# Trying to use data as an initial condition for a 1D diffusion problem with DiffEqOperators.jl

**URL:** <https://discourse.julialang.org/t/trying-to-use-data-as-an-initial-condition-for-a-1d-diffusion-problem-with-diffeqoperators-jl/70433>\
**Category:** New to Julia\
**Tags:** pde\
**Created:** [October 26, 2021, 8:18pm UTC](https://discourse.julialang.org/t/trying-to-use-data-as-an-initial-condition-for-a-1d-diffusion-problem-with-diffeqoperators-jl/70433 "2021-10-26T20:18:36Z")\
**Posts on this page:** 14\
**Page:** 1

<div class="post-metadata">

**Author:** ![thompsonmj](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/thompsonmj/32/25172_2.png) [@thompsonmj](https://discourse.julialang.org/u/thompsonmj)\
**Post date:** [October 26, 2021, 8:18pm UTC](https://discourse.julialang.org/t/trying-to-use-data-as-an-initial-condition-for-a-1d-diffusion-problem-with-diffeqoperators-jl/70433/1 "2021-10-26T20:18:36Z")

</div>

Using code from [Example 1](https://github.com/SciML/DiffEqOperators.jl) in the library repo README to get started.

I’m getting `ERROR: MethodError: no method matching zero(::Type{Vector{Float64}})` and not clear how to decode the Stacktrace …

```julia
using OrdinaryDiffEq, ModelingToolkit, DiffEqOperators, DomainSets, DifferentialEquations, Interpolations
###
function uniform_linear_sample(data_in, n_samples)
        # Resample a 1D dataset using a given number of sample points using linear interpolation.
    
        nodes_in = range(1, size(data_in)[1], length=length(data_in))
        nodes_eval = range(1, Int(nodes_in[end]), length = Int(n_samples))
    
        int = interpolate((nodes_in,), data_in, Gridded(Linear()))
    
        data_out = zeros(length(nodes_eval))
        idx = trues(length(nodes_eval))
    
        data_out[idx] = int(nodes_eval[idx])
    
        return data_out
end

n_nodes = 1000

x_ic = range(0,Float64(2pi),length=10000)
data_vector = cos.(x_ic) .+ 1

ic() = uniform_linear_sample(data_vector,n_nodes)

@register ic()
###
# Parameters, variables, and derivatives
@parameters t x
@variables u(..)
Dt = Differential(t)
Dxx = Differential(x)^2

# 1D PDE and boundary conditions
eq = Dt(u(t,x)) ~ Dxx(u(t,x))
bcs = [u(0,x) ~ ic(),
       u(t,0) ~ exp(-t),
       u(t,Float64(pi)) ~ -exp(-t)]

# Space and time domains
domains = [t ∈ Interval(0.0,1.0),
           x ∈ Interval(0.0,Float64(2pi))]

# PDE system
@named pdesys = PDESystem(eq,bcs,domains,[t,x],[u(t,x)])

# Method of lines discretization
dx = 0.1
order = 2
discretization = MOLFiniteDifference([x=>dx],t;centered_order=order)

# Convert the PDE problem into an ODE problem
prob = discretize(pdesys,discretization)

# Solve ODE problem
sol = solve(prob,saveat=0.1)

```

```julia
ERROR: LoadError: MethodError: no method matching zero(::Type{Vector{Float64}})
Closest candidates are:
  zero(::Union{Type{P}, P}) where P<:Dates.Period at C:\buildbot\worker\package_win64\build\usr\share\julia\stdlib\v1.6\Dates\src\periods.jl:53
  zero(::ExtendedJumpArray) at C:\Users\thompsmj.X-MJIS3050PC09\.julia\packages\DiffEqJump\x05Qi\src\extended_jump_array.jl:26
  zero(::Unitful.AbstractQuantity{T, D, U} where {T, D, U<:(Unitful.Units{N, D, A} where {N, D, A<:Unitful.Affine})}) at C:\Users\thompsmj.X-MJIS3050PC09\.julia\packages\Unitful\yI5QN\src\quantities.jl:374
  ...
Stacktrace:
 [1] zero(x::Vector{Vector{Float64}})
   @ Base .\abstractarray.jl:1085

```

---

<div class="post-metadata">

**Author:** ![ChrisRackauckas](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/chrisrackauckas/32/77_2.png) [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)\
**Post date:** [October 27, 2021, 10:51am UTC](https://discourse.julialang.org/t/trying-to-use-data-as-an-initial-condition-for-a-1d-diffusion-problem-with-diffeqoperators-jl/70433/2 "2021-10-27T10:51:52Z")

</div>

> [@thompsonmj](#):
>
> `u(0,x) ~ ic()`

make it `ic(x)` and use a callable.

