125 lines
3.4 KiB
C
125 lines
3.4 KiB
C
#include "lizfcm.h"
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#include <math.h>
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#include <stdio.h>
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#include <stdlib.h>
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double f(double x) { return (x - 1) / (x + 1); }
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int main() {
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char s[2048];
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printf("Basic Routines\n");
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printf("smaceps(): %.10e\n", smaceps());
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printf("dmaceps(): %.10e\n", dmaceps());
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printf("========\n");
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printf("Norm, Distance\n");
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Array_double *v = InitArray(double, {3, 1, -4});
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strcpy(s, "");
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format_vector_into(v, s);
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printf("v: %s", s);
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Array_double *w = InitArray(double, {-2, 7, 1});
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strcpy(s, "");
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format_vector_into(w, s);
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printf("w: %s", s);
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printf("l1_norm(v): %f\n", l1_norm(v));
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printf("l2_norm(v): %f\n", l2_norm(v));
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printf("linf_norm(v): %f\n", linf_norm(v));
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printf("l1_dist(v, w): %f\n", l1_distance(v, w));
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printf("l2_dist(v, w): %f\n", l2_distance(v, w));
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printf("linf_dist(v, w): %f\n", linf_distance(v, w));
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printf("========\n");
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double h = 0.001;
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printf("Derivative Approxs\n");
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printf("f(x) = (x-1)/(x+1)\n");
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printf("approx f'(1) w/ c.d.: %f\n", central_derivative_at(&f, 1, h));
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printf("approx f'(1) w/ fw.d.: %f\n", forward_derivative_at(&f, 1, h));
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printf("approx f'(1) w/ bw.d.: %f\n", backward_derivative_at(&f, 1, h));
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printf("========\n");
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printf("Least Squares\n");
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v = InitArray(double, {1, 2, 3, 4, 5});
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strcpy(s, "");
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format_vector_into(v, s);
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printf("v: %s", s);
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w = InitArray(double, {2, 3, 4, 5, 6});
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strcpy(s, "");
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format_vector_into(w, s);
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printf("w: %s", s);
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Line *line = least_squares_lin_reg(v, w);
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printf("least_squares_lin_reg(v, w): (%f)x + %f\n", line->m, line->a);
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v = InitArray(double, {1, 2, 3, 4, 5, 6, 7});
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strcpy(s, "");
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format_vector_into(v, s);
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printf("v: %s", s);
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w = InitArray(double, {0.5, 3, 2, 3.5, 5, 6, 7.5});
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strcpy(s, "");
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format_vector_into(w, s);
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printf("w: %s", s);
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line = least_squares_lin_reg(v, w);
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printf("least_squares_lin_reg(v, w): (%f)x + %f\n", line->m, line->a);
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free(line);
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printf("========\n");
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printf("LU Decomp\n");
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uint32_t n = 10;
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Matrix_double *a = InitMatrixWithSize(double, n, n, 0.0);
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for (int i = 0; i < n; i++) {
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for (int j = 0; j < n; j++)
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a->data[i]->data[j] = (100 - rand() % 200);
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}
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strcpy(s, "");
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format_matrix_into(a, s);
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printf("a = %s", s);
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uint32_t solution = 1;
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Array_double *y = InitArrayWithSize(double, n, (double)solution);
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Array_double *b = m_dot_v(a, y); // q8 steps
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Matrix_double **u_l = lu_decomp(a);
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Matrix_double *u = u_l[0];
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Matrix_double *l = u_l[1];
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strcpy(s, "");
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format_matrix_into(u, s);
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printf("u = %s", s);
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strcpy(s, "");
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format_matrix_into(l, s);
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printf("l = %s", s);
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strcpy(s, "");
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format_vector_into(b, s);
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printf("(after following q8) b = %s", s);
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printf("========\n");
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printf("Forward / Backward Substitution Solution to ax=b\n");
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Array_double *b_fsub = fsubst(l, b);
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strcpy(s, "");
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format_vector_into(b_fsub, s);
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printf("b_fsub: %s", s);
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Array_double *x_bsub = bsubst(u, b_fsub);
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strcpy(s, "");
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format_vector_into(x_bsub, s);
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printf("x_bsub: %s", s);
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Array_double *x_solve_matrix = solve_matrix(a, b);
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free_vector(b);
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strcpy(s, "");
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format_vector_into(x_solve_matrix, s);
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printf("\\--> == x_solve_matrix: %s", s);
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free_vector(b_fsub);
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free_vector(x_solve_matrix);
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printf("Verifications\n");
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for (size_t i = 0; i < x_bsub->size; i++)
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printf("in row %zu, solution = %f, true value err=%.10e\n", i,
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x_bsub->data[i], fabs(x_bsub->data[i] - solution));
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return 0;
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}
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