dlib C++ Library - matrix4.cpp

// Copyright (C) 2010 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.matrix4");
 void matrix_test (
 )
 /*!
 ensures
 - runs tests on the matrix stuff compliance with the specs
 !*/
 { 
 print_spinner();
 {
 matrix<double,3,3> m = round(10*randm(3,3));
 matrix<double,3,1> v = round(10*randm(3,1));
 DLIB_TEST(equal( m*diagm(v) , m*tmp(diagm(v)) ));
 DLIB_TEST(equal( scale_columns(m,v) , m*tmp(diagm(v)) ));
 DLIB_TEST(equal( diagm(v)*m , tmp(diagm(v))*m )); 
 DLIB_TEST(equal( scale_rows(m,v) , tmp(diagm(v))*m )); 
 }
 {
 matrix<double,3,3> m = round(10*randm(3,3));
 matrix<double,1,3> v = round(10*randm(1,3));
 DLIB_TEST(equal( m*diagm(v) , m*tmp(diagm(v)) ));
 DLIB_TEST(equal( scale_columns(m,v) , m*tmp(diagm(v)) ));
 DLIB_TEST(equal( diagm(v)*m , tmp(diagm(v))*m )); 
 DLIB_TEST(equal( scale_rows(m,v) , tmp(diagm(v))*m )); 
 }
 {
 matrix<double> m = round(10*randm(3,3));
 matrix<double,1,3> v = round(10*randm(1,3));
 DLIB_TEST(equal( m*diagm(v) , m*tmp(diagm(v)) ));
 DLIB_TEST(equal( scale_columns(m,v) , m*tmp(diagm(v)) ));
 DLIB_TEST(equal( diagm(v)*m , tmp(diagm(v))*m )); 
 DLIB_TEST(equal( scale_rows(m,v) , tmp(diagm(v))*m )); 
 }
 {
 matrix<double> m = round(10*randm(3,3));
 matrix<double,0,3> v = round(10*randm(1,3));
 DLIB_TEST(equal( m*diagm(v) , m*tmp(diagm(v)) ));
 DLIB_TEST(equal( scale_columns(m,v) , m*tmp(diagm(v)) ));
 DLIB_TEST(equal( diagm(v)*m , tmp(diagm(v))*m )); 
 DLIB_TEST(equal( scale_rows(m,v) , tmp(diagm(v))*m )); 
 }
 {
 matrix<double> m = round(10*randm(3,3));
 matrix<double,1,0> v = round(10*randm(1,3));
 DLIB_TEST(equal( m*diagm(v) , m*tmp(diagm(v)) ));
 DLIB_TEST(equal( scale_columns(m,v) , m*tmp(diagm(v)) ));
 DLIB_TEST(equal( diagm(v)*m , tmp(diagm(v))*m )); 
 DLIB_TEST(equal( scale_rows(m,v) , tmp(diagm(v))*m )); 
 }
 {
 matrix<double> m = round(10*randm(3,3));
 matrix<double,3,0> v = round(10*randm(3,1));
 DLIB_TEST(equal( m*diagm(v) , m*tmp(diagm(v)) ));
 DLIB_TEST(equal( scale_columns(m,v) , m*tmp(diagm(v)) ));
 DLIB_TEST(equal( diagm(v)*m , tmp(diagm(v))*m )); 
 DLIB_TEST(equal( scale_rows(m,v) , tmp(diagm(v))*m )); 
 }
 {
 matrix<double> m = round(10*randm(3,3));
 matrix<double,0,1> v = round(10*randm(3,1));
 DLIB_TEST(equal( m*diagm(v) , m*tmp(diagm(v)) ));
 DLIB_TEST(equal( scale_columns(m,v) , m*tmp(diagm(v)) ));
 DLIB_TEST(equal( diagm(v)*m , tmp(diagm(v))*m )); 
 DLIB_TEST(equal( scale_rows(m,v) , tmp(diagm(v))*m )); 
 }
 {
 matrix<double,3,3> m = round(10*randm(3,3));
 matrix<double,3,0> v = round(10*randm(3,1));
 DLIB_TEST(equal( m*diagm(v) , m*tmp(diagm(v)) ));
 DLIB_TEST(equal( scale_columns(m,v) , m*tmp(diagm(v)) ));
 DLIB_TEST(equal( diagm(v)*m , tmp(diagm(v))*m )); 
 DLIB_TEST(equal( scale_rows(m,v) , tmp(diagm(v))*m )); 
 }
 {
 matrix<double,3,3> m = round(10*randm(3,3));
 matrix<double,0,1> v = round(10*randm(3,1));
 DLIB_TEST(equal( m*diagm(v) , m*tmp(diagm(v)) ));
 DLIB_TEST(equal( scale_columns(m,v) , m*tmp(diagm(v)) ));
 DLIB_TEST(equal( diagm(v)*m , tmp(diagm(v))*m )); 
 DLIB_TEST(equal( scale_rows(m,v) , tmp(diagm(v))*m )); 
 }
 {
 matrix<double,3,5> m = round(10*randm(3,5));
 matrix<double,0,1> v1 = round(10*randm(5,1));
 matrix<double,0,1> v2 = round(10*randm(3,1));
 DLIB_TEST(equal( m*diagm(v1) , m*tmp(diagm(v1)) ));
 DLIB_TEST(equal( scale_columns(m,v1) , m*tmp(diagm(v1)) ));
