// Copyright (C) 2006 Davis E. King (davis@dlib.net)
// License: Boost Software License See LICENSE.txt for the full license.
#include <dlib/matrix.h>
#include <sstream>
#include <string>
#include <cstdlib>
#include <ctime>
#include <vector>
#include "../stl_checked.h"
#include "../array.h"
#include "../rand.h"
#include "tester.h"
#include <dlib/memory_manager_stateless.h>
#include <dlib/array2d.h>
namespace
{
using namespace test;
using namespace dlib;
using namespace std;
logger dlog("test.matrix");
void matrix_test (
)
/*!
ensures
- runs tests on the matrix stuff compliance with the specs
!*/
{
typedef memory_manager_stateless<char>::kernel_2_2a MM;
print_spinner();
{
matrix<complex<double>,2,2,MM> m;
set_all_elements(m,complex<double>(1,2));
DLIB_TEST((conj(m) == uniform_matrix<complex<double>,2,2>(conj(m(0,0)))));
DLIB_TEST((real(m) == uniform_matrix<double,2,2>(1)));
DLIB_TEST((imag(m) == uniform_matrix<double,2,2>(2)));
DLIB_TEST_MSG((sum(abs(norm(m) - uniform_matrix<double,2,2>(5))) < 1e-10 ),norm(m));
}
{
matrix<double,5,5,MM,column_major_layout> m(5,5);
for (long r = 0; r < m.nr(); ++r)
{
for (long c = 0; c < m.nc(); ++c)
{
m(r,c) = r*c;
}
}
m = cos(exp(m));
matrix<double> mi = pinv(m );
DLIB_TEST(mi.nr() == m.nc());
DLIB_TEST(mi.nc() == m.nr());
DLIB_TEST((equal(round_zeros(mi*m,0.000001) , identity_matrix<double,5>())));
DLIB_TEST((equal(round_zeros(m*mi,0.000001) , identity_matrix<double,5>())));
DLIB_TEST((equal(round_zeros(mi*m,0.000001) , identity_matrix(m))));
DLIB_TEST((equal(round_zeros(m*mi,0.000001) , identity_matrix(m))));
mi = pinv(m,1e-12);
DLIB_TEST(mi.nr() == m.nc());
DLIB_TEST(mi.nc() == m.nr());
DLIB_TEST((equal(round_zeros(mi*m,0.000001) , identity_matrix<double,5>())));
DLIB_TEST((equal(round_zeros(m*mi,0.000001) , identity_matrix<double,5>())));
DLIB_TEST((equal(round_zeros(mi*m,0.000001) , identity_matrix(m))));
DLIB_TEST((equal(round_zeros(m*mi,0.000001) , identity_matrix(m))));
m = diagm(diag(m));
mi = pinv(diagm(diag(m)),1e-12);
DLIB_TEST(mi.nr() == m.nc());
DLIB_TEST(mi.nc() == m.nr());
DLIB_TEST((equal(round_zeros(mi*m,0.000001) , identity_matrix<double,5>())));
DLIB_TEST((equal(round_zeros(m*mi,0.000001) , identity_matrix<double,5>())));
DLIB_TEST((equal(round_zeros(mi*m,0.000001) , identity_matrix(m))));
DLIB_TEST((equal(round_zeros(m*mi,0.000001) , identity_matrix(m))));
mi = pinv(m,0);
DLIB_TEST(mi.nr() == m.nc());
DLIB_TEST(mi.nc() == m.nr());
DLIB_TEST((equal(round_zeros(mi*m,0.000001) , identity_matrix<double,5>())));
DLIB_TEST((equal(round_zeros(m*mi,0.000001) , identity_matrix<double,5>())));
DLIB_TEST((equal(round_zeros(mi*m,0.000001) , identity_matrix(m))));
DLIB_TEST((equal(round_zeros(m*mi,0.000001) , identity_matrix(m))));
m = diagm(diag(m));
mi = pinv(diagm(diag(m)),0);
DLIB_TEST(mi.nr() == m.nc());
DLIB_TEST(mi.nc() == m.nr());
DLIB_TEST((equal(round_zeros(mi*m,0.000001) , identity_matrix<double,5>())));
DLIB_TEST((equal(round_zeros(m*mi,0.000001) , identity_matrix<double,5>())));
DLIB_TEST((equal(round_zeros(mi*m,0.000001) , identity_matrix(m))));
DLIB_TEST((equal(round_zeros(m*mi,0.000001) , identity_matrix(m))));
}
{
matrix<double,5,0,MM> m(5,5);
for (long r = 0; r < m.nr(); ++r)
{
for (long c = 0; c < m.nc(); ++c)
{
m(r,c) = r*c;
}
}
m = cos(exp(m));
matrix<double> mi = pinv(m );
DLIB_TEST((equal(round_zeros(mi*m,0.000001) , identity_matrix<double,5>())));
}
{
matrix<double,0,5,MM> m(5,5);
for (long r = 0; r < m.nr(); ++r)
{
for (long c = 0; c < m.nc(); ++c)
{
m(r,c) = r*c;
}
}
m = cos(exp(m));
matrix<double> mi = pinv(m );
DLIB_TEST((equal(round_zeros(mi*m,0.000001) , identity_matrix<double,5>())));
}
{
matrix<double> m(5,5);
for (long r = 0; r < m.nr(); ++r)
{
for (long c = 0; c < m.nc(); ++c)
{
m(r,c) = r*c;
}
}
m = cos(exp(m));
matrix<double> mi = pinv(m );
DLIB_TEST((equal(round_zeros(mi*m,0.000001) , identity_matrix<double,5>())));
