📄 qwt__spline_8cpp-source.html
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<a name="l00201"></a>00201 <a name="l00206"></a>00206 <span class="preprocessor">#if QT_VERSION < 0x040000</span><a name="l00207"></a>00207 <span class="preprocessor"></span><span class="keywordtype">bool</span> <a class="code" href="class_qwt_spline.html#1cdf09e841dd6a721eb788914273c484">QwtSpline::buildNaturalSpline</a>(<span class="keyword">const</span> QwtArray<QwtDoublePoint> &points)<a name="l00208"></a>00208 <span class="preprocessor">#else</span><a name="l00209"></a><a class="code" href="class_qwt_spline.html#1cdf09e841dd6a721eb788914273c484">00209</a> <span class="preprocessor"></span><span class="keywordtype">bool</span> <a class="code" href="class_qwt_spline.html#1cdf09e841dd6a721eb788914273c484">QwtSpline::buildNaturalSpline</a>(<span class="keyword">const</span> QPolygonF &points)<a name="l00210"></a>00210 <span class="preprocessor">#endif</span><a name="l00211"></a>00211 <span class="preprocessor"></span>{<a name="l00212"></a>00212 <span class="keywordtype">int</span> i;<a name="l00213"></a>00213 <a name="l00214"></a>00214 <span class="preprocessor">#if QT_VERSION < 0x040000</span><a name="l00215"></a>00215 <span class="preprocessor"></span> <span class="keyword">const</span> QwtDoublePoint *p = points.data();<a name="l00216"></a>00216 <span class="preprocessor">#else</span><a name="l00217"></a>00217 <span class="preprocessor"></span> <span class="keyword">const</span> QPointF *p = points.data();<a name="l00218"></a>00218 <span class="preprocessor">#endif</span><a name="l00219"></a>00219 <span class="preprocessor"></span> <span class="keyword">const</span> <span class="keywordtype">int</span> size = points.size();<a name="l00220"></a>00220 <a name="l00221"></a>00221 <span class="keywordtype">double</span> *a = d_data->a.data();<a name="l00222"></a>00222 <span class="keywordtype">double</span> *b = d_data->b.data();<a name="l00223"></a>00223 <span class="keywordtype">double</span> *c = d_data->c.data();<a name="l00224"></a>00224 <a name="l00225"></a>00225 <span class="comment">// set up tridiagonal equation system; use coefficient</span><a name="l00226"></a>00226 <span class="comment">// vectors as temporary buffers</span><a name="l00227"></a>00227 QwtArray<double> h(size-1);<a name="l00228"></a>00228 <span class="keywordflow">for</span> (i = 0; i < size - 1; i++) <a name="l00229"></a>00229 {<a name="l00230"></a>00230 h[i] = p[i+1].x() - p[i].x();<a name="l00231"></a>00231 <span class="keywordflow">if</span> (h[i] <= 0)<a name="l00232"></a>00232 <span class="keywordflow">return</span> <span class="keyword">false</span>;<a name="l00233"></a>00233 }<a name="l00234"></a>00234 <a name="l00235"></a>00235 QwtArray<double> d(size-1);<a name="l00236"></a>00236 <span class="keywordtype">double</span> dy1 = (p[1].y() - p[0].y()) / h[0];<a name="l00237"></a>00237 <span class="keywordflow">for</span> (i = 1; i < size - 1; i++)<a name="l00238"></a>00238 {<a name="l00239"></a>00239 b[i] = c[i] = h[i];<a name="l00240"></a>00240 a[i] = 2.0 * (h[i-1] + h[i]);<a name="l00241"></a>00241 <a name="l00242"></a>00242 <span class="keyword">const</span> <span class="keywordtype">double</span> dy2 = (p[i+1].y() - p[i].y()) / h[i];<a name="l00243"></a>00243 d[i] = 6.0 * ( dy1 - dy2);<a name="l00244"></a>00244 dy1 = dy2;<a name="l00245"></a>00245 }<a name="l00246"></a>00246 <a name="l00247"></a>00247 <span class="comment">//</span><a name="l00248"></a>00248 <span class="comment">// solve it</span><a name="l00249"></a>00249 <span class="comment">//</span><a name="l00250"></a>00250 <a name="l00251"></a>00251 <span class="comment">// L-U Factorization</span><a name="l00252"></a>00252 <span class="keywordflow">for</span>(i = 1; i < size - 2;i++)<a name="l00253"></a>00253 {<a name="l00254"></a>00254 c[i] /= a[i];<a name="l00255"></a>00255 a[i+1] -= b[i] * c[i]; <a name="l00256"></a>00256 }<a name="l00257"></a>00257 <a name="l00258"></a>00258 <span class="comment">// forward elimination</span><a name="l00259"></a>00259 QwtArray<double> s(size);<a name="l00260"></a>00260 s[1] = d[1];<a name="l00261"></a>00261 <span class="keywordflow">for</span> ( i = 2; i < size - 1; i++)<a name="l00262"></a>00262 s[i] = d[i] - c[i-1] * s[i-1];<a name="l00263"></a>00263 <a name="l00264"></a>00264 <span class="comment">// backward elimination</span><a name="l00265"></a>00265 s[size - 2] = - s[size - 2] / a[size - 2];<a name="l00266"></a>00266 <span class="keywordflow">for</span> (i = size -3; i > 0; i--)<a name="l00267"></a>00267 s[i] = - (s[i] + b[i] * s[i+1]) / a[i];<a name="l00268"></a>00268 s[size - 1] = s[0] = 0.0;<a name="l00269"></a>00269 <a name="l00270"></a>00270 <span class="comment">//</span><a name="l00271"></a>00271 <span class="comment">// Finally, determine the spline coefficients</span><a name="l00272"></a>00272 <span class="comment">//</span><a name="l00273"></a>00273 <span class="keywordflow">for</span> (i = 0; i < size - 1; i++)<a name="l00274"></a>00274 {<a name="l00275"></a>00275 a[i] = ( s[i+1] - s[i] ) / ( 6.0 * h[i]);<a name="l00276"></a>00276 b[i] = 0.5 * s[i];<a name="l00277"></a>00277 c[i] = ( p[i+1].y() - p[i].y() ) / h[i] <a name="l00278"></a>00278 - (s[i+1] + 2.0 * s[i] ) * h[i] / 6.0; <a name="l00279"></a>00279 }<a name="l00280"></a>00280 <a name="l00281"></a>00281 <span class="keywordflow">return</span> <span class="keyword">true</span>;<a name="l00282"></a>00282 }<a name="l00283"></a>00283 <a name="l00288"></a>00288 <span class="preprocessor">#if QT_VERSION < 0x040000</span><a name="l00289"></a>00289 <span class="preprocessor"></span><span class="keywordtype">bool</span> <a class="code" href="class_qwt_spline.html#8184717f8c018e69fabd1e33ac68ef19">QwtSpline::buildPeriodicSpline</a>(<a name="l00290"></a>00290 <span class="keyword">const</span> QwtArray<QwtDoublePoint> &points)<a name="l00291"></a>00291 <span class="preprocessor">#else</span><a name="l00292"></a><a class="code" href="class_qwt_spline.html#8184717f8c018e69fabd1e33ac68ef19">00292</a> <span class="preprocessor"></span><span class="keywordtype">bool</span> <a class="code" href="class_qwt_spline.html#8184717f8c018e69fabd1e33ac68ef19">QwtSpline::buildPeriodicSpline</a>(<span class="keyword">const</span> QPolygonF &points)<a name="l00293"></a>00293 <span class="preprocessor">#endif</span><a name="l00294"></a>00294 <span class="preprocessor"></span>{<a name="l00295"></a>00295 <span class="keywordtype">int</span> i;<a name="l00296"></a>00296 <a name="l00297"></a>00297 <span class="preprocessor">#if QT_VERSION < 0x040000</span><a name="l00298"></a>00298 <span class="preprocessor"></span> <span class="keyword">const</span> QwtDoublePoint *p = points.data();<a name="l00299"></a>00299 <span class="preprocessor">#else</span><a name="l00300"></a>00300 <span class="preprocessor"></span> <span class="keyword">const</span> QPointF *p = points.data();<a name="l00301"></a>00301 <span class="preprocessor">#endif</span><a name="l00302"></a>00302 <span class="preprocessor"></span> <span class="keyword">const</span> <span class="keywordtype">int</span> size = points.size();<a name="l00303"></a>00303 <a name="l00304"></a>00304 <span class="keywordtype">double</span> *a = d_data->a.data();<a name="l00305"></a>00305 <span class="keywordtype">double</span> *b = d_data->b.data();<a name="l00306"></a>00306 <span class="keywordtype">double</span> *c = d_data->c.data();<a name="l00307"></a>00307 <a name="l00308"></a>00308 QwtArray<double> d(size-1);<a name="l00309"></a>00309 QwtArray<double> h(size-1);<a name="l00310"></a>00310 QwtArray<double> s(size);<a name="l00311"></a>00311 <a name="l00312"></a>00312 <span class="comment">//</span><a name="l00313"></a>00313 <span class="comment">// setup equation system; use coefficient</span><a name="l00314"></a>00314 <span class="comment">// vectors as temporary buffers</span><a name="l00315"></a>00315 <span class="comment">//</span><a name="l00316"></a>00316 <span class="keywordflow">for</span> (i = 0; i < size - 1; i++)<a name="l00317"></a>00317 {<a name="l00318"></a>00318 h[i] = p[i+1].x() - p[i].x();<a name="l00319"></a>00319 <span class="keywordflow">if</span> (h[i] <= 0.0)<a name="l00320"></a>00320 <span class="keywordflow">return</span> <span class="keyword">false</span>;<a