 DLIB_TEST(equal( diagm(v2)*m , tmp(diagm(v2))*m )); 
 DLIB_TEST(equal( scale_rows(m,v2) , tmp(diagm(v2))*m )); 
 }
 {
 matrix<double,3,5> m = round(10*randm(3,5));
 matrix<double,5,1> v1 = round(10*randm(5,1));
 matrix<double,3,1> v2 = round(10*randm(3,1));
 DLIB_TEST(equal( m*diagm(v1) , m*tmp(diagm(v1)) ));
 DLIB_TEST(equal( scale_columns(m,v1) , m*tmp(diagm(v1)) ));
 DLIB_TEST(equal( diagm(v2)*m , tmp(diagm(v2))*m )); 
 DLIB_TEST(equal( scale_rows(m,v2) , tmp(diagm(v2))*m )); 
 }
 }
 void test_stuff()
 {
 print_spinner();
 {
 matrix<double> m(3,3), lr(3,3), ud(3,3);
 m = 1,2,3,
 4,5,6,
 7,8,9;
 lr = 3,2,1,
 6,5,4,
 9,8,7;
 ud = 7,8,9,
 4,5,6,
 1,2,3;
 DLIB_TEST(lr == fliplr(m));
 DLIB_TEST(ud == flipud(m));
 }
 {
 matrix<double> m(3,2), lr(3,2), ud(3,2);
 m = 1,2,
 3,4,
 5,6;
 lr = 2,1,
 4,3,
 6,5;
 ud = 5,6,
 3,4,
 1,2;
 DLIB_TEST(lr == fliplr(m));
 DLIB_TEST(ud == flipud(m));
 }
 {
 matrix<int> a, b;
 a = matrix_cast<int>(round(10*randm(3,3)));
 b = a;
 b *= b;
 DLIB_TEST(b == a*a);
 }
 {
 matrix<double> m(2,3), m2(2,3);
 m = 1,2,3,
 4,5,6;
 m2 = 3,4,5,
 6,7,8;
 DLIB_TEST(m + 2 == m2);
 DLIB_TEST(2 + m == m2);
 m += 2;
 DLIB_TEST(m == m2);
 m -= 2;
 m2 = 0,1,2,
 3,4,5;
 DLIB_TEST(m - 1 == m2);
 m -= 1;
 DLIB_TEST(m == m2);
 m += 1;
 m2 = 5,4,3,
 2,1,0;
 DLIB_TEST(6 - m == m2);
 }
 {
 matrix<float> m(2,3), m2(2,3);
 m = 1,2,3,
 4,5,6;
 m2 = 3,4,5,
 6,7,8;
 DLIB_TEST(m + 2 == m2);
 DLIB_TEST(2 + m == m2);
 m += 2;
 DLIB_TEST(m == m2);
 m -= 2;
 m2 = 0,1,2,
 3,4,5;
 DLIB_TEST(m - 1 == m2);
 m -= 1;
 DLIB_TEST(m == m2);
 m += 1;
 m2 = 5,4,3,
 2,1,0;
 DLIB_TEST(6 - m == m2);
 }
 {
 matrix<int> m(2,3), m2(2,3);
 m = 1,2,3,
 4,5,6;
 m2 = 3,4,5,
 6,7,8;
 DLIB_TEST(m + 2 == m2);
 DLIB_TEST(2 + m == m2);
 m += 2;
 DLIB_TEST(m == m2);
 m -= 2;
 m2 = 0,1,2,
 3,4,5;
 DLIB_TEST(m - 1 == m2);
 m -= 1;
 DLIB_TEST(m == m2);
 m += 1;
 m2 = 5,4,3,
 2,1,0;
 DLIB_TEST(6 - m == m2);
 }
 {
 matrix<int,2,3> m, m2;
 m = 1,2,3,
 4,5,6;
 m2 = 3,4,5,
 6,7,8;
 DLIB_TEST(m + 2 == m2);
 DLIB_TEST(2 + m == m2);
 m += 2;
 DLIB_TEST(m == m2);
 m -= 2;
 m2 = 0,1,2,
 3,4,5;
 DLIB_TEST(m - 1 == m2);
 m -= 1;
 DLIB_TEST(m == m2);
 m += 1;
 m2 = 5,4,3,
 2,1,0;
 DLIB_TEST(6 - m == m2);
 }
 {
 matrix<double> m(2,3), m2(3,2);
 m = 1,2,3,
 4,5,6;
 m2 = 2,5,
 3,6,
 4,7;
 DLIB_TEST(trans(m+1) == m2);
 DLIB_TEST(trans(m)+1 == m2);
 DLIB_TEST(1+trans(m) == m2);
 DLIB_TEST(1+m-1 == m);
 m = trans(m+1);
 DLIB_TEST(m == m2);
 m = trans(m-1);
 DLIB_TEST(trans(m+1) == m2);
 m = trans(m)+1;
 DLIB_TEST(m == m2);
 }
 {
 matrix<double> d(3,1), di(3,1);
 matrix<double> m(3,3);
 
 m = 1,2,3,
 4,5,6,
 7,8,9;
 d = 1,2,3;
 di = 1, 1/2.0, 1/3.0;
 DLIB_TEST(inv(diagm(d)) == diagm(di));
 DLIB_TEST(pinv(diagm(d)) == diagm(di));
 DLIB_TEST(inv(diagm(d))*m == tmp(diagm(di))*m);
 DLIB_TEST(m*inv(diagm(d)) == m*tmp(diagm(di)));
 DLIB_TEST(equal(inv(diagm(d)) + m , tmp(diagm(di)) + m));
 DLIB_TEST(equal(m + inv(diagm(d)) , tmp(diagm(di)) + m));
 DLIB_TEST((m + identity_matrix<double>(3) == m + tmp(identity_matrix<double>(3))));
 DLIB_TEST((m + identity_matrix<double,3>() == m + tmp(identity_matrix<double,3>())));
 DLIB_TEST((m + 2*identity_matrix<double>(3) == m + 2*tmp(identity_matrix<double>(3))));
 DLIB_TEST((m + 2*identity_matrix<double,3>() == m + 2*tmp(identity_matrix<double,3>())));
