This is the error message
MethodError: no method matching Lagrange_Polynomials(::Float64, ::LinRange{Float64}, ::Array{Float64,1})
Closest candidates are:Lagrange_Polynomials(::T, !Matched::Array{T,1}, ::Array{T,1}) where T<:AbstractFloat at In[17]:3
This is the code:
using PyPlot
function Lagrange_Polynomials(x::T,vector_x::Vector{T},vector_y::Vector{T}) where T <: AbstractFloat # define an infinitely many large set of functions
n = length(vector_x)
length(vector_y)==n || error("Incompatible vector size")
S = zero(T)
for i ∈ 1:n
P = one(T)
for j ∈ 1:n
if j != i
P*=(x-vector_x[j])/(vector_x[i]-vector_x[j])
end #chiude l'if
end #chiude il ciclo for interno
S += vector_y[i]*P
end #chiude il ciclo for esterno
return S
f(x) = 1/sqrt(2π)*exp(-x^2/2);
a=-2; #estremi dell' intervallo
b = 2;
n = 12 #number of interpolating points
vector_x = LinRange(a,b,n); #suddivisione dell' intervallo [a,b] in n punti equispaziati
xinterval = LinRange(a,b,1024); #Una suddivisione più precisa dell' intervallo
ypoly = [Lagrange_Polynomials(x,vector_x,f.(vector_x)) for x in xinterval]
plot(xinterval, ypoly)
plot(xinterval, f.(xinterval), "k");
plot(vector_x, f.(vector_x), "ro");
plt[:legend](["f(x)","interpolation points",L"L_{n-1}(x)"])
you should change Vector{T}
to AbstractVector{T}
or even delete it
julia> LinRange(1,2,10) isa Vector
false
julia> LinRange(1,2,10) isa AbstractVector
true