# Regresion: Eigvals of bigfloat symmetric matrices does not work anymore

**URL:** <https://discourse.julialang.org/t/regresion-eigvals-of-bigfloat-symmetric-matrices-does-not-work-anymore/63947>\
**Category:** New to Julia\
**Created:** [July 2, 2021, 4:05pm UTC](https://discourse.julialang.org/t/regresion-eigvals-of-bigfloat-symmetric-matrices-does-not-work-anymore/63947 "2021-07-02T16:05:48Z")\
**Posts on this page:** 3\
**Page:** 1

<div class="post-metadata">

**Author:** ![lrnv](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/lrnv/32/19373_2.png) [@lrnv](https://discourse.julialang.org/u/lrnv)\
**Post date:** [July 2, 2021, 4:05pm UTC](https://discourse.julialang.org/t/regresion-eigvals-of-bigfloat-symmetric-matrices-does-not-work-anymore/63947/1 "2021-07-02T16:05:48Z")

</div>

Hi,

I have troubles to get eigenvalues of Symmetric matrices. Here is an example :

```julia
julia> X = big.(rand(10,10));

julia> X = X .+ X';

julia> eigvals(X)
ERROR: UndefVarError: eigvals not defined
Stacktrace:
 [1] top-level scope
   @ REPL[7]:1

julia> using LinearAlgebra

julia> eigvals(X)
ERROR: MethodError: no method matching eigvals!(::Matrix{BigFloat})
Closest candidates are:
  eigvals!(::SymTridiagonal{var"#s832", V} where {var"#s832"<:Union{Float32, Float64}, V<:AbstractVector{var"#s832"}}) at C:\buildbot\worker\package_win64\build\usr\share\julia\stdlib\v1.6\LinearAlgebra\src\tridiag.jl:293
  eigvals!(::SymTridiagonal{var"#s832", V} where {var"#s832"<:Union{Float32, Float64}, V<:AbstractVector{var"#s832"}}, ::UnitRange) at C:\buildbot\worker\package_win64\build\usr\share\julia\stdlib\v1.6\LinearAlgebra\src\tridiag.jl:296
  eigvals!(::SymTridiagonal{var"#s832", V} where {var"#s832"<:Union{Float32, Float64}, V<:AbstractVector{var"#s832"}}, ::Real, ::Real) at C:\buildbot\worker\package_win64\build\usr\share\julia\stdlib\v1.6\LinearAlgebra\src\tridiag.jl:301
  ...
Stacktrace:
 [1] eigvals(A::Matrix{BigFloat}; kws::Base.Iterators.Pairs{Union{}, Union{}, Tuple{}, NamedTuple{(), Tuple{}}})
   @ LinearAlgebra C:\buildbot\worker\package_win64\build\usr\share\julia\stdlib\v1.6\LinearAlgebra\src\eigen.jl:326
 [2] eigvals(A::Matrix{BigFloat})
   @ LinearAlgebra C:\buildbot\worker\package_win64\build\usr\share\julia\stdlib\v1.6\LinearAlgebra\src\eigen.jl:326
 [3] top-level scope
   @ REPL[9]:1

julia> using GenericLinearAlgebra

julia> eigvals(X)
10-element Vector{BigFloat}:
 -1.40896494093833723000919442666358694782060277534420585719212498189431446573352
 -0.9628570629553533920427015265454329908211049396906281502199649555971476817879393
 -0.765572319270339668165400589029211855446345366148112121821247891083801835348516
 -0.4988457885526648034975679430523053256471389136676962921706146821259835194905027
 -0.04967253288626804519859817605198605470194529038496302903243869042530808557833691
  0.7331486204381298592384410093739200409781239753824975991067791372244422807346604
  0.8346942215521769622694146059645529605227057642425001766162913257146661200708872
  1.089539314412129190793027457231843700294486594865326765338587929055980425160901
  2.201640880358843793326393001708644130370018951703733240381220100406889408981475
  9.844172310877760484923259844070267149553296139666547668993512708724577352991

julia> Y = Symmetric(X)
10×10 Symmetric{BigFloat, Matrix{BigFloat}}:
 1.81304 0.688118 1.22362 1.34483 1.22881 1.32082 1.00047 0.88352 1.64804 0.619048
 0.688118 0.243196 0.816204 0.573237 0.963247 0.381922 0.862619 0.123559 0.502359 0.979202
