```// Copyright (C) 2013  Davis E. King (davis@dlib.net)

#include <dlib/statistics.h>
#include <dlib/sparse_vector.h>
#include <dlib/timing.h>
#include <map>

#include "tester.h"

namespace
{
using namespace test;
using namespace dlib;
using namespace std;

logger dlog("test.cca");

dlib::rand rnd;
// ----------------------------------------------------------------------------------------

/*
std::vector<std::map<unsigned long, double> > make_really_big_test_matrix (
)
{
std::vector<std::map<unsigned long,double> > temp(30000);
for (unsigned long i = 0; i < temp.size(); ++i)
{
for (int k = 0; k < 30; ++k)
temp[i][rnd.get_random_32bit_number()%10000] = 1;
}
return temp;
}
*/

template <typename T>
std::vector<std::map<unsigned long, T> > mat_to_sparse (
const matrix<T>& A
)
{
std::vector<std::map<unsigned long,T> > temp(A.nr());
for (long r = 0; r < A.nr(); ++r)
{
for (long c = 0; c < A.nc(); ++c)
{
temp[r][c] = A(r,c);
}
}
return temp;
}

// ----------------------------------------------------------------------------------------

template <typename EXP>
matrix<typename EXP::type> rm_zeros (
const matrix_exp<EXP>& m
)
{
// Do this to avoid trying to correlate super small numbers that are really just
// zero.  Doing this avoids some potential false alarms in the unit tests below.
return round_zeros(m, max(abs(m))*1e-14);
}

// ----------------------------------------------------------------------------------------

/*
void check_correlation (
matrix<double> L,
matrix<double> R,
const matrix<double>& Ltrans,
const matrix<double>& Rtrans,
const matrix<double,0,1>& correlations
)
{
// apply the transforms
L = L*Ltrans;
R = R*Rtrans;

// compute the real correlation values. Store them in A.
matrix<double> A = compute_correlations(L, R);

for (long i = 0; i < correlations.size(); ++i)
{
// compare what the measured correlation values are (in A) to the
// predicted values.
cout << "error: "<< A(i) - correlations(i);
}
}
*/

// ----------------------------------------------------------------------------------------

void test_cca3()
{
print_spinner();
const unsigned long rank = rnd.get_random_32bit_number()%10 + 1;
const unsigned long m = rank + rnd.get_random_32bit_number()%15;
const unsigned long n = rank + rnd.get_random_32bit_number()%15;
const unsigned long n2 = rank + rnd.get_random_32bit_number()%15;
const unsigned long rank2 = rank + rnd.get_random_32bit_number()%5;

dlog << LINFO << "m:  " << m;
dlog << LINFO << "n:  " << n;
dlog << LINFO << "n2: " << n2;
dlog << LINFO << "rank:  " << rank;
dlog << LINFO << "rank2: " << rank2;

matrix<double> L = randm(m,rank, rnd)*randm(rank,n, rnd);
//matrix<double> R = randm(m,rank, rnd)*randm(rank,n2, rnd);
matrix<double> R = L*randm(n,n2, rnd);
//matrix<double> L = randm(m,n, rnd);
//matrix<double> R = randm(m,n2, rnd);

matrix<double> Ltrans, Rtrans;
matrix<double,0,1> correlations;

{
correlations = cca(L, R, Ltrans, Rtrans, min(m,n), max(n,n2));
DLIB_TEST(Ltrans.nc() == Rtrans.nc());
dlog << LINFO << "correlations: "<< trans(correlations);

const double corr_error = max(abs(compute_correlations(rm_zeros(L*Ltrans), rm_zeros(R*Rtrans)) - correlations));
dlog << LINFO << "correlation error: "<< corr_error;
DLIB_TEST_MSG(corr_error < 1e-13, Ltrans << "\n\n" << Rtrans);

const double trans_error = max(abs(L*Ltrans - R*Rtrans));
dlog << LINFO << "trans_error: "<< trans_error;
DLIB_TEST_MSG(trans_error < 1e-9, trans_error);
}
{
correlations = cca(mat_to_sparse(L), mat_to_sparse(R), Ltrans, Rtrans, min(m,n), max(n,n2)+6, 4);
DLIB_TEST(Ltrans.nc() == Rtrans.nc());
dlog << LINFO << "correlations: "<< trans(correlations);