}
{
matrix<double,5,2,MM,column_major_layout> m;
for (long r = 0; r < m.nr(); ++r)
{
for (long c = 0; c < m.nc(); ++c)
{
m(r,c) = r*c;
}
}
m = cos(exp(m));
matrix<double> mi = pinv(m );
DLIB_TEST(mi.nr() == m.nc());
DLIB_TEST(mi.nc() == m.nr());
DLIB_TEST((equal(round_zeros(mi*m,0.000001) , identity_matrix<double,2>())));
}
{
matrix<double> m(5,2);
for (long r = 0; r < m.nr(); ++r)
{
for (long c = 0; c < m.nc(); ++c)
{
m(r,c) = r*c;
}
}
m = cos(exp(m));
matrix<double> mi = pinv(m );
DLIB_TEST(mi.nr() == m.nc());
DLIB_TEST(mi.nc() == m.nr());
DLIB_TEST((equal(round_zeros(mi*m,0.000001) , identity_matrix<double,2>())));
}
{
matrix<double,5,2,MM,column_major_layout> m;
for (long r = 0; r < m.nr(); ++r)
{
for (long c = 0; c < m.nc(); ++c)
{
m(r,c) = r*c;
}
}
m = cos(exp(m));
matrix<double> mi = trans(pinv(trans(m) ));
DLIB_TEST(mi.nr() == m.nc());
DLIB_TEST(mi.nc() == m.nr());
DLIB_TEST((equal(round_zeros(mi*m,0.000001) , identity_matrix<double,2>())));
}
{
matrix<double> m(5,2);
for (long r = 0; r < m.nr(); ++r)
{
for (long c = 0; c < m.nc(); ++c)
{
m(r,c) = r*c;
}
}
m = cos(exp(m));
matrix<double> mi = trans(pinv(trans(m) ));
DLIB_TEST(mi.nr() == m.nc());
DLIB_TEST(mi.nc() == m.nr());
DLIB_TEST((equal(round_zeros(mi*m,0.000001) , identity_matrix<double,2>())));
}
{
matrix<long> a1(5,1);
matrix<long,0,0,MM,column_major_layout> a2(1,5);
matrix<long,5,1> b1(5,1);
matrix<long,1,5> b2(1,5);
matrix<long,0,1> c1(5,1);
matrix<long,1,0> c2(1,5);
matrix<long,0,1,MM,column_major_layout> d1(5,1);
matrix<long,1,0,MM> d2(1,5);
for (long i = 0; i < 5; ++i)
{
a1(i) = i;
a2(i) = i;
b1(i) = i;
b2(i) = i;
c1(i) = i;
c2(i) = i;
d1(i) = i;
d2(i) = i;
}
DLIB_TEST(a1 == trans(a2));
DLIB_TEST(a1 == trans(b2));
DLIB_TEST(a1 == trans(c2));
DLIB_TEST(a1 == trans(d2));
DLIB_TEST(a1 == b1);
DLIB_TEST(a1 == c1);
DLIB_TEST(a1 == d1);
DLIB_TEST(trans(a1) == c2);
DLIB_TEST(trans(b1) == c2);
DLIB_TEST(trans(c1) == c2);
DLIB_TEST(trans(d1) == c2);
DLIB_TEST(sum(a1) == 10);
DLIB_TEST(sum(a2) == 10);
DLIB_TEST(sum(b1) == 10);
DLIB_TEST(sum(b2) == 10);
DLIB_TEST(sum(c1) == 10);
DLIB_TEST(sum(c2) == 10);
DLIB_TEST(sum(d1) == 10);
DLIB_TEST(sum(d2) == 10);
const matrix<long> orig1 = a1;
const matrix<long> orig2 = a2;
ostringstream sout;
serialize(a1,sout);
serialize(a2,sout);
serialize(b1,sout);
serialize(b2,sout);
serialize(c1,sout);
serialize(c2,sout);
serialize(d1,sout);
serialize(d2,sout);
DLIB_TEST(a1 == orig1);
DLIB_TEST(a2 == orig2);
DLIB_TEST(b1 == orig1);
DLIB_TEST(b2 == orig2);
DLIB_TEST(c1 == orig1);
DLIB_TEST(c2 == orig2);
DLIB_TEST(d1 == orig1);
DLIB_TEST(d2 == orig2);
set_all_elements(a1,99);
set_all_elements(a2,99);
set_all_elements(b1,99);
set_all_elements(b2,99);
set_all_elements(c1,99);
set_all_elements(c2,99);
set_all_elements(d1,99);
set_all_elements(d2,99);
DLIB_TEST(a1 != orig1);
DLIB_TEST(a2 != orig2);
DLIB_TEST(b1 != orig1);
DLIB_TEST(b2 != orig2);
DLIB_TEST(c1 != orig1);
DLIB_TEST(c2 != orig2);
DLIB_TEST(d1 != orig1);
DLIB_TEST(d2 != orig2);
istringstream sin(sout.str());
deserialize(a1,sin);
deserialize(a2,sin);
deserialize(b1,sin);
deserialize(b2,sin);
deserialize(c1,sin);
deserialize(c2,sin);
deserialize(d1,sin);
deserialize(d2,sin);
DLIB_TEST(a1 == orig1);
DLIB_TEST(a2 == orig2);
DLIB_TEST(b1 == orig1);
DLIB_TEST(b2 == orig2);
DLIB_TEST(c1 == orig1);
DLIB_TEST(c2 == orig2);
DLIB_TEST(d1 == orig1);
DLIB_TEST(d2 == orig2);
}
{
matrix<double,1,0> a(5);
matrix<double,0,1> b(5);
matrix<double,1,5> c(5);
matrix<double,5,1> d(5);
DLIB_TEST(a.nr() == 1);
DLIB_TEST(a.nc() == 5);
DLIB_TEST(c.nr() == 1);
DLIB_TEST(c.nc() == 5);
DLIB_TEST(b.nc() == 1);
DLIB_TEST(b.nr() == 5);
DLIB_TEST(d.nc() == 1);
DLIB_TEST(d.nr() == 5);
}
{
matrix<double,1,0> a;
matrix<double,0,1> b;
matrix<double,1,5> c;
matrix<double,5,1> d;
a.set_size(5);
b.set_size(5);
c.set_size(5);