 DLIB_TEST((m + identity_matrix<double>(3)*2 == m + 2*tmp(identity_matrix<double>(3))));
 DLIB_TEST((m + identity_matrix<double,3>()*2 == m + 2*tmp(identity_matrix<double,3>())));
 DLIB_TEST((identity_matrix<double>(3) + m == m + tmp(identity_matrix<double>(3))));
 DLIB_TEST((identity_matrix<double,3>() + m == m + tmp(identity_matrix<double,3>())));
 DLIB_TEST((2*identity_matrix<double>(3) + m == m + 2*tmp(identity_matrix<double>(3))));
 DLIB_TEST((2*identity_matrix<double,3>() + m == m + 2*tmp(identity_matrix<double,3>())));
 }
 {
 matrix<double,3,1> d(3,1), di(3,1);
 matrix<double,3,3> m(3,3);
 
 m = 1,2,3,
 4,5,6,
 7,8,9;
 d = 1,2,3;
 di = 1, 1/2.0, 1/3.0;
 DLIB_TEST(equal(inv(diagm(d)) , diagm(di)));
 DLIB_TEST(equal(inv(diagm(d)) , diagm(di)));
 DLIB_TEST(equal(inv(diagm(d))*m , tmp(diagm(di))*m));
 DLIB_TEST(equal(m*inv(diagm(d)) , m*tmp(diagm(di))));
 DLIB_TEST_MSG(equal(inv(diagm(d)) + m , tmp(diagm(di)) + m), 
 (inv(diagm(d)) + m) - (tmp(diagm(di)) + m) );
 DLIB_TEST(equal(m + inv(diagm(d)) , tmp(diagm(di)) + m));
 DLIB_TEST((m + identity_matrix<double>(3) == m + tmp(identity_matrix<double>(3))));
 DLIB_TEST((m + identity_matrix<double,3>() == m + tmp(identity_matrix<double,3>())));
 DLIB_TEST((m + 2*identity_matrix<double>(3) == m + 2*tmp(identity_matrix<double>(3))));
 DLIB_TEST((m + 2*identity_matrix<double,3>() == m + 2*tmp(identity_matrix<double,3>())));
 DLIB_TEST((m + identity_matrix<double>(3)*2 == m + 2*tmp(identity_matrix<double>(3))));
 DLIB_TEST((m + identity_matrix<double,3>()*2 == m + 2*tmp(identity_matrix<double,3>())));
 DLIB_TEST((identity_matrix<double>(3) + m == m + tmp(identity_matrix<double>(3))));
 DLIB_TEST((identity_matrix<double,3>() + m == m + tmp(identity_matrix<double,3>())));
 DLIB_TEST((2*identity_matrix<double>(3) + m == m + 2*tmp(identity_matrix<double>(3))));
 DLIB_TEST((2*identity_matrix<double,3>() + m == m + 2*tmp(identity_matrix<double,3>())));
 }
 {
 matrix<double,1,3> d(1,3), di(1,3);
 matrix<double,3,3> m(3,3);
 
 m = 1,2,3,
 4,5,6,
 7,8,9;
 d = 1,2,3;
 di = 1, 1/2.0, 1/3.0;
 DLIB_TEST(equal(inv(diagm(d)) , diagm(di)));
 DLIB_TEST(equal(inv(diagm(d)) , diagm(di)));
 DLIB_TEST(equal(inv(diagm(d))*m , tmp(diagm(di))*m));
 DLIB_TEST(equal(m*inv(diagm(d)) , m*tmp(diagm(di))));
 DLIB_TEST(equal(inv(diagm(d)) + m , tmp(diagm(di)) + m));
 DLIB_TEST(equal(m + inv(diagm(d)) , tmp(diagm(di)) + m));
 DLIB_TEST((m + identity_matrix<double>(3) == m + tmp(identity_matrix<double>(3))));
 DLIB_TEST((m + identity_matrix<double,3>() == m + tmp(identity_matrix<double,3>())));
 DLIB_TEST((m + 2*identity_matrix<double>(3) == m + 2*tmp(identity_matrix<double>(3))));
 DLIB_TEST((m + 2*identity_matrix<double,3>() == m + 2*tmp(identity_matrix<double,3>())));
 DLIB_TEST((m + identity_matrix<double>(3)*2 == m + 2*tmp(identity_matrix<double>(3))));
 DLIB_TEST((m + identity_matrix<double,3>()*2 == m + 2*tmp(identity_matrix<double,3>())));
 DLIB_TEST((identity_matrix<double>(3) + m == m + tmp(identity_matrix<double>(3))));
 DLIB_TEST((identity_matrix<double,3>() + m == m + tmp(identity_matrix<double,3>())));
 DLIB_TEST((2*identity_matrix<double>(3) + m == m + 2*tmp(identity_matrix<double>(3))));
 DLIB_TEST((2*identity_matrix<double,3>() + m == m + 2*tmp(identity_matrix<double,3>())));
 }
 {
 matrix<double,1,0> d(1,3), di(1,3);
