```// Copyright (C) 2006  Davis E. King (davis@dlib.net)

#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.matrix2");

dlib::rand rnd;

void matrix_test1 (
)
{
typedef memory_manager_stateless<char>::kernel_2_2a MM;
print_spinner();

const double ident[] = {
1, 0, 0, 0,
0, 1, 0, 0,
0, 0, 1, 0,
0, 0, 0, 1 };

const double uniform3[] = {
3, 3, 3, 3,
3, 3, 3, 3,
3, 3, 3, 3,
3, 3, 3, 3
};

const double uniform1[] = {
1, 1, 1, 1,
1, 1, 1, 1,
1, 1, 1, 1,
1, 1, 1, 1
};

const double uniform0[] = {
0, 0, 0, 0,
0, 0, 0, 0,
0, 0, 0, 0,
0, 0, 0, 0
};

const int array[] = {
42, 58, 9, 1,
9, 5, 8, 2,
98, 28, 4, 77,
9, 2, 44, 88 };

const int array2[] = {
1, 22, 3,
4, 52, 6,
7, 8, 9 };

const int array2_r[] = {
52, 6, 4,
8, 9, 7,
22, 3, 1
};

const double array_f[] = {
-0.99,
0.99};

matrix<double,2,1,MM> fm(array_f);

DLIB_TEST(fm.size() == 2);
matrix<double> dfm(fm);
DLIB_TEST(round(fm)(0) == -1);
DLIB_TEST(round(fm)(1) == 1);
DLIB_TEST(round(dfm)(0) == -1);
DLIB_TEST(round(dfm)(1) == 1);
DLIB_TEST(round(dfm).size() == dfm.size());

const int array3[] = { 1, 2, 3, 4 };

matrix<double,3,3,MM> m3(array2);
matrix<double> dm3;
DLIB_TEST(dm3.size() == 0);
DLIB_TEST(dm3.nr() == 0);
DLIB_TEST(dm3.nc() == 0);
dm3.set_size(3,4);
DLIB_TEST(dm3.nr() == 3);
DLIB_TEST(dm3.nc() == 4);
DLIB_TEST(dm3.size() == 3*4);
dm3.set_size(3,3);
DLIB_TEST(dm3.nr() == 3);
DLIB_TEST(dm3.nc() == 3);
dm3 = m3;
dm3(0,0)++;
DLIB_TEST( dm3 != m3);
dm3 = m3;
DLIB_TEST( dm3 == m3);
DLIB_TEST( abs(sum(squared(normalize(dm3))) - 1.0) < 1e-10);

matrix<double,3,4> mrc;
mrc.set_size(3,4);

set_all_elements(mrc,1);

DLIB_TEST(diag(mrc) == uniform_matrix<double>(3,1,1));
DLIB_TEST(diag(matrix<double>(mrc)) == uniform_matrix<double>(3,1,1));

matrix<double,2,3> mrc2;
set_all_elements(mrc2,1);
DLIB_TEST((removerc<1,1>(mrc) == mrc2));
DLIB_TEST((removerc(mrc,1,1) == mrc2));

matrix<int,3,3> m4, m5, m6;
set_all_elements(m4, 4);
set_all_elements(m5, 4);
set_all_elements(m6, 1);

DLIB_TEST(squared(m4) == pointwise_multiply(m4,m4));
DLIB_TEST(cubed(m4) == pointwise_multiply(m4,m4,m4));
DLIB_TEST(pow(matrix_cast<double>(m4),2) == squared(matrix_cast<double>(m4)));
DLIB_TEST(pow(matrix_cast<double>(m4),3) == cubed(matrix_cast<double>(m4)));

matrix<int> dm4;
matrix<int,0,0,memory_manager_stateless<char>::kernel_2_2a> dm5;
dm4 = dm4;
dm4 = dm5;
DLIB_TEST(dm4.nr() == 0);
dm4 = m4;
dm5 = m5;
DLIB_TEST(dm4 == dm5);

DLIB_TEST(m4 == m5);
DLIB_TEST(m6 != m5);
m4.swap(m6);
DLIB_TEST(m6 == m5);
DLIB_TEST(m4 != m5);

DLIB_TEST(m3.nr() == 3);
DLIB_TEST(m3.nc() == 3);

matrix<double,4,1> v(array3), v2;
DLIB_TEST(v.nr() == 4);
DLIB_TEST(v.nc() == 1);

std::vector<double> stdv(4);
std_vector_c<double> stdv_c(4);
dlib::array<double> arr;
arr.resize(4);
for (long i = 0; i < 4; ++i)
stdv[i] = stdv_c[i] = arr[i] = i+1;

DLIB_TEST(mat(stdv)(0) == 1);
DLIB_TEST(mat(stdv)(1) == 2);
DLIB_TEST(mat(stdv)(2) == 3);
DLIB_TEST(mat(stdv)(3) == 4);
DLIB_TEST(mat(stdv).nr() == 4);
DLIB_TEST(mat(stdv).nc() == 1);
DLIB_TEST(mat(stdv).size() == 4);
DLIB_TEST(equal(trans(mat(stdv))*mat(stdv), trans(v)*v));
DLIB_TEST(equal(trans(mat(stdv))*mat(stdv), tmp(trans(v)*v)));

DLIB_TEST(mat(stdv_c)(0) == 1);
DLIB_TEST(mat(stdv_c)(1) == 2);
DLIB_TEST(mat(stdv_c)(2) == 3);
DLIB_TEST(mat(stdv_c)(3) == 4);
