I have been handed some IDL code to port to C++ for a project (http://dream3d.bluequartz.net). In this code the curvature of a patch of triangles is being calculated by fitting a polynomial to the set of points where each point is the centroid of a triangle. The equation is of the form:

z=A * 0.5*x^2 + B*x*y + C*0.5*y^2.

The system is over constrained as I have lots and lots of triangles (at least 70 in most cases) and I need to be able to solve for A, B and C. Using LAPACK/BLAS I can use the "dgels" function to get A, B, and C. What function/template am I looking for in Eigen?

Also after I solve for A,B and C I need to solve the Eigen value problem for the matrix [AB][BC] along with the accompanying Eigen Vectors. We think the equivalent BLAS/LAPCK function is "DSPEV". What function would I be looking for in the Eigen library?

Thank for any help or pointers to the docs (which I am starting to read through).
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Mike Jackson
Principal Software Engineer - BlueQuartz Software (www.bluequartz.net)

I would like to use Eigen instead of BLAS/LAPACK as we are trying to use purely Open Source libraries where we can and attempting to actually get a usable BLAS/LAPACK on Windows with MSVC is basically a non-starter (at least it was for me). I could go a "paid" route and use the Intel MKL for example but I would really rather NOT have to do that.

Hi,

your first problem is a standard least squares problem that you can solve using either the normal equation and the LLT method, or using a QR factorization or even a SVD. See this page:

http://eigen.tuxfamily.org/dox/Tutorial ... gebra.html

For the eigenvalue problem, you can use:
Matrix2d M;
M << A, B, B, C;
SelfAdjointEigenSolver<Matrix2d> eig(M);
eig.eigenvalues();
eig.eigenvectors();

See this section: http://eigen.tuxfamily.org/dox/Tutorial ... gensolving