# Multi variables in lsqfit

**URL:** <https://discourse.julialang.org/t/multi-variables-in-lsqfit/112210>\
**Category:** Optimization (Mathematical)\
**Tags:** curve-fitting\
**Created:** [March 28, 2024, 5:04am UTC](https://discourse.julialang.org/t/multi-variables-in-lsqfit/112210 "2024-03-28T05:04:52Z")\
**Posts on this page:** 7\
**Page:** 1

<div class="post-metadata">

**Author:** ![Stephen](https://avatars.discourse-cdn.com/v4/letter/s/96bed5/32.png) [@Stephen](https://discourse.julialang.org/u/Stephen)\
**Post date:** [March 28, 2024, 5:04am UTC](https://discourse.julialang.org/t/multi-variables-in-lsqfit/112210/1 "2024-03-28T05:04:52Z")

</div>

```julia
using XLSX, DataFrames, LsqFit

df = DataFrame(XLSX.readtable("SMB.xlsx","平衡吸附量", infer_eltypes = true))

function Com_Langmuir(p, x)
    Ha, bA, bC, Hc = p
    CA = @view x[:, 1]
    CC = @view x[:, 2]
    @. qA = Ha*CA / (1 + bA*CA + bC*CC)
    @. qC = Hc*CC / (1 + bA*CA + bC*CC)
    vcat(qA, qC) #返回一个列向量
end

xdata = [df.CA df.CC]

ydata = vcat(df.qA_303K, df.qC_303K)

p0 = [1.983, 0.0067, 0.1951, 1.61]

ret = curve_fit(Com_Langmuir, xdata, ydata, p0)

```

```julia
ERROR: BoundsError: attempt to access 4-element Vector{Float64} at index [1:4, 2]
Stacktrace:
  [1] throw_boundserror(A::Vector{Float64}, I::Tuple{Base.Slice{Base.OneTo{Int64}}, Int64}) @ Base .\abstractarray.jl:737
  [2] checkbounds
    @ .\abstractarray.jl:702 [inlined]
  [3] view
    @ .\subarray.jl:184 [inlined]
  [4] Com_Langmuir(p::Matrix{Float64}, x::Vector{Float64})
    @ Main e:\06325\Julialang\test.jl:30
  [5] #18
    @ C:\Users\admin\.julia\packages\LsqFit\OglWj\src\curve_fit.jl:139 [inlined]
  [6] lmfit(f::LsqFit.var"#18#20"{…}, p0::Vector{…}, wt::Vector{…}; autodiff::Symbol, kwargs::@Kwargs{})
    @ LsqFit C:\Users\admin\.julia\packages\LsqFit\OglWj\src\curve_fit.jl:69
  [7] lmfit
    @ C:\Users\admin\.julia\packages\LsqFit\OglWj\src\curve_fit.jl:54 [inlined]
  [8] curve_fit(model::typeof(Com_Langmuir), xdata::Matrix{…}, ydata::Vector{…}, p0::Vector{…}; inplace::Bool, kwargs::@Kwargs{})
    @ LsqFit C:\Users\admin\.julia\packages\LsqFit\OglWj\src\curve_fit.jl:140
  [9] curve_fit(model::Function, xdata::Matrix{Float64}, ydata::Vector{Float64}, p0::Vector{Float64})
    @ LsqFit C:\Users\admin\.julia\packages\LsqFit\OglWj\src\curve_fit.jl:123
 [10] top-level scope
    @ e:\06325\Julialang\test.jl:42
Some type information was truncated. Use `show(err)` to see complete types.

```

In this function，there is two variables: CA & CC, both are vectors， what syntax should I use?

---

<div class="post-metadata">

**Author:** ![odow](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/odow/32/28685_2.png) [@odow](https://discourse.julialang.org/u/odow)\
**Post date:** [March 28, 2024, 5:21am UTC](https://discourse.julialang.org/t/multi-variables-in-lsqfit/112210/2 "2024-03-28T05:21:57Z")

</div>

Question reposted from: [Least square with multi-value function - #3 by Stephen](https://discourse.julialang.org/t/least-square-with-multi-value-function/47943/3)

Take a look at what the input to `Com_Langmuir` is. The error is saying that `x` is a vector, and you are trying to access the second column.

Do you mean `function Com_Langmuir(x, p)`?

