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< div class = "headertitle" > < div class = "title" > durand_kerner_roots.c File Reference< / div > < / div >
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< / div > <!-- header -->
< div class = "contents" >
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< p > Compute all possible approximate roots of any given polynomial using < a href = "https://en.wikipedia.org/wiki/Durand%E2%80%93Kerner_method" target = "_blank" > Durand Kerner algorithm< / a >
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< a href = "#details" > More...< / a > < / p >
< div class = "textblock" > < code > #include < complex.h> < / code > < br / >
< code > #include < limits.h> < / code > < br / >
< code > #include < math.h> < / code > < br / >
< code > #include < stdio.h> < / code > < br / >
< code > #include < stdlib.h> < / code > < br / >
< code > #include < string.h> < / code > < br / >
< code > #include < time.h> < / code > < br / >
< / div > < div class = "textblock" > < div class = "dynheader" >
Include dependency graph for durand_kerner_roots.c:< / div >
< div class = "dyncontent" >
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< div class = "center" > < iframe scrolling = "no" frameborder = "0" src = "../../db/dff/durand__kerner__roots_8c__incl.svg" width = "616" height = "124" > < p > < b > This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.< / b > < / p > < / iframe >
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< / div >
< / div >
< / div > < table class = "memberdecls" >
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< tr class = "heading" > < td colspan = "2" > < h2 class = "groupheader" > < a id = "define-members" name = "define-members" > < / a >
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Macros< / h2 > < / td > < / tr >
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< tr class = "memitem:af270a96662132d0385cb6b4637c5a689" > < td class = "memItemLeft" align = "right" valign = "top" > < a id = "af270a96662132d0385cb6b4637c5a689" name = "af270a96662132d0385cb6b4637c5a689" > < / a >
#define  < / td > < td class = "memItemRight" valign = "bottom" > < b > ACCURACY< / b >       1e-10< / td > < / tr >
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< tr class = "memdesc:af270a96662132d0385cb6b4637c5a689" > < td class = "mdescLeft" >   < / td > < td class = "mdescRight" > maximum accuracy limit < br / > < / td > < / tr >
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< tr class = "separator:af270a96662132d0385cb6b4637c5a689" > < td class = "memSeparator" colspan = "2" >   < / td > < / tr >
< / table > < table class = "memberdecls" >
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< tr class = "heading" > < td colspan = "2" > < h2 class = "groupheader" > < a id = "func-members" name = "func-members" > < / a >
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Functions< / h2 > < / td > < / tr >
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< tr class = "memitem:a321f9781a9744ccdaf0aba89f35ec29c" > < td class = "memItemLeft" align = "right" valign = "top" > long double complex  < / td > < td class = "memItemRight" valign = "bottom" > < a class = "el" href = "../../da/d38/durand__kerner__roots_8c.html#a321f9781a9744ccdaf0aba89f35ec29c" > poly_function< / a > (long double *coeffs, unsigned int degree, long double complex x)< / td > < / tr >
< tr class = "memdesc:a321f9781a9744ccdaf0aba89f35ec29c" > < td class = "mdescLeft" >   < / td > < td class = "mdescRight" > Evaluate the value of a polynomial with given coefficients. < a href = "../../da/d38/durand__kerner__roots_8c.html#a321f9781a9744ccdaf0aba89f35ec29c" > More...< / a > < br / > < / td > < / tr >
< tr class = "separator:a321f9781a9744ccdaf0aba89f35ec29c" > < td class = "memSeparator" colspan = "2" >   < / td > < / tr >
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< tr class = "memitem:a46197e91f478e99a2229562aaaac311e" > < td class = "memItemLeft" align = "right" valign = "top" > const char *  < / td > < td class = "memItemRight" valign = "bottom" > < a class = "el" href = "../../da/d38/durand__kerner__roots_8c.html#a46197e91f478e99a2229562aaaac311e" > complex_str< / a > (long double complex x)< / td > < / tr >
< tr class = "memdesc:a46197e91f478e99a2229562aaaac311e" > < td class = "mdescLeft" >   < / td > < td class = "mdescRight" > create a textual form of complex number < a href = "../../da/d38/durand__kerner__roots_8c.html#a46197e91f478e99a2229562aaaac311e" > More...< / a > < br / > < / td > < / tr >
< tr class = "separator:a46197e91f478e99a2229562aaaac311e" > < td class = "memSeparator" colspan = "2" >   < / td > < / tr >
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< tr class = "memitem:a26d5695ebed0818a3e7cf4b10aacab52" > < td class = "memItemLeft" align = "right" valign = "top" > char  < / td > < td class = "memItemRight" valign = "bottom" > < a class = "el" href = "../../da/d38/durand__kerner__roots_8c.html#a26d5695ebed0818a3e7cf4b10aacab52" > check_termination< / a > (long double delta)< / td > < / tr >
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< tr class = "memdesc:a26d5695ebed0818a3e7cf4b10aacab52" > < td class = "mdescLeft" >   < / td > < td class = "mdescRight" > check for termination condition < a href = "../../da/d38/durand__kerner__roots_8c.html#a26d5695ebed0818a3e7cf4b10aacab52" > More...< / a > < br / > < / td > < / tr >