---

<div class="post-metadata">

**Author:** ![thompsonmj](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/thompsonmj/32/25172_2.png) [@thompsonmj](https://discourse.julialang.org/u/thompsonmj)\
**Post date:** [October 27, 2021, 9:30pm UTC](https://discourse.julialang.org/t/trying-to-use-data-as-an-initial-condition-for-a-1d-diffusion-problem-with-diffeqoperators-jl/70433/3 "2021-10-27T21:30:46Z")

</div>

Hi Chris, thanks for trying to help, but I’m still unclear. I can interpolate the data fine, but I don’t understand what to do to “use a callable,” though I’ve been going through the [docs](https://docs.julialang.org/en/v1/manual/methods/#Function-like-objects) to try to get the hang of it.

I tried using exactly what I have posted above, and swapping in this line as you suggest:

```julia
bcs = [u(0,x) ~ ic(x),
       u(t,0) ~ exp(-t),
       u(t,Float64(pi)) ~ -exp(-t)]

```

And I get

```julia
ERROR: LoadError: MethodError: no method matching ic(::Num)

```

on that line.

Above that, I then tried

```julia
ic(x) = uniform_linear_sample(data_vector,n_nodes)

```

which gets through to the end and gives this error at the `solve` line

```julia
sol = solve(prob,saveat=0.1)

ERROR: LoadError: MethodError: no method matching zero(::Type{Vector{Float64}})

```

Edit: fixed link to wrong place.

---

<div class="post-metadata">

**Author:** ![ChrisRackauckas](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/chrisrackauckas/32/77_2.png) [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)\
**Post date:** [October 28, 2021, 9:27pm UTC](https://discourse.julialang.org/t/trying-to-use-data-as-an-initial-condition-for-a-1d-diffusion-problem-with-diffeqoperators-jl/70433/4 "2021-10-28T21:27:31Z")

</div>

Why not just use the DataInterpolations.jl linear interpolation?

---

<div class="post-metadata">

**Author:** ![thompsonmj](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/thompsonmj/32/25172_2.png) [@thompsonmj](https://discourse.julialang.org/u/thompsonmj)\
**Post date:** [October 29, 2021, 2:03pm UTC](https://discourse.julialang.org/t/trying-to-use-data-as-an-initial-condition-for-a-1d-diffusion-problem-with-diffeqoperators-jl/70433/5 "2021-10-29T14:03:58Z")

</div>

Didn’t know about it! Looks like a useful library.

Trying it out though I’m getting `LoadError: UndefVarError: LinearInterpolation not defined` with the current v3.6.1.

---

<div class="post-metadata">

**Author:** ![ChrisRackauckas](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/chrisrackauckas/32/77_2.png) [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)\
**Post date:** [October 29, 2021, 2:14pm UTC](https://discourse.julialang.org/t/trying-to-use-data-as-an-initial-condition-for-a-1d-diffusion-problem-with-diffeqoperators-jl/70433/6 "2021-10-29T14:14:22Z")

</div>

Show what you ran.

---

<div class="post-metadata">

**Author:** ![thompsonmj](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/thompsonmj/32/25172_2.png) [@thompsonmj](https://discourse.julialang.org/u/thompsonmj)\
**Post date:** [October 29, 2021, 2:45pm UTC](https://discourse.julialang.org/t/trying-to-use-data-as-an-initial-condition-for-a-1d-diffusion-problem-with-diffeqoperators-jl/70433/7 "2021-10-29T14:45:36Z")

</div>

OK, the issue with `LinearInterpolation not defined` is resolved if I don’t load `Interpolations` and `DataInterpolations` together.

```julia
using DataInterpolations, Interpolations
u = rand(5)
t = 0:4
interp = LinearInterpolation(u,t)

ERROR: LoadError: UndefVarError: LinearInterpolation not defined

```

```julia
using DataInterpolations
u = rand(5)
t = 0:4
interp = LinearInterpolation(u,t)

10-element LinearInterpolation{Vector{Float64}, UnitRange{Int64}, true, Float64}:

```

This is where I’m unfamiliar with symbolic programming, so the final line gives `LoadError: MethodError: no method matching munge_data(::Vector{Float64}, ::Float64)`

running:

```julia
using OrdinaryDiffEq, ModelingToolkit, DiffEqOperators, DomainSets, DifferentialEquations, DataInterpolations

x_dense = range(0,Float64(2pi),length=10000)
data = cos.(x_dense) .+ 1.0 .+ 0.05*randn(10000)

# Parameters, variables, and derivatives
@parameters t x
@variables u(..)
Dt = Differential(t)
Dxx = Differential(x)^2

# 1D PDE and boundary conditions
ic(x) = LinearInterpolation(data, x)
@register ic(x)
eq = Dt(u(t,x)) ~ Dxx(u(t,x))
bcs = [u(0,x) ~ ic(x),
       u(t,0) ~ exp(-t),
       u(t,Float64(pi)) ~ -exp(-t)]

# Space and time domains
domains = [t ∈ Interval(0.0,1.0),
           x ∈ Interval(0.0,Float64(2pi))]

# PDE system
@named pdesys = PDESystem(eq,bcs,domains,[t,x],[u(t,x)])

# Method of lines discretization
dx = 0.1
order = 2
discretization = MOLFiniteDifference([x=>dx],t;centered_order=order)

# Convert the PDE problem into an ODE problem
prob = discretize(pdesys,discretization)

```

---

<div class="post-metadata">

**Author:** ![thompsonmj](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/thompsonmj/32/25172_2.png) [@thompsonmj](https://discourse.julialang.org/u/thompsonmj)\
**Post date:** [October 29, 2021, 3:00pm UTC](https://discourse.julialang.org/t/trying-to-use-data-as-an-initial-condition-for-a-1d-diffusion-problem-with-diffeqoperators-jl/70433/8 "2021-10-29T15:00:53Z")

</div>

Also tried `ic(x) = LinearInterpolation(data, 0:Float64(2pi))` with all else the same, and running `prob = discretize(pdesys,discretization)` succeeds, giving:

```julia
ODEProblem with uType Vector{LinearInterpolation{Vector{Float64}, StepRangeLen{Float64, Base.TwicePrecision{Float64}, Base.TwicePrecision{Float64}}, true, Float64}} and tType Float64. In-place: true

```

but `sol = solve(prob,Tsit5(),saveat=0.1)` gives:

```julia
ERROR: LoadError: MethodError: Cannot `convert` an object of type Vector{Float64} to an object of type LinearInterpolation{Vector{Float64}, StepRangeLen{Float64, Base.TwicePrecision{Float64}, Base.TwicePrecision{Float64}}, true, Float64}

```

---

<div class="post-metadata">

**Author:** ![ChrisRackauckas](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/chrisrackauckas/32/77_2.png) [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)\
**Post date:** [October 29, 2021, 3:04pm UTC](https://discourse.julialang.org/t/trying-to-use-data-as-an-initial-condition-for-a-1d-diffusion-problem-with-diffeqoperators-jl/70433/9 "2021-10-29T15:04:26Z")

</div>

No, LinearInterpolation is a callable. Look at the documentation.

```julia
using DataInterpolations
u = rand(5)
t = 0:4
interp = LinearInterpolation(u,t)
interp(t)

```

Because of that, you do:

```julia
ic = LinearInterpolation(data, x_dense)

```

now `ic(x)` is the interpolation function over the data, which means

```julia
@register ic(x)
bcs = [u(0,x) ~ ic(x),
       u(t,0) ~ exp(-t),
       u(t,Float64(pi)) ~ -exp(-t)]

```

will work.

---

<div class="post-metadata">

**Author:** ![thompsonmj](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/thompsonmj/32/25172_2.png) [@thompsonmj](https://discourse.julialang.org/u/thompsonmj)\
**Post date:** [October 29, 2021, 4:06pm UTC](https://discourse.julialang.org/t/trying-to-use-data-as-an-initial-condition-for-a-1d-diffusion-problem-with-diffeqoperators-jl/70433/10 "2021-10-29T16:06:30Z")

</div>

```julia
using OrdinaryDiffEq, ModelingToolkit, DiffEqOperators, DomainSets, DifferentialEquations, DataInterpolations

x_dense = range(0,Float64(2pi),length=10000)
data = cos.(x_dense) .+ 1.0 

# Parameters, variables, and derivatives
@parameters t x
@variables u(..)
Dt = Differential(t)
Dxx = Differential(x)^2

# 1D PDE and boundary conditions
ic = LinearInterpolation(data, x_dense)
@register ic(x)

```

```julia
ERROR: LoadError: cannot define function ic; it already has a value

