## Adding Generalized Eigenvalue functions to IT++

I have added a functions call to lapack DGGEV and ZGGEV functions to solve generalized eigenvalue problem. There are three files to modify: lapack.h, eigen.h, and eigen.cpp. The diff files can be obtained from this link.

To test the code, I ran an example for generalized complex eigenvalue problem found in the NAG site. The test program is shown below:

``` #include using namespace itpp; //These lines are needed for use of cout and endl using std::cout; using std::endl; int main() { cmat cA,cB; cA="-21.10-22.50i 53.50-50.50i -34.50+127.50i 7.50+0.50i; -0.46-7.78i -3.50-37.50i -15.50+58.50i -10.50-1.50i; 4.30-5.50i 39.70-17.10i -68.50+12.50i -7.50-3.50i; 5.50+4.40i 14.40+43.30i -32.50-46.00i -19.00-32.50i"; cB="1.00-5.00i 1.60+1.20i -3.00+0.00i 0.00-1.00i; 0.80-0.60i 3.00-5.00i -4.00+3.00i -2.40-3.20i; 1.00+0.00i 2.40+1.80i -4.00-5.00i 0.00-3.00i; 0.00+1.00i -1.80+2.40i 0.00-4.00i 4.00-5.00i"; cout<< "cA = " << cA<<endl; cout<< "cB = " << cB<<endl; cvec lambda; cmat evecs; eig(cA,cB,lambda,evecs); cout<< "eig(cA,cB)\n"; cout << "lambda = "<<lambda<<endl; cout << "evecs = "<<evecs<<endl; //Exit program: return 0; } ```

And the output is:

``` cA = [[-21.1-22.5i 53.5-50.5i -34.5+127.5i 7.5+0.5i] [-0.46-7.78i -3.5-37.5i -15.5+58.5i -10.5-1.5i] [4.3-5.5i 39.7-17.1i -68.5+12.5i -7.5-3.5i] [5.5+4.4i 14.4+43.3i -32.5-46i -19-32.5i]] cB = [[1-5i 1.6+1.2i -3+0i 0-1i] [0.8-0.6i 3-5i -4+3i -2.4-3.2i] [1+0i 2.4+1.8i -4-5i 0-3i] [0+1i -1.8+2.4i 0-4i 4-5i]] eig(cA,cB) lambda = [3-9i 2-5i 3-1i 4-5i] evecs = [[-0.823768-0.176232i 0.639741+0.360259i 0.977535+0.0224645i -0.906234+0.0937662i] [-0.152951+0.0706552i 0.0041597-0.000546503i 0.159101-0.11371i -0.0074303+0.00687504i] [-0.0706552-0.152951i 0.0402123+0.0226448i 0.120899-0.15371i 0.0302078-0.00312554i] [0.152951-0.0706552i -0.0226448+0.0402123i 0.15371+0.120899i -0.0145859-0.14097i]] ```