exp 7-9: init

Signed-off-by: Amneesh Singh <natto@weirdnatto.in>

7.c

@@ -0,0 +1,26 @@
+#include <math.h>
+#include <stdio.h>
+
+#define f(x) ((352 * x * x * x) - (64 * x * x) + (198 * x) - 36)
+
+double simpsons_1_3(double a, double b, double n) {
+  double h = (b - a) / n;
+
+  double s = f(a) + f(b);
+
+  // Add the other heights
+
+  for (int i = 1; i < n; i += 2)
+    s += 4 * f(a + i * h);
+
+  for (int i = 2; i < n; i += 2)
+    s += 2 * f(a + i * h);
+
+  return (h / 3) * s;
+}
+
+int main() {
+  printf("The area under the curve f(x) = 352x^3 - 64x^2 + 198x - 36 from x=3 "
+         "to x=4 is %lf",
+         simpsons_1_3(3, 4, 10000));
+}

8.c

@@ -0,0 +1,26 @@
+#include <math.h>
+#include <stdio.h>
+
+#define f(x) ((352 * x * x * x) - (64 * x * x) + (198 * x) - 36)
+
+double simpsons_1_3(double a, double b, double n) {
+  double h = (b - a) / n;
+
+  double s = f(a) + f(b);
+
+  // Add the other heights
+
+  for (int i = 1; i < n; i++)
+    s += 3 * f(a + i * h);
+
+  for (int i = 3; i < n; i += 3)
+    s -= f(a + i * h);
+
+  return (h / 8) * 3 * s;
+}
+
+int main() {
+  printf("The area under the curve f(x) = 352x^3 - 64x^2 + 198x - 36 from x=3 "
+         "to x=4 is %lf",
+         simpsons_1_3(3, 4, 10000));
+}

9.c

@@ -0,0 +1,54 @@
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+
+double **inverse(double **matrix, int order) {
+  double **inverse = calloc(order, sizeof(double *));
+  for (int i = 0; i < order; i++) {
+    inverse[i] = calloc(2 * order, sizeof(double));
+    inverse[i][order + i] = 1;
+    memcpy(inverse[i], matrix[i], order * sizeof(double));
+  }
+
+  for (int i = 0; i < order; i++) {
+    for (int j = 0; j < order; j++) {
+      if (i == j)
+        continue;
+      double r = inverse[j][i] / inverse[i][i];
+
+      for (int k = 0; k < order * 2; k++)
+        inverse[j][k] -= r * inverse[i][k];
+    }
+  }
+
+  for (int i = 0; i < order; i++) {
+    for (int j = 0; j < order; j++)
+      inverse[i][j + order] /= inverse[i][i];
+  }
+
+  return inverse;
+}
+
+int main() {
+  const int ORDER = 3;
+
+  double **matrix = malloc(ORDER * sizeof(double *));
+  for (int i = 0; i < ORDER; i++)
+    matrix[i] = malloc(ORDER * sizeof(double));
+
+  matrix[0][0] = 92, matrix[0][1] = 4.5, matrix[0][2] = 61; // 92x + 4.5y + 61z = 0
+  matrix[1][0] = -2, matrix[1][1] = 0, matrix[1][2] = 92387; // -2x + 92387z = 0
+  matrix[2][0] = -2, matrix[2][1] = 0, matrix[2][2] = -23; // -2x - 23z = 0
+
+  double **inv = inverse(matrix, ORDER);
+
+  for (int i = 0; i < ORDER; i++) {
+    for (int j = 0; j < ORDER; j++)
+      printf("%lf ", inv[i][j + ORDER]);
+    printf("\n");
+    free(inv[i]);
+    free(matrix[i]);
+  }
+  free(inv);
+  free(matrix);
+}

