struct matrix rref (struct matrix M) {
// TODO: Fails on matrix with 0s leading first rows
/* Algorithm description:
Find a row with zero in previous column values and non-zero entry in current column
multiply row to change non-zero entry to 1
zero all other row's column entry
repeat for each column
*/
struct matrix R = copy_of_matrix(M);
int c,r;
int pivot = 1;
for(c=1; c<=R.columns && pivot < R.rows; c++) {
for(r=pivot; r<=R.rows; r++) { // iterate over column
if(get_element(R,r,c).p != 0) { // find non-zero value
_multiply_row(R,r_divide(int_to_r(1),get_element(R,r,c)),r); // change pivot to 1
for(int m=1; m<=R.rows; m++) { // zero all other values in that column
if (m != r) {
_add_multiple(R, r_multiply(int_to_r(-1),get_element(R,m,c)), r,m);
}
}
pivot++;
break;
}
}
}
_sort_matrix_rows(R);
return R;
}
void multiply_test() {
int p,q,s,t;
for ( p = -100; p <= 100; p+=5) {
for ( q = -100; q <= 100; q+=5) {
for ( s = -100; s <= 100; s+=5) {
for ( t = -100; t <= 100; t+=5) {
if (q != 0 && t != 0) {
struct rational r = new_rational(p,q);
struct rational u = new_rational(s,t);
struct rational product= r_multiply(r,u);
if ((product.p*1.0)/(product.q*1.0) < (p*1.0/q*1.0*s*1.0/t*1.0)-1e-5 || (product.p*1.0)/(product.q*1.0) > (p*1.0/q*1.0*s*1.0/t*1.0)+1e-5) {
printf("\nMultiply failed: %d/%d %d/%d\n",p,q,s,t);
printf("%.19g %.19g\n",(product.p*1.0)/(product.q*1.0),(p*1.0/q*1.0+s*1.0/t*1.0));
return;
}
if (r.q ==0) {
printf("0 denominator failure\n");
return;
}
}
}
if(p%500 == 0){
printf(".");
fflush(stdout);
}
}
}
}
}
struct rational cofactor (struct matrix M, int row, int column){
//TODO: test function
if ((row%2) == (column%2)) {
return(determinant(submatrix(M,row,column)));
} else {
return(r_multiply(int_to_r(-1), determinant(submatrix(M,row,column))));
}
}
void _multiply_row(struct matrix M, struct rational factor, int row){
set_error(NONE);
if(row >0 && row<=M.rows){
int col;
for(col=1; col<=M.columns; col++){
set_element(M,row,col,r_multiply(factor,get_element(M,row,col)));
}
} else
set_error(INCOMPATIBLE_MATRIX);
}
struct matrix scalar_multiply(struct rational a, struct matrix B){ //a * B
struct matrix C = new_matrix(B.rows, B.columns);
int i,j;
for (i=1; i<=C.rows; i++) {
for (j=1; j<=C.columns; j++) {
set_element(C, i, j, r_multiply(a, get_element(B,i,j)));
}
}
return C;
}
struct rational row_times_column(struct matrix A, int row, struct matrix B, int column){
int i;
struct rational sum = new_rational(0,1);
//sum A[row][i]*B[j][column]
if (A.columns == B.rows){
for (i=1; i<=A.columns; i++) {
sum = r_add(sum, r_multiply( get_element(A,row,i), get_element(B,i,column)));
}
}
return sum;
}
void _add_multiple(struct matrix M, struct rational factor, int input_row, int modified_row){
set_error(NONE);
if(input_row > 0 && modified_row > 0 && input_row <= M.rows && modified_row <= M.rows){
struct rational temp;
int col;
for(col=1; col<=M.columns; col++){
temp = r_multiply(factor, get_element(M,input_row,col));
temp = r_add(temp, get_element(M,modified_row,col));
set_element(M,modified_row,col,temp);
}
} else
set_error(INCOMPATIBLE_MATRIX);
}
struct matrix ref ( struct matrix M) {
//TODO: this
struct matrix R = copy_of_matrix(M);
int c,r;
int pivot = 1;
for(c=1; c<=R.columns && pivot < R.rows; c++) {
_sort_matrix_rows(R);
for(r=pivot; r<=R.rows; r++) { // iterate over column
if(get_element(R,r,c).p != 0) { // find non-zero value
for(int m=1; m<=R.rows; m++) { // zero all other values in that column
if (m > r) {
_add_multiple(R, r_multiply(get_element(R,r,c),r_reciprocal(get_element(R,m,c))), r,m);
}
}
pivot++;
break;
}
}
}
_sort_matrix_rows(R);
return R;
}
rsexp r_divide (RState* r, rsexp lhs, rsexp rhs)
{
ensure (rhs = r_invert (r, rhs));
return r_multiply (r, lhs, rhs);
}
