/* should output:
* print_matrix:
* 3 1 -1
* 0 -2 0
* 5 0 0
* matrix minor:
* 0 0
* 5 0
* ineff_det: -10
* eff_det: 10
* lu decomposition is not unique, output can be checked manually
* invert_lower_tri_matrix:
* 1.000000 0.000000 0.000000
* 0.000000 1.000000 0.000000
* -1.666667 -0.833333 1.000000
* invert_upper_tri_matrix:
* 0.333333 0.166667 0.200000
* 0.000000 -0.500000 0.000000
* 0.000000 -0.000000 0.600000
* invert_matrix:
* 0.000000 0.000000 0.200000
* 0.000000 -0.500000 0.000000
* -1.000000 -0.500000 0.600000 */
void test_matrix_functions() {
matrix *a = identity_matrix(3);
a->entries[0][0] = 3.0;
a->entries[0][1] = 1.0;
a->entries[0][2] = -1.0;
a->entries[1][1] = -2.0;
a->entries[2][0] = 5.0;
a->entries[2][2] = 0.0;
printf("print_matrix: \n");
print_matrix(*a);
printf("matrix_minor: \n");
print_matrix(*matrix_minor(*a, 1));
printf("ineff_det: %lf\n", (double) ineff_det(*a));
printf("eff_det: %lf\n", (double) eff_det(*a));
matrix *a_cpy = copy_matrix(*a);
printf("lu_decomp: \n");
matrix **pl = lu_decomp(a_cpy, (int*) NULL);
print_matrix(*pl[0]); // prints p
print_matrix(*pl[1]); // prints l
print_matrix(*a_cpy); // prints u
printf("invert_lower_tri_matrix: \n");
print_matrix(*invert_lower_tri_matrix(*pl[1]));
printf("invert_upper_tri_matrix: \n");
print_matrix(*invert_upper_tri_matrix(*a_cpy));
printf("invert_matrix: \n");
print_matrix(*invert_matrix(*a));
}
/** Computes the determinant of a matrix
*
* @param m a Matrix pointer
*
* @return the determinant of m
*/
scalar_t matrix_det(Matrix *m) {
Matrix *minor;
unsigned int j;
scalar_t rdet, sign;
assert(MATRIX_IS_SQUARE(m));
if(m->cols == 2) {
return ((matrix_get(m,0,0) * matrix_get(m,1,1))
- (matrix_get(m,0,1) * matrix_get(m,1,0)));
}
else {
rdet = 0;
for(j=0; j < m->cols; j++) {
minor = matrix_minor(m, 0, j);
sign = (j%2) ? S_LITERAL(1.0) : S_LITERAL(-1.0);
rdet += sign * matrix_get(m, 0, j) * matrix_det(minor);
matrix_free(minor);
}
return rdet;
}
return 0;
}
// inefficient determinant algorithm
// runtime: O(n!)
