rename muller and add hw2

hws/hw2/main.c

@@ -1,20 +1,35 @@
+#include <math.h>
 #include <stdio.h>
 #include <stdlib.h>
 
+#include "muller.h"
 #include "nr.h"
-#include "rtmuller.h"
 
 void dbessj0(float x, float *y, float *dy) {
     *y = bessj0(x);
     *dy = -bessj1(x);
 }
 
+float test_func(float x) {
+    return x * sin(x) - 1;
+}
+
+float test_func_derivative(float x) {
+    return sin(x) + x * cos(x);
+}
+
+void test_funcd(float x, float *y, float *dy) {
+    *y = test_func(x);
+    *dy = test_func_derivative(x);
+}
+
 int main() {
     /*
     1. using zbrak, find all possible intervals with roots.
     2. and use routines and enumerate all roots.
     */
-
+    printf("=== A Program that find bessj0 roots in [1, 10] ===\n");
+    printf("--------------------------------\n");
     float a = 1.0, b = 10.0;
     float xacc = 0.000001;
 
@@ -94,6 +109,35 @@ int main() {
     free(roots_newt);
     free(roots_newtsafe);
     free(roots_muller);
+    printf("\n");
+    printf("=== Solve one interesting nonlinear equation ===\n");
+    printf(": using the routine of rtsafe.c in NR in C\n");
+    printf("--------------------------------\n");
+    n = 21;
+    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);
+
+    for (i = 0; i < nb; i++) {
+        float l = xb1[i + 1];
+        float r = xb2[i + 1];
+
+        roots_interesting[i] = rtsafe(test_funcd, l, r, xacc);
+    }
+
+    printf("I want to find roots of `x * sin(x) - 1`\n");
+    printf("roots: ");
+    for (i = 0; i < nb; i++) {
+        printf("%f ", roots_interesting[i]);
+    }
+    printf("\n");
+
+    free(xb1);
+    free(xb2);
+    free(roots_interesting);
 
     return 0;
 }

hws/hw2/muller.c

@@ -1,6 +1,6 @@
 #include "nrutil.h"
 
-#include "rtmuller.h"
+#include "muller.h"
 #include <math.h>
 
 float rtmuller(float (*func)(float), float x1, float x2, float xacc) {