dlog << LINFO << "computed cors: " << trans(compute_correlations(rm_zeros(L*Ltrans), rm_zeros(R*Rtrans)));

const double trans_error = max(abs(L*Ltrans - R*Rtrans));
dlog << LINFO << "trans_error: "<< trans_error;
const double corr_error = max(abs(compute_correlations(rm_zeros(L*Ltrans), rm_zeros(R*Rtrans)) - correlations));
dlog << LINFO << "correlation error: "<< corr_error;
DLIB_TEST_MSG(corr_error < 1e-13, Ltrans << "\n\n" << Rtrans);

DLIB_TEST(trans_error < 2e-9);
}

dlog << LINFO << "*****************************************************";
}

void test_cca2()
{
print_spinner();
const unsigned long rank = rnd.get_random_32bit_number()%10 + 1;
const unsigned long m = rank + rnd.get_random_32bit_number()%15;
const unsigned long n = rank + rnd.get_random_32bit_number()%15;
const unsigned long n2 = rank + rnd.get_random_32bit_number()%15;

dlog << LINFO << "m:  " << m;
dlog << LINFO << "n:  " << n;
dlog << LINFO << "n2: " << n2;
dlog << LINFO << "rank:  " << rank;

matrix<double> L = randm(m,n, rnd);
matrix<double> R = randm(m,n2, rnd);

matrix<double> Ltrans, Rtrans;
matrix<double,0,1> correlations;

{
correlations = cca(L, R, Ltrans, Rtrans, min(n,n2), max(n,n2)-min(n,n2));
DLIB_TEST(Ltrans.nc() == Rtrans.nc());
dlog << LINFO << "correlations: "<< trans(correlations);

if (Ltrans.nc() > 1)
{
// The CCA projection directions are supposed to be uncorrelated for
// non-matching pairs of projections.
const double corr_rot1_error = max(abs(compute_correlations(rm_zeros(L*rotate<0,1>(Ltrans)), rm_zeros(R*Rtrans))));
dlog << LINFO << "corr_rot1_error: "<< corr_rot1_error;
DLIB_TEST(std::abs(corr_rot1_error) < 1e-10);
}
// Matching projection directions should be correlated with the amount of
// correlation indicated by the return value of cca().
const double corr_error = max(abs(compute_correlations(rm_zeros(L*Ltrans), rm_zeros(R*Rtrans)) - correlations));
dlog << LINFO << "correlation error: "<< corr_error;
DLIB_TEST(corr_error < 1e-13);
}
{
correlations = cca(mat_to_sparse(L), mat_to_sparse(R), Ltrans, Rtrans, min(n,n2), max(n,n2)-min(n,n2));
DLIB_TEST(Ltrans.nc() == Rtrans.nc());
dlog << LINFO << "correlations: "<< trans(correlations);

if (Ltrans.nc() > 1)
{
// The CCA projection directions are supposed to be uncorrelated for
// non-matching pairs of projections.
const double corr_rot1_error = max(abs(compute_correlations(rm_zeros(L*rotate<0,1>(Ltrans)), rm_zeros(R*Rtrans))));
dlog << LINFO << "corr_rot1_error: "<< corr_rot1_error;
DLIB_TEST(std::abs(corr_rot1_error) < 1e-10);
}
// Matching projection directions should be correlated with the amount of
// correlation indicated by the return value of cca().
const double corr_error = max(abs(compute_correlations(rm_zeros(L*Ltrans), rm_zeros(R*Rtrans)) - correlations));
dlog << LINFO << "correlation error: "<< corr_error;
DLIB_TEST(corr_error < 1e-13);
}

dlog << LINFO << "*****************************************************";
}

void test_cca1()
{
print_spinner();
const unsigned long rank = rnd.get_random_32bit_number()%10 + 1;
const unsigned long m = rank + rnd.get_random_32bit_number()%15;
const unsigned long n = rank + rnd.get_random_32bit_number()%15;

dlog << LINFO << "m: " << m;
dlog << LINFO << "n: " << n;
dlog << LINFO << "rank: " << rank;

matrix<double> T = randm(n,n, rnd);

matrix<double> L = randm(m,rank, rnd)*randm(rank,n, rnd);
//matrix<double> L = randm(m,n, rnd);
matrix<double> R = L*T;

matrix<double> Ltrans, Rtrans;
matrix<double,0,1> correlations;

{
correlations = cca(L, R, Ltrans, Rtrans, rank);
DLIB_TEST(Ltrans.nc() == Rtrans.nc());
if (Ltrans.nc() > 1)
{
// The CCA projection directions are supposed to be uncorrelated for
// non-matching pairs of projections.
