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277 lines
7.7 KiB
C++
277 lines
7.7 KiB
C++
// The contents of this file are in the public domain. See LICENSE_FOR_EXAMPLE_PROGRAMS.txt
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/*
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This is an example illustrating the use of the matrix object
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from the dlib C++ Library.
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*/
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#include <iostream>
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#include <dlib/matrix.h>
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using namespace dlib;
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using namespace std;
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// ----------------------------------------------------------------------------------------
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int main()
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{
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// Let's begin this example by using the library to solve a simple
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// linear system.
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//
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// We will find the value of x such that y = M*x where
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//
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// 3.5
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// y = 1.2
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// 7.8
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//
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// and M is
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//
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// 54.2 7.4 12.1
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// M = 1 2 3
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// 5.9 0.05 1
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// First let's declare these 3 matrices.
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// This declares a matrix that contains doubles and has 3 rows and 1 column.
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// Moreover, it's size is a compile time constant since we put it inside the <>.
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matrix<double,3,1> y;
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// Make a 3 by 3 matrix of doubles for the M matrix. In this case, M is
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// sized at runtime and can therefore be resized later by calling M.set_size().
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matrix<double> M(3,3);
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// You may be wondering why someone would want to specify the size of a
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// matrix at compile time when you don't have to. The reason is two fold.
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// First, there is often a substantial performance improvement, especially
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// for small matrices, because it enables a number of optimizations that
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// otherwise would be impossible. Second, the dlib::matrix object checks
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// these compile time sizes to ensure that the matrices are being used
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// correctly. For example, if you attempt to compile the expression y*y you
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// will get a compiler error since that is not a legal matrix operation (the
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// matrix dimensions don't make sense as a matrix multiplication). So if
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// you know the size of a matrix at compile time then it is always a good
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// idea to let the compiler know about it.
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// Now we need to initialize the y and M matrices and we can do so like this:
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M = 54.2, 7.4, 12.1,
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1, 2, 3,
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5.9, 0.05, 1;
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y = 3.5,
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1.2,
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7.8;
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// The solution to y = M*x can be obtained by multiplying the inverse of M
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// with y. As an aside, you should *NEVER* use the auto keyword to capture
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// the output from a matrix expression. So don't do this: auto x = inv(M)*y;
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// To understand why, read the matrix_expressions_ex.cpp example program.
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matrix<double> x = inv(M)*y;
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cout << "x: \n" << x << endl;
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// We can check that it really worked by plugging x back into the original equation
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// and subtracting y to see if we get a column vector with values all very close
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// to zero (Which is what happens. Also, the values may not be exactly zero because
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// there may be some numerical error and round off).
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cout << "M*x - y: \n" << M*x - y << endl;
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// Also note that we can create run-time sized column or row vectors like so
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matrix<double,0,1> runtime_sized_column_vector;
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matrix<double,1,0> runtime_sized_row_vector;
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// and then they are sized by saying
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runtime_sized_column_vector.set_size(3);
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// Similarly, the x matrix can be resized by calling set_size(num rows, num columns). For example
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x.set_size(3,4); // x now has 3 rows and 4 columns.
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// The elements of a matrix are accessed using the () operator like so:
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cout << M(0,1) << endl;
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// The above expression prints out the value 7.4. That is, the value of
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// the element at row 0 and column 1.
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// If we have a matrix that is a row or column vector. That is, it contains either
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// a single row or a single column then we know that any access is always either
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// to row 0 or column 0 so we can omit that 0 and use the following syntax.
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cout << y(1) << endl;
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// The above expression prints out the value 1.2
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// Let's compute the sum of elements in the M matrix.