static matrix_entry ineff_det(matrix a) {
if (a.n == 1)
return a.entries[0][0];
matrix_entry result = 0;
for (int i=0; i<a.n; i++) {
result += ((matrix_entry) alt(i)) * a.entries[0][i] * ineff_det(*matrix_minor(a, i));
}
return result;
}
int main()
{
DoubleMatrix X(3,3);
DoubleInterval A(2,5);
X = A;
DoubleMatrix Y(3,3);
DoubleInterval B(5,9);
Y = B;
std::cout << X << std::endl;
std::cout << Y << std::endl;
DoubleMatrix Z(3,3);
Z = mtl::mat::trans(X);
std::cout << Z << std::endl;
mtl::mat::swap_row(Z,1,2);
std::cout << Z << std::endl;
DoubleInterval C;
C = boost::numeric::max(A,B);
std::cout << C << std::endl;
std::cout << "============== Test 1 ==============" << std::endl << std::endl;
DoubleInterval A00(2,3);
DoubleInterval A01(0,1);
DoubleInterval A10(1,2);
DoubleInterval A11(2,3);
DoubleMatrix *Test = new DoubleMatrix(2,2);
(*Test)(0,0) = A00;
(*Test)(0,1) = A01;
(*Test)(1,0) = A10;
(*Test)(1,1) = A11;
std::cout << "Test: " << std::endl;
std::cout << *Test << std::endl;
bool diag = diagonally_dominant(*Test);
if(diag == true)
std::cout << "Test is diagonally dominant" << std::endl << std::endl;
else
std::cout << "Test is NOT diagonally dominant" << std::endl << std::endl;
std::cout << "Max on row 2 is " << row_max_element(*Test,1,0) << std::endl;
std::cout << "The max is located on element " << row_max_term(*Test,1,0) << std::endl;
std::cout << std::endl;
std::cout << "determinant = " << det(*Test) << std::endl;
delete Test;
std::cout << "============== Test 2 ==============" << std::endl << std::endl;
Test = new DoubleMatrix(3,3);
(*Test)(0,0) = 1;
(*Test)(0,1) = 2;
(*Test)(0,2) = 3;
(*Test)(1,0) = 4;
(*Test)(1,1) = 5;
(*Test)(1,2) = 6;
(*Test)(2,0) = 7;
(*Test)(2,1) = 8;
(*Test)(2,2) = 9;
std::cout << "Test: " << std::endl;
std::cout << *Test << std::endl;
diag = diagonally_dominant(*Test);
if(diag == true)
std::cout << "Test is diagonally dominant" << std::endl << std::endl;
else
std::cout << "Test is NOT diagonally dominant" << std::endl << std::endl;
for(unsigned int i = 0; i < mtl::mat::num_rows(*Test); i++)
{
std::cout << "Max on row " << i << " is " << row_max_element(*Test,i,0) << std::endl;
std::cout << "The max is located on element " << row_max_term(*Test,i,0) << std::endl;
}
std::cout << std::endl;
std::cout << "determinant = " << det(*Test) << std::endl;
delete Test;
std::cout << "============== Test 3 ==============" << std::endl << std::endl;
Test = new DoubleMatrix(3,3);
(*Test)(0,0) = 1;
(*Test)(0,1) = 2;
(*Test)(0,2) = 3;
(*Test)(1,0) = 10;
(*Test)(1,1) = 5;
(*Test)(1,2) = 6;
(*Test)(2,0) = 10;
(*Test)(2,1) = 8;
(*Test)(2,2) = 9;
std::cout << "Test: " << std::endl;
std::cout << *Test << std::endl;
diag = diagonally_dominant(*Test);
if(diag == true)
std::cout << "Test is diagonally dominant" << std::endl << std::endl;
else
std::cout << "Test is NOT diagonally dominant" << std::endl << std::endl;
for(unsigned int i = 0; i < mtl::mat::num_cols(*Test); i++)
{
std::cout << "Max on col " << i << " is " << col_max_element(*Test,i,0) << std::endl;
std::cout << "The max is located on element " << col_max_term(*Test,i,0) << std::endl;
}
std::cout << std::endl;
std::cout << "DoubleMatrix minor(1,0) = " << std::endl;
std::cout << matrix_minor(*Test,1,0) << std::endl;
std::cout << "determinant = " << det(*Test) << std::endl;
delete Test;
std::cout << "============== Test 4 ==============" << std::endl << std::endl;
Test = new DoubleMatrix(2,2);
(*Test)(0,0) = A10;
(*Test)(0,1) = A11;
(*Test)(1,0) = A00;
(*Test)(1,1) = A01;
std::cout << "Test: " << std::endl;
std::cout << *Test << std::endl;
diag = diagonally_dominant(*Test);
if(diag == true)
std::cout << "Test is diagonally dominant" << std::endl << std::endl;
else
std::cout << "Test is NOT diagonally dominant" << std::endl << std::endl;
std::cout << "The midpoint Doublematrix m(Test): " << std::endl;
std::cout << m(*Test) << std::endl;
std::cout << "determinant = " << det(*Test) << std::endl;
delete Test;
return 0;
}