```

`ic` iteself is:

```julia
julia> ic
20000-element LinearInterpolation{Vector{Float64}, StepRangeLen{Float64, Base.TwicePrecision{Float64}, Base.TwicePrecision{Float64}}, true, Float64}:

```

`ic(x)` is:

```julia
julia> ic(x)
ERROR: MethodError: isless(::Num, ::Float64) is ambiguous. Candidates:
  isless(x::Real, y::AbstractFloat) in Base at operators.jl:168
  isless(a::Num, b::Real) in Symbolics at C:\Users\thompsmj.X-MJIS3050PC09\.julia\packages\Symbolics\Cmx10\src\num.jl:130
Possible fix, define
  isless(::Num, ::AbstractFloat)

```

---

<div class="post-metadata">

**Author:** ![ChrisRackauckas](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/chrisrackauckas/32/77_2.png) [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)\
**Post date:** [November 1, 2021, 10:42pm UTC](https://discourse.julialang.org/t/trying-to-use-data-as-an-initial-condition-for-a-1d-diffusion-problem-with-diffeqoperators-jl/70433/11 "2021-11-01T22:42:04Z")

</div>

The answer is in [https://github.com/PumasAI/DataInterpolations.jl/pull/93](https://github.com/PumasAI/DataInterpolations.jl/pull/93) .

```julia
import Symbolics
(interp::DataInterpolations.AbstractInterpolation)(t::Symbolics.Num) = Symbolics.SymbolicUtils.term(interp,t)

```

and the release with that will make it automatic.

---

<div class="post-metadata">

**Author:** ![bclyons12](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/bclyons12/32/33734_2.png) [@bclyons12](https://discourse.julialang.org/u/bclyons12)\
**Post date:** [November 2, 2021, 8:04pm UTC](https://discourse.julialang.org/t/trying-to-use-data-as-an-initial-condition-for-a-1d-diffusion-problem-with-diffeqoperators-jl/70433/12 "2021-11-02T20:04:28Z")

