add conv for hw2 and complement main.c

hws/hw2/convergence.c

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

hws/hw2/convergence.h

@@ -0,0 +1,16 @@
+#pragma once
+
+#include "nr.h"
+#include "nrutil.h"
+
+typedef struct ConvergenceData {
+    int size;
+    float data[200];
+} ConvergenceData;
+
+ConvergenceData rtbis_with_conv(float (*func)(float), float x1, float x2, float xacc);
+ConvergenceData rtflsp_with_conv(float (*func)(float), float x1, float x2, float xacc);
+ConvergenceData rtsec_with_conv(float (*func)(float), float x1, float x2, float xacc);
+ConvergenceData rtnewt_with_conv(void (*funcd)(float, float *, float *), float x1, float x2, float xacc);
+ConvergenceData rtsafe_with_conv(void (*funcd)(float, float *, float *), float x1, float x2, float xacc);
+ConvergenceData rtmuller_with_conv(float (*func)(float), float x1, float x2, float xacc);

hws/hw2/main.c

@@ -2,6 +2,7 @@
 #include <stdio.h>
 #include <stdlib.h>
 
+#include "convergence.h"
 #include "muller.h"
 #include "nr.h"
 
@@ -28,6 +29,10 @@ int main() {
     1. using zbrak, find all possible intervals with roots.
     2. and use routines and enumerate all roots.
     */
+    printf("===============================\n");
+    printf("A report of root-finding\n");
+    printf("student name: Hajin Ju, id: 2024062806\n");
+    printf("--------------------------------\n");
     printf("=== A Program that find bessj0 roots in [1, 10] ===\n");
     printf("--------------------------------\n");
     float a = 1.0, b = 10.0;
@@ -41,10 +46,6 @@ int main() {
     int i;
     zbrak(bessj0, a, b, n, xb1, xb2, &nb);
 
-    /* for (i = 1; i <= nb; i++) {
-        printf("[%f, %f]\n", xb1[i], xb2[i]);
-    } */
-
     float *roots_bisect = calloc(sizeof(float), nb);
     float *roots_linter = calloc(sizeof(float), nb);
     float *roots_secant = calloc(sizeof(float), nb);
@@ -117,7 +118,7 @@ int main() {
     xb1 = calloc(sizeof(float), n);
     xb2 = calloc(sizeof(float), n);
     nb = 0;
-    
+
     zbrak(test_func, a, b, n, xb1, xb2, &nb);
     float *roots_interesting = calloc(sizeof(float), nb);
 
@@ -128,7 +129,8 @@ int main() {
         roots_interesting[i] = rtsafe(test_funcd, l, r, xacc);
     }
 
-    printf("I want to find roots of `x * sin(x) - 1`\n");
+    printf("I want to find roots of `x * sin(x) - 1`\nwhere x in [%.02f, %.02f]\n", a, b);
+    printf("-------------------------------\n");
     printf("roots: ");
     for (i = 0; i < nb; i++) {
         printf("%f ", roots_interesting[i]);
@@ -139,5 +141,134 @@ int main() {
     free(xb2);
     free(roots_interesting);
 
