matrix_ex.cpp

// The contents of this file are in the public domain. See LICENSE_FOR_EXAMPLE_PROGRAMS.txt

/*
    This is an example illustrating the use of the matrix object 
    from the dlib C++ Library.
*/


#include <iostream>
#include "dlib/matrix.h"

using namespace dlib;
using namespace std;

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

int main()
{
    // Lets begin this example by using the library to solve a simple 
    // linear system.
    // 
    // We will find the value of x such that y = M*x where
    //
    //      3.5
    // y =  1.2
    //      7.8
    //
    // and M is
    //
    //      54.2   7.4   12.1
    // M =  1      2     3
    //      5.9    0.05  1


    // First lets declare these 3 matrices.
    // This declares a matrix that contains doubles and has 3 rows and 1 column.
    matrix<double,3,1> y;
    // Make a 3 by 3 matrix of doubles for the M matrix.
    matrix<double,3,3> M;
    // Make a matrix of doubles that has unknown dimensions (the dimensions are
    // decided at runtime unlike the above two matrices which are bound at compile
    // time).  We could declare x the same way as y but I'm doing it differently
    // for the purposes of illustration.
    matrix<double> x;
    
    // You may be wondering why someone would want to specify the size of a matrix
    // at compile time when you don't have to.  The reason is two fold.  First,
    // there is often a substantial performance improvement, especially for small
    // matrices, because the compiler is able to perform loop unrolling if it knows
    // the sizes of matrices.  Second, the dlib::matrix object checks these compile
    // time sizes to ensure that the matrices are being used correctly.  For example,
    // if you attempt to compile the expression y = M; or x = y*y; you will get
    // a compiler error on those lines since those are not legal matrix operations.
    // So if you know the size of a matrix at compile time then it is always a good
    // idea to let the compiler know about it.




    // now we need to initialize the y and M matrices and we can do so like this:
    M = 54.2,  7.4,  12.1,
        1,     2,    3,
        5.9,   0.05, 1;

    y = 3.5,  
        1.2,    
        7.8;


    // the solution can be obtained now by multiplying the inverse of M with y
    x = inv(M)*y;

    cout << "x: \n" << x << endl;

    // We can check that it really worked by plugging x back into the original equation 
    // and subtracting y to see if we get a column vector with values all very close
    // to zero (Which is what happens.  Also, the values may not be exactly zero because 
    // there may be some numerical error and round off).
    cout << "M*x - y: \n" << M*x - y << endl;


    // Also note that we can create run-time sized column or row vectors like so
    matrix<double,0,1> runtime_sized_column_vector;
    matrix<double,1,0> runtime_sized_row_vector;
    // and then they are sized by saying
    runtime_sized_column_vector.set_size(3);

    // Similarly, the x matrix can be resized by calling set_size(num rows, num columns).  For example
    x.set_size(3,4);  // x now has 3 rows and 4 columns.



    // The elements of a matrix are accessed using the () operator like so
    cout << M(0,1) << endl;
    // The above expression prints out the value 7.4.  That is, the value of
    // the element at row 0 and column 1.


    // Let's compute the sum of elements in the M matrix.
    double M_sum = 0;
    // loop over all the rows
    for (long r = 0; r < M.nr(); ++r)
    {
        // loop over all the columns
        for (long c = 0; c < M.nc(); ++c)
        {
            M_sum += M(r,c);
        }
    }
    cout << "sum of all elements in M is " << M_sum << endl;

    // The above code is just to show you how to loop over the elements of a matrix.  An 
    // easier way to find this sum is to do the following:
    cout << "sum of all elements in M is " << sum(M) << endl;


    // If we have a matrix that is a row or column vector.  That is, it contains either 
    // a single row or a single column then we know that any access is always either 
    // to row 0 or column 0 so we can omit that 0 and use the following syntax.
    cout << y(1) << endl;
    // The above expression prints out the value 1.2




    // ---------------------------------  Comparison with MATLAB ---------------------------------
    // Here I list a set of Matlab commands and their equivalent expressions using the dlib matrix.

    matrix<double> A, B, C, D, E;
    matrix<int> Aint;
    matrix<long> Blong;

    // MATLAB: A = eye(3)
    A = identity_matrix<double>(3);

    // MATLAB: B = ones(3,4)
    B = ones_matrix<double>(3,4);

    // MATLAB: B = rand(3,4)
    B = randm(3,4);

    // MATLAB: C = 1.4*A
    C = 1.4*A;

    // MATLAB: D = A.*C
    D = pointwise_multiply(A,C);

    // MATLAB: E = A * B
    E = A*B;

    // MATLAB: E = A + B
    E = A + C;

    // MATLAB: E = A + 5
    E = A + 5;

    // MATLAB: E = E'
    E = trans(E);  // Note that if you want a conjugate transpose then you need to say conj(trans(E))

    // MATLAB: E = B' * B
    E = trans(B)*B;

    double var;
    // MATLAB: var = A(1,2)
    var = A(0,1); // dlib::matrix is 0 indexed rather than starting at 1 like Matlab.

    // MATLAB: C = round(C)
    C = round(C);

    // MATLAB: C = floor(C)
    C = floor(C);

    // MATLAB: C = ceil(C)
    C = ceil(C);

    // MATLAB: C = diag(B)
    C = diag(B);

    // MATLAB: B = cast(A, "int32")
    Aint = matrix_cast<int>(A);

    // MATLAB: A = B(1,:)
    A = rowm(B,0);

    // MATLAB: A = B([1:2],:)
    A = rowm(B,range(0,1));

    // MATLAB: A = B(:,1)
    A = colm(B,0);

    // MATLAB: A = [1:5]
    Blong = range(1,5);

    // MATLAB: A = [1:2:5]
    Blong = range(1,2,5);

    // MATLAB: A = B([1:3], [1:2])
    A = subm(B, range(0,2), range(0,1));
    // or equivalently
    A = subm(B, rectangle(0,0,1,2));


    // MATLAB: A = B([1:3], [1:2:4])
    A = subm(B, range(0,2), range(0,2,3));

    // MATLAB: B(:,:) = 5
    B = 5;
    // or equivalently
    set_all_elements(B,5);


    // MATLAB: B([1:2],[1,2]) = 7
    set_subm(B,range(0,1), range(0,1)) = 7;

    // MATLAB: B([1:3],[2:3]) = A
    set_subm(B,range(0,2), range(1,2)) = A;

    // MATLAB: B(:,1) = 4
    set_colm(B,0) = 4;

    // MATLAB: B(:,[1:2]) = 4
    set_colm(B,range(0,1)) = 4;

    // MATLAB: B(:,1) = B(:,2)
    set_colm(B,0) = colm(B,1);

    // MATLAB: B(1,:) = 4
    set_rowm(B,0) = 4;

    // MATLAB: B(1,:) = B(2,:)
    set_rowm(B,0) = rowm(B,1);

    // MATLAB: var = det(E' * E)
    var = det(trans(E)*E);

    // MATLAB: C = pinv(E)
    C = pinv(E);

    // MATLAB: C = inv(E)
    C = inv(E);

    // MATLAB: [A,B,C] = svd(E)
    svd(E,A,B,C);

    // MATLAB: A = chol(E,'lower') 
    A = chol(E);

    // MATLAB: var = min(min(A))
    var = min(A);
}

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