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< tr class = "separator:a26d5695ebed0818a3e7cf4b10aacab52" > < td class = "memSeparator" colspan = "2" >   < / td > < / tr >
< tr class = "memitem:a3c04138a5bfe5d72780bb7e82a18e627" > < td class = "memItemLeft" align = "right" valign = "top" > int  < / td > < td class = "memItemRight" valign = "bottom" > < a class = "el" href = "../../da/d38/durand__kerner__roots_8c.html#a3c04138a5bfe5d72780bb7e82a18e627" > main< / a > (int argc, char **argv)< / td > < / tr >
< tr class = "separator:a3c04138a5bfe5d72780bb7e82a18e627" > < td class = "memSeparator" colspan = "2" >   < / td > < / tr >
< / table >
< a name = "details" id = "details" > < / a > < h2 class = "groupheader" > Detailed Description< / h2 >
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< div class = "textblock" > < p > Compute all possible approximate roots of any given polynomial using < a href = "https://en.wikipedia.org/wiki/Durand%E2%80%93Kerner_method" target = "_blank" > Durand Kerner algorithm< / a > < / p >
< dl class = "section author" > < dt > Author< / dt > < dd > < a href = "https://github.com/kvedala" target = "_blank" > Krishna Vedala< / a > < / dd > < / dl >
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< p > Test the algorithm online: < a href = "https://gist.github.com/kvedala/27f1b0b6502af935f6917673ec43bcd7" > https://gist.github.com/kvedala/27f1b0b6502af935f6917673ec43bcd7< / a > < / p >
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< p > Try the highly unstable Wilkinson's polynomial: < / p > < div class = "fragment" > < div class = "line" > ./numerical_methods/durand_kerner_roots.c 1 -210 20615 -1256850 53327946< / div >
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< div class = "line" > -1672280820 40171771630 -756111184500 11310276995381 -135585182899530< / div >
< div class = "line" > 1307535010540395 -10142299865511450 63030812099294896 -311333643161390640< / div >
< div class = "line" > 1206647803780373360 -3599979517947607200 8037811822645051776< / div >
< div class = "line" > -12870931245150988800 13803759753640704000 -8752948036761600000< / div >
< div class = "line" > 2432902008176640000< / div >
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< / div > <!-- fragment --> < p > Sample implementation results to compute approximate roots of the equation \(x^4-1=0\):< br / >
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< img src = "https://raw.githubusercontent.com/TheAlgorithms/C/docs/images/numerical_methods/durand_kerner_error.svg" alt = "Error evolution during root approximations computed every
iteration." style="pointer-events: none;" width="400" class="inline"/> < img src = "https://raw.githubusercontent.com/TheAlgorithms/C/docs/images/numerical_methods/durand_kerner_roots.svg" alt = "Roots evolution - shows the initial approximation of the
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roots and their convergence to a final approximation along with the iterative
approximations" style="pointer-events: none;" width="400" class="inline"/> < / p >
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< / div > < h2 class = "groupheader" > Function Documentation< / h2 >
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< a id = "a26d5695ebed0818a3e7cf4b10aacab52" name = "a26d5695ebed0818a3e7cf4b10aacab52" > < / a >
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< h2 class = "memtitle" > < span class = "permalink" > < a href = "#a26d5695ebed0818a3e7cf4b10aacab52" > ◆   < / a > < / span > check_termination()< / h2 >
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< div class = "memitem" >
< div class = "memproto" >
< table class = "memname" >
< tr >
< td class = "memname" > char check_termination < / td >
< td > (< / td >
< td class = "paramtype" > long double  < / td >
< td class = "paramname" > < em > delta< / em > < / td > < td > )< / td >
< td > < / td >
< / tr >
< / table >
< / div > < div class = "memdoc" >
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< p > check for termination condition < / p >
< dl class = "params" > < dt > Parameters< / dt > < dd >
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< table class = "params" >
< tr > < td class = "paramdir" > [in]< / td > < td class = "paramname" > delta< / td > < td > point at which to evaluate the polynomial < / td > < / tr >
< / table >
< / dd >
< / dl >
< dl class = "section return" > < dt > Returns< / dt > < dd > 0 if termination not reached < / dd >
< dd >
1 if termination reached < / dd > < / dl >
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< div class = "fragment" > < div class = "line" > < span class = "lineno" > 84< / span > {< / div >
< div class = "line" > < span class = "lineno" > 85< / span > < span class = "keyword" > static< / span > < span class = "keywordtype" > long< / span > < span class = "keywordtype" > double< / span > past_delta = INFINITY;< / div >
< div class = "line" > < span class = "lineno" > 86< / span > < span class = "keywordflow" > if< / span > (fabsl(past_delta - delta) < = < a class = "code hl_define" href = "../../da/d38/durand__kerner__roots_8c.html#af270a96662132d0385cb6b4637c5a689" > ACCURACY< / a > || delta < < a class = "code hl_define" href = "../../da/d38/durand__kerner__roots_8c.html#af270a96662132d0385cb6b4637c5a689" > ACCURACY< / a > )< / div >
