a00106.html

This library defines basic operation on polynomials, and contains also 3 different roots (zeroes)-fi

<a name="l00161"></a>00161                     <span class="keywordflow">if</span> (E == Complex(0)) {
<a name="l00162"></a>00162                         <span class="comment">//printf("e");</span>
<a name="l00163"></a>00163                         <span class="keywordflow">break</span>;
<a name="l00164"></a>00164                     }
<a name="l00165"></a>00165                     h = (pz + pz) / E;
<a name="l00166"></a>00166                 }
<a name="l00167"></a>00167                 <span class="keywordflow">else</span> {
<a name="l00168"></a>00168                     <span class="comment">//  if we've lost convergence, reduce step by half until we converge again</span>
<a name="l00169"></a>00169                     <span class="comment">//printf("h");</span>
<a name="l00170"></a>00170                     h = h * Float(.5);
<a name="l00171"></a>00171                 }
<a name="l00172"></a>00172 
<a name="l00173"></a>00173                 x = z - h;
<a name="l00174"></a>00174 
<a name="l00175"></a>00175                 <span class="keywordflow">if</span> (x == z) {
<a name="l00176"></a>00176                     <span class="keywordflow">if</span> (j == 1)
<a name="l00177"></a>00177                         <a class="code" href="a00100.html#g0a6fc89686a91e3c8c99923a7b0247e3">evalAndDeflate</a>(p, z, q);
<a name="l00178"></a>00178                     <span class="comment">//printf("a");</span>
<a name="l00179"></a>00179                     <span class="keywordflow">break</span>;
<a name="l00180"></a>00180                 }
<a name="l00181"></a>00181 
<a name="l00182"></a>00182                 px = <a class="code" href="a00100.html#g0a6fc89686a91e3c8c99923a7b0247e3">evalAndDeflate</a>(p, x, q, e);
<a name="l00183"></a>00183                 mpx = abs(px);
<a name="l00184"></a>00184 
<a name="l00185"></a>00185                 <span class="keywordflow">if</span> (_isnan(mpx)) {
<a name="l00186"></a>00186                     <span class="comment">//printf("b");</span>
<a name="l00187"></a>00187                     <span class="keywordflow">break</span>;
<a name="l00188"></a>00188                 }
<a name="l00189"></a>00189                 <span class="keywordflow">else</span> <span class="keywordflow">if</span> (mpx &lt;= (mpz + mpz))
<a name="l00190"></a>00190                     conv = 0;
<a name="l00191"></a>00191                 <span class="keywordflow">else</span>
<a name="l00192"></a>00192                     ++conv;
<a name="l00193"></a>00193                 <span class="keywordflow">if</span> (conv &gt; 5) {
<a name="l00194"></a>00194                     <span class="comment">//printf("g");</span>
<a name="l00195"></a>00195                     conv = 0;
<a name="l00196"></a>00196                     <span class="keywordflow">break</span>;
<a name="l00197"></a>00197                 }
<a name="l00198"></a>00198 
<a name="l00199"></a>00199                 <span class="keywordflow">if</span> (!started || conv == 0) {
<a name="l00200"></a>00200                     conv = 0;
<a name="l00201"></a>00201 
<a name="l00202"></a>00202                     mpz = mpx;
<a name="l00203"></a>00203 
<a name="l00204"></a>00204                     z2 = z1;
<a name="l00205"></a>00205                     z1 = z;
<a name="l00206"></a>00206                     z = x;
<a name="l00207"></a>00207 
<a name="l00208"></a>00208                     <span class="keywordflow">if</span> (mpz &lt; e)
<a name="l00209"></a>00209                         <span class="keywordflow">break</span>;
<a name="l00210"></a>00210 
<a name="l00211"></a>00211                     pz2 = pz1;
<a name="l00212"></a>00212                     pz1 = pz;
<a name="l00213"></a>00213                     pz = px;
<a name="l00214"></a>00214 
<a name="l00215"></a>00215                     h1 = h2;
<a name="l00216"></a>00216                     d1 = d2;
<a name="l00217"></a>00217                     h2 = z - z1;
<a name="l00218"></a>00218                     <span class="keywordflow">if</span> (h2 == Complex(0)) {
<a name="l00219"></a>00219                         <span class="comment">//printf("c");</span>
<a name="l00220"></a>00220                         <span class="keywordflow">break</span>;
<a name="l00221"></a>00221                     }
<a name="l00222"></a>00222                     d2 = (pz - pz1) / h2;
<a name="l00223"></a>00223                     <span class="keywordflow">if</span> ((h2 + h1) == Complex(0)) {
<a name="l00224"></a>00224                         <span class="comment">//printf("d");</span>
<a name="l00225"></a>00225                         <span class="keywordflow">break</span>;
<a name="l00226"></a>00226                     }
<a name="l00227"></a>00227                     d = (d2 - d1) / (h2 + h1);
<a name="l00228"></a>00228                 }
<a name="l00229"></a>00229             }
<a name="l00230"></a>00230 
<a name="l00231"></a>00231             <span class="comment">//printf("j:%d%s", j, (mpz &lt; e) ? "\n" : "f ");</span>