d.set_size(5);
DLIB_TEST(a.nr() == 1);
DLIB_TEST(a.nc() == 5);
DLIB_TEST(c.nr() == 1);
DLIB_TEST(c.nc() == 5);
DLIB_TEST(b.nc() == 1);
DLIB_TEST(b.nr() == 5);
DLIB_TEST(d.nc() == 1);
DLIB_TEST(d.nr() == 5);
}
{
matrix<double> a(1,5);
matrix<double> b(5,1);
set_all_elements(a,1);
set_all_elements(b,1);
a = a*b;
DLIB_TEST(a(0) == 5);
}
{
matrix<double,0,0,MM,column_major_layout> a(6,7);
for (long r = 0; r < a.nr(); ++r)
{
for (long c = 0; c < a.nc(); ++c)
{
a(r,c) = r*a.nc() + c;
}
}
DLIB_TEST(rowm(a,1).nr() == 1);
DLIB_TEST(rowm(a,1).nc() == a.nc());
DLIB_TEST(colm(a,1).nr() == a.nr());
DLIB_TEST(colm(a,1).nc() == 1);
for (long c = 0; c < a.nc(); ++c)
{
DLIB_TEST( rowm(a,1)(c) == 1*a.nc() + c);
}
for (long r = 0; r < a.nr(); ++r)
{
DLIB_TEST( colm(a,1)(r) == r*a.nc() + 1);
}
rectangle rect(2, 1, 3+2-1, 2+1-1);
DLIB_TEST(get_rect(a).contains(get_rect(a)));
DLIB_TEST(get_rect(a).contains(rect));
for (long r = 0; r < 2; ++r)
{
for (long c = 0; c < 3; ++c)
{
DLIB_TEST(subm(a,1,2,2,3)(r,c) == (r+1)*a.nc() + c+2);
DLIB_TEST(subm(a,1,2,2,3) == subm(a,rect));
DLIB_TEST(subm_clipped(a,1,2,2,3) == subm(a,rect));
DLIB_TEST(subm_clipped(a,1,2,2,3) == subm_clipped(a,rect));
}
}
DLIB_TEST(subm(a,rectangle()).nr() == 0);
DLIB_TEST(subm(a,rectangle()).nc() == 0);
}
{
array2d<double> a;
a.set_size(6,7);
for (long r = 0; r < a.nr(); ++r)
{
for (long c = 0; c < a.nc(); ++c)
{
a[r][c] = r*a.nc() + c;
}
}
DLIB_TEST(rowm(mat(a),1).nr() == 1);
DLIB_TEST(rowm(mat(a),1).nc() == a.nc());
DLIB_TEST(colm(mat(a),1).nr() == a.nr());
DLIB_TEST(colm(mat(a),1).nc() == 1);
for (long c = 0; c < a.nc(); ++c)
{
DLIB_TEST( rowm(mat(a),1)(c) == 1*a.nc() + c);
}
for (long r = 0; r < a.nr(); ++r)
{
DLIB_TEST( colm(mat(a),1)(r) == r*a.nc() + 1);
}
for (long r = 0; r < 2; ++r)
{
for (long c = 0; c < 3; ++c)
{
DLIB_TEST(subm(mat(a),1,2,2,3)(r,c) == (r+1)*a.nc() + c+2);
}
}
}
{
array2d<double> m;
m.set_size(5,5);
for (long r = 0; r < m.nr(); ++r)
{
for (long c = 0; c < m.nc(); ++c)
{
m[r][c] = r*c;
}
}
matrix<double> mi = pinv(cos(exp(mat(m))) );
DLIB_TEST(mi.nr() == m.nc());
DLIB_TEST(mi.nc() == m.nr());
DLIB_TEST((equal(round_zeros(mi*cos(exp(mat(m))),0.000001) , identity_matrix<double,5>())));
DLIB_TEST((equal(round_zeros(cos(exp(mat(m)))*mi,0.000001) , identity_matrix<double,5>())));
}
{
matrix<long,5,5,MM,column_major_layout> m1, res;
matrix<long,2,2> m2;
set_all_elements(m1,0);
long res_vals[] = {
9, 9, 9, 9, 9,
0, 1, 1, 0, 0,
0, 1, 1, 0, 2,
0, 0, 2, 2, 2,
0, 0, 2, 2, 0
};
res = res_vals;
set_all_elements(m2, 1);
set_subm(m1, range(1,2), range(1,2)) = subm(m2,0,0,2,2);
set_all_elements(m2, 2);
set_subm(m1, 3,2,2,2) = m2;
set_colm(m1,4) = trans(rowm(m1,4));
set_rowm(m1,0) = 9;
DLIB_TEST_MSG(m1 == res, "m1: \n" << m1 << "\nres: \n" << res);
set_subm(m1,0,0,5,5) = m1*m1;
DLIB_TEST_MSG(m1 == res*res, "m1: \n" << m1 << "\nres*res: \n" << res*res);
m1 = res;
set_subm(m1,1,1,2,2) = subm(m1,0,0,2,2);
long res_vals2[] = {
9, 9, 9, 9, 9,
0, 9, 9, 0, 0,
0, 0, 1, 0, 2,
0, 0, 2, 2, 2,
0, 0, 2, 2, 0
};
res = res_vals2;
DLIB_TEST_MSG(m1 == res, "m1: \n" << m1 << "\nres: \n" << res);
}
{
matrix<long,5,5> m1, res;
matrix<long,2,2> m2;
set_all_elements(m1,0);
long res_vals[] = {
9, 9, 9, 9, 9,
0, 1, 1, 0, 0,
0, 1, 1, 0, 2,
0, 0, 2, 2, 2,
0, 0, 2, 2, 0
};
res = res_vals;
set_all_elements(m2, 1);
set_subm(m1, rectangle(1,1,2,2)) = subm(m2,0,0,2,2);
set_all_elements(m2, 2);
set_subm(m1, 3,2,2,2) = m2;
set_colm(m1,4) = trans(rowm(m1,4));
set_rowm(m1,0) = 9;
DLIB_TEST_MSG(m1 == res, "m1: \n" << m1 << "\nres: \n" << res);
set_subm(m1,0,0,5,5) = m1*m1;
DLIB_TEST_MSG(m1 == res*res, "m1: \n" << m1 << "\nres*res: \n" << res*res);
m1 = res;
set_subm(m1,1,1,2,2) = subm(m1,0,0,2,2);
long res_vals2[] = {
9, 9, 9, 9, 9,
0, 9, 9, 0, 0,
0, 0, 1, 0, 2,
0, 0, 2, 2, 2,
0, 0, 2, 2, 0
};
res = res_vals2;
DLIB_TEST_MSG(m1 == res, "m1: \n" << m1 << "\nres: \n" << res);