< div class = "line" > < span class = "lineno" > 87< / span > < span class = "keywordflow" > return< / span > 1;< / div >
< div class = "line" > < span class = "lineno" > 88< / span > past_delta = delta;< / div >
< div class = "line" > < span class = "lineno" > 89< / span > < span class = "keywordflow" > return< / span > 0;< / div >
< div class = "line" > < span class = "lineno" > 90< / span > }< / div >
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< div class = "ttc" id = "adurand__kerner__roots_8c_html_af270a96662132d0385cb6b4637c5a689" > < div class = "ttname" > < a href = "../../da/d38/durand__kerner__roots_8c.html#af270a96662132d0385cb6b4637c5a689" > ACCURACY< / a > < / div > < div class = "ttdeci" > #define ACCURACY< / div > < div class = "ttdoc" > maximum accuracy limit< / div > < div class = "ttdef" > < b > Definition:< / b > durand_kerner_roots.c:41< / div > < / div >
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< / div > <!-- fragment -->
< / div >
< / div >
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< a id = "a46197e91f478e99a2229562aaaac311e" name = "a46197e91f478e99a2229562aaaac311e" > < / a >
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< h2 class = "memtitle" > < span class = "permalink" > < a href = "#a46197e91f478e99a2229562aaaac311e" > ◆   < / a > < / span > complex_str()< / h2 >
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< div class = "memitem" >
< div class = "memproto" >
< table class = "memname" >
< tr >
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< td class = "memname" > const char * complex_str < / td >
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< td > (< / td >
< td class = "paramtype" > long double complex  < / td >
< td class = "paramname" > < em > x< / em > < / td > < td > )< / td >
< td > < / td >
< / tr >
< / table >
< / div > < div class = "memdoc" >
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< p > create a textual form of complex number < / p >
< dl class = "params" > < dt > Parameters< / dt > < dd >
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< table class = "params" >
< tr > < td class = "paramdir" > [in]< / td > < td class = "paramname" > x< / td > < td > point at which to evaluate the polynomial < / td > < / tr >
< / table >
< / dd >
< / dl >
< dl class = "section return" > < dt > Returns< / dt > < dd > pointer to converted string < / dd > < / dl >
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< div class = "fragment" > < div class = "line" > < span class = "lineno" > 67< / span > {< / div >
< div class = "line" > < span class = "lineno" > 68< / span > < span class = "keyword" > static< / span > < span class = "keywordtype" > char< / span > msg[50];< / div >
< div class = "line" > < span class = "lineno" > 69< / span > < span class = "keywordtype" > double< / span > r = creal(x);< / div >
< div class = "line" > < span class = "lineno" > 70< / span > < span class = "keywordtype" > double< / span > c = cimag(x);< / div >
< div class = "line" > < span class = "lineno" > 71< / span > < / div >
< div class = "line" > < span class = "lineno" > 72< / span > sprintf(msg, < span class = "stringliteral" > " % 7.04g%+7.04gj" < / span > , r, c);< / div >
< div class = "line" > < span class = "lineno" > 73< / span > < / div >
< div class = "line" > < span class = "lineno" > 74< / span > < span class = "keywordflow" > return< / span > msg;< / div >
< div class = "line" > < span class = "lineno" > 75< / span > }< / div >
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< / div > <!-- fragment -->
< / div >
< / div >
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< a id = "a3c04138a5bfe5d72780bb7e82a18e627" name = "a3c04138a5bfe5d72780bb7e82a18e627" > < / a >
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< h2 class = "memtitle" > < span class = "permalink" > < a href = "#a3c04138a5bfe5d72780bb7e82a18e627" > ◆   < / a > < / span > main()< / h2 >
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< div class = "memitem" >
< div class = "memproto" >
< table class = "memname" >
< tr >
< td class = "memname" > int main < / td >
< td > (< / td >
< td class = "paramtype" > int  < / td >
< td class = "paramname" > < em > argc< / em > , < / td >
< / tr >
< tr >
< td class = "paramkey" > < / td >
< td > < / td >
< td class = "paramtype" > char **  < / td >
< td class = "paramname" > < em > argv< / em >   < / td >
< / tr >
< tr >
< td > < / td >
< td > )< / td >
< td > < / td > < td > < / td >
< / tr >
< / table >
< / div > < div class = "memdoc" >
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< p > store intermediate values to a CSV file< / p >
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< div class = "fragment" > < div class = "line" > < span class = "lineno" > 96< / span > {< / div >
< div class = "line" > < span class = "lineno" > 97< / span > < span class = "keywordtype" > long< / span > < span class = "keywordtype" > double< / span > *coeffs = NULL;< / div >
< div class = "line" > < span class = "lineno" > 98< / span > < span class = "keywordtype" > long< / span > < span class = "keywordtype" > double< / span > complex *s0 = NULL;< / div >
< div class = "line" > < span class = "lineno" > 99< / span > < span class = "keywordtype" > unsigned< / span > < span class = "keywordtype" > int< / span > degree = 0;< / div >