+    printf("\n");
+
+    printf("=== Discuss the convergence speed ===\n");
+    printf("--------------------------------\n");
+
+    a = 2.0f;
+    b = 3.0f;
+    printf("Find a root of bessj0(x) where x in [%.02f, %.02f].\n", a, b);
+    printf("We want to get convergence speed(iteration count).\n");
+    printf("-------------------------------\n");
+
+    ConvergenceData conv_bisect = rtbis_with_conv(bessj0, a, b, xacc);
+    ConvergenceData conv_flsp = rtflsp_with_conv(bessj0, a, b, xacc);
+    ConvergenceData conv_secant = rtsec_with_conv(bessj0, a, b, xacc);
+    ConvergenceData conv_newt = rtnewt_with_conv(dbessj0, a, b, xacc);
+    ConvergenceData conv_newtsafe = rtsafe_with_conv(dbessj0, a, b, xacc);
+    ConvergenceData conv_muller = rtmuller_with_conv(bessj0, a, b, xacc);
+
+    printf("Convergence History(where root ~ 2.404825):\n");
+
+    printf("bisect iteration count: %d\n", conv_bisect.size);
+    printf("bisect iteration history: ");
+    for (i = 0; i < conv_bisect.size; i++) {
+        printf("%f ", conv_bisect.data[i]);
+    }
+    printf("\n");
+
+    printf("lin-interpoalation iteration count: %d\n", conv_flsp.size);
+    printf("lin-interpoalation iteration history: ");
+    for (i = 0; i < conv_flsp.size; i++) {
+        printf("%f ", conv_flsp.data[i]);
+    }
+    printf("\n");
+
+    printf("secant iteration count: %d\n", conv_secant.size);
+    printf("secant iteration history: ");
+    for (i = 0; i < conv_secant.size; i++) {
+        printf("%f ", conv_secant.data[i]);
+    }
+    printf("\n");
+
+    printf("newton-raphson iteration count: %d\n", conv_newt.size);
+    printf("newton-raphson iteration history: ");
+    for (i = 0; i < conv_newt.size; i++) {
+        printf("%f ", conv_newt.data[i]);
+    }
+    printf("\n");
+
+    printf("newton with bracketing iteration count: %d\n", conv_newtsafe.size);
+    printf("newton with bracketing iteration history: ");
+    for (i = 0; i < conv_newtsafe.size; i++) {
+        printf("%f ", conv_newtsafe.data[i]);
+    }
+    printf("\n");
+
+    printf("muller method iteration count: %d\n", conv_muller.size);
+    printf("muller method iteration history: ");
+    for (i = 0; i < conv_muller.size; i++) {
+        printf("%f ", conv_muller.data[i]);
+    }
+    printf("\n");
+
+    printf("-------------------------------\n");
+    printf("Convergence Error\n");
+    float res;
+    
+    printf("bisect convergence error: ");
+    res = conv_bisect.data[conv_bisect.size - 1];
+    for (i =0;i < conv_bisect.size; i++) {
+        printf("%f ", fabs(conv_bisect.data[i] - res) / res);
+    }
+    printf("\n");
+
+    printf("flsp convergence error: ");
+    res = conv_flsp.data[conv_flsp.size - 1];
+    for (i =0;i < conv_flsp.size; i++) {
+        printf("%f ", fabs(conv_flsp.data[i] - res) / res);
+    }
+    printf("\n");
+
+    printf("secant convergence error: ");
+    res = conv_secant.data[conv_secant.size - 1];
+    for (i =0;i < conv_secant.size; i++) {
+        printf("%f ", fabs(conv_secant.data[i] - res) / res);
+    }
+    printf("\n");
+
+    printf("newton-raphson convergence error: ");
+    res = conv_newt.data[conv_newt.size - 1];
+    for (i =0;i < conv_newt.size; i++) {
+        printf("%f ", fabs(conv_newt.data[i] - res) / res);
+    }
+    printf("\n");
+
+    printf("newton with bracketing convergence error: ");
+    res = conv_newtsafe.data[conv_newtsafe.size - 1];
+    for (i =0;i < conv_newtsafe.size; i++) {
+        printf("%f ", fabs(conv_newtsafe.data[i] - res) / res);
+    }
+    printf("\n");
+
+    printf("muller method convergence error: ");
+    res = conv_muller.data[conv_muller.size - 1];
+    for (i =0;i < conv_muller.size; i++) {
+        printf("%f ", fabs(conv_muller.data[i] - res) / res);
+    }
+    printf("\n");
+
+    printf("-------------------------------\n");
+
+    printf("Convergence Iteration Counts Table:\n");
+    printf("--------------------------------------------------------------\n");
+    printf("| Method                   | Iter |\n");
+    printf("--------------------------------------------------------------\n");
+    printf("| Bisection                | %-04d |\n", conv_bisect.size);
+    printf("| Linear Interpolation     | %-04d |\n", conv_flsp.size);
+    printf("| Secant                   | %-04d |\n", conv_secant.size);
+    printf("| Newton-Raphson           | %-04d |\n", conv_newt.size);
+    printf("| Newton with Bracketing   | %-04d |\n", conv_newtsafe.size);
+    printf("| Muller                   | %-04d |\n", conv_muller.size);
+    printf("--------------------------------------------------------------\n");
+
+    printf("As a result, In order of performance(faster convergence speed),\n");
+    printf("Newton-Raphson, Newton with Bracketing, Muller, Secant, Linear Interpolation, Bisection\n");
+
+    printf("-------------------------------\n");
+
+    printf("===============================\n");
+
     return 0;
 }

hws/hw2/muller.c

@@ -29,7 +29,7 @@ float rtmuller(float (*func)(float), float x1, float x2, float xacc) {
         c = d2;
 
         float disc = b * b - 4 * a * c;
-        if (disc < 0) nrerror("Muller's method: complex roots encountered");
+        if (disc < 0) nrerror("MullerMethodError: complex roots encountered");
 
         float denom1 = b + sqrt(disc);
         float denom2 = b - sqrt(disc);
@@ -46,6 +46,6 @@ float rtmuller(float (*func)(float), float x1, float x2, float xacc) {
         x_prev = x_curr;
         x_curr = x_next;
     }
-    nrerror("Too many iterations in rtmuller");
+    nrerror("MullerMethodError: too many iterations");
     return 0.0;
 }