mirror of https://github.com/davisking/dlib.git
You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
277 lines
7.7 KiB
277 lines
7.7 KiB
// 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()
|
|
{
|
|
// Let's 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 let's declare these 3 matrices.
|
|
// This declares a matrix that contains doubles and has 3 rows and 1 column.
|
|
// Moreover, its size is a compile time constant since we put it inside the <>.
|
|
matrix<double,3,1> y;
|
|
// Make a 3 by 3 matrix of doubles for the M matrix. In this case, M is
|
|
// sized at runtime and can therefore be resized later by calling M.set_size().
|
|
matrix<double> M(3,3);
|
|
|
|
// 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 it enables a number of optimizations that
|
|
// otherwise would be impossible. 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*y you
|
|
// will get a compiler error since that is not a legal matrix operation (the
|
|
// matrix dimensions don't make sense as a matrix multiplication). 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 to y = M*x can be obtained by multiplying the inverse of M
|
|
// with y. As an aside, you should *NEVER* use the auto keyword to capture
|
|
// the output from a matrix expression. So don't do this: auto x = inv(M)*y;
|
|
// To understand why, read the matrix_expressions_ex.cpp example program.
|
|
matrix<double> 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.
|
|
|
|
// 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
|
|
|
|
|
|
// 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;
|
|
|
|
|
|
|
|
|
|
// 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 + C
|
|
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);
|
|
}
|
|
|
|
// ----------------------------------------------------------------------------------------
|
|
|
|
|