< div class = "line" > < span class = "lineno" > 100< / span > < span class = "keywordtype" > unsigned< / span > < span class = "keywordtype" > int< / span > n, i;< / div >
< div class = "line" > < span class = "lineno" > 101< / span > < / div >
< div class = "line" > < span class = "lineno" > 102< / span > < span class = "keywordflow" > if< / span > (argc < 2)< / div >
< div class = "line" > < span class = "lineno" > 103< / span > {< / div >
< div class = "line" > < span class = "lineno" > 104< / span > printf(< / div >
< div class = "line" > < span class = "lineno" > 105< / span > < span class = "stringliteral" > " Please pass the coefficients of the polynomial as commandline " < / span > < / div >
< div class = "line" > < span class = "lineno" > 106< / span > < span class = "stringliteral" > " arguments.\n" < / span > );< / div >
< div class = "line" > < span class = "lineno" > 107< / span > < span class = "keywordflow" > return< / span > 0;< / div >
< div class = "line" > < span class = "lineno" > 108< / span > }< / div >
< div class = "line" > < span class = "lineno" > 109< / span > < / div >
< div class = "line" > < span class = "lineno" > 110< / span > degree = argc - 1; < span class = "comment" > /* detected polynomial degree */< / span > < / div >
< div class = "line" > < span class = "lineno" > 111< / span > coeffs = (< span class = "keywordtype" > long< / span > < span class = "keywordtype" > double< / span > *)< a class = "code hl_define" href = "../../d2/ddd/malloc__dbg_8h.html#a725f50ecaf1959d96de79b36b4788fee" > malloc< / a > (< / div >
< div class = "line" > < span class = "lineno" > 112< / span > degree * < span class = "keyword" > sizeof< / span > (< span class = "keywordtype" > long< / span > < span class = "keywordtype" > double< / span > )); < span class = "comment" > /* store all input coefficients */< / span > < / div >
< div class = "line" > < span class = "lineno" > 113< / span > s0 = (< span class = "keywordtype" > long< / span > < span class = "keywordtype" > double< / span > complex *)< a class = "code hl_define" href = "../../d2/ddd/malloc__dbg_8h.html#a725f50ecaf1959d96de79b36b4788fee" > malloc< / a > (< / div >
< div class = "line" > < span class = "lineno" > 114< / span > (degree - 1) *< / div >
< div class = "line" > < span class = "lineno" > 115< / span > < span class = "keyword" > sizeof< / span > (< span class = "keywordtype" > long< / span > < span class = "keywordtype" > double< / span > complex)); < span class = "comment" > /* number of roots = degree-1 */< / span > < / div >
< div class = "line" > < span class = "lineno" > 116< / span > < / div >
< div class = "line" > < span class = "lineno" > 117< / span > < span class = "comment" > /* initialize random seed: */< / span > < / div >
< div class = "line" > < span class = "lineno" > 118< / span > srand(time(NULL));< / div >
< div class = "line" > < span class = "lineno" > 119< / span > < / div >
< div class = "line" > < span class = "lineno" > 120< / span > < span class = "keywordflow" > if< / span > (!coeffs || !s0)< / div >
< div class = "line" > < span class = "lineno" > 121< / span > {< / div >
< div class = "line" > < span class = "lineno" > 122< / span > perror(< span class = "stringliteral" > " Unable to allocate memory!" < / span > );< / div >
< div class = "line" > < span class = "lineno" > 123< / span > < span class = "keywordflow" > if< / span > (coeffs)< / div >
< div class = "line" > < span class = "lineno" > 124< / span > < a class = "code hl_define" href = "../../d2/ddd/malloc__dbg_8h.html#a9cc854374299a1dd933bf62029761768" > free< / a > (coeffs);< / div >
< div class = "line" > < span class = "lineno" > 125< / span > < span class = "keywordflow" > if< / span > (s0)< / div >
< div class = "line" > < span class = "lineno" > 126< / span > < a class = "code hl_define" href = "../../d2/ddd/malloc__dbg_8h.html#a9cc854374299a1dd933bf62029761768" > free< / a > (s0);< / div >
< div class = "line" > < span class = "lineno" > 127< / span > < span class = "keywordflow" > return< / span > EXIT_FAILURE;< / div >
< div class = "line" > < span class = "lineno" > 128< / span > }< / div >
< div class = "line" > < span class = "lineno" > 129< / span > < / div >
< div class = "line" > < span class = "lineno" > 130< / span > < span class = "preprocessor" > #if defined(DEBUG) || !defined(NDEBUG)< / span > < span class = "comment" > < / span > < / div >
< div class = "line" > < span class = "lineno" > 131< / span > < span class = "comment" > /**< / span > < / div >
< div class = "line" > < span class = "lineno" > 132< / span > < span class = "comment" > * store intermediate values to a CSV file< / span > < / div >
< div class = "line" > < span class = "lineno" > 133< / span > < span class = "comment" > */< / span > < span class = "preprocessor" > < / span > < / div >
< div class = "line" > < span class = "lineno" > 134< / span > FILE *log_file = fopen(< span class = "stringliteral" > " durand_kerner.log.csv" < / span > , < span class = "stringliteral" > " wt" < / span > );< / div >
< div class = "line" > < span class = "lineno" > 135< / span > < span class = "keywordflow" > if< / span > (!log_file)< / div >
< div class = "line" > < span class = "lineno" > 136< / span > {< / div >
