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#include "lizfcm.h"
#include <assert.h>
#include <stdio.h>
#include <string.h>
Array_double *m_dot_v(Matrix_double *m, Array_double *v) {
assert(v->size == m->cols);
Array_double *product = copy_vector(v);
for (size_t row = 0; row < v->size; ++row)
product->data[row] = v_dot_v(m->data[row], v);
return product;
}
Matrix_double *put_identity_diagonal(Matrix_double *m) {
assert(m->rows == m->cols);
Matrix_double *copy = copy_matrix(m);
for (size_t y = 0; y < m->rows; ++y)
copy->data[y]->data[y] = 1.0;
return copy;
}
Matrix_double *copy_matrix(Matrix_double *m) {
Matrix_double *copy = InitMatrixWithSize(double, m->rows, m->cols, 0.0);
for (size_t y = 0; y < copy->rows; y++) {
free_vector(copy->data[y]);
copy->data[y] = copy_vector(m->data[y]);
}
return copy;
}
Matrix_double **lu_decomp(Matrix_double *m) {
assert(m->cols == m->rows);
Matrix_double *u = copy_matrix(m);
Matrix_double *l = InitMatrixWithSize(double, m->rows, m->cols, 0.0);
put_identity_diagonal(l);
Matrix_double **u_l = malloc(sizeof(Matrix_double *) * 2);
for (size_t y = 0; y < m->rows; y++) {
if (u->data[y]->data[y] == 0) {
printf("ERROR: a pivot is zero in given matrix\n");
exit(-1);
}
}
if (u && l) {
for (size_t x = 0; x < m->cols; x++) {
for (size_t y = x + 1; y < m->rows; y++) {
double denom = u->data[x]->data[x];
if (denom == 0) {
printf("ERROR: non-factorable matrix\n");
exit(-1);
}
double factor = -(u->data[y]->data[x] / denom);
Array_double *scaled = scale_v(u->data[x], factor);
Array_double *added = add_v(scaled, u->data[y]);
free_vector(scaled);
free_vector(u->data[y]);
u->data[y] = added;
l->data[y]->data[x] = -factor;
}
}
}
u_l[0] = u;
u_l[1] = 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;
}
Array_double *solve_matrix(Matrix_double *m, Array_double *b) {
assert(b->size == m->rows);
assert(m->rows == m->cols);
Array_double *x = copy_vector(b);
Matrix_double **u_l = lu_decomp(m);
Matrix_double *u = u_l[0];
Matrix_double *l = u_l[1];
Array_double *b_fsub = fsubst(l, b);
x = bsubst(u, b_fsub);
free_vector(b_fsub);
free_matrix(u);
free_matrix(l);
return x;
}
void free_matrix(Matrix_double *m) {
for (size_t y = 0; y < m->rows; ++y)
free_vector(m->data[y]);
free(m);
}
void format_matrix_into(Matrix_double *m, char *s) {
if (m->rows == 0)
strcpy(s, "empty");
for (size_t y = 0; y < m->rows; ++y) {
char row_s[256];
strcpy(row_s, "");
format_vector_into(m->data[y], row_s);
strcat(s, row_s);
}
strcat(s, "\n");
}
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