implement hw2/rtmuller

hws/hw2/main.c

@@ -2,6 +2,7 @@
 #include <stdlib.h>
 
 #include "nr.h"
+#include "rtmuller.h"
 
 void dbessj0(float x, float *y, float *dy) {
     *y = bessj0(x);
@@ -25,15 +26,16 @@ int main() {
     int i;
     zbrak(bessj0, a, b, n, xb1, xb2, &nb);
 
-    for (i = 1; i <= nb; i++) {
+    /* 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);
     float *roots_newt = calloc(sizeof(float), nb);
     float *roots_newtsafe = calloc(sizeof(float), nb);
+    float *roots_muller = calloc(sizeof(float), nb);
 
     for (i = 0; i < nb; i++) {
         float l = xb1[i + 1];
@@ -43,6 +45,7 @@ int main() {
         roots_secant[i] = rtsec(bessj0, l, r, xacc);
         roots_newt[i] = rtnewt(dbessj0, l, r, xacc);
         roots_newtsafe[i] = rtsafe(dbessj0, l, r, xacc);
+        roots_muller[i] = rtmuller(bessj0, l, r, xacc);
     }
 
     printf("besection roots: ");
@@ -75,6 +78,12 @@ int main() {
     }
     printf("\n");
 
+    printf("muller method roots: ");
+    for (i = 0; i < nb; i++) {
+        printf("%f ", roots_muller[i]);
+    }
+    printf("\n");
+
     /* free */
     free(xb1);
     free(xb2);
@@ -83,6 +92,8 @@ int main() {
     free(roots_linter);
     free(roots_secant);
     free(roots_newt);
+    free(roots_newtsafe);
+    free(roots_muller);
 
     return 0;
 }

hws/hw2/rtmuller.c

@@ -0,0 +1,51 @@
+#include "nrutil.h"
+
+#include "rtmuller.h"
+#include <math.h>
+
+float rtmuller(float (*func)(float), float x1, float x2, float xacc) {
+    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;
+
+    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("Muller's method: 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;
+        }
+
+        if (fabs(x_next - x_curr) < xacc) return x_next;
+
+        x0 = x_prev;
+        x_prev = x_curr;
+        x_curr = x_next;
+    }
+    nrerror("Too many iterations in rtmuller");
+    return 0.0;
+}

hws/hw2/rtmuller.h

@@ -0,0 +1,3 @@
+#pragma once
+
+float rtmuller(float (*func)(float), float x1, float x2, float xacc);