DLIB_TEST(mat(stdv_c).nr() == 4);
DLIB_TEST(mat(stdv_c).nc() == 1);
DLIB_TEST(mat(stdv_c).size() == 4);
DLIB_TEST(equal(trans(mat(stdv_c))*mat(stdv_c), trans(v)*v));

DLIB_TEST(mat(arr)(0) == 1);
DLIB_TEST(mat(arr)(1) == 2);
DLIB_TEST(mat(arr)(2) == 3);
DLIB_TEST(mat(arr)(3) == 4);
DLIB_TEST(mat(arr).nr() == 4);
DLIB_TEST(mat(arr).nc() == 1);
DLIB_TEST(mat(arr).size() == 4);
DLIB_TEST(equal(trans(mat(arr))*mat(arr), trans(v)*v));

DLIB_TEST(v(0) == 1);
DLIB_TEST(v(1) == 2);
DLIB_TEST(v(2) == 3);
DLIB_TEST(v(3) == 4);
matrix<double> dv = v;
DLIB_TEST((trans(v)*v).size() == 1);
DLIB_TEST((trans(v)*v).nr() == 1);
DLIB_TEST((trans(v)*dv).nr() == 1);
DLIB_TEST((trans(dv)*dv).nr() == 1);
DLIB_TEST((trans(dv)*v).nr() == 1);
DLIB_TEST((trans(v)*v).nc() == 1);
DLIB_TEST((trans(v)*dv).nc() == 1);
DLIB_TEST((trans(dv)*dv).nc() == 1);
DLIB_TEST((trans(dv)*v).nc() == 1);
DLIB_TEST((trans(v)*v)(0) == 1*1 + 2*2 + 3*3 + 4*4);
DLIB_TEST((trans(dv)*v)(0) == 1*1 + 2*2 + 3*3 + 4*4);
DLIB_TEST((trans(dv)*dv)(0) == 1*1 + 2*2 + 3*3 + 4*4);
DLIB_TEST((trans(v)*dv)(0) == 1*1 + 2*2 + 3*3 + 4*4);

dv = trans(dv)*v;
DLIB_TEST(dv.nr() == 1);
DLIB_TEST(dv.nc() == 1);

dm3 = m3;
DLIB_TEST(floor(det(m3)+0.01) == -444);
DLIB_TEST(floor(det(dm3)+0.01) == -444);
DLIB_TEST(min(m3) == 1);
DLIB_TEST(m3(min_point(m3).y(),min_point(m3).x()) == 1);
DLIB_TEST(min(dm3) == 1);
DLIB_TEST(max(m3) == 52);
DLIB_TEST(m3(max_point(m3).y(),max_point(m3).x()) == 52);
DLIB_TEST(max(dm3) == 52);
DLIB_TEST(sum(m3) == 112);
DLIB_TEST(sum(dm3) == 112);
DLIB_TEST(prod(m3) == 41513472);
DLIB_TEST(prod(dm3) == 41513472);
DLIB_TEST(prod(diag(m3)) == 1*52*9);
DLIB_TEST(prod(diag(dm3)) == 1*52*9);
DLIB_TEST(sum(diag(m3)) == 1+52+9);
DLIB_TEST(sum(diag(dm3)) == 1+52+9);
DLIB_TEST(equal(round(10000*m3*inv(m3))/10000 , identity_matrix<double,3>()));
DLIB_TEST(equal(round(10000*dm3*inv(m3))/10000 , identity_matrix<double,3>()));
DLIB_TEST(equal(round(10000*dm3*inv(dm3))/10000 , identity_matrix<double,3>()));
DLIB_TEST(equal(round(10000*m3*inv(dm3))/10000 , identity_matrix<double,3>()));
DLIB_TEST(equal(round(10000*tmp(m3*inv(m3)))/10000 , identity_matrix<double,3>()));
DLIB_TEST(equal(round(10000*tmp(dm3*inv(m3)))/10000 , identity_matrix<double,3>()));
DLIB_TEST(equal(round(10000*tmp(dm3*inv(dm3)))/10000 , identity_matrix<double,3>()));
DLIB_TEST(equal(round(10000*tmp(m3*inv(dm3)))/10000 , identity_matrix<double,3>()));
DLIB_TEST(-1*m3 == -m3);
DLIB_TEST(-1*dm3 == -m3);
DLIB_TEST(-1*m3 == -dm3);
DLIB_TEST(-1*dm3 == -dm3);

DLIB_TEST(m3 == dm3);
m3(1,1) = 99;
DLIB_TEST(m3 != dm3);
m3 = dm3;
DLIB_TEST(m3 == dm3);

matrix<double,4,4,MM> mident(ident);
matrix<double,4,4> muniform0(uniform0);
matrix<double,4,4> muniform1(uniform1);
matrix<double,4,4> muniform3(uniform3);
matrix<double,4,4> m1(array), m2;
DLIB_TEST(m1.nr() == 4);
DLIB_TEST(m1.nc() == 4);

DLIB_TEST(muniform1 + muniform1 + muniform1 == muniform3);
DLIB_TEST(muniform1*2 + muniform1 + muniform1 - muniform1 == muniform3);
DLIB_TEST(2*muniform1 + muniform1 + muniform1 - muniform1 == muniform3);
DLIB_TEST(muniform1 + muniform1 + muniform1 - muniform3 == muniform0);
DLIB_TEST(equal(muniform3/3 , muniform1));
DLIB_TEST(v != m1);
DLIB_TEST(v == v);
DLIB_TEST(m1 == m1);

muniform0.swap(muniform1);
