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#include "matrix.h"
matrix *newMatrix(int rows, int cols){
matrix *m = malloc(sizeof(matrix));
m->rows = rows;
m->cols = cols;
m->data = malloc(rows*sizeof(double*));
for(int i = 0; i < rows; ++i){
m->data[i] = malloc(cols*sizeof(double));
}
return m;
}
void freeMatrix(matrix **m){
for(int i = 0; i < (*m)->rows; ++i){
free((*m)->data[i]);
(*m)->data[i] = NULL;
}
free((*m)->data);
(*m)->data = NULL;
free(*m);
*m = NULL;
}
matrix *copyMatrix(matrix *m){
matrix *c = newMatrix(m->rows, m->cols);
for(int i = 0; i < m->rows; ++i){
for(int j = 0; j < m->cols; ++j){
c->data[i][j] = m->data[i][j];
}
}
return c;
}
matrix *identityMatrix(int order){
matrix *im = newMatrix(order, order);
for(int i = 0; i < im->rows; ++i){
for(int j = 0; j < im->cols; ++j){
im->data[i][j] = (i == j);
}
}
return im;
}
matrix *fillMatrix(matrix *m, double n){
matrix *r = newMatrix(m->rows, m->cols);
for(int i = 0; i < r->rows; ++i){
for(int j = 0; j < r->cols; ++j){
r->data[i][j] = n;
}
}
return r;
}
matrix *addMatrix(matrix *m, double n){
for(int i = 0; i < m->rows; ++i){
for(int j = 0; j < m->cols; ++j){
m->data[i][j] += n;
}
}
}
matrix *subtractMatrix(matrix *m, double n){
return addMatrix(m, -n);
}
matrix *scaleMatrix(matrix *m, double n){
matrix *r = copyMatrix(m);
for(int i = 0; i < r->rows; ++i){
for(int j = 0; j < r->cols; ++j){
r->data[i][j] *= n;
}
}
return r;
}
static inline bool sameDimensions(matrix *m1, matrix *m2){
return (m1->rows == m2->rows) && (m1->cols == m2->cols);
}
matrix *addMatrices(matrix *m1, matrix *m2){
if(!sameDimensions(m1, m2)){
fprintf(stderr, "Wrong dimensions (%dx%d != %dx%d)\n", m1->rows, m1->cols, m2->rows, m2->cols);
return NULL;
}
matrix *r = newMatrix(m1->rows, m1->cols);
for(int i = 0; i < m1->rows; ++i){
for(int j = 0; j < m1->cols; ++j){
r->data[i][j] = m1->data[i][j] + m2->data[i][j];
}
}
return r;
}
matrix *subtractMatrices(matrix *m1, matrix *m2){
m2 = scaleMatrix(m2, (double)-1);
return addMatrices(m1, m2);
}
matrix *multiplyMatrices(matrix *m1, matrix *m2){
if(m1->cols != m2->rows){
fprintf(stderr, "Wrong dimensions (%dx%d != %dx%d)\n", m1->rows, m1->cols, m2->rows, m2->cols);
return NULL;
}
matrix *r = newMatrix(m1->rows, m2->cols);
for(int i = 0; i < r->rows; ++i){
for(int j = 0; j < r->cols; ++j){
double sum = 0;
for(int n = 0; n < m1->cols; ++n){
sum += m1->data[i][n] * m2->data[n][j];
}
r->data[i][j] = sum;
}
}
return r;
}
static inline bool isSquare(matrix *m){
return m->rows == m->cols;
}
matrix *subMatrix(matrix *m, int row, int col){
matrix *r = newMatrix(m->rows-1, m->cols-1);
int ri = 0, rj = 0;
for(int i = 0; i < m->rows; ++i){
if(i == row){ continue; }
rj = 0;
for(int j = 0; j < m->cols; ++j){
if(j == col){ continue; }
r->data[ri][rj] = m->data[i][j];
++rj;
}
++ri;
}
return r;
}
double determinant(matrix *m){
if(!isSquare(m)){
fprintf(stderr, "Matrix is not square (%dx%d)\n", m->rows, m->cols);
exit(EXIT_FAILURE);
}
double d = 0;
if(m->rows == 1){
return m->data[0][0];
}else{
for(int i = 0; i < m->rows; ++i){
matrix *s = subMatrix(m, 0, i);
double v = determinant(s)*m->data[0][i];
d += !(i%2) ? v : -v;
}
return d;
}
}
matrix *cofactor(matrix *m){
if(!isSquare(m)){
fprintf(stderr, "Matrix is not square (%dx%d)\n", m->rows, m->cols);
return NULL;
}
matrix *r = newMatrix(m->rows, m->cols);
for(int i = 0; i < r->rows; ++i){
for(int j = 0; j < r->cols; ++j){
double v = determinant(subMatrix(m, i, j));
r->data[i][j] = !((i+j)%2) ? v : -v;
}
}
return r;
}
matrix *transpose(matrix *m){
matrix *r = newMatrix(m->cols, m->rows);
for(int i = 0; i < r->rows; ++i){
for(int j = 0; j < r->cols; ++j){
r->data[i][j] = m->data[j][i];
}
}
return r;
}
matrix *adjugate(matrix *m){
return transpose(cofactor(m));
}
matrix *inverse(matrix *m){
double d = determinant(m);
if(d == 0){
fprintf(stderr, "Determinant is 0, the matrix is not invertible\n");
return NULL;
}
return scaleMatrix(adjugate(m), 1/d);
}
matrix *raiseMatrix(matrix *m, int n){
if(!isSquare(m)){
fprintf(stderr, "Matrix is not square (%dx%d)\n", m->rows, m->cols);
return NULL;
}
if(n < 0){
m = inverse(m);
n = -n;
}
matrix *r = identityMatrix(m->rows);
for(int i = 0; i < n; ++i){
r = multiplyMatrices(r, m);
}
return r;
}
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