< div class = "line" > < span class = "lineno" > 137< / span > perror(< span class = "stringliteral" > " Unable to create a storage log file!" < / span > );< / div >
< div class = "line" > < span class = "lineno" > 138< / span > < a class = "code hl_define" href = "../../d2/ddd/malloc__dbg_8h.html#a9cc854374299a1dd933bf62029761768" > free< / a > (coeffs);< / div >
< div class = "line" > < span class = "lineno" > 139< / span > < a class = "code hl_define" href = "../../d2/ddd/malloc__dbg_8h.html#a9cc854374299a1dd933bf62029761768" > free< / a > (s0);< / div >
< div class = "line" > < span class = "lineno" > 140< / span > < span class = "keywordflow" > return< / span > EXIT_FAILURE;< / div >
< div class = "line" > < span class = "lineno" > 141< / span > }< / div >
< div class = "line" > < span class = "lineno" > 142< / span > fprintf(log_file, < span class = "stringliteral" > " iter#," < / span > );< / div >
< div class = "line" > < span class = "lineno" > 143< / span > < span class = "preprocessor" > #endif< / span > < / div >
< div class = "line" > < span class = "lineno" > 144< / span > < / div >
< div class = "line" > < span class = "lineno" > 145< / span > printf(< span class = "stringliteral" > " Computing the roots for:\n\t" < / span > );< / div >
< div class = "line" > < span class = "lineno" > 146< / span > < span class = "keywordflow" > for< / span > (n = 0; n < degree; n++)< / div >
< div class = "line" > < span class = "lineno" > 147< / span > {< / div >
< div class = "line" > < span class = "lineno" > 148< / span > coeffs[n] = strtod(argv[n + 1], NULL);< / div >
< div class = "line" > < span class = "lineno" > 149< / span > < span class = "keywordflow" > if< / span > (n < degree - 1 & & coeffs[n] != 0)< / div >
< div class = "line" > < span class = "lineno" > 150< / span > printf(< span class = "stringliteral" > " (%Lg) x^%d + " < / span > , coeffs[n], degree - n - 1);< / div >
< div class = "line" > < span class = "lineno" > 151< / span > < span class = "keywordflow" > else< / span > < span class = "keywordflow" > if< / span > (coeffs[n] != 0)< / div >
< div class = "line" > < span class = "lineno" > 152< / span > printf(< span class = "stringliteral" > " (%Lg) x^%d = 0\n" < / span > , coeffs[n], degree - n - 1);< / div >
< div class = "line" > < span class = "lineno" > 153< / span > < / div >
< div class = "line" > < span class = "lineno" > 154< / span > < span class = "keywordtype" > double< / span > tmp;< / div >
< div class = "line" > < span class = "lineno" > 155< / span > < span class = "keywordflow" > if< / span > (n > 0)< / div >
< div class = "line" > < span class = "lineno" > 156< / span > coeffs[n] /= tmp; < span class = "comment" > /* numerical errors less when the first< / span > < / div >
< div class = "line" > < span class = "lineno" > 157< / span > < span class = "comment" > coefficient is " 1" */< / span > < / div >
< div class = "line" > < span class = "lineno" > 158< / span > < span class = "keywordflow" > else< / span > < / div >
< div class = "line" > < span class = "lineno" > 159< / span > {< / div >
< div class = "line" > < span class = "lineno" > 160< / span > tmp = coeffs[0];< / div >
< div class = "line" > < span class = "lineno" > 161< / span > coeffs[0] = 1;< / div >
< div class = "line" > < span class = "lineno" > 162< / span > }< / div >
< div class = "line" > < span class = "lineno" > 163< / span > < / div >
< div class = "line" > < span class = "lineno" > 164< / span > < span class = "comment" > /* initialize root approximations with random values */< / span > < / div >
< div class = "line" > < span class = "lineno" > 165< / span > < span class = "keywordflow" > if< / span > (n < degree - 1)< / div >
< div class = "line" > < span class = "lineno" > 166< / span > {< / div >
< div class = "line" > < span class = "lineno" > 167< / span > s0[n] = (< span class = "keywordtype" > long< / span > double)rand() + (< span class = "keywordtype" > long< / span > double)rand() * I;< / div >
< div class = "line" > < span class = "lineno" > 168< / span > < span class = "preprocessor" > #if defined(DEBUG) || !defined(NDEBUG)< / span > < / div >
< div class = "line" > < span class = "lineno" > 169< / span > fprintf(log_file, < span class = "stringliteral" > " root_%d," < / span > , n);< / div >
< div class = "line" > < span class = "lineno" > 170< / span > < span class = "preprocessor" > #endif< / span > < / div >
< div class = "line" > < span class = "lineno" > 171< / span > }< / div >
< div class = "line" > < span class = "lineno" > 172< / span > }< / div >
< div class = "line" > < span class = "lineno" > 173< / span > < / div >
< div class = "line" > < span class = "lineno" > 174< / span > < span class = "preprocessor" > #if defined(DEBUG) || !defined(NDEBUG)< / span > < / div >
< div class = "line" > < span class = "lineno" > 175< / span > fprintf(log_file, < span class = "stringliteral" > " avg. correction" < / span > );< / div >
< div class = "line" > < span class = "lineno" > 176< / span > fprintf(log_file, < span class = "stringliteral" > " \n0," < / span > );< / div >
< div class = "line" > < span class = "lineno" > 177< / span > < span class = "keywordflow" > for< / span > (n = 0; n < degree - 1; n++)< / div >
< div class = "line" > < span class = "lineno" > 178< / span > fprintf(log_file, < span class = "stringliteral" > " %s," < / span > , < a class = "code hl_function" href = "../../da/d38/durand__kerner__roots_8c.html#a46197e91f478e99a2229562aaaac311e" > complex_str< / a > (s0[n]));< / div >
