# Eigenvalues of symmetric matrix in packed format (upper triangular entries stacked in vector)

**URL:** https://discourse.julialang.org/t/eigenvalues-of-symmetric-matrix-in-packed-format-upper-triangular-entries-stacked-in-vector/18323
**Category:** Performance
**Tags:** linearalgebra, lapack
**Created:** [December 5, 2018, 2:46pm UTC](https://discourse.julialang.org/t/eigenvalues-of-symmetric-matrix-in-packed-format-upper-triangular-entries-stacked-in-vector/18323 "2018-12-05T14:46:20Z")
**Posts on this page:** 1
**Page:** 1

<div class="post-metadata">

### Author: ![migarstka](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/migarstka/32/3828_2.png) [@migarstka](https://discourse.julialang.org/u/migarstka)
#### Post date: [December 5, 2018, 2:46pm UTC](https://discourse.julialang.org/t/eigenvalues-of-symmetric-matrix-in-packed-format-upper-triangular-entries-stacked-in-vector/18323/1 "2018-12-05T14:46:20Z")

</div>

I am trying to compute the eigenvalues of a symmetric matrix in packed format, i.e. you stack the upper triangular entries in a vector ([Packed Storage](http://www.netlib.org/lapack/lug/node123.html) )

It seems like there exists a LAPACK function for that, e.g. `spev`.  
However, it seems like that function is not yet supported in Julia’s LAPACK package.

Another way would be to recreate the original matrix and then call `eigen!` or `LAPACK.syevr!`, like so:

```julia

using LinearAlgebra

# represent the matrix [1 2 4; 2 3 5; 4 5 6] in packed form
x_packed = [1;2;3;4;5;6]

function populate_upper_triangle!(A::AbstractMatrix, x::AbstractVector)
    k = 0
    for j in 1:size(A,1)
        for i in 1:j
            k += 1
            A[i,j] = x[k]
        end
    end
    nothing
end

function packed_eigen(x)

  # compute original matrix size
  n = Int(sqrt(0.25 + 2 * length(x)) - 0.5)
  # allocate memory for orignal matrix
  X = zeros(n, n)
  populate_upper_triangle!(X, x)
  # solve eigenvalue problem
  (W, Z) = LAPACK.syevr!('V', 'A', 'U', X, 0.0, 0.0, 0, 0, -1.0);
  return W
end

packed_eigen(x_packed)

```

My question is, what is the most efficient way to do this without allocating a lot of memory (I want to compute the eigenvalues hundreds of times)? I want to avoid

```julia
 X = zeros(n, n)
 populate_upper_triangle!(X, x)

```

and was envisioning something like `reshape` to create a view-based upper triangular matrix that can be passed to `LAPACK.syevr!`.