244 lines
6.1 KiB
C
244 lines
6.1 KiB
C
#include "convergence.h"
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#define JMAX 80
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ConvergenceData rtbis_with_conv(float (*func)(float), float x1, float x2, float xacc) {
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void nrerror(char error_text[]);
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ConvergenceData data;
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data.size = 0;
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int j;
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float dx, f, fmid, xmid, rtb;
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f = (*func)(x1);
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fmid = (*func)(x2);
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if (f * fmid >= 0.0) nrerror("Root must be bracketed for bisection in rtbis");
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rtb = f < 0.0 ? (dx = x2 - x1, x1) : (dx = x1 - x2, x2);
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for (j = 1; j <= JMAX; j++) {
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fmid = (*func)(xmid = rtb + (dx *= 0.5));
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if (fmid <= 0.0) rtb = xmid;
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data.data[data.size++] = rtb;
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if (fabs(dx) < xacc || fmid == 0.0) {
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return data;
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};
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}
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nrerror("Too many bisections in rtbis");
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return data;
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}
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ConvergenceData rtflsp_with_conv(float (*func)(float), float x1, float x2, float xacc) {
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void nrerror(char error_text[]);
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ConvergenceData data;
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data.size = 0;
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int j;
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float fl, fh, xl, xh, swap, dx, del, f, rtf;
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fl = (*func)(x1);
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fh = (*func)(x2);
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if (fl * fh > 0.0) nrerror("Root must be bracketed in rtflsp");
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if (fl < 0.0) {
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xl = x1;
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xh = x2;
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} else {
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xl = x2;
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xh = x1;
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swap = fl;
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fl = fh;
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fh = swap;
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}
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dx = xh - xl;
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for (j = 1; j <= JMAX; j++) {
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rtf = xl + dx * fl / (fl - fh);
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f = (*func)(rtf);
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if (f < 0.0) {
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del = xl - rtf;
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xl = rtf;
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fl = f;
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} else {
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del = xh - rtf;
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xh = rtf;
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fh = f;
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}
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dx = xh - xl;
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data.data[data.size++] = rtf;
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if (fabs(del) < xacc || f == 0.0) return data;
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}
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nrerror("Maximum number of iterations exceeded in rtflsp");
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return data;
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}
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ConvergenceData rtsec_with_conv(float (*func)(float), float x1, float x2, float xacc) {
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void nrerror(char error_text[]);
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ConvergenceData data;
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data.size = 0;
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int j;
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float fl, f, dx, swap, xl, rts;
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fl = (*func)(x1);
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f = (*func)(x2);
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if (fabs(fl) < fabs(f)) {
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rts = x1;
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xl = x2;
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swap = fl;
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fl = f;
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f = swap;
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} else {
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xl = x1;
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rts = x2;
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}
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for (j = 1; j <= JMAX; j++) {
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dx = (xl - rts) * f / (f - fl);
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xl = rts;
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fl = f;
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rts += dx;
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f = (*func)(rts);
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data.data[data.size++] = rts;
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if (fabs(dx) < xacc || f == 0.0) return data;
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}
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nrerror("Maximum number of iterations exceeded in rtsec");
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return data;
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}
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ConvergenceData rtnewt_with_conv(void (*funcd)(float, float *, float *), float x1, float x2,
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float xacc) {
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void nrerror(char error_text[]);
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ConvergenceData data;
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data.size = 0;
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int j;
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float df, dx, f, rtn;
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rtn = 0.5 * (x1 + x2);
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for (j = 1; j <= JMAX; j++) {
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(*funcd)(rtn, &f, &df);
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dx = f / df;
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rtn -= dx;
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if ((x1 - rtn) * (rtn - x2) < 0.0)
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nrerror("Jumped out of brackets in rtnewt");
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data.data[data.size++] = rtn;
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if (fabs(dx) < xacc) return data;
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}
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nrerror("Maximum number of iterations exceeded in rtnewt");
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return data;
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}
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ConvergenceData rtsafe_with_conv(void (*funcd)(float, float *, float *), float x1, float x2,
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float xacc) {
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void nrerror(char error_text[]);
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ConvergenceData data;
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data.size = 0;
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int j;
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float df, dx, dxold, f, fh, fl;
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float temp, xh, xl, rts;
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(*funcd)(x1, &fl, &df);
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(*funcd)(x2, &fh, &df);
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if ((fl > 0.0 && fh > 0.0) || (fl < 0.0 && fh < 0.0))
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nrerror("Root must be bracketed in rtsafe");
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if (fl == 0.0) {
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data.data[data.size++] = x1;
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return data;
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}
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if (fh == 0.0) {
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data.data[data.size++] = x2;
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return data;
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}
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if (fl < 0.0) {
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xl = x1;
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xh = x2;
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} else {
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xh = x1;
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xl = x2;
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}
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rts = 0.5 * (x1 + x2);
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dxold = fabs(x2 - x1);
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dx = dxold;
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(*funcd)(rts, &f, &df);
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for (j = 1; j <= JMAX; j++) {
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if ((((rts - xh) * df - f) * ((rts - xl) * df - f) > 0.0) || (fabs(2.0 * f) > fabs(dxold * df))) {
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dxold = dx;
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dx = 0.5 * (xh - xl);
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rts = xl + dx;
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data.data[data.size++] = rts;
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if (xl == rts) return data;
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} else {
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dxold = dx;
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dx = f / df;
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temp = rts;
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rts -= dx;
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data.data[data.size++] = rts;
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if (temp == rts) return data;
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}
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if (fabs(dx) < xacc) return data;
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(*funcd)(rts, &f, &df);
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if (f < 0.0)
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xl = rts;
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else
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xh = rts;
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}
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nrerror("Maximum number of iterations exceeded in rtsafe");
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return data;
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}
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ConvergenceData rtmuller_with_conv(float (*func)(float), float x1, float x2, float xacc) {
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void nrerror(char error_text[]);
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int j;
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float fh, fl, fm, fnew, s, xl, r, x3, x0, x_prev, x_curr, x_next;
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float d0, d1, d2, a, b, c;
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ConvergenceData data;
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data.size = 0;
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x0 = x1;
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x_prev = x2;
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x_curr = (x0 + x_prev) / 2.0;
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if (x_prev == x_curr) x_curr += xacc;
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if (x0 == x_curr) x0 -= xacc;
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for (j = 1; j <= 200; j++) {
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d0 = func(x0);
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d1 = func(x_prev);
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d2 = func(x_curr);
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float h1 = x_prev - x0;
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float h2 = x_curr - x_prev;
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float delta1 = (d1 - d0) / h1;
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float delta2 = (d2 - d1) / h2;
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a = (delta2 - delta1) / (h2 + h1);
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b = a * h2 + delta2;
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c = d2;
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float disc = b * b - 4 * a * c;
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if (disc < 0) nrerror("MullerMethodError: Complex roots encountered");
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float denom1 = b + sqrt(disc);
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float denom2 = b - sqrt(disc);
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if (fabs(denom1) < fabs(denom2)) {
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x_next = x_curr - (2 * c) / denom2;
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} else {
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x_next = x_curr - (2 * c) / denom1;
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}
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data.data[data.size++] = x_next;
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if (fabs(x_next - x_curr) < xacc) return data;
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x0 = x_prev;
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x_prev = x_curr;
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x_curr = x_next;
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}
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nrerror("MullerMethodError: Too many iterations");
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return data;
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}
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#undef JMAX |