const double corr_rot1_error = max(abs(compute_correlations(rm_zeros(L*rotate<0,1>(Ltrans)), rm_zeros(R*Rtrans))));
dlog << LINFO << "corr_rot1_error: "<< corr_rot1_error;
DLIB_TEST(std::abs(corr_rot1_error) < 2e-9);
}
// Matching projection directions should be correlated with the amount of
// correlation indicated by the return value of cca().
const double corr_error = max(abs(compute_correlations(rm_zeros(L*Ltrans), rm_zeros(R*Rtrans)) - correlations));
dlog << LINFO << "correlation error: "<< corr_error;
DLIB_TEST(corr_error < 1e-13);

const double trans_error = max(abs(L*Ltrans - R*Rtrans));
dlog << LINFO << "trans_error: "<< trans_error;
DLIB_TEST(trans_error < 2e-9);

dlog << LINFO << "correlations: "<< trans(correlations);
}
{
correlations = cca(mat_to_sparse(L), mat_to_sparse(R), Ltrans, Rtrans, rank);
DLIB_TEST(Ltrans.nc() == Rtrans.nc());
if (Ltrans.nc() > 1)
{
// The CCA projection directions are supposed to be uncorrelated for
// non-matching pairs of projections.
const double corr_rot1_error = max(abs(compute_correlations(rm_zeros(L*rotate<0,1>(Ltrans)), rm_zeros(R*Rtrans))));
dlog << LINFO << "corr_rot1_error: "<< corr_rot1_error;
DLIB_TEST(std::abs(corr_rot1_error) < 2e-9);
}
// Matching projection directions should be correlated with the amount of
// correlation indicated by the return value of cca().
const double corr_error = max(abs(compute_correlations(rm_zeros(L*Ltrans), rm_zeros(R*Rtrans)) - correlations));
dlog << LINFO << "correlation error: "<< corr_error;
DLIB_TEST(corr_error < 1e-13);

const double trans_error = max(abs(L*Ltrans - R*Rtrans));
dlog << LINFO << "trans_error: "<< trans_error;
DLIB_TEST(trans_error < 2e-9);

dlog << LINFO << "correlations: "<< trans(correlations);
}

dlog << LINFO << "*****************************************************";
}

// ----------------------------------------------------------------------------------------

void test_svd_fast(
long rank,
long m,
long n
)
{
print_spinner();
matrix<double> A = randm(m,rank,rnd)*randm(rank,n,rnd);
matrix<double> u,v;
matrix<double,0,1> w;

dlog << LINFO << "rank: "<< rank;
dlog << LINFO << "m: "<< m;
dlog << LINFO << "n: "<< n;

svd_fast(A, u, w, v, rank, 2);
DLIB_TEST(u.nr() == m);
DLIB_TEST(u.nc() == rank);
DLIB_TEST(w.nr() == rank);
DLIB_TEST(w.nc() == 1);
DLIB_TEST(v.nr() == n);
DLIB_TEST(v.nc() == rank);
DLIB_TEST(max(abs(trans(u)*u - identity_matrix<double>(u.nc()))) < 1e-13);
DLIB_TEST(max(abs(trans(v)*v - identity_matrix<double>(u.nc()))) < 1e-13);

DLIB_TEST(max(abs(tmp(A - u*diagm(w)*trans(v)))) < 1e-13);
svd_fast(mat_to_sparse(A), u, w, v, rank, 2);
DLIB_TEST(u.nr() == m);
DLIB_TEST(u.nc() == rank);
DLIB_TEST(w.nr() == rank);
DLIB_TEST(w.nc() == 1);
DLIB_TEST(v.nr() == n);
DLIB_TEST(v.nc() == rank);
DLIB_TEST(max(abs(trans(u)*u - identity_matrix<double>(u.nc()))) < 1e-13);
DLIB_TEST(max(abs(trans(v)*v - identity_matrix<double>(u.nc()))) < 1e-13);
DLIB_TEST(max(abs(tmp(A - u*diagm(w)*trans(v)))) < 1e-13);

svd_fast(A, u, w, v, rank, 0);
DLIB_TEST(u.nr() == m);
DLIB_TEST(u.nc() == rank);
DLIB_TEST(w.nr() == rank);
DLIB_TEST(w.nc() == 1);
DLIB_TEST(v.nr() == n);
DLIB_TEST(v.nc() == rank);
DLIB_TEST(max(abs(trans(u)*u - identity_matrix<double>(u.nc()))) < 1e-13);
DLIB_TEST(max(abs(trans(v)*v - identity_matrix<double>(u.nc()))) < 1e-13);