DLIB_TEST((muniform1 == matrix_cast<double>(uniform_matrix<long,4,4,0>())));
DLIB_TEST((muniform0 == matrix_cast<double>(uniform_matrix<long,4,4,1>())));
DLIB_TEST((muniform1 == matrix_cast<double>(uniform_matrix<long>(4,4,0))));
DLIB_TEST((muniform0 == matrix_cast<double>(uniform_matrix<long>(4,4,1))));
swap(muniform0,muniform1);

DLIB_TEST((mident == identity_matrix<double,4>()));
DLIB_TEST((muniform0 == matrix_cast<double>(uniform_matrix<long,4,4,0>())));
DLIB_TEST((muniform1 == matrix_cast<double>(uniform_matrix<long,4,4,1>())));
DLIB_TEST((muniform3 == matrix_cast<double>(uniform_matrix<long,4,4,3>())));
DLIB_TEST((muniform1*8 == matrix_cast<double>(uniform_matrix<long,4,4,8>())));

set_all_elements(m2,7);
DLIB_TEST(m2 == muniform1*7);
m2 = array;
DLIB_TEST(m2 == m1);

const double m1inv[] = {
-0.00946427624, 0.0593272941,  0.00970564379,  -0.00973323731,
0.0249312057,   -0.0590122427, -0.00583102756, 0.00616002729,
-0.00575431149, 0.110081189,   -0.00806792253, 0.00462297692,
0.00327847478,  -0.0597669712, 0.00317386196,  0.00990759201
};

m2 = m1inv;
DLIB_TEST((round(m2*m1) == identity_matrix<double,4>()));
DLIB_TEST((round(tmp(m2*m1)) == identity_matrix<double,4>()));

DLIB_TEST_MSG(round(m2*10000) == round(inv(m1)*10000),
round(m2*10000) - round(inv(m1)*10000)
<< "\n\n" << round(m2*10000)
<< "\n\n" << round(inv(m1)*10000)
<< "\n\n" << m2
<< "\n\n" << inv(m1)
);
DLIB_TEST(m1 == abs(-1*m1));
DLIB_TEST(abs(m2) == abs(-1*m2));

DLIB_TEST_MSG(floor(det(m1)+0.01) == 3297875,"\nm1: \n" << m1 << "\ndet(m1): " << det(m1));

ostringstream sout;
m1 = m2;
serialize(m1,sout);
set_all_elements(m1,0);
istringstream sin(sout.str());
deserialize(m1,sin);
DLIB_TEST_MSG(round(100000*m1) == round(100000*m2),"m1: \n" << m1 << endl << "m2: \n" << m2);

set_all_elements(v,2);
v2 =  pointwise_multiply(v, v*2);
set_all_elements(v,8);
DLIB_TEST(v == v2);
DLIB_TEST(v == tmp(v2));
DLIB_TEST((v == rotate<2,0>(v)));

m4 = array2;
m5 = array2_r;
DLIB_TEST((m5 == rotate<1,1>(m4)));

m5 = array2;
DLIB_TEST((m5*2 == pointwise_multiply(m5,uniform_matrix<int,3,3,2>())));
DLIB_TEST((tmp(m5*2) == tmp(pointwise_multiply(m5,uniform_matrix<int,3,3,2>()))));

v = tmp(v);

matrix<double> dm10(10,5);
DLIB_TEST(dm10.nr() == 10);
DLIB_TEST(dm10.nc() == 5);
set_all_elements(dm10,4);
DLIB_TEST(dm10.nr() == 10);
DLIB_TEST(dm10.nc() == 5);
matrix<double,10,5> m10;
DLIB_TEST(m10.nr() == 10);
DLIB_TEST(m10.nc() == 5);
set_all_elements(m10,4);
DLIB_TEST(dm10 == m10);
DLIB_TEST((clamp<0,3>(dm10) == clamp<0,3>(m10)));
DLIB_TEST((clamp<0,3>(dm10)(0,2) == 3));

set_all_elements(dm10,1);
set_all_elements(m10,4);
DLIB_TEST(4*dm10 == m10);
DLIB_TEST(5*dm10 - dm10 == m10);
DLIB_TEST((16*dm10)/4 == m10);
DLIB_TEST(dm10+dm10+2*dm10 == m10);
DLIB_TEST(dm10+tmp(dm10+2*dm10) == m10);
set_all_elements(dm10,4);
DLIB_TEST(dm10 == m10);
DLIB_TEST_MSG(sum(abs(sigmoid(dm10) -sigmoid(m10))) < 1e-10,sum(abs(sigmoid(dm10) -sigmoid(m10))) );

{
matrix<double,2,1> x, l, u, out;
x = 3,4;

l = 1,1;
u = 2,2.2;

out = 2, 2.2;
DLIB_TEST(equal(dlib::clamp(x, l, u) , out));
out = 3, 2.2;
DLIB_TEST(!equal(dlib::clamp(x, l, u) , out));
out = 2, 4.2;
DLIB_TEST(!equal(dlib::clamp(x, l, u) , out));

x = 1.5, 1.5;
out = x;
DLIB_TEST(equal(dlib::clamp(x, l, u) , out));

