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< div class = "headertitle" > < div class = "title" > newton_raphson_root.c File Reference< / div > < / div >
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< / div > <!-- header -->
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< p > Find approximate solution for \(f(x) = 0\) using Newton-Raphson interpolation algorithm.
< 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 < time.h> < / code > < br / >
< / div > < div class = "textblock" > < div class = "dynheader" >
Include dependency graph for newton_raphson_root.c:< / div >
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< div class = "center" > < iframe scrolling = "no" frameborder = "0" src = "../../d8/d11/newton__raphson__root_8c__incl.svg" width = "526" 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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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" > solution accuracy < br / > < / td > < / tr >
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Functions< / h2 > < / td > < / tr >
< tr class = "memitem:a72f87d423a488946b319627a454d3925" > < td class = "memItemLeft" align = "right" valign = "top" > double complex  < / td > < td class = "memItemRight" valign = "bottom" > < a class = "el" href = "../../dd/d08/newton__raphson__root_8c.html#a72f87d423a488946b319627a454d3925" > func< / a > (double complex x)< / td > < / tr >
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< tr class = "memdesc:a72f87d423a488946b319627a454d3925" > < td class = "mdescLeft" >   < / td > < td class = "mdescRight" > Return value of the function to find the root for. < br / > < / td > < / tr >
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< tr class = "separator:a72f87d423a488946b319627a454d3925" > < td class = "memSeparator" colspan = "2" >   < / td > < / tr >
< tr class = "memitem:ae713a1fd0c275fbec7edf263ac2c0337" > < td class = "memItemLeft" align = "right" valign = "top" > double complex  < / td > < td class = "memItemRight" valign = "bottom" > < a class = "el" href = "../../dd/d08/newton__raphson__root_8c.html#ae713a1fd0c275fbec7edf263ac2c0337" > d_func< / a > (double complex x)< / td > < / tr >
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< tr class = "memdesc:ae713a1fd0c275fbec7edf263ac2c0337" > < td class = "mdescLeft" >   < / td > < td class = "mdescRight" > Return first order derivative of the function. < br / > < / td > < / tr >
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< tr class = "separator:ae713a1fd0c275fbec7edf263ac2c0337" > < td class = "memSeparator" colspan = "2" >   < / td > < / tr >
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< tr class = "memitem:a3c04138a5bfe5d72780bb7e82a18e627" > < td class = "memItemLeft" align = "right" valign = "top" > int  < / td > < td class = "memItemRight" valign = "bottom" > < a class = "el" href = "../../dd/d08/newton__raphson__root_8c.html#a3c04138a5bfe5d72780bb7e82a18e627" > main< / a > (int argc, char **argv)< / td > < / tr >
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< tr class = "memdesc:a3c04138a5bfe5d72780bb7e82a18e627" > < td class = "mdescLeft" >   < / td > < td class = "mdescRight" > main function < br / > < / td > < / tr >
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< 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 > Find approximate solution for \(f(x) = 0\) using Newton-Raphson interpolation algorithm. < / p >
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< 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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< / div > < h2 class = "groupheader" > Function Documentation< / h2 >
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< a id = "ae713a1fd0c275fbec7edf263ac2c0337" name = "ae713a1fd0c275fbec7edf263ac2c0337" > < / a >
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< h2 class = "memtitle" > < span class = "permalink" > < a href = "#ae713a1fd0c275fbec7edf263ac2c0337" > ◆   < / a > < / span > d_func()< / h2 >
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< div class = "memitem" >
< div class = "memproto" >
< table class = "memname" >
< tr >
< td class = "memname" > double complex d_func < / td >
< td > (< / td >
< td class = "paramtype" > 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 > Return first order derivative of the function. < / p >