---

<div class="post-metadata">

**Author:** ![Stephen](https://avatars.discourse-cdn.com/v4/letter/s/96bed5/32.png) [@Stephen](https://discourse.julialang.org/u/Stephen)\
**Post date:** [March 28, 2024, 5:27am UTC](https://discourse.julialang.org/t/multi-variables-in-lsqfit/112210/3 "2024-03-28T05:27:40Z")

</div>

Yes, CC & CA has number values, Shouldn’t I use matrix in function definition? Just leave x as a vector? But how to pass the valuse of CC & CA to Com\_Langmuir function in `curve_fit` ?

here is the data:

| Column 1 | Column 2 | Column 3 | Column 4 | E | F | G | H |
| --- | --- | --- | --- | --- | --- | --- | --- |
| CA | CC | qA\_293k | qA\_303K | qA\_313K | qC\_293K | qC\_303K | qC\_313K |
| 3.46 | 0.34 | 7.27 | 7.00 | 5.50 | 0.54 | 0.51 | 0.48 |
| 5.19 | 0.51 | 9.67 | 9.36 | 7.80 | 0.77 | 0.69 | 0.64 |
| 6.93 | 0.68 | 12.70 | 11.44 | 9.99 | 1.02 | 0.94 | 0.89 |
| 8.66 | 0.85 | 15.09 | 13.96 | 12.44 | 1.22 | 1.12 | 1.03 |
| 10.39 | 1.02 | 16.88 | 15.67 | 14.81 | 1.42 | 1.25 | 1.22 |
| 12.12 | 1.19 | 20.01 | 19.36 | 17.46 | 1.61 | 1.51 | 1.42 |

---

<div class="post-metadata">

**Author:** ![Stephen](https://avatars.discourse-cdn.com/v4/letter/s/96bed5/32.png) [@Stephen](https://discourse.julialang.org/u/Stephen)\
**Post date:** [March 28, 2024, 5:42am UTC](https://discourse.julialang.org/t/multi-variables-in-lsqfit/112210/4 "2024-03-28T05:42:23Z")

</div>

If I change the code as:

```julia
function Com_Langmuir(p, x)
    Ha, bA, bC, Hc = p
    CA = x[1]
    CC = x[2]
    qA = Ha*CA ./ (1 .+ bA*CA .+ bC*CC)
    qC = Hc*CC ./ (1 .+ bA*CA .+ bC*CC)
    vcat(qA, qC) #返回一个列向量
end

xdata = [df.CA, df.CC]

```

new error appears:

```julia
ERROR: MethodError: no method matching isinf(::Vector{Float64})

Closest candidates are:
  isinf(::BigFloat)
   @ Base mpfr.jl:978
  isinf(::Missing)
   @ Base missing.jl:101
  isinf(::ForwardDiff.Dual)
   @ ForwardDiff C:\Users\admin\.julia\packages\ForwardDiff\PcZ48\src\dual.jl:386
  ...

Stacktrace:
 [1] _any
   @ .\reduce.jl:1220 [inlined]
 [2] any
   @ .\reducedim.jl:1020 [inlined]
 [3] check_data_health(xdata::Vector{Vector{Float64}}, ydata::Vector{Float64})
   @ LsqFit C:\Users\admin\.julia\packages\LsqFit\OglWj\src\curve_fit.jl:23
 [4] curve_fit(model::typeof(Com_Langmuir), xdata::Vector{…}, ydata::Vector{…}, p0::Vector{…}; inplace::Bool, kwargs::@Kwargs{})
   @ LsqFit C:\Users\admin\.julia\packages\LsqFit\OglWj\src\curve_fit.jl:131
 [5] curve_fit(model::Function, xdata::Vector{Vector{Float64}}, ydata::Vector{Float64}, p0::Vector{Float64})
   @ LsqFit C:\Users\admin\.julia\packages\LsqFit\OglWj\src\curve_fit.jl:123
 [6] top-level scope
   @ e:\06325\Julialang\test.jl:42
Some type information was truncated. Use `show(err)` to see complete types.

```

---

<div class="post-metadata">

**Author:** ![odow](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/odow/32/28685_2.png) [@odow](https://discourse.julialang.org/u/odow)\
**Post date:** [March 28, 2024, 6:06am UTC](https://discourse.julialang.org/t/multi-variables-in-lsqfit/112210/5 "2024-03-28T06:06:22Z")

</div>

> Do you mean `function Com_Langmuir(x, p)` ?