</div>

I’ve been running into similar issues using DataInterpolations’s `CubicSplines` in ModelingToolkit. The pull request provided by @ChrisRackauckas looks like it may fix my problems, but I can’t update Symbolics to the latest version. There’s some sort of incompatibility with the packages in ModelingToolkit. Any thoughts?

```julia
pkg> add Symbolics@4.0
   Resolving package versions...
ERROR: Unsatisfiable requirements detected for package ModelingToolkit [961ee093]:
 ModelingToolkit [961ee093] log:
 ├─possible versions are: 0.0.1-6.7.1 or uninstalled
 ├─restricted to versions * by QED [03dc1bc1], leaving only versions 0.0.1-6.7.1
 │ └─QED [03dc1bc1] log:
 │ ├─possible versions are: 0.1.0 or uninstalled
 │ └─QED [03dc1bc1] is fixed to version 0.1.0
 ├─restricted by compatibility requirements with Symbolics [0c5d862f] to versions: 0.0.1-5.9.1 or uninstalled, leaving only versions: 0.0.1-5.9.1
 │ └─Symbolics [0c5d862f] log:
 │ ├─possible versions are: 0.1.0-4.0.0 or uninstalled
 │ ├─restricted to versions * by QED [03dc1bc1], leaving only versions 0.1.0-4.0.0
 │ │ └─QED [03dc1bc1] log: see above
 │ └─restricted to versions 4.0 by an explicit requirement, leaving only versions 4.0.0
 ├─restricted by compatibility requirements with RuntimeGeneratedFunctions [7e49a35a] to versions: [0.0.1-3.21.0, 4.5.0-6.7.1] or uninstalled, leaving only versions: [0.0.1-3.21.0, 4.5.0-5.9.1]
 │ └─RuntimeGeneratedFunctions [7e49a35a] log:
 │ ├─possible versions are: 0.1.0-0.5.3 or uninstalled
 │ └─restricted by compatibility requirements with Symbolics [0c5d862f] to versions: 0.5.0-0.5.3
 │ └─Symbolics [0c5d862f] log: see above
 ├─restricted by compatibility requirements with Latexify [23fbe1c1] to versions: [0.0.1-0.8.0, 1.2.7-6.7.1] or uninstalled, leaving only versions: [0.0.1-0.8.0, 1.2.7-3.21.0, 4.5.0-5.9.1]
 │ └─Latexify [23fbe1c1] log:
 │ ├─possible versions are: 0.5.0-0.15.9 or uninstalled
 │ ├─restricted by compatibility requirements with Symbolics [0c5d862f] to versions: 0.11.0-0.15.9
 │ │ └─Symbolics [0c5d862f] log: see above
 │ └─restricted by compatibility requirements with Requires [ae029012] to versions: 0.13.0-0.15.9 or uninstalled, leaving only versions: 0.13.0-0.15.9
 │ └─Requires [ae029012] log:
 │ ├─possible versions are: 0.5.0-1.1.3 or uninstalled
 │ └─restricted by compatibility requirements with Symbolics [0c5d862f] to versions: 1.1.0-1.1.3
 │ └─Symbolics [0c5d862f] log: see above
 ├─restricted by compatibility requirements with StaticArrays [90137ffa] to versions: 4.0.7-6.7.1 or uninstalled, leaving only versions: 4.5.0-5.9.1
 │ └─StaticArrays [90137ffa] log:
 │ ├─possible versions are: 0.8.0-1.2.13 or uninstalled
 │ ├─restricted to versions * by Equilibrium [187daef3], leaving only versions 0.8.0-1.2.13
 │ │ └─Equilibrium [187daef3] log:
 │ │ ├─possible versions are: 0.1.0 or uninstalled
 │ │ └─Equilibrium [187daef3] is fixed to version 0.1.0
 │ ├─restricted by compatibility requirements with ForwardDiff [f6369f11] to versions: 0.8.3-1.2.13
 │ │ └─ForwardDiff [f6369f11] log:
 │ │ ├─possible versions are: 0.9.0-0.10.21 or uninstalled
 │ │ ├─restricted to versions * by Equilibrium [187daef3], leaving only versions 0.9.0-0.10.21
 │ │ │ └─Equilibrium [187daef3] log: see above
 │ │ ├─restricted by compatibility requirements with DiffRules [b552c78f] to versions: 0.10.6-0.10.21 or uninstalled, leaving only versions: 0.10.6-0.10.21
 │ │ │ └─DiffRules [b552c78f] log:
 │ │ │ ├─possible versions are: 0.0.8-1.3.1 or uninstalled
 │ │ │ ├─restricted by compatibility requirements with ForwardDiff [f6369f11] to versions: [0.0.8-1.0.2, 1.2.1-1.3.1]
 │ │ │ │ └─ForwardDiff [f6369f11] log: see above
 │ │ │ └─restricted by compatibility requirements with Symbolics [0c5d862f] to versions: 0.1.0-1.3.1, leaving only versions: [0.1.0-1.0.2, 1.2.1-1.3.1]
 │ │ │ └─Symbolics [0c5d862f] log: see above
 │ │ └─restricted by compatibility requirements with StaticArrays [90137ffa] to versions: 0.10.13-0.10.21 or uninstalled, leaving only versions: 0.10.13-0.10.21
 │ │ └─StaticArrays [90137ffa] log: see above
 │ └─restricted by compatibility requirements with Symbolics [0c5d862f] to versions: 1.1.0-1.2.13
 │ └─Symbolics [0c5d862f] log: see above
 └─restricted by compatibility requirements with SymbolicUtils [d1185830] to versions: 0.0.1-3.1.1 or uninstalled — no versions left
   └─SymbolicUtils [d1185830] log:
     ├─possible versions are: 0.1.0-0.18.0 or uninstalled
     └─restricted by compatibility requirements with Symbolics [0c5d862f] to versions: 0.18.0
       └─Symbolics [0c5d862f] log: see above

```

---

<div class="post-metadata">

**Author:** ![ChrisRackauckas](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/chrisrackauckas/32/77_2.png) [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)\
**Post date:** [November 2, 2021, 8:06pm UTC](https://discourse.julialang.org/t/trying-to-use-data-as-an-initial-condition-for-a-1d-diffusion-problem-with-diffeqoperators-jl/70433/13 "2021-11-02T20:06:07Z")

</div>

Symbolics.jl v4 was just released, and this requires that update. So some downstream updates will need to be done before this can really be used everywhere. Working on it 😅

---

<div class="post-metadata">

**Author:** ![bclyons12](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/bclyons12/32/33734_2.png) [@bclyons12](https://discourse.julialang.org/u/bclyons12)\
**Post date:** [November 2, 2021, 8:12pm UTC](https://discourse.julialang.org/t/trying-to-use-data-as-an-initial-condition-for-a-1d-diffusion-problem-with-diffeqoperators-jl/70433/14 "2021-11-02T20:12:59Z")

</div>

Sounds good, thanks!