x = 0.5, 1.5;
out = 1, 1.5;
DLIB_TEST(equal(dlib::clamp(x, l, u) , out));

x = 1.5, 0.5;
out = 1.5, 1.0;
DLIB_TEST(equal(dlib::clamp(x, l, u) , out));

}

matrix<double, 7, 7,MM,column_major_layout> m7;
matrix<double> dm7(7,7);
dm7 = randm(7,7, rnd);
m7 = dm7;

DLIB_TEST_MSG(max(abs(dm7*inv(dm7) - identity_matrix<double>(7))) < 1e-12, max(abs(dm7*inv(dm7) - identity_matrix<double>(7))));
DLIB_TEST(equal(inv(dm7),  inv(m7)));
DLIB_TEST(abs(det(dm7) - det(m7)) < 1e-14);
DLIB_TEST(abs(min(dm7) - min(m7)) < 1e-14);
DLIB_TEST(abs(max(dm7) - max(m7)) < 1e-14);
DLIB_TEST_MSG(abs(sum(dm7) - sum(m7)) < 1e-13,sum(dm7) - sum(m7));
DLIB_TEST(abs(prod(dm7) -prod(m7)) < 1e-14);
DLIB_TEST(equal(diag(dm7) , diag(m7)));
DLIB_TEST(equal(trans(dm7) , trans(m7)));
DLIB_TEST(equal(abs(dm7) , abs(m7)));
DLIB_TEST(equal(round(dm7) , round(m7)));
DLIB_TEST(matrix_cast<int>(dm7) == matrix_cast<int>(m7));
DLIB_TEST((rotate<2,3>(dm7) == rotate<2,3>(m7)));
DLIB_TEST((sum(pointwise_multiply(dm7,dm7) - pointwise_multiply(m7,m7))) < 1e-10);
DLIB_TEST((sum(pointwise_multiply(dm7,dm7,dm7) - pointwise_multiply(m7,m7,m7))) < 1e-10);
DLIB_TEST_MSG((sum(pointwise_multiply(dm7,dm7,dm7,dm7) - pointwise_multiply(m7,m7,m7,m7))) < 1e-10,
(sum(pointwise_multiply(dm7,dm7,dm7,dm7) - pointwise_multiply(m7,m7,m7,m7)))
);

matrix<double> temp(5,5);
matrix<double> dsm(5,5);
matrix<double,5,5,MM> sm;

set_all_elements(dsm,1);
set_all_elements(sm,1);
set_all_elements(temp,1);

dsm += dsm;
sm += sm;
DLIB_TEST(dsm == 2*temp);
DLIB_TEST(sm == 2*temp);
temp = dsm*sm + dsm;
dsm += dsm*sm;
DLIB_TEST_MSG(temp == dsm,temp - dsm);

set_all_elements(dsm,1);
set_all_elements(sm,1);
set_all_elements(temp,1);

dsm += dsm;
sm += sm;
DLIB_TEST(dsm == 2*temp);
DLIB_TEST(sm == 2*temp);
temp = dsm*sm + dsm;
sm += dsm*sm;
DLIB_TEST_MSG(temp == sm,temp - sm);

set_all_elements(dsm,1);
set_all_elements(sm,1);
set_all_elements(temp,1);

dsm += dsm;
sm += sm;
DLIB_TEST(dsm == 2*temp);
DLIB_TEST(sm == 2*temp);
temp = sm - dsm*sm ;
sm -= dsm*sm;
DLIB_TEST_MSG(temp == sm,temp - sm);

set_all_elements(dsm,1);
set_all_elements(sm,1);
set_all_elements(temp,1);

dsm += dsm;
sm += sm;
DLIB_TEST(dsm == 2*temp);
DLIB_TEST(sm == 2*temp);
temp = dsm - dsm*sm ;
dsm -= dsm*sm;
DLIB_TEST_MSG(temp == dsm,temp - dsm);

set_all_elements(dsm,1);
set_all_elements(sm,1);
set_all_elements(temp,2);

dsm *= 2;
sm *= 2;
DLIB_TEST(dsm == temp);
DLIB_TEST(sm == temp);
dsm /= 2;
sm /= 2;
DLIB_TEST(dsm == temp/2);
DLIB_TEST(sm == temp/2);

dsm += dsm;
sm += sm;
DLIB_TEST(dsm == temp);
DLIB_TEST(sm == temp);
dsm += sm;
sm += dsm;
DLIB_TEST(dsm == 2*temp);
DLIB_TEST(sm == temp*3);
dsm -= sm;
sm -= dsm;
DLIB_TEST(dsm == -temp);
DLIB_TEST(sm == 4*temp);
sm -= sm;
dsm -= dsm;
DLIB_TEST(dsm == 0*temp);
DLIB_TEST(sm == 0*temp);

set_all_elements(dsm,1);
set_all_elements(sm,1);
set_all_elements(temp,3);
dsm += sm+sm;
DLIB_TEST(dsm == temp);

set_all_elements(dsm,1);
set_all_elements(sm,1);
set_all_elements(temp,-1);
dsm -= sm+sm;
DLIB_TEST(dsm == temp);

set_all_elements(dsm,1);
set_all_elements(sm,1);
set_all_elements(temp,-1);
sm -= dsm+dsm;
DLIB_TEST(sm == temp);

set_all_elements(dsm,1);
set_all_elements(sm,1);
set_all_elements(temp,3);
sm += dsm+dsm;
DLIB_TEST(sm == temp);

