create hw2 and some commit

hws/hw2/main.c

@@ -0,0 +1,88 @@
+#include <stdio.h>
+#include <stdlib.h>
+
+#include "nr.h"
+
+void dbessj0(float x, float *y, float *dy) {
+    *y = bessj0(x);
+    *dy = -bessj1(x);
+}
+
+int main() {
+    /*
+    1. using zbrak, find all possible intervals with roots.
+    2. and use routines and enumerate all roots.
+    */
+
+    float a = 1.0, b = 10.0;
+    float xacc = 0.000001;
+
+    int n = 23;
+    float *xb1 = calloc(sizeof(float), n);
+    float *xb2 = calloc(sizeof(float), n);
+    int nb;
+
+    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);
+    float *roots_newt = calloc(sizeof(float), nb);
+    float *roots_newtsafe = calloc(sizeof(float), nb);
+    
+    for (i = 0; i < nb; i++) {
+        float l = xb1[i + 1];
+        float r = xb2[i + 1];
+        roots_bisect[i] = rtbis(bessj0, l, r, xacc);
+        roots_linter[i] = rtflsp(bessj0, l, r, xacc);
+        roots_secant[i] = rtsec(bessj0, l, r, xacc);
+        roots_newt[i] = rtnewt(dbessj0, l, r, xacc);
+        roots_newtsafe[i] = rtsafe(dbessj0, l, r, xacc);
+    }
+
+    printf("besection roots: ");
+    for (i = 0; i < nb; i++) {
+        printf("%f ", roots_bisect[i]);
+    }
+    printf("\n");
+
+    printf("lin-interpoalation roots: ");
+    for (i = 0; i < nb; i++) {
+        printf("%f ", roots_linter[i]);
+    }
+    printf("\n");
+
+    printf("secant roots: ");
+    for (i = 0; i < nb; i++) {
+        printf("%f ", roots_secant[i]);
+    }
+    printf("\n");
+
+    printf("newton-raphson roots: ");
+    for (i = 0; i < nb; i++) {
+        printf("%f ", roots_newt[i]);
+    }
+    printf("\n");
+
+    printf("newton with bracketing roots: ");
+    for (i = 0; i < nb; i++) {
+        printf("%f ", roots_newtsafe[i]);
+    }
+    printf("\n");
+
+    /* free */
+    free(xb1);
+    free(xb2);
+
+    free(roots_bisect);
+    free(roots_linter);
+    free(roots_secant);
+    free(roots_newt);
+
+    return 0;
+}