 matrix<double,0,3> m(3,3);
 
 m = 1,2,3,
 4,5,6,
 7,8,9;
 d = 1,2,3;
 di = 1, 1/2.0, 1/3.0;
 DLIB_TEST(equal(inv(diagm(d)) , diagm(di)));
 DLIB_TEST(equal(inv(diagm(d)) , diagm(di)));
 DLIB_TEST(equal(inv(diagm(d))*m , tmp(diagm(di))*m));
 DLIB_TEST(equal(m*inv(diagm(d)) , m*tmp(diagm(di))));
 DLIB_TEST(equal(inv(diagm(d)) + m , tmp(diagm(di)) + m));
 DLIB_TEST(equal(m + inv(diagm(d)) , tmp(diagm(di)) + m));
 DLIB_TEST((m + identity_matrix<double>(3) == m + tmp(identity_matrix<double>(3))));
 DLIB_TEST((m + identity_matrix<double,3>() == m + tmp(identity_matrix<double,3>())));
 DLIB_TEST((m + 2*identity_matrix<double>(3) == m + 2*tmp(identity_matrix<double>(3))));
 DLIB_TEST((m + 2*identity_matrix<double,3>() == m + 2*tmp(identity_matrix<double,3>())));
 DLIB_TEST((m + identity_matrix<double>(3)*2 == m + 2*tmp(identity_matrix<double>(3))));
 DLIB_TEST((m + identity_matrix<double,3>()*2 == m + 2*tmp(identity_matrix<double,3>())));
 DLIB_TEST((identity_matrix<double>(3) + m == m + tmp(identity_matrix<double>(3))));
 DLIB_TEST((identity_matrix<double,3>() + m == m + tmp(identity_matrix<double,3>())));
 DLIB_TEST((2*identity_matrix<double>(3) + m == m + 2*tmp(identity_matrix<double>(3))));
 DLIB_TEST((2*identity_matrix<double,3>() + m == m + 2*tmp(identity_matrix<double,3>())));
 }
 {
 matrix<double,3,1> d1, d2;
 d1 = 1,2,3;
 d2 = 2,3,4;
 matrix<double,3,3> ans;
 ans = 2, 0, 0,
 0, 6, 0,
 0, 0, 12;
 DLIB_TEST(ans == diagm(d1)*diagm(d2));
 }
 dlib::rand rnd;
 for (int i = 0; i < 1; ++i)
 {
 matrix<double> d1 = randm(4,1,rnd);
 matrix<double,5,1> d2 = randm(5,1,rnd);
 matrix<double,4,5> m = randm(4,5,rnd);
 DLIB_TEST_MSG(equal(pointwise_multiply(d1*trans(d2), m) , diagm(d1)*m*diagm(d2)),
 pointwise_multiply(d1*trans(d2), m) - diagm(d1)*m*diagm(d2)
 );
 DLIB_TEST(equal(pointwise_multiply(d1*trans(d2), m) , diagm(d1)*(m*diagm(d2))));
 DLIB_TEST(equal(pointwise_multiply(d1*trans(d2), m) , (diagm(d1)*m)*diagm(d2)));
 DLIB_TEST(equal(pointwise_multiply(reciprocal(d1)*trans(reciprocal(d2)), m) , inv(diagm(d1))*m*inv(diagm(d2))));
 DLIB_TEST(equal(pointwise_multiply(reciprocal(d1)*trans(reciprocal(d2)), m) , inv(diagm(d1))*(m*inv(diagm(d2)))));
 DLIB_TEST(equal(pointwise_multiply(reciprocal(d1)*trans(reciprocal(d2)), m) , (inv(diagm(d1))*m)*inv(diagm(d2))));
 DLIB_TEST(equal(pointwise_multiply(reciprocal(d1)*trans((d2)), m) , inv(diagm(d1))*m*(diagm(d2))));
 DLIB_TEST(equal(pointwise_multiply(reciprocal(d1)*trans((d2)), m) , inv(diagm(d1))*(m*(diagm(d2)))));
 DLIB_TEST(equal(pointwise_multiply(reciprocal(d1)*trans((d2)), m) , (inv(diagm(d1))*m)*(diagm(d2))));
 DLIB_TEST(equal(pointwise_multiply((d1)*trans(reciprocal(d2)), m) , (diagm(d1))*m*inv(diagm(d2))));
 DLIB_TEST(equal(pointwise_multiply((d1)*trans(reciprocal(d2)), m) , (diagm(d1))*(m*inv(diagm(d2)))));
 DLIB_TEST(equal(pointwise_multiply((d1)*trans(reciprocal(d2)), m) , ((diagm(d1))*m)*inv(diagm(d2))));
 }
 for (int i = 0; i < 1; ++i)
 {
 matrix<double,4,1> d1 = randm(4,1,rnd);
 matrix<double,5,1> d2 = randm(5,1,rnd);
 matrix<double,4,5> m = randm(4,5,rnd);
 DLIB_TEST(equal(pointwise_multiply(d1*trans(d2), m) , diagm(d1)*m*diagm(d2)));
 DLIB_TEST(equal(pointwise_multiply(d1*trans(d2), m) , diagm(d1)*(m*diagm(d2))));
 DLIB_TEST(equal(pointwise_multiply(d1*trans(d2), m) , (diagm(d1)*m)*diagm(d2)));
