fix subst

This commit is contained in:
Elizabeth Hunt 2023-10-13 17:20:17 -06:00
parent 0ce79392c3
commit e16dc49abc
Signed by: simponic
GPG Key ID: 52B3774857EB24B1
5 changed files with 102 additions and 40 deletions

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@ -30,7 +30,9 @@ extern Line *least_squares_lin_reg(Array_double *x, Array_double *y);
extern void put_identity_diagonal(Matrix_double *m); extern void put_identity_diagonal(Matrix_double *m);
extern Matrix_double *copy_matrix(Matrix_double *m); extern Matrix_double *copy_matrix(Matrix_double *m);
extern void free_matrix(Matrix_double *m); extern void free_matrix(Matrix_double *m);
extern Matrix_double **put_lu_decomp(Matrix_double *m); extern Matrix_double **lu_decomp(Matrix_double *m);
extern Array_double *bsubst(Matrix_double *u, Array_double *b);
extern Array_double *fsubst(Matrix_double *l, Array_double *b);
extern void format_matrix_into(Matrix_double *m, char *s); extern void format_matrix_into(Matrix_double *m, char *s);

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8
notes/Oct-13.org Normal file
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@ -0,0 +1,8 @@
* Root Finding
Finx x \in R such that f(x) = 0
If g(x) is a function and we want to find x such that g(x) is
extremal then we find x \in R such that g'(x) = 0
Hanging Cable Problem y(x) = c_1 cosh(\frac{x- c_2}{c_2})

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@ -1,7 +1,7 @@
#include "lizfcm.h" #include "lizfcm.h"
#include <assert.h> #include <assert.h>
#include <string.h>
#include <stdio.h> #include <stdio.h>
#include <string.h>
void put_identity_diagonal(Matrix_double *m) { void put_identity_diagonal(Matrix_double *m) {
assert(m->rows == m->cols); assert(m->rows == m->cols);
@ -19,7 +19,7 @@ Matrix_double *copy_matrix(Matrix_double *m) {
return copy; return copy;
} }
Matrix_double **put_lu_decomp(Matrix_double *m) { Matrix_double **lu_decomp(Matrix_double *m) {
assert(m->cols == m->rows); assert(m->cols == m->rows);
Matrix_double *u = copy_matrix(m); Matrix_double *u = copy_matrix(m);
@ -63,6 +63,32 @@ Matrix_double **put_lu_decomp(Matrix_double *m) {
return u_l; return u_l;
} }
Array_double *bsubst(Matrix_double *u, Array_double *b) {
assert(u->rows == b->size && u->cols == u->rows);
Array_double *x = copy_vector(b);
for (int64_t row = b->size - 1; row >= 0; row--) {
for (size_t col = b->size - 1; col > row; col--)
x->data[row] -= x->data[col] * u->data[row]->data[col];
x->data[row] /= u->data[row]->data[row];
}
return x;
}
Array_double *fsubst(Matrix_double *l, Array_double *b) {
assert(l->rows == b->size && l->cols == l->rows);
Array_double *x = copy_vector(b);
for (size_t row = 0; row < b->size; row++) {
for (size_t col = 0; col < row; col++)
x->data[row] -= x->data[col] * l->data[row]->data[col];
x->data[row] /= l->data[row]->data[row];
}
return x;
}
void free_matrix(Matrix_double *m) { void free_matrix(Matrix_double *m) {
for (size_t y = 0; y < m->rows; ++y) for (size_t y = 0; y < m->rows; ++y)
free_vector(m->data[y]); free_vector(m->data[y]);

