📄 a00104.html
字号:
<!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: jenkinstraub.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>jenkinstraub.h</h1><a href="a00093.html">Go to the documentation of this file.</a><div class="fragment"><pre class="fragment"><a name="l00001"></a>00001 <span class="preprocessor">#ifndef JENKINSTRAUB_H</span><a name="l00002"></a>00002 <span class="preprocessor"></span><span class="preprocessor">#define JENKINSTRAUB_H</span><a name="l00003"></a>00003 <span class="preprocessor"></span><a name="l00029"></a>00029 <span class="preprocessor">#include "<a class="code" href="a00097.html">polyzero.h</a>"</span><a name="l00030"></a>00030 <a name="l00054"></a>00054 <span class="keyword">template</span><<span class="keyword">class</span> T, <span class="keyword">class</span> U><a name="l00055"></a><a class="code" href="a00102.html#g38785df759bdb907a923c48b208f4e0d">00055</a> <span class="keywordtype">int</span> <a class="code" href="a00102.html#g38785df759bdb907a923c48b208f4e0d">jenkinsTraubZeros</a>(<span class="keyword">const</span> Polynomial< T >& P, std::vector< std::complex < U > >& zeros, <span class="keywordtype">bool</span> polish) {<a name="l00056"></a>00056 <a name="l00057"></a>00057 <span class="keyword">typedef</span> U Float;<a name="l00058"></a>00058 <span class="keyword">typedef</span> std::complex<Float> Complex;<a name="l00059"></a>00059 <span class="keyword">typedef</span> Polynomial<Complex> ComplexPolynomial;<a name="l00060"></a>00060 <span class="keyword">typedef</span> Polynomial<Float> FloatPolynomial;<a name="l00061"></a>00061 <a name="l00062"></a>00062 <span class="keyword">class </span>local {<a name="l00063"></a>00063 <span class="keyword">public</span>:<a name="l00064"></a>00064 <span class="keyword">static</span> <span class="keywordtype">void</span> noShift(<span class="keyword">const</span> ComplexPolynomial& p, ComplexPolynomial& h) {<a name="l00065"></a>00065 <span class="keyword">const</span> <span class="keywordtype">unsigned</span> M = 5;<a name="l00066"></a>00066 <span class="keywordtype">int</span> m = p.degree();<a name="l00067"></a>00067 Float ii = Float(1);<a name="l00068"></a>00068 Float dd = Float(m);<a name="l00069"></a>00069 h.resize(m);<a name="l00070"></a>00070 <span class="comment">// first evalutate H0 = p'</span><a name="l00071"></a>00071 <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < m; ++i, ii += Float(1))<a name="l00072"></a>00072 h[i] = p[i + 1] * (ii / dd);<a name="l00073"></a>00073 <a name="l00074"></a>00074 <span class="comment">// Hl+1(z) = 1/z * (Hl(z) - (Hl(0)/p(0)) * p(z));</span><a name="l00075"></a>00075 <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> i = 0; i < M; ++i) {<a name="l00076"></a>00076 Complex k = -h[0] / p[0];<a name="l00077"></a>00077 <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j < m - 1; ++j)<a name="l00078"></a>00078 h[j] = h[j + 1] + (k * p[j + 1]);<a name="l00079"></a>00079 h[m - 1] = k * p[m];<a name="l00080"></a>00080 }<a name="l00081"></a>00081 }<a name="l00082"></a>00082 <a name="l00083"></a>00083 <span class="keyword">static</span> <span class="keywordtype">bool</span> fixedShift(<span class="keywordtype">unsigned</span> pass, <span class="keyword">const</span> ComplexPolynomial& p, ComplexPolynomial& h, ComplexPolynomial& qp, Complex& s) {<a