< div class = "line" > < span class = "lineno" > 179< / span > < span class = "preprocessor" > #endif< / span > < / div >
< div class = "line" > < span class = "lineno" > 180< / span > < / div >
< div class = "line" > < span class = "lineno" > 181< / span > < span class = "keywordtype" > double< / span > tol_condition = 1;< / div >
< div class = "line" > < span class = "lineno" > 182< / span > < span class = "keywordtype" > unsigned< / span > < span class = "keywordtype" > long< / span > iter = 0;< / div >
< div class = "line" > < span class = "lineno" > 183< / span > < / div >
< div class = "line" > < span class = "lineno" > 184< / span > clock_t end_time, start_time = clock();< / div >
< div class = "line" > < span class = "lineno" > 185< / span > < span class = "keywordflow" > while< / span > (!< a class = "code hl_function" href = "../../da/d38/durand__kerner__roots_8c.html#a26d5695ebed0818a3e7cf4b10aacab52" > check_termination< / a > (tol_condition) & & iter < INT_MAX)< / div >
< div class = "line" > < span class = "lineno" > 186< / span > {< / div >
< div class = "line" > < span class = "lineno" > 187< / span > < span class = "keywordtype" > long< / span > < span class = "keywordtype" > double< / span > complex delta = 0;< / div >
< div class = "line" > < span class = "lineno" > 188< / span > tol_condition = 0;< / div >
< div class = "line" > < span class = "lineno" > 189< / span > iter++;< / div >
< div class = "line" > < span class = "lineno" > 190< / span > < / div >
< div class = "line" > < span class = "lineno" > 191< / span > < span class = "preprocessor" > #if defined(DEBUG) || !defined(NDEBUG)< / span > < / div >
< div class = "line" > < span class = "lineno" > 192< / span > fprintf(log_file, < span class = "stringliteral" > " \n%ld," < / span > , iter);< / div >
< div class = "line" > < span class = "lineno" > 193< / span > < span class = "preprocessor" > #endif< / span > < / div >
< div class = "line" > < span class = "lineno" > 194< / span > < / div >
< div class = "line" > < span class = "lineno" > 195< / span > < span class = "keywordflow" > for< / span > (n = 0; n < degree - 1; n++)< / div >
< div class = "line" > < span class = "lineno" > 196< / span > {< / div >
< div class = "line" > < span class = "lineno" > 197< / span > < span class = "keywordtype" > long< / span > < span class = "keywordtype" > double< / span > complex numerator =< / div >
< div class = "line" > < span class = "lineno" > 198< / span > < a class = "code hl_function" href = "../../da/d38/durand__kerner__roots_8c.html#a321f9781a9744ccdaf0aba89f35ec29c" > poly_function< / a > (coeffs, degree, s0[n]);< / div >
< div class = "line" > < span class = "lineno" > 199< / span > < span class = "keywordtype" > long< / span > < span class = "keywordtype" > double< / span > complex denominator = 1.0;< / div >
< div class = "line" > < span class = "lineno" > 200< / span > < span class = "keywordflow" > for< / span > (i = 0; i < degree - 1; i++)< / div >
< div class = "line" > < span class = "lineno" > 201< / span > < span class = "keywordflow" > if< / span > (i != n)< / div >
< div class = "line" > < span class = "lineno" > 202< / span > denominator *= s0[n] - s0[i];< / div >
< div class = "line" > < span class = "lineno" > 203< / span > < / div >
< div class = "line" > < span class = "lineno" > 204< / span > delta = numerator / denominator;< / div >
< div class = "line" > < span class = "lineno" > 205< / span > < / div >
< div class = "line" > < span class = "lineno" > 206< / span > < span class = "keywordflow" > if< / span > (isnan(cabsl(delta)) || isinf(cabsl(delta)))< / div >
< div class = "line" > < span class = "lineno" > 207< / span > {< / div >
< div class = "line" > < span class = "lineno" > 208< / span > printf(< span class = "stringliteral" > " \n\nOverflow/underrun error - got value = %Lg" < / span > ,< / div >
< div class = "line" > < span class = "lineno" > 209< / span > cabsl(delta));< / div >
< div class = "line" > < span class = "lineno" > 210< / span > < span class = "keywordflow" > goto< / span > end;< / div >
< div class = "line" > < span class = "lineno" > 211< / span > }< / div >
< div class = "line" > < span class = "lineno" > 212< / span > < / div >
< div class = "line" > < span class = "lineno" > 213< / span > s0[n] -= delta;< / div >
< div class = "line" > < span class = "lineno" > 214< / span > < / div >
< div class = "line" > < span class = "lineno" > 215< / span > tol_condition = fmaxl(tol_condition, fabsl(cabsl(delta)));< / div >
< div class = "line" > < span class = "lineno" > 216< / span > < / div >
< div class = "line" > < span class = "lineno" > 217< / span > < span class = "preprocessor" > #if defined(DEBUG) || !defined(NDEBUG)< / span > < / div >
< div class = "line" > < span class = "lineno" > 218< / span > fprintf(log_file, < span class = "stringliteral" > " %s," < / span > , < a class = "code hl_function" href = "../../da/d38/durand__kerner__roots_8c.html#a46197e91f478e99a2229562aaaac311e" > complex_str< / a > (s0[n]));< / div >
< div class = "line" > < span class = "lineno" > 219< / span > < span class = "preprocessor" > #endif< / span > < / div >
< div class = "line" > < span class = "lineno" > 220< / span > }< / div >