}
{
matrix<long,5,5> m1, res;
matrix<long,2,2> m2;
set_all_elements(m1,0);
long res_vals[] = {
9, 0, 3, 3, 0,
9, 2, 2, 2, 0,
9, 2, 2, 2, 0,
4, 4, 4, 4, 4,
9, 0, 3, 3, 0
};
long res_vals_c3[] = {
9, 0, 3, 0,
9, 2, 2, 0,
9, 2, 2, 0,
4, 4, 4, 4,
9, 0, 3, 0
};
long res_vals_r2[] = {
9, 0, 3, 3, 0,
9, 2, 2, 2, 0,
4, 4, 4, 4, 4,
9, 0, 3, 3, 0
};
matrix<long> temp;
res = res_vals;
temp = matrix<long,4,5>(res_vals_r2);
DLIB_TEST(remove_row<2>(res) == temp);
DLIB_TEST(remove_row<2>(res)(3,3) == 3);
DLIB_TEST(remove_row<2>(res).nr() == 4);
DLIB_TEST(remove_row<2>(res).nc() == 5);
DLIB_TEST(remove_row(res,2) == temp);
DLIB_TEST(remove_row(res,2)(3,3) == 3);
DLIB_TEST(remove_row(res,2).nr() == 4);
DLIB_TEST(remove_row(res,2).nc() == 5);
temp = matrix<long,5,5>(res_vals);
temp = remove_row(res,2);
DLIB_TEST((temp == matrix<long,4,5>(res_vals_r2)));
temp = matrix<long,5,5>(res_vals);
temp = remove_col(res,3);
DLIB_TEST((temp == matrix<long,5,4>(res_vals_c3)));
matrix<long,3,1> vect;
set_all_elements(vect,1);
temp = identity_matrix<long>(3);
temp = temp*vect;
DLIB_TEST(temp == vect);
temp = matrix<long,5,4>(res_vals_c3);
DLIB_TEST(remove_col(res,3) == temp);
DLIB_TEST(remove_col(res,3)(2,3) == 0);
DLIB_TEST(remove_col(res,3).nr() == 5);
DLIB_TEST(remove_col(res,3).nc() == 4);
set_all_elements(m2, 1);
set_subm(m1, rectangle(1,1,3,2)) = 2;
set_all_elements(m2, 2);
set_subm(m1, 3,2,2,2) = 3;
set_colm(m1,0) = 9;
set_rowm(m1,0) = rowm(m1,4);
set_rowm(m1,3) = 4;
DLIB_TEST_MSG(m1 == res, "m1: \n" << m1 << "\nres: \n" << res);
}
}
void matrix_test2()
{
print_spinner();
{
const double stuff[] = {
1, 2, 3,
6, 3, 3,
7, 3, 9};
matrix<double,3,3> m(stuff);
// make m be symmetric
m = m*trans(m);
matrix<double> L = chol(m);
DLIB_TEST(equal(L*trans(L), m));
DLIB_TEST_MSG(equal(inv(m), inv_upper_triangular(trans(L))*inv_lower_triangular((L))), "");
DLIB_TEST(equal(round_zeros(inv_upper_triangular(trans(L))*trans(L),1e-10), identity_matrix<double>(3), 1e-10));
DLIB_TEST(equal(round_zeros(inv_lower_triangular((L))*(L),1e-10) ,identity_matrix<double>(3),1e-10));
}
{
const double stuff[] = {
1, 2, 3, 6, 3, 4,
6, 3, 3, 1, 2, 3,
7, 3, 9, 54.3, 5, 3,
-6, 3, -3, 1, 2, 3,
1, 2, 3, 5, -3, 3,
7, 3, -9, 54.3, 5, 3
};
matrix<double,6,6> m(stuff);
// make m be symmetric
m = m*trans(m);
matrix<double> L = chol(m);
DLIB_TEST_MSG(equal(L*trans(L), m, 1e-10), L*trans(L)-m);
DLIB_TEST_MSG(equal(inv(m), inv_upper_triangular(trans(L))*inv_lower_triangular((L))), "");
DLIB_TEST_MSG(equal(inv(m), trans(inv_lower_triangular(L))*inv_lower_triangular((L))), "");
DLIB_TEST_MSG(equal(inv(m), trans(inv_lower_triangular(L))*trans(inv_upper_triangular(trans(L)))), "");
DLIB_TEST_MSG(equal(round_zeros(inv_upper_triangular(trans(L))*trans(L),1e-10) , identity_matrix<double>(6), 1e-10),
round_zeros(inv_upper_triangular(trans(L))*trans(L),1e-10));
DLIB_TEST_MSG(equal(round_zeros(inv_lower_triangular((L))*(L),1e-10) ,identity_matrix<double>(6), 1e-10),
round_zeros(inv_lower_triangular((L))*(L),1e-10));
}
{
matrix<int> m(3,4), m2;
m = 1,2,3,4,
4,5,6,6,
6,1,8,0;
m2 = m;
DLIB_TEST(round(m) == m2);
DLIB_TEST(round_zeros(m) == m2);
m2 = 0,2,3,4,
4,5,6,6,
6,0,8,0;
DLIB_TEST(round_zeros(m,2) == m2);
}
{
matrix<double,6,6> m(identity_matrix<double>(6)*4.5);
matrix<double> L = chol(m);
DLIB_TEST_MSG(equal(L*trans(L), m, 1e-10), L*trans(L)-m);
DLIB_TEST_MSG(equal(inv(m), inv_upper_triangular(trans(L))*inv_lower_triangular((L))), "");
DLIB_TEST_MSG(equal(round_zeros(inv_upper_triangular(trans(L))*trans(L),1e-10) , identity_matrix<double>(6), 1e-10),
round_zeros(inv_upper_triangular(trans(L))*trans(L),1e-10));
DLIB_TEST_MSG(equal(round_zeros(inv_lower_triangular((L))*(L),1e-10) ,identity_matrix<double>(6), 1e-10),
round_zeros(inv_lower_triangular((L))*(L),1e-10));
}
{
matrix<double,6,6> m(identity_matrix<double>(6)*4.5);