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double M_sum = 0;
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// loop over all the rows
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for (long r = 0; r < M.nr(); ++r)
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{
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// loop over all the columns
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for (long c = 0; c < M.nc(); ++c)
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{
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M_sum += M(r,c);
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}
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}
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cout << "sum of all elements in M is " << M_sum << endl;
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// The above code is just to show you how to loop over the elements of a matrix. An
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// easier way to find this sum is to do the following:
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cout << "sum of all elements in M is " << sum(M) << endl;
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// Note that you can always print a matrix to an output stream by saying:
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cout << M << endl;
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// which will print:
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// 54.2 7.4 12.1
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// 1 2 3
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// 5.9 0.05 1
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// However, if you want to print using comma separators instead of spaces you can say:
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cout << csv << M << endl;
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// and you will instead get this as output:
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// 54.2, 7.4, 12.1
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// 1, 2, 3
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// 5.9, 0.05, 1
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// Conversely, you can also read in a matrix that uses either space, tab, or comma
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// separated values by uncommenting the following:
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// cin >> M;
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// ----------------------------- Comparison with MATLAB ------------------------------
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// Here I list a set of Matlab commands and their equivalent expressions using the dlib
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// matrix. Note that there are a lot more functions defined for the dlib::matrix. See
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// the HTML documentation for a full listing.
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matrix<double> A, B, C, D, E;
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matrix<int> Aint;
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matrix<long> Blong;
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// MATLAB: A = eye(3)
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A = identity_matrix<double>(3);
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// MATLAB: B = ones(3,4)
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B = ones_matrix<double>(3,4);
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// MATLAB: B = rand(3,4)
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B = randm(3,4);
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// MATLAB: C = 1.4*A
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C = 1.4*A;
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// MATLAB: D = A.*C
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D = pointwise_multiply(A,C);
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// MATLAB: E = A * B
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E = A*B;
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// MATLAB: E = A + B
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E = A + C;
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// MATLAB: E = A + 5
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E = A + 5;
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// MATLAB: E = E'
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E = trans(E); // Note that if you want a conjugate transpose then you need to say conj(trans(E))
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// MATLAB: E = B' * B
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E = trans(B)*B;
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double var;
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// MATLAB: var = A(1,2)
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var = A(0,1); // dlib::matrix is 0 indexed rather than starting at 1 like Matlab.
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// MATLAB: C = round(C)
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C = round(C);
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// MATLAB: C = floor(C)
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C = floor(C);
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// MATLAB: C = ceil(C)
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C = ceil(C);
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// MATLAB: C = diag(B)
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C = diag(B);
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// MATLAB: B = cast(A, "int32")
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Aint = matrix_cast<int>(A);
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// MATLAB: A = B(1,:)
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A = rowm(B,0);
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// MATLAB: A = B([1:2],:)
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A = rowm(B,range(0,1));
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// MATLAB: A = B(:,1)
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A = colm(B,0);
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// MATLAB: A = [1:5]
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Blong = range(1,5);
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// MATLAB: A = [1:2:5]
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Blong = range(1,2,5);
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// MATLAB: A = B([1:3], [1:2])
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A = subm(B, range(0,2), range(0,1));
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// or equivalently
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A = subm(B, rectangle(0,0,1,2));
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// MATLAB: A = B([1:3], [1:2:4])
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A = subm(B, range(0,2), range(0,2,3));
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// MATLAB: B(:,:) = 5
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B = 5;
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// or equivalently
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set_all_elements(B,5);
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// MATLAB: B([1:2],[1,2]) = 7
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set_subm(B,range(0,1), range(0,1)) = 7;
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// MATLAB: B([1:3],[2:3]) = A
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set_subm(B,range(0,2), range(1,2)) = A;
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// MATLAB: B(:,1) = 4
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set_colm(B,0) = 4;
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// MATLAB: B(:,[1:2]) = 4
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set_colm(B,range(0,1)) = 4;
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// MATLAB: B(:,1) = B(:,2)
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set_colm(B,0) = colm(B,1);
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// MATLAB: B(1,:) = 4
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set_rowm(B,0) = 4;
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// MATLAB: B(1,:) = B(2,:)
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set_rowm(B,0) = rowm(B,1);
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// MATLAB: var = det(E' * E)
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var = det(trans(E)*E);
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// MATLAB: C = pinv(E)
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C = pinv(E);
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// MATLAB: C = inv(E)
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C = inv(E);
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// MATLAB: [A,B,C] = svd(E)
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svd(E,A,B,C);
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// MATLAB: A = chol(E,'lower')
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A = chol(E);
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// MATLAB: var = min(min(A))
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var = min(A);
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}
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// ----------------------------------------------------------------------------------------
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