DLIB_TEST_MSG(max(abs(tmp(A - u*diagm(w)*trans(v)))) < 1e-9,max(abs(tmp(A - u*diagm(w)*trans(v)))));
svd_fast(mat_to_sparse(A), u, w, v, rank, 0);
DLIB_TEST(u.nr() == m);
DLIB_TEST(u.nc() == rank);
DLIB_TEST(w.nr() == rank);
DLIB_TEST(w.nc() == 1);
DLIB_TEST(v.nr() == n);
DLIB_TEST(v.nc() == rank);
DLIB_TEST(max(abs(trans(u)*u - identity_matrix<double>(u.nc()))) < 1e-13);
DLIB_TEST(max(abs(trans(v)*v - identity_matrix<double>(u.nc()))) < 1e-13);
DLIB_TEST(max(abs(tmp(A - u*diagm(w)*trans(v)))) < 1e-10);

svd_fast(A, u, w, v, rank+5, 0);
DLIB_TEST(max(abs(trans(u)*u - identity_matrix<double>(u.nc()))) < 1e-13);
DLIB_TEST(max(abs(trans(v)*v - identity_matrix<double>(u.nc()))) < 1e-13);
DLIB_TEST(max(abs(tmp(A - u*diagm(w)*trans(v)))) < 1e-11);
svd_fast(mat_to_sparse(A), u, w, v, rank+5, 0);
DLIB_TEST(max(abs(trans(u)*u - identity_matrix<double>(u.nc()))) < 1e-13);
DLIB_TEST(max(abs(trans(v)*v - identity_matrix<double>(u.nc()))) < 1e-13);
DLIB_TEST(max(abs(tmp(A - u*diagm(w)*trans(v)))) < 1e-11);
svd_fast(A, u, w, v, rank+5, 1);
DLIB_TEST(max(abs(trans(u)*u - identity_matrix<double>(u.nc()))) < 1e-13);
DLIB_TEST(max(abs(trans(v)*v - identity_matrix<double>(u.nc()))) < 1e-13);
DLIB_TEST(max(abs(tmp(A - u*diagm(w)*trans(v)))) < 1e-12);
svd_fast(mat_to_sparse(A), u, w, v, rank+5, 1);
DLIB_TEST(max(abs(trans(u)*u - identity_matrix<double>(u.nc()))) < 1e-13);
DLIB_TEST(max(abs(trans(v)*v - identity_matrix<double>(u.nc()))) < 1e-13);
DLIB_TEST(max(abs(tmp(A - u*diagm(w)*trans(v)))) < 1e-12);
}

void test_svd_fast()
{
for (int iter = 0; iter < 1000; ++iter)
{
const unsigned long rank = rnd.get_random_32bit_number()%10 + 1;
const unsigned long m = rank + rnd.get_random_32bit_number()%10;
const unsigned long n = rank + rnd.get_random_32bit_number()%10;

test_svd_fast(rank, m, n);

}
test_svd_fast(1, 1, 1);
test_svd_fast(1, 2, 2);
test_svd_fast(1, 1, 2);
test_svd_fast(1, 2, 1);
}

// ----------------------------------------------------------------------------------------

/*
typedef std::vector<std::pair<unsigned int, float>> sv;
sv rand_sparse_vector()
{
static dlib::rand rnd;
sv v;
for (int i = 0; i < 50; ++i)
v.push_back(make_pair(rnd.get_integer(400000), rnd.get_random_gaussian()*100));

make_sparse_vector_inplace(v);
return v;
}

sv rand_basis_combo(const std::vector<sv>& basis)
{
static dlib::rand rnd;
sv result;

for (int i = 0; i < 5; ++i)
{
sv temp = basis[rnd.get_integer(basis.size())];
scale_by(temp, rnd.get_random_gaussian());
}
return result;
}

void big_sparse_speed_test()
{
cout << "making A" << endl;
std::vector<sv> basis;
for (int i = 0; i < 100; ++i)
basis.emplace_back(rand_sparse_vector());

std::vector<sv> A;
for (int i = 0; i < 500000; ++i)
A.emplace_back(rand_basis_combo(basis));

cout << "done making A" << endl;

matrix<float> u,v;
matrix<float,0,1> w;
{
timing::block aosijdf(0,"call it");
svd_fast(A, u,w,v, 100, 5);
}

timing::print();
}
*/

// ----------------------------------------------------------------------------------------

class test_cca : public tester
{
public:
test_cca (
) :
tester ("test_cca",
"Runs tests on the cca() and svd_fast() routines.")
{}

void perform_test (
)
{
//big_sparse_speed_test();
for (int i = 0; i < 200; ++i)
{
test_cca1();
test_cca2();
test_cca3();
}
test_svd_fast();
}
} a;

}

```