 1.22362 0.816204 0.639077 0.421363 1.01484 0.63954 0.83318 0.446309 1.56783 1.09914
 1.34483 0.573237 0.421363 1.59545 1.44708 0.526422 0.828333 0.49427 1.2904 0.719624
 1.22881 0.963247 1.01484 1.44708 1.96836 0.9886 0.345132 0.791248 1.5455 0.984035
 1.32082 0.381922 0.63954 0.526422 0.9886 1.34552 0.953025 1.38539 1.04277 1.62095
 1.00047 0.862619 0.83318 0.828333 0.345132 0.953025 0.858865 0.851573 0.425886 1.67392
 0.88352 0.123559 0.446309 0.49427 0.791248 1.38539 0.851573 0.0927274 1.02034 0.827739
 1.64804 0.502359 1.56783 1.2904 1.5455 1.04277 0.425886 1.02034 0.734844 1.08006
 0.619048 0.979202 1.09914 0.719624 0.984035 1.62095 1.67392 0.827739 1.08006 1.72621

julia> eigvals(Y)
ERROR: MethodError: no method matching eigvals!(::Symmetric{BigFloat, Matrix{BigFloat}})
Closest candidates are:
  eigvals!(::StridedMatrix{var"#s829"} where var"#s829"<:Union{Float32, Float64}; permute, scale, sortby) at C:\buildbot\worker\package_win64\build\usr\share\julia\stdlib\v1.6\LinearAlgebra\src\eigen.jl:291
  eigvals!(::StridedMatrix{var"#s830"} where var"#s830"<:Union{ComplexF32, ComplexF64}; permute, scale, sortby) at C:\buildbot\worker\package_win64\build\usr\share\julia\stdlib\v1.6\LinearAlgebra\src\eigen.jl:296
  eigvals!(::StridedMatrix{T}, ::StridedMatrix{T}; sortby) where T<:Union{Float32, Float64} at C:\buildbot\worker\package_win64\build\usr\share\julia\stdlib\v1.6\LinearAlgebra\src\eigen.jl:544
  ...
Stacktrace:
 [1] eigvals(A::Symmetric{BigFloat, Matrix{BigFloat}})
   @ LinearAlgebra C:\buildbot\worker\package_win64\build\usr\share\julia\stdlib\v1.6\LinearAlgebra\src\symmetric.jl:740
 [2] top-level scope
   @ REPL[13]:1

julia> Z = Hermitian(X)
10×10 Hermitian{BigFloat, Matrix{BigFloat}}:
 1.81304 0.688118 1.22362 1.34483 1.22881 1.32082 1.00047 0.88352 1.64804 0.619048
 0.688118 0.243196 0.816204 0.573237 0.963247 0.381922 0.862619 0.123559 0.502359 0.979202
 1.22362 0.816204 0.639077 0.421363 1.01484 0.63954 0.83318 0.446309 1.56783 1.09914
 1.34483 0.573237 0.421363 1.59545 1.44708 0.526422 0.828333 0.49427 1.2904 0.719624
 1.22881 0.963247 1.01484 1.44708 1.96836 0.9886 0.345132 0.791248 1.5455 0.984035
 1.32082 0.381922 0.63954 0.526422 0.9886 1.34552 0.953025 1.38539 1.04277 1.62095
 1.00047 0.862619 0.83318 0.828333 0.345132 0.953025 0.858865 0.851573 0.425886 1.67392
 0.88352 0.123559 0.446309 0.49427 0.791248 1.38539 0.851573 0.0927274 1.02034 0.827739
 1.64804 0.502359 1.56783 1.2904 1.5455 1.04277 0.425886 1.02034 0.734844 1.08006
 0.619048 0.979202 1.09914 0.719624 0.984035 1.62095 1.67392 0.827739 1.08006 1.72621

julia> eigvals(Z)
10-element Vector{BigFloat}:
 -1.40896494093833723000919442666358694782060277534420585719212498189431446573352
 -0.9628570629553533920427015265454329908211049396906281502199649555971476817879393
 -0.765572319270339668165400589029211855446345366148112121821247891083801835348516
 -0.4988457885526648034975679430523053256471389136676962921706146821259835194905027
 -0.04967253288626804519859817605198605470194529038496302903243869042530808557833691
  0.7331486204381298592384410093739200409781239753824975991067791372244422807346604
  0.8346942215521769622694146059645529605227057642425001766162913257146661200708872
  1.089539314412129190793027457231843700294486594865326765338587929055980425160901
  2.201640880358843793326393001708644130370018951703733240381220100406889408981475
  9.844172310877760484923259844070267149553296139666547668993512708724577352991

julia> 

