# Inv() producing NaNs when called on a Tridiagonal

**URL:** <https://discourse.julialang.org/t/inv-producing-nans-when-called-on-a-tridiagonal/16269>\
**Category:** Numerics\
**Created:** [October 13, 2018, 8:06am UTC](https://discourse.julialang.org/t/inv-producing-nans-when-called-on-a-tridiagonal/16269 "2018-10-13T08:06:32Z")\
**Posts on this page:** 3\
**Page:** 1

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**Author:** ![mdsalerno](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/mdsalerno/32/5539_2.png) [@mdsalerno](https://discourse.julialang.org/u/mdsalerno)\
**Post date:** [October 13, 2018, 8:06am UTC](https://discourse.julialang.org/t/inv-producing-nans-when-called-on-a-tridiagonal/16269/1 "2018-10-13T08:06:32Z")

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I’m creating a 90x90 tridiagonal matrix using the function below, which I store in the variable `A90`. When I call `inv(A90)`, I get a matrix of all NaNs, but if I call `inv(Matrix(A90))`, the inverse is successfully computed. Is this behavior expected?

```julia
using LinearAlgebra
function central_difference_discretization(N; dfunc = x -> 12x^2 - 2N^2,
                                           dufunc = x -> N^2 + 4N*x,
                                           dlfunc = x -> N^2 - 4N*x,
                                           bfunc = x -> 114ℯ^-x * (1 + 3x),
                                           b0 = 0, bf = 57/ℯ,
                                           x0 = 0, xf = 1)
    h = 1/N
    d, du, dl, b = map(dfunc, (x0+h):h:(xf-h)), map(dufunc, (x0+h):h:(xf-2h)), 
                   map(dlfunc, (x0+2h):h:(xf-h)), map(bfunc, (x0+h):h:(xf-h))
    b[1] -= dlfunc(x0)*b0 # subtract the boundary term 
    b[end] -= dufunc(xf)*bf # subtract the boundary term 
    Tridiagonal(dl, d, du), b
end

A90, b90 = central_difference_discretization(90)

typeof(A90) # Tridiagonal{Float64,Array{Float64,1}}

inv(A90) # Produces a matrix of all NaNs
inv(Matrix(A90)) # Successfully computes the inverse

A80, b80 = central_difference_discretization(80)
inv(A80) # Works fine on Tridiagonals smaller than 82x82

```

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<div class="post-metadata">

**Author:** ![Tamas\_Papp](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/tamas_papp/32/25949_2.png) [@Tamas\_Papp](https://discourse.julialang.org/u/Tamas_Papp)\
**Post date:** [October 13, 2018, 3:32pm UTC](https://discourse.julialang.org/t/inv-producing-nans-when-called-on-a-tridiagonal/16269/2 "2018-10-13T15:32:43Z")

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Did not investigate in detail, but could be a conditioning issue with the special method used for inverting `Tridiagonal`. I would suggest that you [open an issue](https://github.com/JuliaLang/julia/issues), and include the nice self-contained example that you have made (which should help a lot).

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<div class="post-metadata">

**Author:** ![mdsalerno](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/mdsalerno/32/5539_2.png) [@mdsalerno](https://discourse.julialang.org/u/mdsalerno)\
**Post date:** [October 13, 2018, 6:53pm UTC](https://discourse.julialang.org/t/inv-producing-nans-when-called-on-a-tridiagonal/16269/3 "2018-10-13T18:53:20Z")

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It’s likely to be a conditioning related problem as I’m deliberately generating an ill-conditioned matrix here. Went ahead and opened an [issue](https://github.com/JuliaLang/julia/issues/29630).