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#include "lizfcm.h"
#include <stdio.h>
#include <stdlib.h>
double f(double x) { return (x - 1) / (x + 1); }
int main() {
printf("Basic Routines\n");
printf("smaceps(): %.10e\n", smaceps());
printf("dmaceps(): %.10e\n", dmaceps());
printf("========\n");
Array_double *v = InitArray(double, {3, 1, -4, 1, 5, -9, 3});
char v_s[256];
strcpy(v_s, "");
format_vector_into(v, v_s);
Array_double *w = InitArray(double, {-2, 7, 1, -8, -2, 8, 5});
char w_s[256];
strcpy(w_s, "");
format_vector_into(w, w_s);
printf("Norm, Distance\n");
printf("v: %s", v_s);
printf("w: %s", w_s);
printf("l1_norm(v): %f\n", l1_norm(v));
printf("l2_norm(v): %f\n", l2_norm(v));
printf("linf_norm(v): %f\n", linf_norm(v));
printf("l1_dist(v, w): %f\n", l1_distance(v, w));
printf("l2_dist(v, w): %f\n", l2_distance(v, w));
printf("linf_dist(v, w): %f\n", linf_distance(v, w));
printf("========\n");
double h = 0.001;
printf("Derivative Approxs\n");
printf("f(x) = (x-1)/(x+1)\n");
printf("approx f'(1) w/ c.d.: %f\n", central_derivative_at(&f, 1, h));
printf("approx f'(1) w/ fw.d.: %f\n", forward_derivative_at(&f, 1, h));
printf("approx f'(1) w/ bw.d.: %f\n", backward_derivative_at(&f, 1, h));
printf("========\n");
v = InitArray(double, {1, 2, 3, 4, 5});
strcpy(v_s, "");
format_vector_into(v, v_s);
w = InitArray(double, {2, 3, 4, 5, 6});
strcpy(w_s, "");
format_vector_into(w, w_s);
Line *line = least_squares_lin_reg(v, w);
printf("Least Squares\n");
printf("v: %s", v_s);
printf("w: %s", w_s);
printf("least_squares_lin_reg(v, w): (%f)x + %f\n", line->m, line->a);
v = InitArray(double, {1, 2, 3, 4, 5, 6, 7});
strcpy(v_s, "");
format_vector_into(v, v_s);
w = InitArray(double, {0.5, 3, 2, 3.5, 5, 6, 7.5});
strcpy(w_s, "");
format_vector_into(w, w_s);
printf("v: %s", v_s);
printf("w: %s", w_s);
line = least_squares_lin_reg(v, w);
printf("least_squares_lin_reg(v, w): (%f)x + %f\n", line->m, line->a);
printf("========\n");
printf("LU Decomp\n");
char m_s[2048];
Matrix_double *m = InitMatrixWithSize(double, 8, 8, 0.0);
for (int i = 0; i < 8; i++) {
for (int j = 0; j < 8; j++) {
m->data[i]->data[j] = (i + 1.0) + j * 3 + (rand() % 12);
}
}
format_matrix_into(m, m_s);
printf("m = %s", m_s);
Matrix_double **u_l = put_lu_decomp(m);
Matrix_double *u = u_l[0];
Matrix_double *l = u_l[1];
strcpy(m_s, "");
format_matrix_into(u, m_s);
printf("u = %s", m_s);
strcpy(m_s, "");
format_matrix_into(l, m_s);
printf("l = %s", m_s);
printf("========\n");
printf("Back Substitution\n");
return 0;
}
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