m(1,4) = 2;
DLIB_TEST_MSG(dlib::equal(inv_upper_triangular(m), inv(m),1e-10), inv_upper_triangular(m)-inv(m));
DLIB_TEST_MSG(dlib::equal(inv_lower_triangular(trans(m)), inv(trans(m)),1e-10), inv_lower_triangular(trans(m))-inv(trans(m)));
}
{
matrix<double> a;
matrix<float> b;
matrix<int> i;
a.set_size(1000,10);
b.set_size(1000,10);
i.set_size(1000,10);
dlib::rand rnd;
for (long r = 0; r < a.nr(); ++r)
{
for (long c = 0; c < a.nc(); ++c)
{
a(r,c) = rnd.get_random_double();
b(r,c) = rnd.get_random_float();
i(r,c) = r+c*r;
}
}
// make sure the multiply optimizations aren't messing things up
DLIB_TEST(trans(i)*i == tmp(trans(i)*i));
DLIB_TEST_MSG(equal(trans(a)*a , tmp(trans(a)*a), 1e-11),max(abs(trans(a)*a - tmp(trans(a)*a))));
DLIB_TEST_MSG(equal(trans(b)*b , tmp(trans(b)*b), 1e-3f),max(abs(trans(b)*b - tmp(trans(b)*b))));
}
{
matrix<int,4> i(4,1);
i(0) = 1;
i(1) = 2;
i(2) = 3;
i(3) = 4;
matrix<int,4,4> m;
set_all_elements(m,0);
m(0,0) = 1;
m(1,1) = 2;
m(2,2) = 3;
m(3,3) = 4;
DLIB_TEST(diagm(i) == m);
}
{
matrix<int,1,4> i;
i(0) = 1;
i(1) = 2;
i(2) = 3;
i(3) = 4;
matrix<int,4,4> m;
set_all_elements(m,0);
m(0,0) = 1;
m(1,1) = 2;
m(2,2) = 3;
m(3,3) = 4;
DLIB_TEST(diagm(i) == m);
}
{
matrix<int> i(4,1);
i(0) = 1;
i(1) = 2;
i(2) = 3;
i(3) = 4;
matrix<int> m(4,4);
set_all_elements(m,0);
m(0,0) = 1;
m(1,1) = 2;
m(2,2) = 3;
m(3,3) = 4;
DLIB_TEST(diagm(i) == m);
}
{
matrix<int> i(1,4);
i(0) = 1;
i(1) = 2;
i(2) = 3;
i(3) = 4;
matrix<int> m(4,4);
set_all_elements(m,0);
m(0,0) = 1;
m(1,1) = 2;
m(2,2) = 3;
m(3,3) = 4;
DLIB_TEST(diagm(i) == m);
}
{
DLIB_TEST(range(0,5).nc() == 6);
DLIB_TEST(range(1,5).nc() == 5);
DLIB_TEST(range(0,5).nr() == 1);
DLIB_TEST(range(1,5).nr() == 1);
DLIB_TEST(trans(range(0,5)).nr() == 6);
DLIB_TEST(trans(range(1,5)).nr() == 5);
DLIB_TEST(trans(range(0,5)).nc() == 1);
DLIB_TEST(trans(range(1,5)).nc() == 1);
DLIB_TEST(range(0,2,5).nc() == 3);
DLIB_TEST(range(1,2,5).nc() == 3);
DLIB_TEST(range(0,2,5).nr() == 1);
DLIB_TEST(range(1,2,5).nr() == 1);
DLIB_TEST(trans(range(0,2,5)).nr() == 3);
DLIB_TEST(trans(range(1,2,5)).nr() == 3);
DLIB_TEST(trans(range(0,2,5)).nc() == 1);
DLIB_TEST(trans(range(1,2,5)).nc() == 1);
DLIB_TEST(range(0,3,6).nc() == 3);
DLIB_TEST(range(1,3,5).nc() == 2);
DLIB_TEST(range(0,3,5).nr() == 1);
DLIB_TEST(range(1,3,5).nr() == 1);
DLIB_TEST(trans(range(0,3,6)).nr() == 3);
DLIB_TEST(trans(range(1,3,5)).nr() == 2);
DLIB_TEST(trans(range(0,3,5)).nc() == 1);
DLIB_TEST(trans(range(1,3,5)).nc() == 1);
DLIB_TEST(range(1,9,5).nc() == 1);
DLIB_TEST(range(1,9,5).nr() == 1);
DLIB_TEST(range(0,0).nc() == 1);
DLIB_TEST(range(0,0).nr() == 1);
DLIB_TEST(range(1,1)(0) == 1);
DLIB_TEST(range(0,5)(0) == 0 && range(0,5)(1) == 1 && range(0,5)(5) == 5);
DLIB_TEST(range(1,2,5)(0) == 1 && range(1,2,5)(1) == 3 && range(1,2,5)(2) == 5);
DLIB_TEST((range<0,5>()(0) == 0 && range<0,5>()(1) == 1 && range<0,5>()(5) == 5));
DLIB_TEST((range<1,2,5>()(0) == 1 && range<1,2,5>()(1) == 3 && range<1,2,5>()(2) == 5));
DLIB_TEST((range<0,5>().nc() == 6));
DLIB_TEST((range<1,5>().nc() == 5));
DLIB_TEST((range<0,5>().nr() == 1));
DLIB_TEST((range<1,5>().nr() == 1));
DLIB_TEST((trans(range<0,5>()).nr() == 6));
DLIB_TEST((trans(range<1,5>()).nr() == 5));
DLIB_TEST((trans(range<0,5>()).nc() == 1));
DLIB_TEST((trans(range<1,5>()).nc() == 1));
DLIB_TEST((range<0,2,5>().nc() == 3));
DLIB_TEST((range<1,2,5>().nc() == 3));
DLIB_TEST((range<0,2,5>().nr() == 1));
DLIB_TEST((range<1,2,5>().nr() == 1));
DLIB_TEST((trans(range<0,2,5>()).nr() == 3));
DLIB_TEST((trans(range<1,2,5>()).nr() == 3));
DLIB_TEST((trans(range<0,2,5>()).nc() == 1));
DLIB_TEST((trans(range<1,2,5>()).nc() == 1));
DLIB_TEST((range<0,3,6>().nc() == 3));
DLIB_TEST((range<1,3,5>().nc() == 2));
DLIB_TEST((range<0,3,5>().nr() == 1));
DLIB_TEST((range<1,3,5>().nr() == 1));
DLIB_TEST((trans(range<0,3,6>()).nr() == 3));