// test the implicit conversion to bool stuff
{
matrix<float> bt1(3,1);
matrix<float,3,1> bt2;
set_all_elements(bt1,2);
set_all_elements(bt2,3);

float val = trans(bt1)*bt2;
DLIB_TEST((float)(trans(bt1)*bt2) == 18);
DLIB_TEST((float)(trans(bt1)*bt2) != 19);
DLIB_TEST(val == 18);
}
{
matrix<float,3,1> bt1;
matrix<float> bt2(3,1);
set_all_elements(bt1,2);
set_all_elements(bt2,3);

float val = trans(bt1)*bt2;
DLIB_TEST((float)(trans(bt1)*bt2) == 18);
DLIB_TEST((float)(trans(bt1)*bt2) != 19);
DLIB_TEST(val == 18);
}
{
matrix<float> bt1(3,1);
matrix<float> bt2(3,1);
set_all_elements(bt1,2);
set_all_elements(bt2,3);

float val = trans(bt1)*bt2;
DLIB_TEST((float)(trans(bt1)*bt2) == 18);
DLIB_TEST((float)(trans(bt1)*bt2) != 19);
DLIB_TEST(val == 18);
}
{
matrix<float,3,1> bt1;
matrix<float,3,1> bt2;
set_all_elements(bt1,2);
set_all_elements(bt2,3);

float val = trans(bt1)*bt2;
DLIB_TEST((float)(trans(bt1)*bt2) == 18);
DLIB_TEST((float)(trans(bt1)*bt2) != 19);
DLIB_TEST(val == 18);
}

{
srand(423452);
const long M = 50;
const long N = 40;

matrix<double> a(M,N);
for (long r = 0; r < a.nr(); ++r)
{
for (long c = 0; c < a.nc(); ++c)
{
a(r,c) = 10*((double)::rand())/RAND_MAX;
}
}

matrix<double> u, u2;
matrix<double> q, q2;
matrix<double> v, v2;

matrix<double> a2;
a2 = tmp(a/2);

svd2(true,true,a2+a2,u,q,v);

double err = max(abs(a - subm(u,get_rect(a2+a2))*diagm(q)*trans(v)));
DLIB_TEST_MSG( err < 1e-11,"err: " << err);
using dlib::equal;
DLIB_TEST((equal(trans(u)*u , identity_matrix<double,M>(), 1e-10)));
DLIB_TEST((equal(trans(v)*v , identity_matrix<double,N>(), 1e-10)));

svd2(false,true,a2+a2,u,q,v2);
svd2(true,false,a2+a2,u2,q,v);
svd2(false,false,a2+a2,u,q2,v);

err = max(abs(a - subm(u2,get_rect(a2+a2))*diagm(q2)*trans(v2)));
DLIB_TEST_MSG( err < 1e-11,"err: " << err);
DLIB_TEST((equal(trans(u2)*u2 , identity_matrix<double,M>(), 1e-10)));
DLIB_TEST((equal(trans(v2)*v2 , identity_matrix<double,N>(), 1e-10)));

}

{
srand(423452);
const long M = 3;
const long N = 3;

matrix<double> a(M,N);
for (long r = 0; r < a.nr(); ++r)
{
for (long c = 0; c < a.nc(); ++c)
{
a(r,c) = 10*((double)::rand())/RAND_MAX;
}
}

matrix<double,M,M> u, u2;
matrix<double> q, q2;
matrix<double,N,N> v, v2;

matrix<double,M,N,MM> a2;
a2 = tmp(a/2);

svd2(true,true,a2+a2,u,q,v);

double err = max(abs(a - subm(u,get_rect(a2+a2))*diagm(q)*trans(v)));
DLIB_TEST_MSG( err < 1e-11,"err: " << err);
using dlib::equal;
DLIB_TEST((equal(trans(u)*u , identity_matrix<double,M>(), 1e-10)));
DLIB_TEST((equal(trans(v)*v , identity_matrix<double,N>(), 1e-10)));

svd2(false,true,a2+a2,u,q,v2);
svd2(true,false,a2+a2,u2,q,v);
svd2(false,false,a2+a2,u,q2,v);

err = max(abs(a - subm(u2,get_rect(a2+a2))*diagm(q2)*trans(v2)));
DLIB_TEST_MSG( err < 1e-11,"err: " << err);
DLIB_TEST((equal(trans(u2)*u2 , identity_matrix<double,M>(), 1e-10)));
DLIB_TEST((equal(trans(v2)*v2 , identity_matrix<double,N>(), 1e-10)));

}

{
srand(423452);
const long M = 3;
const long N = 3;

matrix<double,0,0,default_memory_manager, column_major_layout> a(M,N);
for (long r = 0; r < a.nr(); ++r)
{
for (long c = 0; c < a.nc(); ++c)
{
a(r,c) = 10*((double)::rand())/RAND_MAX;
}
}

matrix<double,M,M,default_memory_manager, column_major_layout> u, u2;
matrix<double,0,0,default_memory_manager, column_major_layout> q, q2;
