1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
|
#include "lizfcm.h"
#include <math.h>
#include <stdio.h>
#include <stdlib.h>
double f(double x) { return (x - 1) / (x + 1); }
int main() {
char s[2048];
printf("Basic Routines\n");
printf("smaceps(): %.10e\n", smaceps());
printf("dmaceps(): %.10e\n", dmaceps());
printf("========\n");
printf("Norm, Distance\n");
Array_double *v = InitArray(double, {3, 1, -4});
strcpy(s, "");
format_vector_into(v, s);
printf("v: %s", s);
Array_double *w = InitArray(double, {-2, 7, 1});
strcpy(s, "");
format_vector_into(w, s);
printf("w: %s", 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");
printf("Least Squares\n");
v = InitArray(double, {1, 2, 3, 4, 5});
strcpy(s, "");
format_vector_into(v, s);
printf("v: %s", s);
w = InitArray(double, {2, 3, 4, 5, 6});
strcpy(s, "");
format_vector_into(w, s);
printf("w: %s", s);
Line *line = least_squares_lin_reg(v, w);
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(s, "");
format_vector_into(v, s);
printf("v: %s", s);
w = InitArray(double, {0.5, 3, 2, 3.5, 5, 6, 7.5});
strcpy(s, "");
format_vector_into(w, s);
printf("w: %s", s);
line = least_squares_lin_reg(v, w);
printf("least_squares_lin_reg(v, w): (%f)x + %f\n", line->m, line->a);
free(line);
printf("========\n");
printf("LU Decomp\n");
uint32_t n = 10;
Matrix_double *a = InitMatrixWithSize(double, n, n, 0.0);
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++)
a->data[i]->data[j] = (100 - rand() % 200);
}
strcpy(s, "");
format_matrix_into(a, s);
printf("a = %s", s);
uint32_t solution = 1;
Array_double *y = InitArrayWithSize(double, n, (double)solution);
Array_double *b = m_dot_v(a, y); // q8 steps
Matrix_double **u_l = lu_decomp(a);
Matrix_double *u = u_l[0];
Matrix_double *l = u_l[1];
strcpy(s, "");
format_matrix_into(u, s);
printf("u = %s", s);
strcpy(s, "");
format_matrix_into(l, s);
printf("l = %s", s);
strcpy(s, "");
format_vector_into(b, s);
printf("(after following q8) b = %s", s);
printf("========\n");
printf("Forward / Backward Substitution Solution to ax=b\n");
Array_double *b_fsub = fsubst(l, b);
strcpy(s, "");
format_vector_into(b_fsub, s);
printf("b_fsub: %s", s);
Array_double *x_bsub = bsubst(u, b_fsub);
strcpy(s, "");
format_vector_into(x_bsub, s);
printf("x_bsub: %s", s);
Array_double *x_solve_matrix = solve_matrix(a, b);
free_vector(b);
strcpy(s, "");
format_vector_into(x_solve_matrix, s);
printf("\\--> == x_solve_matrix: %s", s);
free_vector(b_fsub);
free_vector(x_solve_matrix);
printf("Verifications\n");
for (size_t i = 0; i < x_bsub->size; i++)
printf("in row %zu, solution = %f, true value err=%.10e\n", i,
x_bsub->data[i], fabs(x_bsub->data[i] - solution));
return 0;
}
|
