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## Diagonalization of symmetric matrices - form of matrix?

I would like to compute the eigenvalues of a symmetric matrix and wanted to use the LAPACKE_dsyev function from the MKL Library in C++ for that.

From the documentation https://software.intel.com/en-us/mkl-developer-reference-c-syev, I concluded that I would have to pass only the upper/lower triangular part of the matrix. It says about the argument that it "is an array containing either upper or lower triangular part of the symmetric matrix A".

However, it seems that actually one needs to pass the pointer to the full matrix to the routine. Say I want to diagonalize the following matrix:

[[-2,   0,     0.5,  0],
[0,     0.5, -2,     0.5],
[0.5,  -2,    0.5,  0],
[0,     0.5,  0,    -1]],
which has eigenvalues [ 2.56,  -2.22, -1.53, -0.81]

Then in the following code, only the first option gives the correct values.

```#include <iostream>
#include"mkl_lapacke.h"
using namespace std;
int main(){
MKL_INT N = 4;
double matrix_ex_full = {-2,0,0.5,0,0,0.5,-2,0.5,0.5, -2, 0.5, 0, 0,0.5,0,-1};
double evals_full;
// Pass over the full matrix
MKL_INT test1 = LAPACKE_dsyev(LAPACK_ROW_MAJOR, 'N', 'U', N, matrix_ex_full,N, evals_full);
cout << "success = " <<test1 << endl;
for (MKL_INT i = 0;i<4;i++)
cout << evals_full << endl;
// Pass only the upper triagonal
double matrix_ex_uppertri = {-2, 0, 0.5, 0, 0.5, -2, 0.5, 0.5, 0, -1};
double evals_uppertri;
MKL_INT test2 = LAPACKE_dsyev(LAPACK_ROW_MAJOR, 'N', 'U', N, matrix_ex_uppertri,N, evals_uppertri);
cout << "success = " <<test2 << endl;
for (MKL_INT i = 0;i<4;i++)
cout << evals_uppertri << endl;

}
//Compiled with g++ test.cpp -o main -m64 -I/share/opt/intel/compilers_and_libraries_2018.0.128/linux/mkl/include -L/share/opt/intel/compilers_and_libraries_2018.0.128/linux/mkl/lib/intel64 -Wl,--no-as-needed -lmkl_intel_lp64 -lmkl_gnu_thread -lmkl_core -lgomp -lpthread -lm -ldl
```

I guess I am missing something obvious here, but why, if the full matrix has to be given anyway, is it necessary at all to specify 'U' or 'L'? Or am I doing something wrong elsewhere?

Thanks for any help, and apologies if this question is trivial (which I have the feeling it must be), I am rather new to using MKL.

2 Replies Beginner
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