);<a name="l00336"></a>00336 }<a name="l00337"></a>00337 <a name="l00349"></a>00349 template <class T><a name="l00350"></a><a class="code" href="a00102.html#g6e9fe1cec8c7ec334d9e21f31b602bde">00350</a> <span class="keyword">inline</span> T <a class="code" href="a00102.html#g6e9fe1cec8c7ec334d9e21f31b602bde">solveDegree1</a>(<span class="keyword">const</span> T& a, <span class="keyword">const</span> T& b) {<a name="l00351"></a>00351 <span class="keywordflow">return</span> -b / a;<a name="l00352"></a>00352 }<a name="l00353"></a>00353 <a name="l00382"></a>00382 <span class="keyword">template</span> <<span class="keyword">class</span> T, <span class="keyword">class</span> U><a name="l00383"></a><a class="code" href="a00102.html#gb88e92200690d2e3f8b0c785c8fa42d3">00383</a> <span class="keywordtype">void</span> <a class="code" href="a00102.html#gb88e92200690d2e3f8b0c785c8fa42d3">solveDegree2</a>(<span class="keyword">const</span> T& a, <span class="keyword">const</span> T& b, <span class="keyword">const</span> T& c, U& z1, U& z2) {<a name="l00384"></a>00384 U sq, sum, dif, q;<a name="l00385"></a>00385 sq = sqrt(U((b * b) - (Float(4) * a * c)));<a name="l00386"></a>00386 sum = b + sq;<a name="l00387"></a>00387 dif = sq - b;<a name="l00388"></a>00388 <span class="keywordflow">if</span> (abs(dif) > abs(sum))<a name="l00389"></a>00389 q = dif;<a name="l00390"></a>00390 <span class="keywordflow">else</span> <a name="l00391"></a>00391 q = -sum;<a name="l00392"></a>00392 <a name="l00393"></a>00393 z1 = (c + c) / q;<a name="l00394"></a>00394 z2 = q / (a + a);<a name="l00395"></a>00395 <a name="l00396"></a>00396 <span class="keywordflow">if</span> (z1 > z2)<a name="l00397"></a>00397 std::swap(z1, z2);<a name="l00398"></a>00398 }<a name="l00400"></a>00400 <span class="preprocessor">#endif // POLYZERO_H </span></pre></div><hr size="1"><address style="align: right;"><small>Generated on Mon Aug 21 21:57:25 2006 for The Polynomials Templates Library by <a href="http://www.doxygen.org/index.html"><img src="doxygen.png" alt="doxygen" align="middle" border="0"></a> 1.4.5 </small></address></body></html>⌨️ 快捷键说明
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