matrix<double,N,N,default_memory_manager, column_major_layout> v, v2;

matrix<double,M,N,MM, column_major_layout> a2;
a2 = tmp(a/2);

svd2(true,true,a2+a2,u,q,v);

double err = max(abs(a - subm(u,get_rect(a2+a2))*diagm(q)*trans(v)));
DLIB_TEST_MSG( err < 1e-11,"err: " << err);
using dlib::equal;
DLIB_TEST((equal(trans(u)*u , identity_matrix<double,M>(), 1e-10)));
DLIB_TEST((equal(trans(v)*v , identity_matrix<double,N>(), 1e-10)));

svd2(false,true,a2+a2,u,q,v2);
svd2(true,false,a2+a2,u2,q,v);
svd2(false,false,a2+a2,u,q2,v);

err = max(abs(a - subm(u2,get_rect(a2+a2))*diagm(q2)*trans(v2)));
DLIB_TEST_MSG( err < 1e-11,"err: " << err);
DLIB_TEST((equal(trans(u2)*u2 , identity_matrix<double,M>(), 1e-10)));
DLIB_TEST((equal(trans(v2)*v2 , identity_matrix<double,N>(), 1e-10)));

}

{
srand(423452);
const long M = 10;
const long N = 7;

matrix<double> a(M,N);
for (long r = 0; r < a.nr(); ++r)
{
for (long c = 0; c < a.nc(); ++c)
{
a(r,c) = 10*((double)::rand())/RAND_MAX;
}
}

matrix<double,M,M> u;
matrix<double> q;
matrix<double,N,N> v;

matrix<double,M,N,MM> a2;
a2 = tmp(a/2);

svd2(true,true,a2+a2,u,q,v);

double err = sum(round(1e10*(a - subm(u,get_rect(a2+a2))*diagm(q)*trans(v))));
DLIB_TEST_MSG(  err == 0,"err: " << err);
DLIB_TEST((round(1e10*trans(u)*u)  == 1e10*identity_matrix<double,M>()));
DLIB_TEST((round(1e10*trans(v)*v)  == 1e10*identity_matrix<double,N>()));
}

}

void matrix_test2 (
)
{
typedef memory_manager_stateless<char>::kernel_2_2a MM;
{
srand(423452);
const long M = 10;
const long N = 7;

matrix<double> a(M,N);
for (long r = 0; r < a.nr(); ++r)
{
for (long c = 0; c < a.nc(); ++c)
{
a(r,c) = 10*((double)::rand())/RAND_MAX;
}
}

matrix<double,M> u(M,N);
matrix<double> w;
matrix<double,N,N> v(N,N);

matrix<double,M,N,MM> a2;
a2 = tmp(a/2);

svd(a2+a2,u,w,v);

DLIB_TEST(  sum(round(1e10*(a - u*w*trans(v)))) == 0);
DLIB_TEST((round(1e10*trans(u)*u)  == 1e10*identity_matrix<double,N>()));
DLIB_TEST((round(1e10*trans(v)*v)  == 1e10*identity_matrix<double,N>()));
}

{
srand(423452);
const long M = 1;
const long N = 1;

matrix<double> a(M,N);
for (long r = 0; r < a.nr(); ++r)
{
for (long c = 0; c < a.nc(); ++c)
{
a(r,c) = 10*((double)::rand())/RAND_MAX;
}
}

matrix<double,M,N> u;
matrix<double> w;
matrix<double,N,N> v;

matrix<double,M,N> a2;
a2 = 0;
a2 = tmp(a/2);

svd(a2+a2,u,w,v);

DLIB_TEST(  sum(round(1e10*(a - u*w*trans(v)))) == 0);
DLIB_TEST((round(1e10*trans(u)*u)  == 1e10*identity_matrix<double,N>()));
DLIB_TEST((round(1e10*trans(v)*v)  == 1e10*identity_matrix<double,N>()));
}

{
srand(53434);
const long M = 5;
const long N = 5;

matrix<double> a(M,N);
for (long r = 0; r < a.nr(); ++r)
{
for (long c = 0; c < a.nc(); ++c)
{
a(r,c) = 10*((double)::rand())/RAND_MAX;
}
}

matrix<double,0,N> u(M,N);
matrix<double,N,N> w;
matrix<double> v;

svd(a,u,w,v);

DLIB_TEST(  sum(round(1e10*(a - u*w*trans(v)))) == 0);
DLIB_TEST((round(1e10*trans(u)*u)  == 1e10*identity_matrix<double,N>()));
DLIB_TEST((round(1e10*trans(v)*v)  == 1e10*identity_matrix<double,N>()));
}

{
srand(11234);
const long M = 9;
const long N = 4;

matrix<double,0,0,MM> a(M,N);
for (long r = 0; r < a.nr(); ++r)
{
for (long c = 0; c < a.nc(); ++c)
{
a(r,c) = 10*((double)::rand())/RAND_MAX;
}
}