 DLIB_TEST(equal(pointwise_multiply(reciprocal(d1)*trans(reciprocal(d2)), m) , inv(diagm(d1))*m*inv(diagm(d2))));
 DLIB_TEST(equal(pointwise_multiply(reciprocal(d1)*trans(reciprocal(d2)), m) , inv(diagm(d1))*(m*inv(diagm(d2)))));
 DLIB_TEST(equal(pointwise_multiply(reciprocal(d1)*trans(reciprocal(d2)), m) , (inv(diagm(d1))*m)*inv(diagm(d2))));
 DLIB_TEST(equal(pointwise_multiply(reciprocal(d1)*trans((d2)), m) , inv(diagm(d1))*m*(diagm(d2))));
 DLIB_TEST(equal(pointwise_multiply(reciprocal(d1)*trans((d2)), m) , inv(diagm(d1))*(m*(diagm(d2)))));
 DLIB_TEST(equal(pointwise_multiply(reciprocal(d1)*trans((d2)), m) , (inv(diagm(d1))*m)*(diagm(d2))));
 DLIB_TEST(equal(pointwise_multiply((d1)*trans(reciprocal(d2)), m) , (diagm(d1))*m*inv(diagm(d2))));
 DLIB_TEST(equal(pointwise_multiply((d1)*trans(reciprocal(d2)), m) , (diagm(d1))*(m*inv(diagm(d2)))));
 DLIB_TEST(equal(pointwise_multiply((d1)*trans(reciprocal(d2)), m) , ((diagm(d1))*m)*inv(diagm(d2))));
 }
 for (int i = 0; i < 1; ++i)
 {
 matrix<double,4,1> d1 = randm(4,1,rnd);
 matrix<double,5,1> d2 = randm(5,1,rnd);
 matrix<double,0,0> m = randm(4,5,rnd);
 DLIB_TEST(equal(pointwise_multiply(d1*trans(d2), m) , diagm(d1)*m*diagm(d2)));
 DLIB_TEST(equal(pointwise_multiply(d1*trans(d2), m) , diagm(d1)*(m*diagm(d2))));
 DLIB_TEST(equal(pointwise_multiply(d1*trans(d2), m) , (diagm(d1)*m)*diagm(d2)));
 DLIB_TEST(equal(pointwise_multiply(reciprocal(d1)*trans(reciprocal(d2)), m) , inv(diagm(d1))*m*inv(diagm(d2))));
 DLIB_TEST(equal(pointwise_multiply(reciprocal(d1)*trans(reciprocal(d2)), m) , inv(diagm(d1))*(m*inv(diagm(d2)))));
 DLIB_TEST(equal(pointwise_multiply(reciprocal(d1)*trans(reciprocal(d2)), m) , (inv(diagm(d1))*m)*inv(diagm(d2))));
 DLIB_TEST(equal(pointwise_multiply(reciprocal(d1)*trans((d2)), m) , inv(diagm(d1))*m*(diagm(d2))));
 DLIB_TEST(equal(pointwise_multiply(reciprocal(d1)*trans((d2)), m) , inv(diagm(d1))*(m*(diagm(d2)))));
 DLIB_TEST(equal(pointwise_multiply(reciprocal(d1)*trans((d2)), m) , (inv(diagm(d1))*m)*(diagm(d2))));
 DLIB_TEST(equal(pointwise_multiply((d1)*trans(reciprocal(d2)), m) , (diagm(d1))*m*inv(diagm(d2))));
 DLIB_TEST(equal(pointwise_multiply((d1)*trans(reciprocal(d2)), m) , (diagm(d1))*(m*inv(diagm(d2)))));
 DLIB_TEST(equal(pointwise_multiply((d1)*trans(reciprocal(d2)), m) , ((diagm(d1))*m)*inv(diagm(d2))));
 }
 {
 for (int i = 0; i < 5; ++i)
 {
 matrix<double> m = randm(3,4) + 1;
 DLIB_TEST(equal(1.0/m , reciprocal(m)));
 DLIB_TEST(equal(0.0/m , zeros_matrix<double>(3,4)));
 }
 }
 {
 matrix<int> m(2,3);
 m = 1,2,3,
 4,5,6;
 matrix<int> M(2,3);
 M = m;
 DLIB_TEST(upperbound(m,6) == M);
 DLIB_TEST(upperbound(m,60) == M);
 DLIB_TEST(lowerbound(m,-2) == M);
 DLIB_TEST(lowerbound(m,0) == M);
 M = 2,2,3,
 4,5,6;
 DLIB_TEST(lowerbound(m,2) == M);
 M = 0,0,0,
 0,0,0;
 DLIB_TEST(upperbound(m,0) == M);
 M = 1,2,3,
 3,3,3;
 DLIB_TEST(upperbound(m,3) == M);
 }
 
 {
 matrix<double,9,5> A = randm(9,5);
 matrix<double> B = A;
 
 orthogonalize(A);
 orthogonalize(B);
 
 DLIB_TEST(equal(A,B));
 }
 {
 matrix<double,9,5> A = randm(9,5);
 matrix<double,9,5> B = randm(9,5);
 matrix<double,9,5> C = pointwise_pow(A, B);
 for (long r = 0; r < C.nr(); ++r)
 {
 for (long c = 0; c < C.nc(); ++c)
 {
 DLIB_TEST(C(r, c) == std::pow(A(r, c), B(r, c)));
 }
 }
 }
 }
 template <
 long D1,
 long D2, 