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< p > \(f' (x)\) < / p >
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< div class = "fragment" > < div class = "line" > < span class = "lineno" > 32< / span > { < span class = "keywordflow" > return< / span > 2. * x; }< / div >
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< / div >
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< a id = "a72f87d423a488946b319627a454d3925" name = "a72f87d423a488946b319627a454d3925" > < / a >
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< h2 class = "memtitle" > < span class = "permalink" > < a href = "#a72f87d423a488946b319627a454d3925" > ◆   < / a > < / span > func()< / h2 >
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< div class = "memitem" >
< div class = "memproto" >
< table class = "memname" >
< tr >
< td class = "memname" > double complex func < / td >
< td > (< / td >
< td class = "paramtype" > 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 > Return value of the function to find the root for. < / p >
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< p > \(f(x)\) < / p >
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< div class = "fragment" > < div class = "line" > < span class = "lineno" > 23< / span > {< / div >
< div class = "line" > < span class = "lineno" > 24< / span > < span class = "keywordflow" > return< / span > x * x - 3.; < span class = "comment" > /* x^2 = 3 - solution is sqrt(3) */< / span > < / div >
< div class = "line" > < span class = "lineno" > 25< / span > < span class = "comment" > // return x * x - 2.; /* x^2 = 2 - solution is sqrt(2) */< / span > < / div >
< div class = "line" > < span class = "lineno" > 26< / span > }< / div >
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< / div > <!-- fragment -->
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< / div >
< / div >
< 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" >
< p > main function < / p >
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< div class = "fragment" > < div class = "line" > < span class = "lineno" > 38< / span > {< / div >
< div class = "line" > < span class = "lineno" > 39< / span > < span class = "keywordtype" > double< / span > delta = 1;< / div >
< div class = "line" > < span class = "lineno" > 40< / span > < span class = "keywordtype" > double< / span > complex cdelta = 1;< / div >
< div class = "line" > < span class = "lineno" > 41< / span > < / div >
< div class = "line" > < span class = "lineno" > 42< / span > < span class = "comment" > /* initialize random seed: */< / span > < / div >
< div class = "line" > < span class = "lineno" > 43< / span > srand(time(NULL));< / div >
< div class = "line" > < span class = "lineno" > 44< / span > < / div >
< div class = "line" > < span class = "lineno" > 45< / span > < span class = "comment" > /* random initial approximation */< / span > < / div >
< div class = "line" > < span class = "lineno" > 46< / span > < span class = "keywordtype" > double< / span > complex root = (rand() % 100 - 50) + (rand() % 100 - 50) * I;< / div >
< div class = "line" > < span class = "lineno" > 47< / span > < / div >
< div class = "line" > < span class = "lineno" > 48< / span > < span class = "keywordtype" > unsigned< / span > < span class = "keywordtype" > long< / span > counter = 0;< / div >
< div class = "line" > < span class = "lineno" > 49< / span > < span class = "comment" > /* iterate till a convergence is reached */< / span > < / div >
< div class = "line" > < span class = "lineno" > 50< / span > < span class = "keywordflow" > while< / span > (delta > < a class = "code hl_define" href = "../../dd/d08/newton__raphson__root_8c.html#af270a96662132d0385cb6b4637c5a689" > ACCURACY< / a > & & counter < ULONG_MAX)< / div >
< div class = "line" > < span class = "lineno" > 51< / span > {< / div >
< div class = "line" > < span class = "lineno" > 52< / span > cdelta = < a class = "code hl_function" href = "../../dd/d08/newton__raphson__root_8c.html#a72f87d423a488946b319627a454d3925" > func< / a > (root) / < a class = "code hl_function" href = "../../dd/d08/newton__raphson__root_8c.html#ae713a1fd0c275fbec7edf263ac2c0337" > d_func< / a > (root);< / div >
< div class = "line" > < span class = "lineno" > 53< / span > root += -cdelta;< / div >