matrix<double> u;
matrix<double,0,0,MM> w;
matrix<double> v;

svd(a,u,w,v);

DLIB_TEST(  sum(round(1e10*(a - u*w*trans(v)))) == 0);
DLIB_TEST((round(1e10*trans(u)*u)  == 1e10*identity_matrix<double,N>()));
DLIB_TEST((round(1e10*trans(v)*v)  == 1e10*identity_matrix<double,N>()));
}

{
srand(53934);
const long M = 2;
const long N = 4;

matrix<double> a(M,N);
for (long r = 0; r < a.nr(); ++r)
{
for (long c = 0; c < a.nc(); ++c)
{
a(r,c) = 10*((double)::rand())/RAND_MAX;
}
}

matrix<double> u;
matrix<double> w;
matrix<double> v;

svd(a,u,w,v);

DLIB_TEST(  sum(round(1e10*(a - u*w*trans(v)))) == 0);
}

{
srand(53234);
const long M = 9;
const long N = 40;

matrix<double> a(M,N);
for (long r = 0; r < a.nr(); ++r)
{
for (long c = 0; c < a.nc(); ++c)
{
a(r,c) = 10*((double)::rand())/RAND_MAX;
}
}

matrix<double> u;
matrix<double> w;
matrix<double> v;

svd(a,u,w,v);

DLIB_TEST(  sum(round(1e10*(a - u*w*trans(v)))) == 0);
}

{
srand(53234);
const long M = 9;
const long N = 40;

typedef matrix<double,0,0,default_memory_manager, column_major_layout> mat;
mat a(M,N);
for (long r = 0; r < a.nr(); ++r)
{
for (long c = 0; c < a.nc(); ++c)
{
a(r,c) = 10*((double)::rand())/RAND_MAX;
}
}

mat u;
mat w;
mat v;

svd(a,u,w,v);

DLIB_TEST(  sum(round(1e10*(a - u*w*trans(v)))) == 0);
}

{
matrix<double> a(3,3);
matrix<double,3,3> b;
set_all_elements(a,0);

a(0,0) = 1;
a(1,1) = 2;
a(2,2) = 3;
b = a;

DLIB_TEST(diag(a)(0) == 1);
DLIB_TEST(diag(a)(1) == 2);
DLIB_TEST(diag(a)(2) == 3);
DLIB_TEST(diag(a).nr() == 3);
DLIB_TEST(diag(a).nc() == 1);

DLIB_TEST(diag(b)(0) == 1);
DLIB_TEST(diag(b)(1) == 2);
DLIB_TEST(diag(b)(2) == 3);
DLIB_TEST(diag(b).nr() == 3);
DLIB_TEST(diag(b).nc() == 1);

DLIB_TEST(pointwise_multiply(a,b)(0,0) == 1);
DLIB_TEST(pointwise_multiply(a,b)(1,1) == 4);
DLIB_TEST(pointwise_multiply(a,b)(2,2) == 9);
DLIB_TEST(pointwise_multiply(a,b)(1,0) == 0);
DLIB_TEST(pointwise_multiply(a,b,a)(1,0) == 0);
DLIB_TEST(pointwise_multiply(a,b,a,b)(1,0) == 0);

DLIB_TEST(complex_matrix(a,b)(0,0) == std::complex<double>(1,1));
DLIB_TEST(complex_matrix(a,b)(2,2) == std::complex<double>(3,3));
DLIB_TEST(complex_matrix(a,b)(2,1) == std::complex<double>(0,0));
}

{
matrix<complex<double> > m(2,2), m2(2,2);
complex<double> val1(1,2), val2(1.0/complex<double>(1,2));
m = val1;
m2 = val2;

DLIB_TEST(equal(reciprocal(m) , m2));
}
{
matrix<complex<float> > m(2,2), m2(2,2);
complex<float> val1(1,2), val2(1.0f/complex<float>(1,2));
m = val1;
m2 = val2;

DLIB_TEST(equal(reciprocal(m) , m2));
}

{
matrix<float,3,1> m1, m2;
set_all_elements(m1,2.0);
set_all_elements(m2,1.0/2.0);
DLIB_TEST(reciprocal(m1) == m2);
DLIB_TEST((reciprocal(uniform_matrix<float,3,1>(2.0)) == m2));
DLIB_TEST((round_zeros(uniform_matrix<float,3,1>(1e-8f)) == uniform_matrix<float,3,1>(0)) );
set_all_elements(m1,2.0);
m2 = m1;
m1(1,0) = static_cast<float>(1e-8);
m2(1,0) = 0;
DLIB_TEST(round_zeros(m1) == m2);
m1 = round_zeros(m1);
DLIB_TEST(m1 == m2);
}

{
matrix<matrix<double,2,2> > m;
m.set_size(3,3);
set_all_elements(m,uniform_matrix<double,2,2>(1));
DLIB_TEST((sum(m) == uniform_matrix<double,2,2>(9)));
DLIB_TEST((round_zeros(sqrt(sum(m)) - uniform_matrix<double,2,2>(3)) == uniform_matrix<double,2,2>(0)));
}

{
matrix<int,2,2> m1;
matrix<int> m2;
m2.set_size(2,2);