 long D3,
 long D4
 >
 void test_conv()
 {
 dlog << LINFO << D1 << " " << D2 << " " << D3 << " " << D4;
 matrix<int,D1,D1> a(1,1);
 matrix<int,D2,D2> b(2,2); 
 matrix<int,D3,D3> c(3,3); 
 matrix<int,D4,D1> d(4,1);
 a = 4;
 b = 1,2,
 3,4;
 c = 1,2,3,
 4,5,6,
 7,8,9;
 d = 1,
 2,
 3,
 4;
 
 matrix<int> temp(4,4), temp2;
 temp = 1, 4, 7, 6,
 7, 23, 33, 24,
 19, 53, 63, 42,
 21, 52, 59, 36;
 DLIB_TEST(conv(b,c) == temp);
 DLIB_TEST(conv(c,b) == temp);
 DLIB_TEST(xcorr(c,flip(b)) == temp);
 temp.set_size(2,2);
 temp = 23, 33,
 53, 63;
 DLIB_TEST(conv_same(b,c) == temp);
 DLIB_TEST(xcorr_same(b,flip(c)) == temp);
 temp2.set_size(2,2);
 temp2 = 63, 53,
 33, 23;
 DLIB_TEST(flip(temp) == temp2);
 DLIB_TEST(flip(temp) == fliplr(flipud(temp)));
 DLIB_TEST(conv_valid(b,c).nr() == 0);
 DLIB_TEST(conv_valid(b,c).nc() == 0);
 DLIB_TEST(conv_valid(c,b) == temp);
 DLIB_TEST(xcorr_valid(c,flip(b)) == temp);
 temp.set_size(1,1);
 temp = 16;
 DLIB_TEST(conv(a,a) == temp);
 DLIB_TEST(conv_same(a,a) == temp);
 DLIB_TEST(conv_valid(a,a) == temp);
 DLIB_TEST(xcorr(a,a) == temp);
 DLIB_TEST(xcorr_same(a,a) == temp);
 DLIB_TEST(xcorr_valid(a,a) == temp);
 temp.set_size(0,0);
 DLIB_TEST(conv(temp,temp).nr() == 0);
 DLIB_TEST(conv(temp,temp).nc() == 0);
 DLIB_TEST(conv_same(temp,temp).nr() == 0);
 DLIB_TEST(conv_same(temp,temp).nc() == 0);
 DLIB_TEST_MSG(conv_valid(temp,temp).nr() == 0, conv_valid(temp,temp).nr());
 DLIB_TEST(conv_valid(temp,temp).nc() == 0);
 DLIB_TEST(conv(c,temp).nr() == 0);
 DLIB_TEST(conv(c,temp).nc() == 0);
 DLIB_TEST(conv_same(c,temp).nr() == 0);
 DLIB_TEST(conv_same(c,temp).nc() == 0);
 DLIB_TEST(conv_valid(c,temp).nr() == 0);
 DLIB_TEST(conv_valid(c,temp).nc() == 0);
 DLIB_TEST(conv(temp,c).nr() == 0);
 DLIB_TEST(conv(temp,c).nc() == 0);
 DLIB_TEST(conv_same(temp,c).nr() == 0);
 DLIB_TEST(conv_same(temp,c).nc() == 0);
 DLIB_TEST(conv_valid(temp,c).nr() == 0);
 DLIB_TEST(conv_valid(temp,c).nc() == 0);
 temp.set_size(5,2);
 temp = 1, 2,
 5, 8,
 9, 14,
 13, 20,
 12, 16;
 DLIB_TEST(conv(b,d) == temp);
 DLIB_TEST(xcorr(b,flip(d)) == temp);
 temp.set_size(2,2);
 temp = 9, 14,
 13, 20;
 DLIB_TEST(conv_same(b,d) == temp);
 DLIB_TEST(xcorr_same(b,flip(d)) == temp);
 DLIB_TEST(conv_valid(b,d).nr() == 0);
 DLIB_TEST(xcorr_valid(b,flip(d)).nr() == 0);
 DLIB_TEST_MSG(conv_valid(b,d).nc() == 0, conv_valid(b,d).nc());
 DLIB_TEST(xcorr_valid(b,flip(d)).nc() == 0);
 temp.set_size(5,5);
 temp = 1, 4, 10, 12, 9,
 8, 26, 56, 54, 36,
 30, 84, 165, 144, 90,
 56, 134, 236, 186, 108,
 49, 112, 190, 144, 81;
 DLIB_TEST(conv(c,c) == temp);
 DLIB_TEST(xcorr(c,flip(c)) == temp);
 matrix<int> temp3 = c;
 temp3 = conv(temp3,c);
 DLIB_TEST(temp3 == temp);
 temp3 = c;
 temp3 = conv(c,temp3);
 DLIB_TEST(temp3 == temp);
 temp.set_size(3,3);
 temp = 26, 56, 54,
 84, 165, 144,
 134, 236, 186;
 DLIB_TEST(conv_same(c,c) == temp);
 DLIB_TEST(xcorr_same(c,flip(c)) == temp);
 temp3 = c;
 temp3 = conv_same(c,temp3);
 DLIB_TEST(temp3 == temp);
 temp3 = c;
 temp3 = conv_same(temp3,c);
 DLIB_TEST(temp3 == temp);
 temp.set_size(1,1);
 temp = 165;
 DLIB_TEST(conv_valid(c,c) == temp);
 DLIB_TEST(xcorr_valid(c,flip(c)) == temp);
 temp3 = c;
 temp3 = conv_valid(c,temp3);
 DLIB_TEST(temp3 == temp);
 temp3 = c;
 temp3 = conv_valid(temp3,c);
 DLIB_TEST(temp3 == temp);
 dlib::rand rnd;
 for (int i = 0; i < 3; ++i)