< div class = "line" > < span class = "lineno" > 221< / span > < span class = "comment" > // tol_condition /= (degree - 1);< / span > < / div >
< div class = "line" > < span class = "lineno" > 222< / span > < / div >
< div class = "line" > < span class = "lineno" > 223< / span > < span class = "preprocessor" > #if defined(DEBUG) || !defined(NDEBUG)< / span > < / div >
< div class = "line" > < span class = "lineno" > 224< / span > < span class = "keywordflow" > if< / span > (iter % 500 == 0)< / div >
< div class = "line" > < span class = "lineno" > 225< / span > {< / div >
< div class = "line" > < span class = "lineno" > 226< / span > printf(< span class = "stringliteral" > " Iter: %lu\t" < / span > , iter);< / div >
< div class = "line" > < span class = "lineno" > 227< / span > < span class = "keywordflow" > for< / span > (n = 0; n < degree - 1; n++) printf(< span class = "stringliteral" > " \t%s" < / span > , < a class = "code hl_function" href = "../../da/d38/durand__kerner__roots_8c.html#a46197e91f478e99a2229562aaaac311e" > complex_str< / a > (s0[n]));< / div >
< div class = "line" > < span class = "lineno" > 228< / span > printf(< span class = "stringliteral" > " \t\tabsolute average change: %.4g\n" < / span > , tol_condition);< / div >
< div class = "line" > < span class = "lineno" > 229< / span > }< / div >
< div class = "line" > < span class = "lineno" > 230< / span > < / div >
< div class = "line" > < span class = "lineno" > 231< / span > fprintf(log_file, < span class = "stringliteral" > " %.4g" < / span > , tol_condition);< / div >
< div class = "line" > < span class = "lineno" > 232< / span > < span class = "preprocessor" > #endif< / span > < / div >
< div class = "line" > < span class = "lineno" > 233< / span > }< / div >
< div class = "line" > < span class = "lineno" > 234< / span > end:< / div >
< div class = "line" > < span class = "lineno" > 235< / span > < / div >
< div class = "line" > < span class = "lineno" > 236< / span > end_time = clock();< / div >
< div class = "line" > < span class = "lineno" > 237< / span > < / div >
< div class = "line" > < span class = "lineno" > 238< / span > < span class = "preprocessor" > #if defined(DEBUG) || !defined(NDEBUG)< / span > < / div >
< div class = "line" > < span class = "lineno" > 239< / span > fclose(log_file);< / div >
< div class = "line" > < span class = "lineno" > 240< / span > < span class = "preprocessor" > #endif< / span > < / div >
< div class = "line" > < span class = "lineno" > 241< / span > < / div >
< div class = "line" > < span class = "lineno" > 242< / span > printf(< span class = "stringliteral" > " \nIterations: %lu\n" < / span > , iter);< / div >
< div class = "line" > < span class = "lineno" > 243< / span > < span class = "keywordflow" > for< / span > (n = 0; n < degree - 1; n++) printf(< span class = "stringliteral" > " \t%s\n" < / span > , < a class = "code hl_function" href = "../../da/d38/durand__kerner__roots_8c.html#a46197e91f478e99a2229562aaaac311e" > complex_str< / a > (s0[n]));< / div >
< div class = "line" > < span class = "lineno" > 244< / span > printf(< span class = "stringliteral" > " absolute average change: %.4g\n" < / span > , tol_condition);< / div >
< div class = "line" > < span class = "lineno" > 245< / span > printf(< span class = "stringliteral" > " Time taken: %.4g sec\n" < / span > ,< / div >
< div class = "line" > < span class = "lineno" > 246< / span > (end_time - start_time) / (< span class = "keywordtype" > double< / span > )CLOCKS_PER_SEC);< / div >
< div class = "line" > < span class = "lineno" > 247< / span > < / div >
< div class = "line" > < span class = "lineno" > 248< / span > < a class = "code hl_define" href = "../../d2/ddd/malloc__dbg_8h.html#a9cc854374299a1dd933bf62029761768" > free< / a > (coeffs);< / div >
< div class = "line" > < span class = "lineno" > 249< / span > < a class = "code hl_define" href = "../../d2/ddd/malloc__dbg_8h.html#a9cc854374299a1dd933bf62029761768" > free< / a > (s0);< / div >
< div class = "line" > < span class = "lineno" > 250< / span > < / div >
< div class = "line" > < span class = "lineno" > 251< / span > < span class = "keywordflow" > return< / span > 0;< / div >
< div class = "line" > < span class = "lineno" > 252< / span > }< / div >
2021-02-06 03:52:57 +08:00
< div class = "ttc" id = "adurand__kerner__roots_8c_html_a26d5695ebed0818a3e7cf4b10aacab52" > < div class = "ttname" > < a href = "../../da/d38/durand__kerner__roots_8c.html#a26d5695ebed0818a3e7cf4b10aacab52" > check_termination< / a > < / div > < div class = "ttdeci" > char check_termination(long double delta)< / div > < div class = "ttdoc" > check for termination condition< / div > < div class = "ttdef" > < b > Definition:< / b > durand_kerner_roots.c:83< / div > < / div >
< div class = "ttc" id = "adurand__kerner__roots_8c_html_a321f9781a9744ccdaf0aba89f35ec29c" > < div class = "ttname" > < a href = "../../da/d38/durand__kerner__roots_8c.html#a321f9781a9744ccdaf0aba89f35ec29c" > poly_function< / a > < / div > < div class = "ttdeci" > long double complex poly_function(long double *coeffs, unsigned int degree, long double complex x)< / div > < div class = "ttdoc" > Evaluate the value of a polynomial with given coefficients.< / div > < div class = "ttdef" > < b > Definition:< / b > durand_kerner_roots.c:50< / div > < / div >
2021-10-26 03:34:27 +08:00
