In [1]:

    

?linspace


    

    




search: linspace LinSpace







    
Out[1]:





linspace(start, stop, n=100)
Construct a range of n linearly spaced elements from start to stop.

In [2]:

    

?collect


    

    




search: collect Collections







    
Out[2]:





collect(collection)
Return an array of all items in a collection. For associative collections, returns Pair{KeyType, ValType}.

collect(element_type, collection)
Return an array of type Array{element_type,1} of all items in a collection.

In [3]:

    

collect(linspace(0, 1, 9))


    

    
Out[3]:





9-element Array{Float64,1}:
 0.0  
 0.125
 0.25 
 0.375
 0.5  
 0.625
 0.75 
 0.875
 1.0  

In [4]:

    

?fill


    

    




search: fill fill! finally filt filt! filter filter! Filter filesize filemode







    
Out[4]:





fill(x, dims)
Create an array filled with the value x. For example, fill(1.0, (10,10)) returns a 10x10 array of floats, with each element initialized to 1.0.
If x is an object reference, all elements will refer to the same object. fill(Foo(), dims) will return an array filled with the result of evaluating Foo() once.

In [5]:

    

?vcat


    

    




search: vcat hvcat VecOrMat DenseVecOrMat StridedVecOrMat AbstractVecOrMat







    
Out[5]:





vcat(A...)
Concatenate along dimension 1

In [6]:

    

?cumsum


    

    




search: cumsum cumsum! cumsum_kbn







    
Out[6]:




..  cumsum(A, [dim])

Cumulative sum along a dimension ``dim`` (defaults to 1).
See also :func:`cumsum!` to use a preallocated output array,
both for performance and to control the precision of the
output (e.g. to avoid overflow).

In [7]:

    

A = [2, 3]
cumsum(A, 1)


    

    
Out[7]:





2-element Array{Int64,1}:
 2
 5

In [11]:

    

[2, 3], [[2, 3]]


    

    
Out[11]:





([2,3],[2,3])

In [12]:

    

?minimum


    

    




search: minimum minimum! DimensionMismatch







    
Out[12]:





minimum(A, dims)
Compute the minimum value of an array over the given dimensions.

minimum(itr)
Returns the smallest element in a collection.

In [14]:

    

minimum(linspace(0, 1, 10))


    

    
Out[14]:





0.0

In [15]:

    

?AbstractVector


    

    




search: AbstractVector AbstractSparseVector AbstractVecOrMat







    
Out[15]:




No documentation found.
Base.AbstractVector is of type TypeConstructor:
Summary:
immutable TypeConstructor <: Type{T}

Fields:
parameters :: SimpleVector
body       :: Any

In [1]:

    

zeros(10)


    

    
Out[1]:





10-element Array{Float64,1}:
 0.0
 0.0
 0.0
 0.0
 0.0
 0.0
 0.0
 0.0
 0.0
 0.0

In [2]:

    

?push!


    

    




search: push! pushdisplay







    
Out[2]:




..  push!(collection, items...) -> collection

Insert one or more ``items`` at the end of ``collection``.

.. doctest::

  julia> push!([1, 2, 3], 4, 5, 6)
  6-element Array{Int64,1}:
   1
   2
   3
   4
   5
   6

Use :func:`append!` to add all the elements of another collection to
``collection``.
The result of the preceding example is equivalent to
``append!([1, 2, 3], [4, 5, 6])``.

In [3]:

    

push!([], 2, 3)


    

    
Out[3]:





2-element Array{Any,1}:
 2
 3

In [4]:

    

push!([2, 3], 4, 5)


    

    
Out[4]:





4-element Array{Int64,1}:
 2
 3
 4
 5

In [6]:

    

?zeros


    

    




search: zeros spzeros nonzeros count_zeros set_zero_subnormals







    
Out[6]:





zeros(type, dims)
Create an array of all zeros of specified type. The type defaults to Float64 if not specified.

zeros(A)
Create an array of all zeros with the same element type and shape as A.

In [7]:

    

zeros(10, 2)


    

    
Out[7]:





10x2 Array{Float64,2}:
 0.0  0.0
 0.0  0.0
 0.0  0.0
 0.0  0.0
 0.0  0.0
 0.0  0.0
 0.0  0.0
 0.0  0.0
 0.0  0.0
 0.0  0.0

In [12]:

    

zeros(2, 2)


    

    
Out[12]:





2x2 Array{Float64,2}:
 0.0  0.0
 0.0  0.0

In [14]:

    

?copy!


    

    




search: copy! unsafe_copy! copy copysign deepcopy







    
Out[14]:





copy!(dest, do, src, so, N)
Copy N elements from collection src starting at offset so, to array dest starting at offset do. Returns dest.

copy!(dest, src)
Copy all elements from collection src to array dest. Returns dest.

In [15]:

    

?vcat


    

    




search: vcat hvcat VecOrMat DenseVecOrMat StridedVecOrMat AbstractVecOrMat







    
Out[15]:





vcat(A...)
Concatenate along dimension 1

In [42]:

    

ygrid0 = linspace(-4, 4, 10)


    

    
Out[42]:





linspace(-4.0,4.0,10)

In [43]:

    

using BasisMatrices

# 1st method
y_basis = Basis(ChebParams(length(ygrid0), minimum(ygrid0), maximum(ygrid0)))


    

    
Out[43]:





1 dimensional Basis on the hypercube formed by [-4.0] × [4.0].
Basis families are BasisMatrices.Cheb

In [44]:

    

S, (ygrid) = nodes(y_basis);


    

In [45]:

    

Φ = BasisMatrix(y_basis, Expanded(), S, 0)


    

    
Out[45]:





BasisMatrix{BasisMatrices.Expanded} of order 1x1 Array{Int64,2}:
 0

In [46]:

    

# Actual function at interpolation nodes
f(x::Vector{Float64}) = 1./(1 .+ 25x.^2)
y = f(S[:,1])

# Get coefficients
c = Φ.vals[1] \ y;


    

In [47]:

    

using QuantEcon

ygridf = linspace(-4, 4, 100)
Sf = gridmake(ygridf)
yf = f(Sf[:, 1])
interp = funeval(c, y_basis, Sf);


    

In [48]:

    

using Plots
plotlyjs()

plt_a = plot(ygridf, [interp[1:length(ygridf)] yf[1:length(ygridf)]], 
             label=["Interpolant", "Original"]',
             lw=2,
             xlabel="a")


    

    
Out[48]:






     


     

In [1]:

    

using QuantEcon


    

In [2]:

    

#Approximated Function
f(x::Array{Float64, 1}) = 1./(1 .+ 25x.^2)


    

    
Out[2]:





f (generic function with 1 method)

In [3]:

    

c_grid = linspace(-1, 1, 1000)
c_basis = Basis(ChebParams(length(c_grid), minimum(c_grid), maximum(c_grid)))

#Approximant
c_S, (c_grid) = nodes(c_basis)
c_phi = BasisMatrix(c_basis, Direct(), c_S)
y = f(c_S[:, 1])
c = c_phi.vals[1] \ y
c_interp = funeval(c, c_basis, c_S)

#Plot
ylims = (-1.1, 1.1)
plot(c_grid, c_interp, ylims=ylims, leg=false)


    

    




LoadError: UndefVarError: Basis not defined
while loading In[3], in expression starting on line 2

In [ ]: