Least Squares fitting matlab code IMPORTANT Include a print

Least Squares fitting - matlab code

IMPORTANT: Include a printout of your code and of the figure for Problem 2 - PLEASE DO

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solve using your own coding style of matlab

Problem 2. Least squares fitting Derive the least-squares fit of the following model. Derive the equations using the method described in class. That is, determine the coefficients that results in the least-squares fit for a second-order polynomial with a zero intercept. Test the approach by using it to fit the following data, which describes force vs velocity measures in a wind tunnel: m/s 10 20 30 40 50 60 70 80 TV, F, N 25 70 380 550 610 1220 830 1450 In order to find the numerical values for the data, write a Matlab function fit QuadraticNolntercept. The inputs should the x and y vectors and the output should be the values of the a1 and a2 coefficients and the r2 value In another function named LastNameFirstNamePS4Pb2, enter the data, call your fitQuadraticNolntercept function and plot the data and the best fit. Both functions should be in the same file named LastName FirstNamePS4Pb2.m.

Solution

#include #include #include #include using namespace std; long int p, q, n, t, flag, e[100], d[100], temp[100], j, m[100], en[100], i; char msg[100]; int prime(long int); void ce(); long int cd(long int); void encrypt(); void decrypt(); int prime(long int pr) { int i; j = sqrt(pr); for (i = 2; i <= j; i++) { if (pr % i == 0) return 0; } return 1; } int main() { cout << \"\ ENTER FIRST PRIME NUMBER\ \"; cin >> p; flag = prime(p); if (flag == 0) { cout << \"\ WRONG INPUT\ \"; exit(1); } cout << \"\ ENTER ANOTHER PRIME NUMBER\ \"; cin >> q; flag = prime(q); if (flag == 0 || p == q) { cout << \"\ WRONG INPUT\ \"; exit(1); } cout << \"\ ENTER MESSAGE\ \"; fflush(stdin); cin >> msg; for (i = 0; msg[i] != NULL; i++) m[i] = msg[i]; n = p * q; t = (p - 1) * (q - 1); ce(); cout << \"\ POSSIBLE VALUES OF e AND d ARE\ \"; for (i = 0; i < j - 1; i++) cout << e[i] << \"\\t\" << d[i] << \"\ \"; encrypt(); decrypt(); return 0; } void ce() { int k; k = 0; for (i = 2; i < t; i++) { if (t % i == 0) continue; flag = prime(i); if (flag == 1 && i != p && i != q) { e[k] = i; flag = cd(e[k]); if (flag > 0) { d[k] = flag; k++; } if (k == 99) break; } } } long int cd(long int x) { long int k = 1; while (1) { k = k + t; if (k % x == 0) return (k / x); } } void encrypt() { long int pt, ct, key = e[0], k, len; i = 0; len = strlen(msg); while (i != len) { pt = m[i]; pt = pt - 96; k = 1; for (j = 0; j < key; j++) { k = k * pt; k = k % n; } temp[i] = k; ct = k + 96; en[i] = ct; i++; } en[i] = -1; cout << \"\ THE ENCRYPTED MESSAGE IS\ \"; for (i = 0; en[i] != -1; i++) printf(\"%c\", en[i]); } void decrypt() { long int pt, ct, key = d[0], k; i = 0; while (en[i] != -1) { ct = temp[i]; k = 1; for (j = 0; j < key; j++) { k = k * ct; k = k % n; } pt = k + 96; m[i] = pt; i++; } m[i] = -1; cout << \"\ THE DECRYPTED MESSAGE IS\ \"; for (i = 0; m[i] != -1; i++) printf(\"%c\", m[i]); }