```

The problem is that this call is far away in my call stack through several packages, and I cannot force the packages to upgrade their matrices to `Hermitian` instead of `Symmetric`.

Which square in the disptch field do you propose I patch on my local environnement to make this work ?

I tried to add :

```julia
GenericLinearAlgebra.eigvals!(X::Symmetric{BigFloat, Matrix{BigFloat}}) = GenericLinearAlgebra.eigvals!(GenericLinearAlgebra.Hermitian(X))

```

But it was’nt enough. The call stack I have on my real code is

```julia
ERROR: MethodError: no method matching geigvals!(::LinearAlgebra.Symmetric{BigFloat, Matrix{BigFloat}}, ::LinearAlgebra.QRIteration)
Closest candidates are:
  geigvals!(::LinearAlgebra.SymTridiagonal{T, V} where V<:AbstractVector{T}, ::Any) where T<:AbstractFloat at C:\Users\u009192\.julia\packages\GenericSchur\i4qpR\src\symtridiag.jl:24
Stacktrace:
 [1] eigvals!(A::LinearAlgebra.Symmetric{BigFloat, Matrix{BigFloat}}, alg::LinearAlgebra.QRIteration; kwargs::Base.Iterators.Pairs{Union{}, Union{}, Tuple{}, NamedTuple{(), Tuple{}}})
   @ GenericSchur ~\.julia\packages\GenericSchur\i4qpR\src\GenericSchur.jl:98
 [2] eigvals!(A::LinearAlgebra.Symmetric{BigFloat, Matrix{BigFloat}}, alg::LinearAlgebra.QRIteration) (repeats 2 times)
   @ GenericSchur ~\.julia\packages\GenericSchur\i4qpR\src\GenericSchur.jl:98
 [3] eigvals(A::LinearAlgebra.Symmetric{BigFloat, Matrix{BigFloat}})
   @ LinearAlgebra C:\buildbot\worker\package_win64\build\usr\share\julia\stdlib\v1.6\LinearAlgebra\src\symmetric.jl:740
 [4] quadform(x::Convex.AdditionAtom, A::Matrix{BigFloat})
   @ Convex ~\.julia\packages\Convex\ubaUN\src\atoms\second_order_cone\quadform.jl:12
 [5] top-level scope
   @ REPL[57]:1

```

I also tried adding :

```julia
LinearAlgebra.eigvals(A::LinearAlgebra.Symmetric{BigFloat, Matrix{BigFloat}}) = GenericLinearAlgebra.eigvals!(GenericLinearAlgebra.Hermitian(A))