DLIB_TEST((trans(range<1,3,5>()).nr() == 2));
DLIB_TEST((trans(range<0,3,5>()).nc() == 1));
DLIB_TEST((trans(range<1,3,5>()).nc() == 1));
}
{
DLIB_TEST(range(5,0).nc() == 6);
DLIB_TEST(range(5,1).nc() == 5);
DLIB_TEST(range(5,0).nr() == 1);
DLIB_TEST(range(5,1).nr() == 1);
DLIB_TEST(trans(range(5,0)).nr() == 6);
DLIB_TEST(trans(range(5,1)).nr() == 5);
DLIB_TEST(trans(range(5,0)).nc() == 1);
DLIB_TEST(trans(range(5,1)).nc() == 1);
DLIB_TEST(range(5,2,0).nc() == 3);
DLIB_TEST(range(5,2,1).nc() == 3);
DLIB_TEST(range(5,2,0).nr() == 1);
DLIB_TEST(range(5,2,1).nr() == 1);
DLIB_TEST(trans(range(5,2,0)).nr() == 3);
DLIB_TEST(trans(range(5,2,1)).nr() == 3);
DLIB_TEST(trans(range(5,2,0)).nc() == 1);
DLIB_TEST(trans(range(5,2,1)).nc() == 1);
DLIB_TEST(range(6,3,0).nc() == 3);
DLIB_TEST(range(5,3,1).nc() == 2);
DLIB_TEST(range(5,3,0).nr() == 1);
DLIB_TEST(range(5,3,1).nr() == 1);
DLIB_TEST(trans(range(6,3,0)).nr() == 3);
DLIB_TEST(trans(range(5,3,1)).nr() == 2);
DLIB_TEST(trans(range(5,3,0)).nc() == 1);
DLIB_TEST(trans(range(5,3,1)).nc() == 1);
DLIB_TEST(range(5,9,1).nc() == 1);
DLIB_TEST(range(5,9,1).nr() == 1);
DLIB_TEST(range(0,0).nc() == 1);
DLIB_TEST(range(0,0).nr() == 1);
DLIB_TEST(range(1,1)(0) == 1);
DLIB_TEST(range(5,0)(0) == 5 && range(5,0)(1) == 4 && range(5,0)(5) == 0);
DLIB_TEST(range(5,2,1)(0) == 5 && range(5,2,1)(1) == 3 && range(5,2,1)(2) == 1);
DLIB_TEST((range<5,0>()(0) == 5 && range<5,0>()(1) == 4 && range<5,0>()(5) == 0));
DLIB_TEST((range<5,2,1>()(0) == 5 && range<5,2,1>()(1) == 3 && range<5,2,1>()(2) == 1));
DLIB_TEST((range<5,0>().nc() == 6));
DLIB_TEST((range<5,1>().nc() == 5));
DLIB_TEST((range<5,0>().nr() == 1));
DLIB_TEST((range<5,1>().nr() == 1));
DLIB_TEST((trans(range<5,0>()).nr() == 6));
DLIB_TEST((trans(range<5,1>()).nr() == 5));
DLIB_TEST((trans(range<5,0>()).nc() == 1));
DLIB_TEST((trans(range<5,1>()).nc() == 1));
DLIB_TEST((range<5,2,0>().nc() == 3));
DLIB_TEST((range<5,2,1>().nc() == 3));
DLIB_TEST((range<5,2,0>().nr() == 1));
DLIB_TEST((range<5,2,1>().nr() == 1));
DLIB_TEST((trans(range<5,2,0>()).nr() == 3));
DLIB_TEST((trans(range<5,2,1>()).nr() == 3));
DLIB_TEST((trans(range<5,2,0>()).nc() == 1));
DLIB_TEST((trans(range<5,2,1>()).nc() == 1));
DLIB_TEST((range<6,3,0>().nc() == 3));
DLIB_TEST((range<5,3,1>().nc() == 2));
DLIB_TEST((range<5,3,0>().nr() == 1));
DLIB_TEST((range<5,3,1>().nr() == 1));
DLIB_TEST((trans(range<6,3,0>()).nr() == 3));
DLIB_TEST((trans(range<5,3,1>()).nr() == 2));
DLIB_TEST((trans(range<5,3,0>()).nc() == 1));
DLIB_TEST((trans(range<5,3,1>()).nc() == 1));
}
{
matrix<double> m(4,3);
for (long r = 0; r < m.nr(); ++r)
{
for (long c = 0; c < m.nc(); ++c)
{
m(r,c) = r*c;
}
}
DLIB_TEST(subm(m,range(0,3),range(0,0)) == colm(m,0));
DLIB_TEST(subm(m,range(0,3),range(1,1)) == colm(m,1));
DLIB_TEST(subm(m,range(0,3),range(2,2)) == colm(m,2));
DLIB_TEST(subm(m,range(0,0),range(0,2)) == rowm(m,0));
DLIB_TEST(subm(m,range(1,1),range(0,2)) == rowm(m,1));
DLIB_TEST(subm(m,range(2,2),range(0,2)) == rowm(m,2));
DLIB_TEST(subm(m,range(3,3),range(0,2)) == rowm(m,3));
DLIB_TEST(subm(m,0,0,2,2) == subm(m,range(0,1),range(0,1)));
DLIB_TEST(subm(m,1,1,2,2) == subm(m,range(1,2),range(1,2)));
matrix<double,2,2> m2 = subm(m,range(0,2,2),range(0,2,2));
DLIB_TEST(m2(0,0) == m(0,0));
DLIB_TEST(m2(0,1) == m(0,2));
DLIB_TEST(m2(1,0) == m(2,0));
DLIB_TEST(m2(1,1) == m(2,2));
}
{
matrix<double,4,3> m(4,3);
for (long r = 0; r < m.nr(); ++r)
{
for (long c = 0; c < m.nc(); ++c)
{
m(r,c) = r*c;
}
}
DLIB_TEST(subm(m,range<0,3>(),range<0,0>()) == colm(m,0));
DLIB_TEST(subm(m,range<0,3>(),range<1,1>()) == colm(m,1));
DLIB_TEST(subm(m,range<0,3>(),range<2,2>()) == colm(m,2));
DLIB_TEST(subm(m,range<0,0>(),range<0,2>()) == rowm(m,0));
DLIB_TEST(subm(m,range<1,1>(),range<0,2>()) == rowm(m,1));
DLIB_TEST(subm(m,range<2,2>(),range<0,2>()) == rowm(m,2));
