    // 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

        // Note that you can always print a matrix to an output stream by saying:
        cout << M << endl;
        // which will print:
        //   54.2  7.4 12.1
        //      1    2    3
        //    5.9 0.05    1

        // However, if you want to print using comma separators instead of spaces you can say:
        cout << csv << M << endl;
        // and you will instead get this as output:
        //   54.2, 7.4, 12.1
        //   1, 2, 3
        //   5.9, 0.05, 1

        // Conversely, you can also read in a matrix that uses either space, tab, or comma
        // separated values by uncommenting the following:
        // cin >> M;

        // -----------------------------  Comparison with MATLAB ------------------------------
        // Here I list a set of Matlab commands and their equivalent expressions using the dlib
        // matrix.  Note that there are a lot more functions defined for the dlib::matrix.  See
        // the HTML documentation for a full listing.

        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);
    }

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