name="l00084"></a>00084 <a name="l00085"></a>00085 <span class="keywordtype">bool</span> failed = <span class="keyword">false</span>;<a name="l00086"></a>00086 <span class="keywordtype">int</span> conv = 0;<a name="l00087"></a>00087 Complex hs, ps, t, tOld, z;<a name="l00088"></a>00088 ComplexPolynomial qh;<a name="l00089"></a>00089 ps = p.evalAndDeflate(s, qp);<a name="l00090"></a>00090 t = nextT(s, ps, h, hs, qh);<a name="l00091"></a>00091 <a name="l00092"></a>00092 <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> i = 0; i < (10 * pass); ++i) {<a name="l00093"></a>00093 tOld = t;<a name="l00094"></a>00094 <span class="comment">// compute next h and new t</span><a name="l00095"></a>00095 nextH(p, h, qp, qh, hs, ps, t);<a name="l00096"></a>00096 t = nextT(s, ps, h, hs, qh);<a name="l00097"></a>00097 z = s + t;<a name="l00098"></a>00098 <a name="l00099"></a>00099 <span class="keywordflow">if</span> (hs == Complex(0))<a name="l00100"></a>00100 <span class="keywordflow">continue</span>;<a name="l00101"></a>00101 <a name="l00102"></a>00102 <span class="comment">// weak convergence test</span><a name="l00103"></a>00103 Float k = abs(tOld - t);<a name="l00104"></a>00104 Float l = Float(.5) * abs(z);<a name="l00105"></a>00105 <span class="keywordflow">if</span> (!failed && abs(t - tOld) < Float(.5) * abs(z)) {<a name="l00106"></a>00106 <span class="keywordflow">if</span> (++conv >= 2) {<a name="l00107"></a>00107 <span class="keywordflow">if</span> (variableShift(p, h, qp, qh, z, t, hs, ps)) {<a name="l00108"></a>00108 s = z;<a name="l00109"></a>00109 <span class="keywordflow">return</span> <span class="keyword">true</span>;<a name="l00110"></a>00110 }<a name="l00111"></a>00111 conv = 0;<a name="l00112"></a>00112 failed = <span class="keyword">true</span>;<a name="l00113"></a>00113 }<a name="l00114"></a>00114 }<a name="l00115"></a>00115 <span class="keywordflow">else</span><a name="l00116"></a>00116 conv = 0;<a name="l00117"></a>00117 }<a name="l00118"></a>00118 <span class="comment">// do a last attempt with final h polynomial</span><a name="l00119"></a>00119 <span class="keywordflow">if</span> (variableShift(p, h, qp, qh, z, t, ps, hs)) {<a name="l00120"></a>00120 s = z;<a name="l00121"></a>00121 <span class="keywordflow">return</span> <span class="keyword">true</span>;<a name="l00122"></a>00122 }<a name="l00123"></a>00123 <span class="keywordflow">return</span> <span class="keyword">false</span>;<a name="l00124"></a>00124 }<a name="l00125"></a>00125 <a name="l00126"></a>00126 <span class="keyword">static</span> <span class="keywordtype">bool</span> variableShift(<span class="keyword">const</span> ComplexPolynomial& p, ComplexPolynomial& h, ComplexPolynomial& qp, ComplexPolynomial& qh, Complex& s, Complex& t, Complex& ps, Complex& hs) {<a name="l00127"></a>00127 <span class="keyword">static</span> FloatSpecs<Float> fpSpecs;<a name="l00128"></a>00128 <span class="keywordtype">bool</span> b = <span class="keyword">false</span>;<a name="l00129"></a>00129 <span class="keywordtype">int</span> i;<a name="l00130"></a>00130 Float step = 0, mpOld = fpSpecs.<a class="code" href="a00089.html#7fce7d8806caf8595e993e7f1258e57d">INFINY</a>, mp = 0, mt = fpSpecs.<a class="code" href="a00089.html#7fce7d8806caf8595e993e7f1258e57d">INFINY</a>, mtOld = fpSpecs.