The syntax for the model is `foo(x, params)`. See the documentation: [GitHub - JuliaNLSolvers/LsqFit.jl: Simple curve fitting in Julia](https://github.com/JuliaNLSolvers/LsqFit.jl?tab=readme-ov-file#basic-usage)

```Julia
julia> import CSV, DataFrames, LsqFit

julia> data = """
       CA,CC,qA_293k,qA_303K,qA_313K,qC_293K,qC_303K,qC_313K
       3.46,0.34,7.27,7.00,5.50,0.54,0.51,0.48
       5.19,0.51,9.67,9.36,7.80,0.77,0.69,0.64
       6.93,0.68,12.70,11.44,9.99,1.02,0.94,0.89
       8.66,0.85,15.09,13.96,12.44,1.22,1.12,1.03
       10.39,1.02,16.88,15.67,14.81,1.42,1.25,1.22
       12.12,1.19,20.01,19.36,17.46,1.61,1.51,1.42
       """
"CA,CC,qA_293k,qA_303K,qA_313K,qC_293K,qC_303K,qC_313K\n3.46,0.34,7.27,7.00,5.50,0.54,0.51,0.48\n5.19,0.51,9.67,9.36,7.80,0.77,0.69,0.64\n6.93,0.68,12.70,11.44,9.99,1.02,0.94,0.89\n8.66,0.85,15.09,13.96,12.44,1.22,1.12,1.03\n10.39,1.02,16.88,15.67,14.81,1.42,1.25,1.22\n12.12,1.19,20.01,19.36,17.46,1.61,1.51,1.42\n"

julia> df = CSV.read(IOBuffer(data), DataFrames.DataFrame)
6×8 DataFrame
 Row │ CA CC qA_293k qA_303K qA_313K qC_293K qC_303K qC_313K 
     │ Float64 Float64 Float64 Float64 Float64 Float64 Float64 Float64 
─────┼────────────────────────────────────────────────────────────────────────
   1 │ 3.46 0.34 7.27 7.0 5.5 0.54 0.51 0.48
   2 │ 5.19 0.51 9.67 9.36 7.8 0.77 0.69 0.64
   3 │ 6.93 0.68 12.7 11.44 9.99 1.02 0.94 0.89
   4 │ 8.66 0.85 15.09 13.96 12.44 1.22 1.12 1.03
   5 │ 10.39 1.02 16.88 15.67 14.81 1.42 1.25 1.22
   6 │ 12.12 1.19 20.01 19.36 17.46 1.61 1.51 1.42

julia> function Com_Langmuir(x, p)
           Ha, bA, bC, Hc = p
           CA = @view x[:, 1]
           CC = @view x[:, 2]
           qA = @. Ha * CA / (1 + bA*CA + bC*CC)
           qC = @. Hc * CC / (1 + bA*CA + bC*CC)
           return vcat(qA, qC)
       end
Com_Langmuir (generic function with 1 method)

julia> xdata = [df.CA df.CC]
6×2 Matrix{Float64}:
  3.46 0.34
  5.19 0.51
  6.93 0.68
  8.66 0.85
 10.39 1.02
 12.12 1.19

julia> ydata = vcat(df.qA_303K, df.qC_303K)
12-element Vector{Float64}:
  7.0
  9.36
 11.44
 13.96
 15.67
 19.36
  0.51
  0.69
  0.94
  1.12
  1.25
  1.51

julia> p0 = [1.983, 0.0067, 0.1951, 1.61]
4-element Vector{Float64}:
 1.983
 0.0067
 0.1951
 1.61

julia> ret = LsqFit.curve_fit(Com_Langmuir, xdata, ydata, p0)
LsqFit.LsqFitResult{Vector{Float64}, Vector{Float64}, Matrix{Float64}, Vector{Float64}, Vector{LsqFit.LMState{LsqFit.LevenbergMarquardt}}}([1.9591016841592197, 13.58216904773464, -138.11627273117097, 1.571176537116358], [-0.44929059679496763, 0.30369611921302386, -0.1765545568040796, -0.08488979377925254, 0.7435466251881575, -0.4782080120029555, 0.006248923887321234, 0.0715774743231512, -0.0536302114136612, -0.027791676070707094, 0.04227536237120133, -0.023189712036286503], [3.3437311886808767 -21.903812996616832 -2.1523978086444178 0.0; 4.932717988715785 -47.668295531028825 -4.68416776783525 0.0; … ; 0.0 -10.826815246805841 -1.0628827270494086 0.8224889640699448; 0.0 -14.329863758728356 -1.4069750692351175 0.9463037748263273], true, Iter Function value Gradient norm 
------ -------------- --------------
, Float64[])

julia> ret.param
4-element Vector{Float64}:
    1.9591016841592197
   13.58216904773464
 -138.11627273117097
    1.571176537116358

```

---

<div class="post-metadata">

**Author:** ![Stephen](https://avatars.discourse-cdn.com/v4/letter/s/96bed5/32.png) [@Stephen](https://discourse.julialang.org/u/Stephen)\
**Post date:** [April 30, 2024, 7:26am UTC](https://discourse.julialang.org/t/multi-variables-in-lsqfit/112210/6 "2024-04-30T07:26:48Z")

</div>

I found that the parameters obtained is different from the article, In fact, the object function is in this form:

 ![圖片](https://global.discourse-cdn.com/julialang/original/3X/a/6/a6c048cd5965f3d8c79794f0fa3b01915fd8f38c.png)

I’m wondering whether the function definition here is correct or not?

> [@Stephen](#):
>
> `vcat(qA, qC)`

---

<div class="post-metadata">

**Author:** ![odow](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/odow/32/28685_2.png) [@odow](https://discourse.julialang.org/u/odow)\
**Post date:** [May 1, 2024, 2:08am UTC](https://discourse.julialang.org/t/multi-variables-in-lsqfit/112210/7 "2024-05-01T02:08:27Z")

</div>

It’s a little hard to tell what you are referring to by a single screenshot, but I assume S is the sum of squares model for fitting that you are trying to replicate. In which case, it probably is correct.

The question should not be whether you find identical parameters, but whether the loss function (the value of S is similar). There might be many parameter settings that lead to near identical loss values.