 {
 matrix<complex<int> > a, b;
 a = complex_matrix(matrix_cast<int>(round(20*randm(2,7,rnd))), 
 matrix_cast<int>(round(20*randm(2,7,rnd))));
 b = complex_matrix(matrix_cast<int>(round(20*randm(3,2,rnd))), 
 matrix_cast<int>(round(20*randm(3,2,rnd))));
 DLIB_TEST(xcorr(a,b) == conv(a, flip(conj(b))));
 DLIB_TEST(xcorr_valid(a,b) == conv_valid(a, flip(conj(b))));
 DLIB_TEST(xcorr_same(a,b) == conv_same(a, flip(conj(b))));
 }
 for (int i = 0; i < 30; ++i)
 {
 auto nr1 = rnd.get_integer_in_range(1,30);
 auto nc1 = rnd.get_integer_in_range(1,30);
 auto nr2 = rnd.get_integer_in_range(1,30);
 auto nc2 = rnd.get_integer_in_range(1,30);
 matrix<double> a, b;
 a = randm(nr1,nc1,rnd);
 b = randm(nr2,nc2,rnd);
 DLIB_TEST(max(abs(xcorr(a,b) - xcorr_fft(a,b))) < 1e-12);
 }
 }
 void test_complex()
 {
 matrix<complex<double> > a, b;
 a = complex_matrix(linspace(1,7,7), linspace(2,8,7));
 b = complex_matrix(linspace(4,10,7), linspace(2,8,7));
 DLIB_TEST(mean(a) == complex<double>(4, 5));
 }
 void test_setsubs()
 {
 {
 matrix<double> m(3,3);
 m = 0;
 set_colm(m,0) += 1;
 set_rowm(m,0) += 1;
 set_subm(m,1,1,2,2) += 5;
 matrix<double> m2(3,3);
 m2 = 2, 1, 1,
 1, 5, 5, 
 1, 5, 5;
 DLIB_TEST(m == m2);
 set_colm(m,0) -= 1;
 set_rowm(m,0) -= 1;
 set_subm(m,1,1,2,2) -= 5;
 m2 = 0;
 DLIB_TEST(m == m2);
 matrix<double,1,3> r;
 matrix<double,3,1> c;
 matrix<double,2,2> b;
 r = 1,2,3;
 c = 2,
 3,
 4;
 b = 2,3,
 4,5;
 set_colm(m,1) += c;
 set_rowm(m,1) += r;
 set_subm(m,1,1,2,2) += b;
 m2 = 0, 2, 0,
 1, 7, 6,
 0, 8, 5;
 DLIB_TEST(m2 == m);
 set_colm(m,1) -= c;
 set_rowm(m,1) -= r;
 set_subm(m,1,1,2,2) -= b;
 m2 = 0;
 DLIB_TEST(m2 == m);
 // check that the code path for destructive aliasing works right.
 m = 2*identity_matrix<double>(3);
 set_colm(m,1) += m*c;
 m2 = 2, 4, 0,
 0, 8, 0,
 0, 8, 2;
 DLIB_TEST(m == m2);
 m = 2*identity_matrix<double>(3);
 set_colm(m,1) -= m*c;
 m2 = 2, -4, 0,
 0, -4, 0,
 0, -8, 2;
 DLIB_TEST(m == m2);
 m = 2*identity_matrix<double>(3);
 set_rowm(m,1) += r*m;
 m2 = 2, 0, 0,
 2, 6, 6,
 0, 0, 2;
 DLIB_TEST(m == m2);
 m = 2*identity_matrix<double>(3);
 set_rowm(m,1) -= r*m;
 m2 = 2, 0, 0,
 -2, -2, -6,
 0, 0, 2;
 DLIB_TEST(m == m2);
 m = identity_matrix<double>(3);
 const rectangle rect(0,0,1,1);
 set_subm(m,rect) += subm(m,rect)*b;
 m2 = 3, 3, 0,
 4, 6, 0,
 0, 0, 1;
 DLIB_TEST(m == m2);
 m = identity_matrix<double>(3);
 set_subm(m,rect) -= subm(m,rect)*b;
 m2 = -1, -3, 0,
 -4, -4, 0,
 0, 0, 1;
 DLIB_TEST(m == m2);
 }
 {
 matrix<double,1,1> a, b;
 a = 2;
 b = 3;
 DLIB_TEST(dot(a,b) == 6);
 }
 {
 matrix<double,1,1> a;
 matrix<double,0,1> b(1);
 a = 2;
 b = 3;
 DLIB_TEST(dot(a,b) == 6);
 DLIB_TEST(dot(b,a) == 6);
 }
 {
 matrix<double,1,1> a;
 matrix<double,1,0> b(1);
 a = 2;
 b = 3;
 DLIB_TEST(dot(a,b) == 6);
 DLIB_TEST(dot(b,a) == 6);
 }
 }
 template <typename T>
 std::vector<int> tovect1(const T& m)
 {
 std::vector<int> temp;
 for (typename T::const_iterator i = m.begin(); i != m.end(); ++i)
 {
 temp.push_back(*i);
 }
 return temp;
 }
 template <typename T>
 std::vector<int> tovect2(const T& m)
 {
 std::vector<int> temp;
 for (typename T::const_iterator i = m.begin(); i != m.end(); i++)
 {
 temp.push_back(*i);
 }
 return temp;
 }
 template <typename T>
 std::vector<int> tovect3(const T& m_)
 {
 matrix<int> m(m_);
 std::vector<int> temp;