<a name="l00232"></a>00232             <span class="keywordflow">if</span> (mpz &lt; e || mpz == 0) {
<a name="l00233"></a>00233                 <span class="keywordflow">if</span> (<span class="keyword">sizeof</span>(T) == <span class="keyword">sizeof</span>(U)) {
<a name="l00234"></a>00234                     z1 = conj(z);
<a name="l00235"></a>00235                     pz1 = <a class="code" href="a00100.html#gc5161c8ecd75b0108d0ea60c92d30d21">eval</a>(q, conj(z), e);
<a name="l00236"></a>00236                     <span class="keywordflow">if</span> (abs(pz1) &lt; e) {
<a name="l00237"></a>00237                         <span class="comment">//if (abs(z.imag()) &gt; abs(z.real()) * 20 * fpSpecs.MRE) {</span>
<a name="l00238"></a>00238                         <span class="keywordflow">if</span> (polish) {
<a name="l00239"></a>00239                             <a class="code" href="a00102.html#g7528de40f73b280a95202bc5b8947424">newtonZero</a>(P, z, pz, mpz, ADAPTIVE);
<a name="l00240"></a>00240                             <a class="code" href="a00100.html#g0a6fc89686a91e3c8c99923a7b0247e3">evalAndDeflate</a>(p, z, q);
<a name="l00241"></a>00241                         }
<a name="l00242"></a>00242                         zeros.push_back(z);
<a name="l00243"></a>00243                         z = conj(z);
<a name="l00244"></a>00244                         <span class="keywordflow">if</span> (polish) {
<a name="l00245"></a>00245                             <a class="code" href="a00102.html#g7528de40f73b280a95202bc5b8947424">newtonZero</a>(P, z, pz, mpz, ADAPTIVE);
<a name="l00246"></a>00246                         }
<a name="l00247"></a>00247                         <a class="code" href="a00100.html#g0a6fc89686a91e3c8c99923a7b0247e3">evalAndDeflate</a>(q, z, q2);
<a name="l00248"></a>00248                         zeros.push_back(z);
<a name="l00249"></a>00249                         n = q2.degree();
<a name="l00250"></a>00250                         <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt;= n; ++i)
<a name="l00251"></a>00251                             * (Float *) &amp; (p[i]) = q2[i].real();
<a name="l00252"></a>00252                         p.resize(n + 1);
<a name="l00253"></a>00253                     }
<a name="l00254"></a>00254                     <span class="keywordflow">else</span> {
<a name="l00255"></a>00255                         <span class="keywordflow">if</span> (polish) {
<a name="l00256"></a>00256                             <a class="code" href="a00102.html#g7528de40f73b280a95202bc5b8947424">newtonZero</a>(P, z, pz, mpz, ADAPTIVE);
<a name="l00257"></a>00257                             <a class="code" href="a00100.html#g0a6fc89686a91e3c8c99923a7b0247e3">evalAndDeflate</a>(p, z, q);
<a name="l00258"></a>00258                         }
<a name="l00259"></a>00259                         zeros.push_back(z);
<a name="l00260"></a>00260                         n = q.degree();
<a name="l00261"></a>00261                         <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt;= n; ++i)
<a name="l00262"></a>00262                             * (Float *) &amp; (p[i]) = q[i].real();
<a name="l00263"></a>00263                         p.resize(n + 1);
<a name="l00264"></a>00264                     }
<a name="l00265"></a>00265                     <span class="keywordflow">break</span>;
<a name="l00266"></a>00266                 }
<a name="l00267"></a>00267                 <span class="keywordflow">else</span> {
<a name="l00268"></a>00268                     <span class="keywordflow">if</span> (polish) {
<a name="l00269"></a>00269                         <a class="code" href="a00102.html#g7528de40f73b280a95202bc5b8947424">newtonZero</a>(P, z, pz, mpz, ADAPTIVE);
<a name="l00270"></a>00270                         <a class="code" href="a00100.html#g0a6fc89686a91e3c8c99923a7b0247e3">evalAndDeflate</a>(p, z, q);
<a name="l00271"></a>00271                     }
<a name="l00272"></a>00272                     zeros.push_back(z);
<a name="l00273"></a>00273                     * (ComplexPolynomial *) &amp; p = q;
<a name="l00274"></a>00274                     <span class="keywordflow">break</span>;
<a name="l00275"></a>00275                 }
<a name="l00276"></a>00276             }
<a name="l00277"></a>00277         }
<a name="l00278"></a>00278         <span class="keywordflow">if</span> (i &gt;= MAXIT)
<a name="l00279"></a>00279             <span class="keywordflow">break</span>;
<a name="l00280"></a>00280     }
<a name="l00281"></a>00281     <a class="code" href="a00102.html#g3536daa88b2578a96cd84d2680ac9d66">sortZeros</a>(zeros);
<a name="l00282"></a>00282     <span class="keywordflow">return</span> (<span class="keywordtype">int</span>)zeros.size();
<a name="l00283"></a>00283 }
<a name="l00284"></a>00284 
<a name="l00285"></a>00285 <span class="preprocessor">#endif //MUELLER_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&nbsp;
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