dlib C++ Library - cca.cpp

// Copyright (C) 2013 Davis E. King (davis@dlib.net)
// License: Boost Software License See LICENSE.txt for the full license.
#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) < 1e-7);
 }
 // 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-11);
 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-9);
 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());
 result = add(result,temp);
 }
 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;
}