```

And still same problem, although different call stack:

```julia
ERROR: MethodError: no method matching geigvals!(::LinearAlgebra.Hermitian{BigFloat, Matrix{BigFloat}}, 
::LinearAlgebra.QRIteration)
Closest candidates are:
  geigvals!(::LinearAlgebra.SymTridiagonal{T, V} where V<:AbstractVector{T}, ::Any) where T<:AbstractFloat at C:\Users\u009192\.julia\packages\GenericSchur\i4qpR\src\symtridiag.jl:24
Stacktrace:
 [1] eigvals!(A::LinearAlgebra.Hermitian{BigFloat, Matrix{BigFloat}}, alg::LinearAlgebra.QRIteration; kwargs::Base.Iterators.Pairs{Union{}, Union{}, Tuple{}, NamedTuple{(), Tuple{}}})
   @ GenericSchur ~\.julia\packages\GenericSchur\i4qpR\src\GenericSchur.jl:98
 [2] eigvals!(A::LinearAlgebra.Hermitian{BigFloat, Matrix{BigFloat}}, alg::LinearAlgebra.QRIteration) (repeats 2 times)
   @ GenericSchur ~\.julia\packages\GenericSchur\i4qpR\src\GenericSchur.jl:98
 [3] eigvals(A::LinearAlgebra.Symmetric{BigFloat, Matrix{BigFloat}})
   @ Main .\REPL[58]:1
 [4] quadform(x::Convex.AdditionAtom, A::Matrix{BigFloat})
   @ Convex ~\.julia\packages\Convex\ubaUN\src\atoms\second_order_cone\quadform.jl:12
 [5] top-level scope
   @ REPL[59]:1

```

Here is my MWE :

```julia
using Convex
x = Variable(3)
y = rand(3)
M = big.(rand(3,3))
M = M+M'

Prob = Convex.minimize(Convex.quadform(x - y, M), numeric_type = BigFloat) # error

using LinearAlgebra
M = Symmetric(M)

Prob = Convex.minimize(Convex.quadform(x - y, M), numeric_type = BigFloat) # error

using GenericLinearAlgebra

Prob = Convex.minimize(Convex.quadform(x - y, M), numeric_type = BigFloat) # error

M = Hermitian(M)

Prob = Convex.minimize(Convex.quadform(x - y, M), numeric_type = BigFloat) # error

M = GenericLinearAlgebra.Hermitian(M)
Prob = Convex.minimize(Convex.quadform(x - y, M), numeric_type = BigFloat) # error

# What should I do ? 

```

* * *

EDIT: By taking a look, I found that :

```julia
julia> Symmetric{BigFloat, Matrix{BigFloat}} <: Hermitian{BigFloat, Matrix{BigFloat}}
false

```

Why is that ?

* * *

In this file : [julia/symmetric.jl at master · JuliaLang/julia · GitHub](https://github.com/JuliaLang/julia/blob/master/stdlib/LinearAlgebra/src/symmetric.jl), it says :

```julia
ishermitian(A::Hermitian) = true
ishermitian(A::Symmetric{<:Real}) = true
ishermitian(A::Symmetric{<:Complex}) = isreal(A)
issymmetric(A::Hermitian{<:Real}) = true
issymmetric(A::Hermitian{<:Complex}) = isreal(A)
issymmetric(A::Symmetric) = true

```

So clearly, for reals, Symmetric matrices could be treated by the same code as Hermitian matrices, which is probably why there is no code specific for them in `GenericLinearAlgebra.jl`.

Even with all this digging around, I still cannot find the right spot in the method field to patch 😕

---

<div class="post-metadata">

**Author:** ![Ralph\_Smith](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/ralph_smith/32/10344_2.png) [@Ralph\_Smith](https://discourse.julialang.org/u/Ralph_Smith)\
**Post date:** [July 3, 2021, 4:04am UTC](https://discourse.julialang.org/t/regresion-eigvals-of-bigfloat-symmetric-matrices-does-not-work-anymore/63947/2 "2021-07-03T04:04:02Z")

</div>

Your “real code” and the examples are using different packages. The “real code” encounters a twisty gap in the method tree of my GenericSchur package, which I will address in the next release. (Thanks for your accidental contribution, and sorry for the inconvenience.)

A possible workaround for now is

```julia
import LinearAlgebra.eigvals
eigvals(A::Symmetric{BigFloat}) = eigen(Hermitian(A)).values

```

---

<div class="post-metadata">

**Author:** ![lrnv](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/lrnv/32/19373_2.png) [@lrnv](https://discourse.julialang.org/u/lrnv)\
**Post date:** [July 5, 2021, 8:20am UTC](https://discourse.julialang.org/t/regresion-eigvals-of-bigfloat-symmetric-matrices-does-not-work-anymore/63947/3 "2021-07-05T08:20:05Z")

</div>

Thanks a lot for the workaround. I’ll check your changes once they are released for sure.