 for (matrix<int>::iterator i = m.begin(); i != m.end(); ++i)
 {
 temp.push_back(*i);
 }
 return temp;
 }
 template <typename T>
 std::vector<int> tovect4(const T& m_)
 {
 matrix<int> m(m_);
 std::vector<int> temp;
 for (matrix<int>::iterator i = m.begin(); i != m.end(); i++)
 {
 temp.push_back(*i);
 }
 return temp;
 }
 void test_iterators()
 {
 matrix<int> m(3,2);
 m = 1,2,3,
 4,5,6;
 std::vector<int> v1 = tovect1(m);
 std::vector<int> v2 = tovect2(m);
 std::vector<int> v3 = tovect3(m);
 std::vector<int> v4 = tovect4(m);
 std::vector<int> v5 = tovect1(m+m);
 std::vector<int> v6 = tovect2(m+m);
 std::vector<int> v7 = tovect3(m+m);
 std::vector<int> v8 = tovect4(m+m);
 std::vector<int> a1, a2;
 for (int i = 1; i <= 6; ++i)
 {
 a1.push_back(i);
 a2.push_back(i*2);
 }
 DLIB_TEST(max(abs(mat(v1) - mat(a1))) == 0);
 DLIB_TEST(max(abs(mat(v2) - mat(a1))) == 0);
 DLIB_TEST(max(abs(mat(v3) - mat(a1))) == 0);
 DLIB_TEST(max(abs(mat(v4) - mat(a1))) == 0);
 DLIB_TEST(max(abs(mat(v5) - mat(a2))) == 0);
 DLIB_TEST(max(abs(mat(v6) - mat(a2))) == 0);
 DLIB_TEST(max(abs(mat(v7) - mat(a2))) == 0);
 DLIB_TEST(max(abs(mat(v8) - mat(a2))) == 0);
 }
 void test_linpiece()
 {
 matrix<double,0,1> temp = linpiece(5, linspace(-1, 9, 2));
 DLIB_CASSERT(temp.size() == 1,"");
 DLIB_CASSERT(std::abs(temp(0) - 6) < 1e-13,"");
 temp = linpiece(5, linspace(-1, 9, 6));
 DLIB_CASSERT(temp.size() == 5,"");
 DLIB_CASSERT(std::abs(temp(0) - 2) < 1e-13,"");
 DLIB_CASSERT(std::abs(temp(1) - 2) < 1e-13,"");
 DLIB_CASSERT(std::abs(temp(2) - 2) < 1e-13,"");
 DLIB_CASSERT(std::abs(temp(3) - 0) < 1e-13,"");
 DLIB_CASSERT(std::abs(temp(4) - 0) < 1e-13,"");
 temp = linpiece(4, linspace(-1, 9, 6));
 DLIB_CASSERT(temp.size() == 5,"");
 DLIB_CASSERT(std::abs(temp(0) - 2) < 1e-13,"");
 DLIB_CASSERT(std::abs(temp(1) - 2) < 1e-13,"");
 DLIB_CASSERT(std::abs(temp(2) - 1) < 1e-13,"");
 DLIB_CASSERT(std::abs(temp(3) - 0) < 1e-13,"");
 DLIB_CASSERT(std::abs(temp(4) - 0) < 1e-13,"");
 temp = linpiece(40, linspace(-1, 9, 6));
 DLIB_CASSERT(temp.size() == 5,"");
 DLIB_CASSERT(std::abs(temp(0) - 2) < 1e-13,"");
 DLIB_CASSERT(std::abs(temp(1) - 2) < 1e-13,"");
 DLIB_CASSERT(std::abs(temp(2) - 2) < 1e-13,"");
 DLIB_CASSERT(std::abs(temp(3) - 2) < 1e-13,"");
 DLIB_CASSERT(std::abs(temp(4) - 2) < 1e-13,"");
 temp = linpiece(-40, linspace(-1, 9, 6));
 DLIB_CASSERT(temp.size() == 5,"");
 DLIB_CASSERT(std::abs(temp(0) - 0) < 1e-13,"");
 DLIB_CASSERT(std::abs(temp(1) - 0) < 1e-13,"");
 DLIB_CASSERT(std::abs(temp(2) - 0) < 1e-13,"");
 DLIB_CASSERT(std::abs(temp(3) - 0) < 1e-13,"");
 DLIB_CASSERT(std::abs(temp(4) - 0) < 1e-13,"");
 temp = linpiece(0, linspace(-1, 9, 6));
 DLIB_CASSERT(temp.size() == 5,"");
 DLIB_CASSERT(std::abs(temp(0) - 1) < 1e-13,"");
 DLIB_CASSERT(std::abs(temp(1) - 0) < 1e-13,"");
 DLIB_CASSERT(std::abs(temp(2) - 0) < 1e-13,"");
 DLIB_CASSERT(std::abs(temp(3) - 0) < 1e-13,"");
 DLIB_CASSERT(std::abs(temp(4) - 0) < 1e-13,"");
 }
 class matrix_tester : public tester
 {
 public:
 matrix_tester (
 ) :
 tester ("test_matrix4",
 "Runs tests on the scale_rows and scale_columns functions.")
 {}
 void perform_test (
 )
 {
 test_iterators();
 test_setsubs();
 test_conv<0,0,0,0>();
 test_conv<1,2,3,4>();
 test_stuff();
 for (int i = 0; i < 10; ++i)
 matrix_test();
 test_complex();
 test_linpiece();
 }
 } a;
}