DLIB_TEST(subm(m,range<3,3>(),range<0,2>()) == rowm(m,3));
DLIB_TEST(subm(m,0,0,2,2) == subm(m,range<0,1>(),range<0,1>()));
DLIB_TEST(subm(m,1,1,2,2) == subm(m,range<1,2>(),range<1,2>()));
matrix<double,2,2> m2 = subm(m,range<0,2,2>(),range<0,2,2>());
DLIB_TEST(m2(0,0) == m(0,0));
DLIB_TEST(m2(0,1) == m(0,2));
DLIB_TEST(m2(1,0) == m(2,0));
DLIB_TEST(m2(1,1) == m(2,2));
}
{
matrix<double> a = randm(3,4);
matrix<double> b = randm(3,4);
matrix<double> m1, m2;
m1 = max_pointwise(a,b);
m2 = min_pointwise(a,b);
DLIB_TEST(m1.nr() == a.nr());
DLIB_TEST(m1.nc() == a.nc());
DLIB_TEST(m2.nr() == a.nr());
DLIB_TEST(m2.nc() == a.nc());
for (long r = 0; r < a.nr(); ++r)
{
for (long c = 0; c < a.nc(); ++c)
{
DLIB_TEST_MSG(m1(r,c) == std::max(a(r,c), b(r,c)), m1(r,c) << " : " << a(r,c) << " " << b(r,c));
DLIB_TEST(m2(r,c) == std::min(a(r,c), b(r,c)));
}
}
}
{
matrix<double,4,5> m;
set_subm(m, range(0,3), range(0,4)) = 4;
DLIB_TEST(min(m) == max(m) && min(m) == 4);
set_subm(m,range(1,1),range(0,4)) = 7;
DLIB_TEST((rowm(m,0) == uniform_matrix<double>(1,5, 4)));
DLIB_TEST((rowm(m,1) == uniform_matrix<double>(1,5, 7)));
DLIB_TEST((rowm(m,2) == uniform_matrix<double>(1,5, 4)));
DLIB_TEST((rowm(m,3) == uniform_matrix<double>(1,5, 4)));
set_subm(m, range(0,2,3), range(0,2,4)) = trans(subm(m,0,0,3,2));
DLIB_TEST(m(0,2) == 7);
DLIB_TEST(m(2,2) == 7);
DLIB_TEST(sum(m) == 7*5+ 7+7 + 4*(4*5 - 7));
}
{
matrix<double> mat(4,5);
DLIB_TEST((uniform_matrix<double>(4,5,1) == ones_matrix<double>(4,5)));
DLIB_TEST((uniform_matrix<double>(4,5,1) == ones_matrix(mat)));
DLIB_TEST((uniform_matrix<double>(4,5,0) == zeros_matrix<double>(4,5)));
DLIB_TEST((uniform_matrix<double>(4,5,0) == zeros_matrix(mat)));
DLIB_TEST((uniform_matrix<float>(4,5,1) == ones_matrix<float>(4,5)));
DLIB_TEST((uniform_matrix<float>(4,5,0) == zeros_matrix<float>(4,5)));
DLIB_TEST((uniform_matrix<complex<double> >(4,5,1) == ones_matrix<complex<double> >(4,5)));
DLIB_TEST((uniform_matrix<complex<double> >(4,5,0) == zeros_matrix<complex<double> >(4,5)));
DLIB_TEST((uniform_matrix<complex<float> >(4,5,1) == ones_matrix<complex<float> >(4,5)));
DLIB_TEST((uniform_matrix<complex<float> >(4,5,0) == zeros_matrix<complex<float> >(4,5)));
DLIB_TEST((complex_matrix(ones_matrix<double>(3,3), zeros_matrix<double>(3,3)) == complex_matrix(ones_matrix<double>(3,3))));
DLIB_TEST((pointwise_multiply(complex_matrix(ones_matrix<double>(3,3)), ones_matrix<double>(3,3)*2) ==
complex_matrix(2*ones_matrix<double>(3,3))));
}
{
DLIB_TEST(( uniform_matrix<double>(303,303, 3)*identity_matrix<double>(303) == uniform_matrix<double,303,303>(3) ) );
DLIB_TEST(( uniform_matrix<double,303,303>(3)*identity_matrix<double,303>() == uniform_matrix<double,303,303>(3) ));
}
{
matrix<double> m(2,3);
m = 1,2,3,
5,6,7;
DLIB_TEST_MSG(m(0,0) == 1 && m(0,1) == 2 && m(0,2) == 3 &&
m(1,0) == 5 && m(1,1) == 6 && m(1,2) == 7,"");
m = 4;
DLIB_TEST((m == uniform_matrix<double,2,3>(4)));
matrix<double,2,3> m2;
m2 = 1,2,3,
5,6,7;
DLIB_TEST_MSG(m2(0,0) == 1 && m2(0,1) == 2 && m2(0,2) == 3 &&
m2(1,0) == 5 && m2(1,1) == 6 && m2(1,2) == 7,"");
matrix<double,2,1> m3;
m3 = 1,
5;
DLIB_TEST(m3(0) == 1 && m3(1) == 5 );
matrix<double,1,2> m4;
m4 = 1, 5;
DLIB_TEST(m3(0) == 1 && m3(1) == 5 );
}
{
matrix<double> m(4,1);
m = 3, 1, 5, 2;
DLIB_TEST(index_of_min(m) == 1);
DLIB_TEST(index_of_max(m) == 2);
DLIB_TEST(index_of_min(trans(m)) == 1);
DLIB_TEST(index_of_max(trans(m)) == 2);
}
{
matrix<double> m1(1,5), m2;
m1 = 3.0000, 3.7500, 4.5000, 5.2500, 6.0000;
m2 = linspace(3, 6, 5);
DLIB_TEST(equal(m1, m2));
m1 = pow(10, m1);
m2 = logspace(3, 6, 5);
DLIB_TEST(equal(m1, m2));
}
{
matrix<long> m = cartesian_product(range(1,3), range(0,1));
matrix<long,2,1> c0, c1, c2, c3, c4, c5;
c0 = 1, 0;
c1 = 1, 1;
c2 = 2, 0;
c3 = 2, 1;
c4 = 3, 0;
c5 = 3, 1;
DLIB_TEST_MSG(colm(m,0) == c0, colm(m,0) << "\n\n" << c0);
