exp 1-6: init

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

.gitignore

@@ -0,0 +1,9 @@
+*tex
+*~
+\#*
+_minted-file/
+.\#
+*html
+lab*/*pdf
+*.in
+*.out

1.c

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+#include <math.h>
+#include <stdio.h>
+#define EPSILON 0.0000001
+#define f(x) ((352 * x * x * x) - (64 * x * x) + (198 * x) - 36)
+#define f1(x) ((1056 * x * x) - (128 * x) + 198)
+double newtonRaphson(double x) {
+  double h = f(x) / f1(x);
+  if (f(x) == 0 || fabs(h) < EPSILON)
+    return x;
+  return newtonRaphson(x - h);
+}
+int main() {
+  printf("Root for f(x) = 352x^3 - 64x^2 + 198x - 36 is %lf",
+         newtonRaphson(-4));
+}

2.c

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+#include <math.h>
+#include <stdio.h>
+#include <stdlib.h>
+#define EPSILON 0.0000001
+#define f(x) ((352 * x * x * x) - (64 * x * x) + (198 * x) - 36)
+double bisection(double a, double b) {
+  double x;
+  if (f(a) * f(b) > 0) {
+    printf("The values of function at the respective initial guesses must have "
+           "opposite signs");
+    exit(1);
+  }
+  x = (a + b) / 2;
+  if (f(x) == 0 || fabs(b - a) < EPSILON)
+    return x;
+  if (f(x) > 0)
+    return bisection(x, b);
+  return bisection(a, x);
+}
+int main() {
+  printf("Root for f(x) = 352x^3 - 64x^2 + 198x - 36 is %lf",
+         bisection(1.6, -4));
+}

3.c

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+#include <math.h>
+#include <stdio.h>
+#define EPSILON 0.0000001
+#define f(x) ((352 * x * x * x) - (64 * x * x) + (198 * x) - 36)
+double secant(double a, double b) {
+  double x1;
+  x1 = (a * f(b) - b * f(a)) / (f(b) - f(a));
+  if (f(x1) == 0 || fabs(a - b) < EPSILON)
+    return x1;
+  return secant(b, x1);
+}
+int main() {
+  printf("Root for f(x) = 352x^3 - 64x^2 + 198x - 36 is %lf", secant(1.6, -4));
+}

4.c

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+#include <stdio.h>
+
+int main() {
+  double xp, yp = 0, p;
+  int i, j, n;
+
+  printf("Number of inputs: ");
+  scanf("%d", &n);
+
+  double x[n], y[n];
+  printf("Input sample space:\n");
+
+  for (i = 0; i < n; i++) {
+    printf("x%d: ", i);
+    scanf("%lf", x + i);
+    printf("y%d: ", i);
+    scanf("%lf", y + i);
+  }
+
+  printf("Enter interpolation point x: ");
+  scanf("%lf", &xp);
+
+  for (i = 0; i < n; i++) {
+    p = 1;
+    for (j = 0; j < n; j++) {
+      if (i != j) {
+        p *= (xp - x[j]) / (x[i] - x[j]);
+      }
+    }
+    yp += p * y[i];
+  }
+  printf("Interpolated value for %lf is %lf.", xp, yp);
+}

5.c

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+#include <stdio.h>
+
+int main() {
+  int n, i, j = 1;
+  double xp, yp, f1, f2 = 0;
+
+  printf("Enter the number of inputs: ");
+  scanf("%d", &n);
+
+  double x[n], y[n];
+
+  printf("Enter input values:\n");
+  for (i = 0; i < n; i++) {
+    printf("x%d=", i);
+    scanf("%lf", x + i);
+    printf("y%d=", i);
+    scanf("%lf", y + i);
+  }
+
+  yp = y[0];
+
+  printf("Enter interpolation point x: ");
+  scanf("%lf", &xp);
+
+  do {
+    for (i = 0; i < n - 1; i++) 
+      y[i] = ((y[i + 1] - y[i]) / (x[i + j] - x[i]));
+
+    f1 = 1;
+
+    for (i = 0; i < j; i++) {
+      f1 *= (xp - x[i]);
+    }
+
+    f2 += (y[0] * f1);
+    j++;
+  } while ((--n) > 1);
+
+  yp += f2;
+  
+  printf("Interpolated value for %lf is %lf.", xp, yp);
+}