file.org

@@ -233,3 +233,125 @@ int main() {
          trapezoidal_integral(3, 4, 10000));
 }
 #+end_src
+
+* Program for solving numerical integration by Simpson's 1/3 rule.
+#+ATTR_LATEX: :options frame=single,breaklines=true
+#+begin_src C  :tangle 7.c :results output :exports both :wrap src text
+#include <math.h>
+#include <stdio.h>
+
+#define f(x) ((352 * x * x * x) - (64 * x * x) + (198 * x) - 36)
+
+double simpsons_1_3(double a, double b, double n) {
+  double h = (b - a) / n;
+
+  double s = f(a) + f(b);
+
+  // Add the other heights
+
+  for (int i = 1; i < n; i += 2)
+    s += 4 * f(a + i * h);
+
+  for (int i = 2; i < n; i += 2)
+    s += 2 * f(a + i * h);
+
+  return (h / 3) * s;
+}
+
+int main() {
+  printf("The area under the curve f(x) = 352x^3 - 64x^2 + 198x - 36 from x=3 "
+         "to x=4 is %lf",
+         simpsons_1_3(3, 4, 10000));
+}
+#+end_src
+
+#+LATEX: \clearpage
+* Program for solving numerical integration by Simpson's 3/8 rule.
+#+ATTR_LATEX: :options frame=single,breaklines=true
+#+begin_src C  :tangle 8.c :results output :exports both :wrap src text
+#include <math.h>
+#include <stdio.h>
+
+#define f(x) ((352 * x * x * x) - (64 * x * x) + (198 * x) - 36)
+
+double simpsons_1_3(double a, double b, double n) {
+  double h = (b - a) / n;
+
+  double s = f(a) + f(b);
+
+  // Add the other heights
+
+  for (int i = 1; i < n; i++)
+    s += 3 * f(a + i * h);
+
+  for (int i = 3; i < n; i += 3)
+    s -= f(a + i * h);
+
+  return (h / 8) * 3 * s;
+}
+
+int main() {
+  printf("The area under the curve f(x) = 352x^3 - 64x^2 + 198x - 36 from x=3 "
+         "to x=4 is %lf",
+         simpsons_1_3(3, 4, 10000));
+}
+#+end_src
+
+* Program for finding inverse of linear equations using Gauss Jordan method.
+#+ATTR_LATEX: :options frame=single,breaklines=true
+#+begin_src C  :tangle 9.c :results output :exports both :wrap src text
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+
+double **inverse(double **matrix, int order) {
+  double **inverse = calloc(order, sizeof(double *));
+  for (int i = 0; i < order; i++) {
+    inverse[i] = calloc(2 * order, sizeof(double));
+    inverse[i][order + i] = 1;
+    memcpy(inverse[i], matrix[i], order * sizeof(double));
+  }
+
+  for (int i = 0; i < order; i++) {
+    for (int j = 0; j < order; j++) {
+      if (i == j)
+        continue;
+      double r = inverse[j][i] / inverse[i][i];
+
+      for (int k = 0; k < order * 2; k++)
+        inverse[j][k] -= r * inverse[i][k];
+    }
+  }
+
+  for (int i = 0; i < order; i++) {
+    for (int j = 0; j < order; j++)
+      inverse[i][j + order] /= inverse[i][i];
+  }
+
+  return inverse;
+}
+
+int main() {
+  const int ORDER = 3;
+
+  double **matrix = malloc(ORDER * sizeof(double *));
+  for (int i = 0; i < ORDER; i++)
+    matrix[i] = malloc(ORDER * sizeof(double));
+
+  matrix[0][0] = 92, matrix[0][1] = 4.5, matrix[0][2] = 61; // 92x + 4.5y + 61z = 0
+  matrix[1][0] = -2, matrix[1][1] = 0, matrix[1][2] = 92387; // -2x + 92387z = 0
+  matrix[2][0] = -2, matrix[2][1] = 0, matrix[2][2] = -23; // -2x - 23z = 0
+
+  double **inv = inverse(matrix, ORDER);
+
+  for (int i = 0; i < ORDER; i++) {
+    for (int j = 0; j < ORDER; j++)
+      printf("%lf ", inv[i][j + ORDER]);
+    printf("\n");
+    free(inv[i]);
+    free(matrix[i]);
+  }
+  free(inv);
+  free(matrix);
+}
+#+end_src