DLIB_TEST(colm(m,1) == c1);
DLIB_TEST(colm(m,2) == c2);
DLIB_TEST(colm(m,3) == c3);
DLIB_TEST(colm(m,4) == c4);
DLIB_TEST(colm(m,5) == c5);
}
{
matrix<double> m(2,2), mr(2,2), mr_max(2,2);
m = 1, 2,
0, 4;
mr = 1, 1.0/2.0,
0, 1.0/4.0;
mr_max = 1, 1.0/2.0,
std::numeric_limits<double>::max(), 1.0/4.0;
DLIB_TEST(equal(reciprocal(m), mr));
DLIB_TEST(equal(reciprocal_max(m), mr_max));
}
{
matrix<double> m1, m2;
m1.set_size(3,1);
m2.set_size(1,3);
m1 = 1,2,3;
m2 = 4,5,6;
DLIB_TEST(dot(m1, m2) == 1*4 + 2*5 + 3*6);
DLIB_TEST(dot(m1, trans(m2)) == 1*4 + 2*5 + 3*6);
DLIB_TEST(dot(trans(m1), m2) == 1*4 + 2*5 + 3*6);
DLIB_TEST(dot(trans(m1), trans(m2)) == 1*4 + 2*5 + 3*6);
}
{
matrix<double,3,1> m1, m2;
m1.set_size(3,1);
m2.set_size(3,1);
m1 = 1,2,3;
m2 = 4,5,6;
DLIB_TEST(dot(m1, m2) == 1*4 + 2*5 + 3*6);
DLIB_TEST(dot(m1, trans(m2)) == 1*4 + 2*5 + 3*6);
DLIB_TEST(dot(trans(m1), m2) == 1*4 + 2*5 + 3*6);
DLIB_TEST(dot(trans(m1), trans(m2)) == 1*4 + 2*5 + 3*6);
}
{
matrix<double,1,3> m1, m2;
m1.set_size(1,3);
m2.set_size(1,3);
m1 = 1,2,3;
m2 = 4,5,6;
DLIB_TEST(dot(m1, m2) == 1*4 + 2*5 + 3*6);
DLIB_TEST(dot(m1, trans(m2)) == 1*4 + 2*5 + 3*6);
DLIB_TEST(dot(trans(m1), m2) == 1*4 + 2*5 + 3*6);
DLIB_TEST(dot(trans(m1), trans(m2)) == 1*4 + 2*5 + 3*6);
}
{
matrix<double,1,3> m1;
matrix<double> m2;
m1.set_size(1,3);
m2.set_size(3,1);
m1 = 1,2,3;
m2 = 4,5,6;
DLIB_TEST(dot(m1, m2) == 1*4 + 2*5 + 3*6);
DLIB_TEST(dot(m1, trans(m2)) == 1*4 + 2*5 + 3*6);
DLIB_TEST(dot(trans(m1), m2) == 1*4 + 2*5 + 3*6);
DLIB_TEST(dot(trans(m1), trans(m2)) == 1*4 + 2*5 + 3*6);
}
{
matrix<double> m1(3,3), m2(3,3);
m1 = 1;
m2 = 1;
m1 = m1*subm(m2,0,0,3,3);
DLIB_TEST(is_finite(m1));
}
{
matrix<double,3,1> m1;
matrix<double> m2(3,3);
m1 = 1;
m2 = 1;
m1 = subm(m2,0,0,3,3)*m1;
}
{
matrix<int> m(2,1);
m = 3,3;
m /= m(0);
DLIB_TEST(m(0) == 1);
DLIB_TEST(m(1) == 1);
}
{
matrix<int> m(2,1);
m = 3,3;
m *= m(0);
DLIB_TEST(m(0) == 9);
DLIB_TEST(m(1) == 9);
}
{
matrix<int> m(2,1);
m = 3,3;
m -= m(0);
DLIB_TEST(m(0) == 0);
DLIB_TEST(m(1) == 0);
}
{
matrix<int> m(2,1);
m = 3,3;
m += m(0);
DLIB_TEST(m(0) == 6);
DLIB_TEST(m(1) == 6);
DLIB_TEST(is_finite(m));
}
{
matrix<double> m(3,3);
m = 3;
m(1,1) = std::numeric_limits<double>::infinity();
DLIB_TEST(is_finite(m) == false);
m(1,1) = -std::numeric_limits<double>::infinity();
DLIB_TEST(is_finite(m) == false);
m(1,1) = 2;
DLIB_TEST(is_finite(m));
}
{
matrix<int> m(4,1), mm, mmm;
mmm = mm = (m = 1,2,3,4);
DLIB_TEST(m(0) == 1);
DLIB_TEST(m(1) == 2);
DLIB_TEST(m(2) == 3);
DLIB_TEST(m(3) == 4);
DLIB_TEST(mm == m);
DLIB_TEST(mmm == m);
DLIB_TEST(mm(0) == 1);
DLIB_TEST(mm(1) == 2);
DLIB_TEST(mm(2) == 3);
DLIB_TEST(mm(3) == 4);
}
{
const long n = 5;
matrix<double> m1, m2, m3, truth;
m1 = randm(n,n);
m2 = randm(n,n);
m3 = randm(n,n);
truth = m1*m2;
m3 = mat(&m1(0,0),n,n)*mat(&m2(0,0),n,n);
DLIB_TEST(max(abs(truth-m3)) < 1e-13);
m3 = 0;
set_ptrm(&m3(0,0),n,n) = mat(&m1(0,0),n,n)*mat(&m2(0,0),n,n);
DLIB_TEST(max(abs(truth-m3)) < 1e-13);
set_ptrm(&m3(0,0),n,n) = m1*m2;
DLIB_TEST(max(abs(truth-m3)) < 1e-13);
// now make sure it deals with aliasing correctly.
truth = m1*m2;
m1 = mat(&m1(0,0),n,n)*mat(&m2(0,0),n,n);
DLIB_TEST(max(abs(truth-m1)) < 1e-13);
m1 = randm(n,n);
truth = m1*m2;
set_ptrm(&m1(0,0),n,n) = mat(&m1(0,0),n,n)*mat(&m2(0,0),n,n);
DLIB_TEST(max(abs(truth-m1)) < 1e-13);
m1 = randm(n,n);
truth = m1*m2;
set_ptrm(&m1(0,0),n,n) = m1*m2;
DLIB_TEST(max(abs(truth-m1)) < 1e-13);
m1 = randm(n,n);
truth = m1+m1*m2;
set_ptrm(&m1(0,0),n,n) += m1*m2;
DLIB_TEST(max(abs(truth-m1)) < 1e-13);
m1 = randm(n,n);
truth = m1-m1*m2;
set_ptrm(&m1(0,0),n,n) -= m1*m2;
DLIB_TEST(max(abs(truth-m1)) < 1e-13);
}
}
class matrix_tester : public tester
{
public:
matrix_tester (
) :
tester ("test_matrix",
"Runs tests on the matrix component.")
{}
void perform_test (
)
{
matrix_test();
matrix_test2();
}
} a;
}