Eigen values/vectors large symetric matrix

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Calculating exact eigenvalues and eigenvectors for large symmetric real matrices can be challenging, particularly when precision is critical. The user initially attempted to use CPPLAPACK's dgeev routine but found that it only provided approximately two-thirds of the required exact results. It was suggested that using the dsyev routine, which is more efficient for real symmetric matrices, could yield better outcomes. The user confirmed they switched to dsyev after discovering that MKL offers a C++ library wrapper for BLAS and LAPACK, which can help achieve the necessary precision. The discussion highlights the importance of selecting the right numerical methods and tools for accurate eigenvalue computations.
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I need to calculate eigen values and eigen vectors of a large symmetric real matrix, but all eigen vectors have to be exact not just 2/3 off all eigenvectors.
I tried with CPPLAPACK and dgeev routine:
http://cpplapack.sourceforge.net/
but only about 2/3 of eigen values and vectors are exact, for my project I need all vectory exactly calculated with the norm of unity, for the time expansion of my system in eigen space. I use MKL and ICC compiler, how can I calculate numerically all eigen vectors exactly in c++, which method would be exact.
 
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If you have MKL then you already have a C++ library wrapper for Blas and Lapack. The MKL manuals will explain how to use them, but as far as I know dgeev is a direct routine, you should get the exact results (or as close as you can get with finite precision). However, since you have a real symmetric matrix, there are more efficient methods, like dsyev.
 
I have contacted Yuki Onishi from CPPLAPACK project.
dgeev had a bug and I reported it on 24.09.2009, the bug was solved, I have also changed my code and started to use dsyev, I didn't know that MKL have c++ library wrapper, thanks for the suggestion.
 
Oh wow... whoops, I didn't notice how old this thread was when I responded first. Well at least you got it figured out then.
 
I am studying the mathematical formalism behind non-commutative geometry approach to quantum gravity. I was reading about Hopf algebras and their Drinfeld twist with a specific example of the Moyal-Weyl twist defined as F=exp(-iλ/2θ^(μν)∂_μ⊗∂_ν) where λ is a constant parametar and θ antisymmetric constant tensor. {∂_μ} is the basis of the tangent vector space over the underlying spacetime Now, from my understanding the enveloping algebra which appears in the definition of the Hopf algebra...

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