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@ -10,19 +10,18 @@ int main() {
printf("dmaceps(): %.10e\n", dmaceps()); printf("dmaceps(): %.10e\n", dmaceps());
printf("========\n"); printf("========\n");
printf("Norm, Distance\n");
Array_double *v = InitArray(double, {3, 1, -4, 1, 5, -9, 3}); Array_double *v = InitArray(double, {3, 1, -4, 1, 5, -9, 3});
char v_s[256]; char s[2048];
strcpy(v_s, ""); strcpy(s, "");
format_vector_into(v, v_s); format_vector_into(v, s);
printf("v: %s", s);
Array_double *w = InitArray(double, {-2, 7, 1, -8, -2, 8, 5}); Array_double *w = InitArray(double, {-2, 7, 1, -8, -2, 8, 5});
char w_s[256]; strcpy(s, "");
strcpy(w_s, ""); format_vector_into(w, s);
format_vector_into(w, w_s); printf("w: %s", 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("l1_norm(v): %f\n", l1_norm(v));
printf("l2_norm(v): %f\n", l2_norm(v)); printf("l2_norm(v): %f\n", l2_norm(v));
printf("linf_norm(v): %f\n", linf_norm(v)); printf("linf_norm(v): %f\n", linf_norm(v));
@ -38,52 +37,79 @@ int main() {
printf("approx f'(1) w/ fw.d.: %f\n", forward_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("approx f'(1) w/ bw.d.: %f\n", backward_derivative_at(&f, 1, h));
printf("========\n"); printf("========\n");
printf("Least Squares\n");
v = InitArray(double, {1, 2, 3, 4, 5}); v = InitArray(double, {1, 2, 3, 4, 5});
strcpy(v_s, ""); strcpy(s, "");
format_vector_into(v, v_s); format_vector_into(v, s);
printf("v: %s", s);
w = InitArray(double, {2, 3, 4, 5, 6}); w = InitArray(double, {2, 3, 4, 5, 6});
strcpy(w_s, ""); strcpy(s, "");
format_vector_into(w, w_s); format_vector_into(w, s);
printf("w: %s", s);
Line *line = least_squares_lin_reg(v, w); 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); 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}); v = InitArray(double, {1, 2, 3, 4, 5, 6, 7});
strcpy(v_s, ""); strcpy(s, "");
format_vector_into(v, v_s); format_vector_into(v, s);
printf("v: %s", s);
w = InitArray(double, {0.5, 3, 2, 3.5, 5, 6, 7.5}); w = InitArray(double, {0.5, 3, 2, 3.5, 5, 6, 7.5});
strcpy(w_s, ""); strcpy(s, "");
format_vector_into(w, w_s); format_vector_into(w, s);
printf("v: %s", v_s); printf("w: %s", s);
printf("w: %s", w_s);
line = least_squares_lin_reg(v, w); line = least_squares_lin_reg(v, w);
printf("least_squares_lin_reg(v, w): (%f)x + %f\n", line->m, line->a); printf("least_squares_lin_reg(v, w): (%f)x + %f\n", line->m, line->a);
printf("========\n"); printf("========\n");
printf("LU Decomp\n"); printf("LU Decomp\n");
char m_s[2048]; Matrix_double *m = InitMatrixWithSize(double, 10, 10, 0.0);
Matrix_double *m = InitMatrixWithSize(double, 8, 8, 0.0); for (int i = 0; i < 10; i++) {
for (int i = 0; i < 8; i++) { for (int j = 0; j < 10; j++)
for (int j = 0; j < 8; j++) m->data[i]->data[j] = (100 - rand() % 200);
m->data[i]->data[j] = (i + 1.0) + j * 3 + (rand() % 12);
} }
format_matrix_into(m, m_s); strcpy(s, "");
printf("m = %s", m_s); format_matrix_into(m, s);
printf("m = %s", s);
Matrix_double **u_l = put_lu_decomp(m); Array_double *b = InitArrayWithSize(double, 10, 100.0);
Matrix_double **u_l = lu_decomp(m);
Matrix_double *u = u_l[0]; Matrix_double *u = u_l[0];
Matrix_double *l = u_l[1]; Matrix_double *l = u_l[1];
strcpy(m_s, ""); strcpy(s, "");
format_matrix_into(u, m_s); format_matrix_into(u, s);
printf("u = %s", m_s); printf("u = %s", s);
strcpy(m_s, ""); strcpy(s, "");
format_matrix_into(l, m_s); format_matrix_into(l, s);
printf("l = %s", m_s); printf("l = %s", s);
strcpy(s, "");
format_vector_into(b, s);
printf("b = %s", s);
printf("========\n"); printf("========\n");
printf("Back Substitution\n"); printf("Backward -> Forward Substitution\n");
Array_double *b_fsub = fsubst(l, b);
strcpy(s, "");
format_vector_into(b_fsub, s);
printf("x: %s\n", s);
Array_double *x_bsub = bsubst(u, b_fsub);
strcpy(s, "");
format_vector_into(x_bsub, s);
printf("x: %s", s);
free_vector(b_fsub);
printf("Verifications (each should be approximately 100)\n");
for (size_t row = 0; row < m->rows; row++) {
double curr = 0;
for (size_t col = 0; col < m->cols; col++)
curr += m->data[row]->data[col] * x_bsub->data[col];
printf("Substitution for row %zu = %f\n", row, curr);
}
return 0; return 0;
} }