< div class = "ttc" id = "adurand__kerner__roots_8c_html_a46197e91f478e99a2229562aaaac311e" > < div class = "ttname" > < a href = "../../da/d38/durand__kerner__roots_8c.html#a46197e91f478e99a2229562aaaac311e" > complex_str< / a > < / div > < div class = "ttdeci" > const char * complex_str(long double complex x)< / div > < div class = "ttdoc" > create a textual form of complex number< / div > < div class = "ttdef" > < b > Definition:< / b > durand_kerner_roots.c:66< / div > < / div >
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< div class = "ttc" id = "amalloc__dbg_8h_html_a725f50ecaf1959d96de79b36b4788fee" > < div class = "ttname" > < a href = "../../d2/ddd/malloc__dbg_8h.html#a725f50ecaf1959d96de79b36b4788fee" > malloc< / a > < / div > < div class = "ttdeci" > #define malloc(bytes)< / div > < div class = "ttdoc" > This macro replace the standard malloc function with malloc_dbg.< / div > < div class = "ttdef" > < b > Definition:< / b > malloc_dbg.h:18< / div > < / div >
< div class = "ttc" id = "amalloc__dbg_8h_html_a9cc854374299a1dd933bf62029761768" > < div class = "ttname" > < a href = "../../d2/ddd/malloc__dbg_8h.html#a9cc854374299a1dd933bf62029761768" > free< / a > < / div > < div class = "ttdeci" > #define free(ptr)< / div > < div class = "ttdoc" > This macro replace the standard free function with free_dbg.< / div > < div class = "ttdef" > < b > Definition:< / b > malloc_dbg.h:26< / div > < / div >
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< div class = "center" > < iframe scrolling = "no" frameborder = "0" src = "../../da/d38/durand__kerner__roots_8c_a3c04138a5bfe5d72780bb7e82a18e627_cgraph.svg" width = "238" height = "135" > < p > < b > This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.< / b > < / p > < / iframe >
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< a id = "a321f9781a9744ccdaf0aba89f35ec29c" name = "a321f9781a9744ccdaf0aba89f35ec29c" > < / a >
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< h2 class = "memtitle" > < span class = "permalink" > < a href = "#a321f9781a9744ccdaf0aba89f35ec29c" > ◆   < / a > < / span > poly_function()< / h2 >
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< div class = "memitem" >
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< td class = "memname" > long double complex poly_function < / td >
< td > (< / td >
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< td class = "paramtype" > long double *  < / td >
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< td class = "paramname" > < em > coeffs< / em > , < / td >
< / tr >
< tr >
< td class = "paramkey" > < / td >
< td > < / td >
< td class = "paramtype" > unsigned int  < / td >
< td class = "paramname" > < em > degree< / em > , < / td >
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< td class = "paramkey" > < / td >
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< td class = "paramtype" > long double complex  < / td >
< td class = "paramname" > < em > x< / em >   < / td >
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< td > < / td >
< td > )< / td >
< td > < / td > < td > < / td >
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< p > Evaluate the value of a polynomial with given coefficients. < / p >
< dl class = "params" > < dt > Parameters< / dt > < dd >
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< table class = "params" >
< tr > < td class = "paramdir" > [in]< / td > < td class = "paramname" > coeffs< / td > < td > coefficients of the polynomial < / td > < / tr >
< tr > < td class = "paramdir" > [in]< / td > < td class = "paramname" > degree< / td > < td > degree of polynomial < / td > < / tr >
< tr > < td class = "paramdir" > [in]< / td > < td class = "paramname" > x< / td > < td > point at which to evaluate the polynomial < / td > < / tr >
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< dl class = "section return" > < dt > Returns< / dt > < dd > \(f(x)\) < / dd > < / dl >
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< div class = "fragment" > < div class = "line" > < span class = "lineno" > 52< / span > {< / div >
< div class = "line" > < span class = "lineno" > 53< / span > < span class = "keywordtype" > long< / span > < span class = "keywordtype" > double< / span > complex out = 0.;< / div >
< div class = "line" > < span class = "lineno" > 54< / span > < span class = "keywordtype" > unsigned< / span > < span class = "keywordtype" > int< / span > n;< / div >
< div class = "line" > < span class = "lineno" > 55< / span > < / div >
< div class = "line" > < span class = "lineno" > 56< / span > < span class = "keywordflow" > for< / span > (n = 0; n < degree; n++) out += coeffs[n] * cpow(x, degree - n - 1);< / div >
< div class = "line" > < span class = "lineno" > 57< / span > < / div >
< div class = "line" > < span class = "lineno" > 58< / span > < span class = "keywordflow" > return< / span > out;< / div >
< div class = "line" > < span class = "lineno" > 59< / span > }< / div >
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< li class = "navelem" > < a class = "el" href = "../../dir_9c6faab82c22511b50177aa2e38e2780.html" > numerical_methods< / a > < / li > < li class = "navelem" > < a class = "el" href = "../../da/d38/durand__kerner__roots_8c.html" > durand_kerner_roots.c< / a > < / li >
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