<a class="code" href="a00089.html#7fce7d8806caf8595e993e7f1258e57d">INFINY</a>;<a name="l00131"></a>00131 ComplexPolynomial _H = h, _QH = qh;<a name="l00132"></a>00132 Complex _s = s, _Hs = hs, _t = t;<a name="l00133"></a>00133 Float e;<a name="l00134"></a>00134 <a name="l00135"></a>00135 <span class="keywordflow">for</span> (i = 1; i <= 12; ++i) {<a name="l00136"></a>00136 ps = <a class="code" href="a00100.html#g0a6fc89686a91e3c8c99923a7b0247e3">evalAndDeflate</a>(p, s, qp, e);<a name="l00137"></a>00137 mpOld = mp;<a name="l00138"></a>00138 mp = abs(ps);<a name="l00139"></a>00139 mtOld = mt;<a name="l00140"></a>00140 mt = abs(t);<a name="l00141"></a>00141 <a name="l00142"></a>00142 <span class="keywordflow">if</span> (_isnan(mp)) {<a name="l00143"></a>00143 <span class="comment">//printf("a");</span><a name="l00144"></a>00144 <span class="keywordflow">break</span>;<a name="l00145"></a>00145 }<a name="l00146"></a>00146 <a name="l00147"></a>00147 <span class="keywordflow">if</span> (mp < e) {<a name="l00148"></a>00148 <span class="comment">//printf("i:%d ", i);</span><a name="l00149"></a>00149 <span class="keywordflow">return</span> <span class="keyword">true</span>;<a name="l00150"></a>00150 }<a name="l00151"></a>00151 <a name="l00152"></a>00152 <span class="keywordflow">if</span> (i != 0) {<a name="l00153"></a>00153 <span class="keywordflow">if</span>(!b && mp > mpOld && step < Float(.05)) {<a name="l00154"></a>00154 <span class="comment">// Iteration has stalled. Probably a cluster of zeros. Do 5 fixed </span><a name="l00155"></a>00155 <span class="comment">// shift steps into the cluster to force one zero to dominate</span><a name="l00156"></a>00156 Float tp = std::max(step, fpSpecs.<a class="code" href="a00089.html#5e567bf650640c58e9455ad2eb4b05bc">ETA</a>);<a name="l00157"></a>00157 b = <span class="keyword">true</span>;<a name="l00158"></a>00158 Complex r(1 + sqrt(tp), sqrt(tp));<a name="l00159"></a>00159 s *= r;<a name="l00160"></a>00160 ps = p.evalAndDeflate(s, qp);<a name="l00161"></a>00161 <span class="keywordflow">for</span>(<span class="keywordtype">unsigned</span> j = 0; j < 5; ++j) {<a name="l00162"></a>00162 t = nextT(s, ps, h, hs, qh);<a name="l00163"></a>00163 nextH(p, h, qp, qh, hs, ps, t);<a name="l00164"></a>00164 }<a name="l00165"></a>00165 mp = fpSpecs.<a class="code" href="a00089.html#7fce7d8806caf8595e993e7f1258e57d">INFINY</a>;<a name="l00166"></a>00166 }<a name="l00167"></a>00167 <span class="comment">// Exit if polynomial value increase significantly</span><a name="l00168"></a>00168 <span class="keywordflow">else</span> <span class="keywordflow">if</span>((mp * Float(0.1)) > mpOld) <a name="l00169"></a>00169 <span class="keywordflow">break</span>;<a name="l00170"></a>00170 }<a name="l00171"></a>00171 <a name="l00172"></a>00172 t = nextT(s, ps, h, hs, qh);<a name="l00173"></a>00173 nextH(p, h, qp, qh, hs, ps, t);<a name="l00174"></a>00174 t = nextT(s, ps, h, hs, qh);<a name="l00175"></a>00175 <span class="keywordflow">if</span> (hs != Complex(0)) {<a name="l00176"></a>00176 step = abs(t) / abs(s);<a name="l00177"></a>00177 s = s + t;<a name="l00178"></a>00178 }<a name="l00179"></a>00179 }<a name="l00180"></a>00180 h = _H;<a name="l00181"></a>00181 qh = _QH;⌨️ 快捷键说明
复制代码
Ctrl + C
搜索代码
Ctrl + F
全屏模式
F11
切换主题
Ctrl + Shift + D
显示快捷键
?
增大字号
Ctrl + =
减小字号
Ctrl + -