OpenCV Mat and Matrix operation examples

example code.

...
Mat Ma = Mat::eye(3, 3, CV_64FC1);
 cout << Ma << endl;
 double dm[3][3] = { { 1, 2, 3 }, { 4, 5, 6 }, { 7, 8, 9 } };
 Mat Mb = Mat(3, 3, CV_64F, dm);
 cout << Mb << endl;
 
 //Matrix - matrix operations :
 Mat Mc;
 cv::add(Ma, Mb, Mc); // Ma+Mb   -> Mc
 cout << Ma+Mb << endl;
 cout << Mc << endl;
 cv::subtract(Ma, Mb, Mc);      // Ma-Mb   -> Mc
 cout << Ma - Mb << endl;
 cout << Mc << endl;
 Mc = Ma*Mb; //Ma*Mb;
 cout << Mc << endl;
 
 //Elementwise matrix operations :
 cv::multiply(Ma, Mb, Mc);   // Ma.*Mb   -> Mc
 cout << Mc << endl;
 Mc = Ma.mul(Mb);
 cout << Mc << endl;
 cv::divide(Ma, Mb, Mc);      // Ma./Mb  -> Mc
 cout << Mc << endl;
 Mc = Ma + 10; //Ma + 10 = Mc
 cout << Mc << endl;

 //Vector products :
 double va[] = { 1, 2, 3 };
 double vb[] = { 0, 0, 1 };
 double vc[3];

 Mat Va(3, 1, CV_64FC1, va);
 Mat Vb(3, 1, CV_64FC1, vb);
 Mat Vc(3, 1, CV_64FC1, vc);

 double res = Va.dot(Vb); // dot product:   Va . Vb -> res
 Vc = Va.cross(Vb);    // cross product: Va x Vb -> Vc
 cout << res << " " << Vc << endl;


 //Single matrix operations :
 Mc = Mb.t();      // transpose(Ma) -> Mb (cannot transpose onto self)
 cout << Mc << endl;
 cv::Scalar t = trace(Ma); // trace(Ma) -> t.val[0] 
 cout << t.val[0] << endl; 
 double d = determinant(Ma); // det(Ma) -> d
 cout << d << endl;
 Mc = Ma.inv();         // inv(Mb) -> Mc
 invert(Ma, Mc);
 cout << Mc << endl;


 //Inhomogeneous linear system solver :
 double dm2[3][3] = { { 1, 2, 3 }, { 4, 5, 6 }, { 7, 8, 9 } };
 Mat A(3, 3, CV_64FC1, dm2);
 Mat x(3, 1, CV_64FC1);
 double vvb[] = { 14, 32, 52 };
 Mat b(3, 1, CV_64FC1, vvb);
 cv::solve(A, b, x, DECOMP_SVD); //// solve (Ax=b) for x
 cout << x << endl;


 //Eigen analysis(of a symmetric matrix) :
 float f11[] = { 1, 0.446, -0.56, 0.446, 1, -0.239, -0.56, 0.239, 1 };
 Mat data(3, 3, CV_32F, f11);
 Mat value, vector;
 eigen(data, value, vector);
 cout << "Eigenvalues" << value << endl;
 cout << "Eigenvectors" << endl;
 cout << vector << endl;


 //Singular value decomposition :
 Mat w, u, v;
 SVDecomp(data, w, u, v); // A = U W V^T
 //The flags cause U and V to be returned transposed(does not work well without the transpose flags).
 cout << w << endl;
 cout << u << endl;
 cout << v << endl;


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