< div class = "line" > < span class = "lineno" > 54< / span > counter++;< / div >
< div class = "line" > < span class = "lineno" > 55< / span > delta = fabs(cabs(cdelta));< / div >
< div class = "line" > < span class = "lineno" > 56< / span > < / div >
< div class = "line" > < span class = "lineno" > 57< / span > < span class = "preprocessor" > #if defined(DEBUG) || !defined(NDEBUG)< / span > < / div >
< div class = "line" > < span class = "lineno" > 58< / span > < span class = "keywordflow" > if< / span > (counter % 50 == 0)< / div >
< div class = "line" > < span class = "lineno" > 59< / span > {< / div >
< div class = "line" > < span class = "lineno" > 60< / span > < span class = "keywordtype" > double< / span > r = creal(root);< / div >
< div class = "line" > < span class = "lineno" > 61< / span > < span class = "keywordtype" > double< / span > c = cimag(root);< / div >
< div class = "line" > < span class = "lineno" > 62< / span > < / div >
< div class = "line" > < span class = "lineno" > 63< / span > printf(< span class = "stringliteral" > " Iter %5lu: Root: %4.4g%c%4.4gi\t\tdelta: %.4g\n" < / span > , counter,< / div >
< div class = "line" > < span class = "lineno" > 64< / span > r, c > = 0 ? < span class = "charliteral" > ' +' < / span > : < span class = "charliteral" > ' -' < / span > , c > = 0 ? c : -c, delta);< / div >
< div class = "line" > < span class = "lineno" > 65< / span > }< / div >
< div class = "line" > < span class = "lineno" > 66< / span > < span class = "preprocessor" > #endif< / span > < / div >
< div class = "line" > < span class = "lineno" > 67< / span > }< / div >
< div class = "line" > < span class = "lineno" > 68< / span > < / div >
< div class = "line" > < span class = "lineno" > 69< / span > < span class = "keywordtype" > double< / span > r = creal(root);< / div >
< div class = "line" > < span class = "lineno" > 70< / span > < span class = "keywordtype" > double< / span > c = fabs(cimag(root)) < < a class = "code hl_define" href = "../../dd/d08/newton__raphson__root_8c.html#af270a96662132d0385cb6b4637c5a689" > ACCURACY< / a > ? 0 : cimag(root);< / div >
< div class = "line" > < span class = "lineno" > 71< / span > < / div >
< div class = "line" > < span class = "lineno" > 72< / span > printf(< span class = "stringliteral" > " Iter %5lu: Root: %4.4g%c%4.4gi\t\tdelta: %.4g\n" < / span > , counter, r,< / div >
< div class = "line" > < span class = "lineno" > 73< / span > c > = 0 ? < span class = "charliteral" > ' +' < / span > : < span class = "charliteral" > ' -' < / span > , c > = 0 ? c : -c, delta);< / div >
< div class = "line" > < span class = "lineno" > 74< / span > < / div >
< div class = "line" > < span class = "lineno" > 75< / span > < span class = "keywordflow" > return< / span > 0;< / div >
< div class = "line" > < span class = "lineno" > 76< / span > }< / div >
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< div class = "ttc" id = "anewton__raphson__root_8c_html_a72f87d423a488946b319627a454d3925" > < div class = "ttname" > < a href = "../../dd/d08/newton__raphson__root_8c.html#a72f87d423a488946b319627a454d3925" > func< / a > < / div > < div class = "ttdeci" > double complex func(double complex x)< / div > < div class = "ttdoc" > Return value of the function to find the root for.< / div > < div class = "ttdef" > < b > Definition:< / b > newton_raphson_root.c:22< / div > < / div >
< div class = "ttc" id = "anewton__raphson__root_8c_html_ae713a1fd0c275fbec7edf263ac2c0337" > < div class = "ttname" > < a href = "../../dd/d08/newton__raphson__root_8c.html#ae713a1fd0c275fbec7edf263ac2c0337" > d_func< / a > < / div > < div class = "ttdeci" > double complex d_func(double complex x)< / div > < div class = "ttdoc" > Return first order derivative of the function.< / div > < div class = "ttdef" > < b > Definition:< / b > newton_raphson_root.c:32< / div > < / div >
< div class = "ttc" id = "anewton__raphson__root_8c_html_af270a96662132d0385cb6b4637c5a689" > < div class = "ttname" > < a href = "../../dd/d08/newton__raphson__root_8c.html#af270a96662132d0385cb6b4637c5a689" > ACCURACY< / a > < / div > < div class = "ttdeci" > #define ACCURACY< / div > < div class = "ttdoc" > solution accuracy< / div > < div class = "ttdef" > < b > Definition:< / b > newton_raphson_root.c:16< / div > < / div >
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