6.c

@@ -0,0 +1,23 @@
+#include <math.h>
+#include <stdio.h>
+
+#define f(x) ((352 * x * x * x) - (64 * x * x) + (198 * x) - 36)
+
+double trapezoidal_integral(double a, double b, double n) {
+  double h = (b - a) / n;
+
+  double s = (f(a) + f(b)) / 2;
+
+  // Add the other heights
+
+  for (int i = 1; i < n; i++)
+    s += f(a + i * h);
+
+  return s * h;
+}
+
+int main() {
+  printf("The area under the curve f(x) = 352x^3 - 64x^2 + 198x - 36 from x=3 "
+         "to x=4 is %lf",
+         trapezoidal_integral(3, 4, 10000));
+}

file.org

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+#+title: Computational Methods Lab
+#+author: Amneesh Singh I6
+#+LATEX_HEADER: \usepackage[margin=0.5in]{geometry}
+
+#+LATEX: \clearpage
+
+|------------------------------------------------------------------------------------------------------------|
+| Programs are followed by their respective inputs and outputs i.e, both stdin and stdout are shown together |
+|------------------------------------------------------------------------------------------------------------|
+
+* Program for finding roots of f(x) = 0 using Newton Raphson Method
+#+ATTR_LATEX: :options frame=single,breaklines=true
+#+begin_src C :tangle 1.c :results output :exports both :wrap src text
+#include <math.h>
+#include <stdio.h>
+#define EPSILON 0.0000001
+#define f(x) ((352 * x * x * x) - (64 * x * x) + (198 * x) - 36)
+#define f1(x) ((1056 * x * x) - (128 * x) + 198)
+double newtonRaphson(double x) {
+  double h = f(x) / f1(x);
+  if (f(x) == 0 || fabs(h) < EPSILON)
+    return x;
+  return newtonRaphson(x - h);
+}
+int main() {
+  printf("Root for f(x) = 352x^3 - 64x^2 + 198x - 36 is %lf",
+         newtonRaphson(-4));
+}
+#+end_src
+
+* Program for nding roots of f(x) = 0 using bisection method
+#+ATTR_LATEX: :options frame=single,breaklines=true
+#+begin_src C :tangle 2.c :results output :exports both :wrap src text
+#include <math.h>
+#include <stdio.h>
+#include <stdlib.h>
+#define EPSILON 0.0000001
+#define f(x) ((352 * x * x * x) - (64 * x * x) + (198 * x) - 36)
+double bisection(double a, double b) {
+  double x;
+  if (f(a) * f(b) > 0) {
+    printf("The values of function at the respective initial guesses must have "
+           "opposite signs");
+    exit(1);
+  }
+  x = (a + b) / 2;
+  if (f(x) == 0 || fabs(b - a) < EPSILON)
+    return x;
+  if (f(x) > 0)
+    return bisection(x, b);
+  return bisection(a, x);
+}
+int main() {
+  printf("Root for f(x) = 352x^3 - 64x^2 + 198x - 36 is %lf",
+         bisection(1.6, -4));
+}
+#+end_src
+
+#+LATEX: \clearpage
+
+* Program for finding roots of f(x) = 0 using secant method
+#+ATTR_LATEX: :options frame=single,breaklines=true
+#+begin_src C :tangle 3.c :results output :exports both :wrap src text
+#include <math.h>
+#include <stdio.h>
+#define EPSILON 0.0000001
+#define f(x) ((352 * x * x * x) - (64 * x * x) + (198 * x) - 36)
+double secant(double a, double b) {
+  double x1;
+  x1 = (a * f(b) - b * f(a)) / (f(b) - f(a));
+  if (f(x1) == 0 || fabs(a - b) < EPSILON)