name="l00321"></a>00321 }<a name="l00322"></a>00322 <a name="l00323"></a>00323 <span class="keyword">const</span> <span class="keywordtype">int</span> imax = size - 2;<a name="l00324"></a>00324 <span class="keywordtype">double</span> htmp = h[imax];<a name="l00325"></a>00325 <span class="keywordtype">double</span> dy1 = (p[0].y() - p[imax].y()) / htmp;<a name="l00326"></a>00326 <span class="keywordflow">for</span> (i = 0; i <= imax; i++)<a name="l00327"></a>00327 {<a name="l00328"></a>00328 b[i] = c[i] = h[i];<a name="l00329"></a>00329 a[i] = 2.0 * (htmp + h[i]);<a name="l00330"></a>00330 <span class="keyword">const</span> <span class="keywordtype">double</span> dy2 = (p[i+1].y() - p[i].y()) / h[i];<a name="l00331"></a>00331 d[i] = 6.0 * ( dy1 - dy2);<a name="l00332"></a>00332 dy1 = dy2;<a name="l00333"></a>00333 htmp = h[i];<a name="l00334"></a>00334 }<a name="l00335"></a>00335 <a name="l00336"></a>00336 <span class="comment">//</span><a name="l00337"></a>00337 <span class="comment">// solve it</span><a name="l00338"></a>00338 <span class="comment">//</span><a name="l00339"></a>00339 <a name="l00340"></a>00340 <span class="comment">// L-U Factorization</span><a name="l00341"></a>00341 a[0] = sqrt(a[0]);<a name="l00342"></a>00342 c[0] = h[imax] / a[0];<a name="l00343"></a>00343 <span class="keywordtype">double</span> sum = 0;<a name="l00344"></a>00344 <a name="l00345"></a>00345 <span class="keywordflow">for</span>( i = 0; i < imax - 1; i++)<a name="l00346"></a>00346 {<a name="l00347"></a>00347 b[i] /= a[i];<a name="l00348"></a>00348 <span class="keywordflow">if</span> (i > 0)<a name="l00349"></a>00349 c[i] = - c[i-1] * b[i-1] / a[i];<a name="l00350"></a>00350 a[i+1] = sqrt( a[i+1] - qwtSqr(b[i]));<a name="l00351"></a>00351 sum += qwtSqr(c[i]);<a name="l00352"></a>00352 }<a name="l00353"></a>00353 b[imax-1] = (b[imax-1] - c[imax-2] * b[imax-2]) / a[imax-1];<a name="l00354"></a>00354 a[imax] = sqrt(a[imax] - qwtSqr(b[imax-1]) - sum);<a name="l00355"></a>00355 <a name="l00356"></a>00356 <a name="l00357"></a>00357 <span class="comment">// forward elimination</span><a name="l00358"></a>00358 s[0] = d[0] / a[0];<a name="l00359"></a>00359 sum = 0;<a name="l00360"></a>00360 <span class="keywordflow">for</span>( i = 1; i < imax; i++)<a name="l00361"></a>00361 {<a name="l00362"></a>00362 s[i] = (d[i] - b[i-1] * s[i-1]) / a[i];<a name="l00363"></a>00363 sum += c[i-1] * s[i-1];<a name="l00364"></a>00364 }<a name="l00365"></a>00365 s[imax] = (d[imax] - b[imax-1] * s[imax-1] - sum) / a[imax];<a name="l00366"></a>00366 <a name="l00367"></a>00367 <a name="l00368"></a>00368 <span class="comment">// backward elimination</span><a name="l00369"></a>00369 s[imax] = - s[imax] / a[imax];<a name="l00370"></a>00370 s[imax-1] = -(s[imax-1] + b[imax-1] * s[imax]) / a[imax-1];<a name="l00371"></a>00371 <span class="keywordflow">for</span> (i= imax - 2; i >= 0; i--)<a name="l00372"></a>00372 s[i] = - (s[i] + b[i] * s[i+1] + c[i] * s[imax]) / a[i];<a name="l00373"></a>00373 <a name="l00374"></a>00374 <span class="comment">//</span><a name="l00375"></a>00375 <span class="comment">// Finally, determine the spline coefficients</span><a name="l00376"></a>00376 <span class="comment">//</span><a name="l00377"></a>00377 s[size-1] = s[0];<a name="l00378"></a>00378 <span class="keywordflow">for</span> ( i=0; i < size-1; i++)<a name="l00379"></a>00379 {<a name="l00380"></a>00380 a[i] = ( s[i+1] - s[i] ) / ( 6.0 * h[i]);<a name="l00381"></a>00381 b[i] = 0.5 * s[i];<a name="l00382"></a>00382 c[i] = ( p[i+1].y() - p[i].y() ) <a name="l00383"></a>00383 / h[i] - (s[i+1] + 2.0 * s[i] ) * h[i] / 6.0; <a name="l00384"></a>00384 }<a name="l00385"></a>00385 <a name="l00386"></a>00386 <span class="keywordflow">return</span> <span class="keyword">true</span>;<a name="l00387"></a>00387 }</pre></div><hr size="1"><address style="align: right;"><small>Generated on Mon Feb 26 21:22:38 2007 for Qwt User's Guide by <a href="http://www.doxygen.org/index.html"><img src="doxygen.png" alt="doxygen" align="middle" border="0"></a> 1.4.6 </small></address></body></html>⌨️ 快捷键说明
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