// 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.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(m4 == pointwise_divide(squared(m4),m4)); DLIB_TEST(m4 == pointwise_divide(cubed(m4),m4,m4)); DLIB_TEST(m4 == pointwise_divide(pointwise_multiply(cubed(m4),m4),m4,m4,m4)); DLIB_TEST(squared(m4) == pointwise_divide(cubed(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_divide(v*2,v); DLIB_TEST(v == v2); DLIB_TEST(v == tmp(v2)); 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>())))); DLIB_TEST((m5/2 == pointwise_divide(m5,uniform_matrix<int,3,3,2>()))); DLIB_TEST((tmp(m5/2) == tmp(pointwise_divide(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)); DLIB_TEST(equal(pointwise_multiply(m,m2),pointwise_divide(m,m))); } { 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)); DLIB_TEST(equal(pointwise_multiply(m,m2),pointwise_divide(m,m))); } { 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; }