+    return x1;
+  return secant(b, x1);
+}
+int main() {
+  printf("Root for f(x) = 352x^3 - 64x^2 + 198x - 36 is %lf", secant(1.6, -4));
+}
+#+end_src
+
+#+LATEX: \clearpage
+
+* Program to implement Langrange Interpolation.
+#+ATTR_LATEX: :options frame=single,breaklines=true
+#+begin_src C :tangle 4.c :results output :wrap src text
+#include <stdio.h>
+
+int main() {
+  double xp, yp = 0, p;
+  int i, j, n;
+
+  printf("Number of inputs: ");
+  scanf("%d", &n);
+
+  double x[n], y[n];
+  printf("Input sample space:\n");
+
+  for (i = 0; i < n; i++) {
+    printf("x%d: ", i);
+    scanf("%lf", x + i);
+    printf("y%d: ", i);
+    scanf("%lf", y + i);
+  }
+
+  printf("Enter interpolation point x: ");
+  scanf("%lf", &xp);
+
+  for (i = 0; i < n; i++) {
+    p = 1;
+    for (j = 0; j < n; j++) {
+      if (i != j) {
+        p *= (xp - x[j]) / (x[i] - x[j]);
+      }
+    }
+    yp += p * y[i];
+  }
+  printf("Interpolated value for %lf is %lf.", xp, yp);
+}
+#+end_src
+
+#+begin_src text
+Number of inputs: 4
+Input sample space:
+x0: 0
+y0: 2
+x1: 1
+y1: 3
+x2: 2
+y2: 12
+x3: 5
+y3: 147
+Enter interpolation point x: 3
+Interpolated value for 3.000000 is 35.000000.
+#+end_src
+
+#+LATEX: \clearpage
+
+* Program to implement Newton's Divided Difference formula.
+#+ATTR_LATEX: :options frame=single,breaklines=true
+#+begin_src C :tangle 5.c :results output :wrap src text
+#include <stdio.h>
+
+int main() {
+  int n, i, j = 1;
+  double xp, yp, f1, f2 = 0;
+
+  printf("Enter the number of inputs: ");
+  scanf("%d", &n);
+
+  double x[n], y[n];
+
+  printf("Enter input values:\n");
+  for (i = 0; i < n; i++) {
+    printf("x%d=", i);
+    scanf("%lf", x + i);
+    printf("y%d=", i);
+    scanf("%lf", y + i);
+  }
+
+  yp = y[0];
+
+  printf("Enter interpolation point x: ");
+  scanf("%lf", &xp);
+
+  do {
+    for (i = 0; i < n - 1; i++) 
+      y[i] = ((y[i + 1] - y[i]) / (x[i + j] - x[i]));
+
+    f1 = 1;
+
+    for (i = 0; i < j; i++) {
+      f1 *= (xp - x[i]);
+    }
+
+    f2 += (y[0] * f1);
+    j++;
+  } while ((--n) > 1);
+
+  yp += f2;
+  
+  printf("Interpolated value for %lf is %lf.", xp, yp);
+}
+#+end_src
+
+#+LATEX: \clearpage
+
+#+begin_src text
+Enter the number of inputs: 4
+Enter input values:
+x0=3
+y0=9
+x1=5
+y1=12 
+x2=9
+y2=666
+x3=15
+y3=10245
+Enter interpolation point x: 999
+Interpolated value for 999.000000 is 9525764925.000002.
+#+end_src
+
+* Program for solving numerical integration by trapezoidal method.
+#+ATTR_LATEX: :options frame=single,breaklines=true
+#+begin_src C  :tangle 6.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 trapezoidal_integral(double a, double b, double n) {
+  double h = (b - a) / n;
+
+  double s = (f(a) + f(b)) / 2;
+
+  // Add the other heights
+
+  for (int i = 1; i < n; i++)
+    s += f(a + i * h);
+
+  return s * h;
+}
+
+int main() {
+  printf("The area under the curve f(x) = 352x^3 - 64x^2 + 198x - 36 from x=3 "
+         "to x=4 is %lf",
+         trapezoidal_integral(3, 4, 10000));
+}
+#+end_src