set_all_elements(m1,2);
m2 = uniform_matrix<int,2,2>(2);

m1 = m1 + m2;
DLIB_TEST((m1 == uniform_matrix<int,2,2>(4)));

set_all_elements(m1,2);
set_all_elements(m2,2);
m1 = m1*m1;
DLIB_TEST((m1 == uniform_matrix<int,2,2>(8)));

m1(1,0) = 1;
set_all_elements(m2,8);
m2(0,1) = 1;
m1 = trans(m1);
DLIB_TEST(m1 == m2);
}

{
matrix<double,2,3> m;
matrix<double> m2(2,3);

set_all_elements(m,1);
DLIB_TEST(mean(m) == 1);
set_all_elements(m,2);
DLIB_TEST(mean(m) == 2);
m(0,0) = 1;
m(0,1) = 1;
m(0,2) = 1;
DLIB_TEST(abs(mean(m) - 1.5) < 1e-10);
DLIB_TEST(abs(variance(m) - 0.3) < 1e-10);

set_all_elements(m2,1);
DLIB_TEST(mean(m2) == 1);
set_all_elements(m2,2);
DLIB_TEST(mean(m2) == 2);
m2(0,0) = 1;
m2(0,1) = 1;
m2(0,2) = 1;
DLIB_TEST(abs(mean(m2) - 1.5) < 1e-10);
DLIB_TEST(abs(variance(m2) - 0.3) < 1e-10);

set_all_elements(m,0);
DLIB_TEST(abs(variance(m)) < 1e-10);
set_all_elements(m,1);
DLIB_TEST(abs(variance(m)) < 1e-10);
set_all_elements(m,23.4);
DLIB_TEST(abs(variance(m)) < 1e-10);
}

{
matrix<matrix<double,3,1,MM>,2,2,MM> m;
set_all_elements(m,uniform_matrix<double,3,1>(1));
DLIB_TEST((round_zeros(variance(m)) == uniform_matrix<double,3,1>(0)));
DLIB_TEST((round_zeros(mean(m)) == uniform_matrix<double,3,1>(1)));
m(0,0) = uniform_matrix<double,3,1>(9);
DLIB_TEST((round_zeros(variance(m)) == uniform_matrix<double,3,1>(16)));
DLIB_TEST((round_zeros(mean(m)) == uniform_matrix<double,3,1>(3)));

matrix<matrix<double> > m2(2,2);
set_all_elements(m2,uniform_matrix<double,3,1>(1));
DLIB_TEST((round_zeros(variance(m2)) == uniform_matrix<double,3,1>(0)));
DLIB_TEST((round_zeros(mean(m2)) == uniform_matrix<double,3,1>(1)));
m2(0,0) = uniform_matrix<double,3,1>(9);
DLIB_TEST((round_zeros(variance(m2)) == uniform_matrix<double,3,1>(16)));
DLIB_TEST((round_zeros(mean(m2)) == uniform_matrix<double,3,1>(3)));
}

{
matrix<double> m(4,4), m2;
m = 1,2,3,4,
1,2,3,4,
4,6,8,10,
4,6,8,10;
m2 = m;

DLIB_TEST(colm(m,range(0,3)) == m);
DLIB_TEST(rowm(m,range(0,3)) == m);
DLIB_TEST(colm(m,range(0,0)) == colm(m,0));
DLIB_TEST(rowm(m,range(0,0)) == rowm(m,0));
DLIB_TEST(colm(m,range(1,1)) == colm(m,1));
DLIB_TEST(rowm(m,range(1,1)) == rowm(m,1));

DLIB_TEST(colm(m,range(2,2)) == colm(m,2));
DLIB_TEST(rowm(m,range(2,2)) == rowm(m,2));

DLIB_TEST(colm(m,range(1,2)) == subm(m,0,1,4,2));
DLIB_TEST(rowm(m,range(1,2)) == subm(m,1,0,2,4));

set_colm(m,range(1,2)) = 9;
set_subm(m2,0,1,4,2) = 9;
DLIB_TEST(m == m2);

set_colm(m,range(1,2)) = 11;
set_subm(m2,0,1,4,2) = 11;
DLIB_TEST(m == m2);
}

{
print_spinner();
matrix<double,1,1> m1;
matrix<double,2,2> m2;
matrix<double,3,3> m3;
matrix<double,4,4> m4;

dlib::rand rnd;
for (int i = 0; i < 50; ++i)
{
m1 = randm(1,1,rnd);
m2 = randm(2,2,rnd);
m3 = randm(3,3,rnd);
m4 = randm(4,4,rnd);

DLIB_TEST(max(abs(m1*inv(m1) - identity_matrix(m1))) < 1e-13);
DLIB_TEST(max(abs(m2*inv(m2) - identity_matrix(m2))) < 1e-12);
DLIB_TEST(max(abs(m3*inv(m3) - identity_matrix(m3))) < 1e-13);
DLIB_TEST_MSG(max(abs(m4*inv(m4) - identity_matrix(m4))) < 1e-12, max(abs(m4*inv(m4) - identity_matrix(m4))));
}
}

}

class matrix_tester : public tester
{
public:
matrix_tester (
) :
tester ("test_matrix2",
"Runs tests on the matrix component.")
{}

void perform_test (
)
{
matrix_test1();
matrix_test2();
}
} a;

}

```