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Fixed how code rendered in some docstrings
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@RJDennis
RJDennis committed Nov 15, 2024
1 parent fe9c636 commit 627a994
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2 changes: 1 addition & 1 deletion Project.toml
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Original file line number Diff line number Diff line change
@@ -1,7 +1,7 @@
name = "ChebyshevApprox"
uuid = "17a596ad-87cd-578c-9b6d-01108c31dc04"
authors = ["Richard Dennis <[email protected]>"]
version = "0.4.5"
version = "0.4.6"

[deps]
LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
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125 changes: 113 additions & 12 deletions src/chebyshev_approx_functions.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -502,6 +502,83 @@ function chebyshev_polynomial(order::S, x::AbstractArray{R,1}) where {S<:Integer

end

"""
Computes the Chebyshev polynomial of degree ```order``` at the scalar point ```x```, which must lie in ```dom```.
Returns a 2d array. The element-type of the polynomial is given by the element-type of ```x```.
Signature
=========
P = chebyshev_polynomial(order,x,dom)
Example
=======
```
julia> P = chebyshev_polynomial(3,0.6,[1.0,-1.0])
[1.0 0.6 -0.28 -0.936]
```
"""
function chebyshev_polynomial(order::S, x::R, dom::Array{T,1}) where {S<:Integer,R<:Number,T<:AbstractFloat}

# x must reside in [-1,1]

point = normalize_node(x,dom)

poly = Array{R}(undef, 1, order + 1)
poly[1] = one(R)

@inbounds for i = 2:order+1
if i == 2
poly[i] = point
else
poly[i] = 2*point*poly[i-1] - poly[i-2]
end
end

return poly

end

"""
Computes the Chebyshev polynomial of degree ```order``` at end point in the vector ```x```. The elements of ```x```
must lie in ```dom```. Returns a 2d array. The element-type of the polynomial is given by the element-type of
```x```.
Signature
=========
P = chebyshev_polynomial(order,x,dom)
Example
=======
```
julia> P = chebyshev_polynomial(3,[0.6,0.4],[1.0,-1.0])
[1.0 0.6 -0.28 -0.936
1.0 0.4 -0.68 -0.944]
```
"""
function chebyshev_polynomial(order::S, x::AbstractArray{R,1}, dom::Array{T,1}) where {S<:Integer,R<:Number,T<:AbstractFloat}

points = normalize_node(x,dom
)
# Elements of x must reside in [-1,1]
poly = Array{R}(undef, length(x), order + 1)
poly[:, 1] .= one(R)

@inbounds for i = 2:order+1
for j in eachindex(x)
if i == 2
poly[j, i] = points[j]
else
poly[j, i] = 2*points[j]*poly[j,i-1] - poly[j,i-2]
end
end
end

return poly

end

"""
Computes the Chebyshev polynomial of degree ```order``` at each point specified in the ```nodes``` struct. The
elements of ```nodes.points``` must lie in [1.0,-1.0]. Returns a ChebPoly type. The element-type of the polynomial
Expand Down Expand Up @@ -916,6 +993,7 @@ julia> weights = chebyshev_weights(y,(nodes1,nodes2),ord,dom)
0.26378 0.0948592 -0.00375743 0.000432628
-0.0246176 -0.00885287 0.000350667 -4.03756e-5
0.00372291 0.00133882 -5.30312e-5 6.10598e-6]
```
"""
function chebyshev_weights(y::Array{T,N}, nodes::NTuple{N,Array{T,1}}, order::Union{NTuple{N,S},Array{S,1}}, domain=[ones(T, 1, N); -ones(T, 1, N)]) where {T<:AbstractFloat,N,S<:Integer}

Expand Down Expand Up @@ -970,6 +1048,7 @@ julia> weights = chebyshev_weights_extrema(y,(nodes1,nodes2),ord,dom)
0.263786 0.0948622 -0.00375987 0.000444808
-0.024647 -0.0088635 0.000351305 -4.15608e-5
0.00386243 0.001389 -5.5053e-5 6.513e-6]
```
"""
function chebyshev_weights_extrema(y::Array{T,N}, nodes::NTuple{N,Array{T,1}}, order::Union{NTuple{N,S},Array{S,1}}, domain=[ones(T, 1, N); -ones(T, 1, N)]) where {T<:AbstractFloat,N,S<:Integer}

Expand Down Expand Up @@ -1035,6 +1114,7 @@ julia> weights = chebyshev_weights_extended(y,(nodes1,nodes2),ord,dom)
0.263837 0.0948909 -0.00378841 0.000439284
-0.0249247 -0.00896435 0.000357891 -4.14991e-5
0.00379791 0.00136595 -5.45338e-5 6.32345e-6]
```
"""
function chebyshev_weights_extended(y::Array{T,N}, nodes::NTuple{N,Array{T,1}}, order::Union{NTuple{N,S},Array{S,1}}, domain=[ones(T, 1, N); -ones(T, 1, N)]) where {T<:AbstractFloat,N,S<:Integer}

Expand Down Expand Up @@ -1085,7 +1165,7 @@ element-type of ```poly```.
Signature
=========
w = chebyshev_weights(y,nodes,order,domain)
w = chebyshev_weights(y,poly,order)
Example
=======
Expand All @@ -1101,6 +1181,7 @@ julia> weights = chebyshev_weights(y,(poly1.poly,poly2.poly),ord)
0.26378 0.0948592 -0.00375743 0.000432628
-0.0246176 -0.00885287 0.000350667 -4.03756e-5
0.00372291 0.00133882 -5.30312e-5 6.10598e-6]
```
"""
function chebyshev_weights(y::Array{T,N}, poly::NTuple{N,Array{T,2}}, order::Union{NTuple{N,S},Array{S,1}}) where {T<:AbstractFloat,N,S<:Integer}

Expand Down Expand Up @@ -1140,7 +1221,7 @@ element-type of ```poly```.
Signature
=========
w = chebyshev_weights_extrema(y,nodes,order,domain)
w = chebyshev_weights_extrema(y,poly,order)
Example
=======
Expand All @@ -1156,6 +1237,7 @@ julia> weights = chebyshev_weights_extrema(y,(poly1.poly,poly2.poly),ord)
0.263786 0.0948622 -0.00375987 0.000444808
-0.024647 -0.0088635 0.000351305 -4.15608e-5
0.00386243 0.001389 -5.5053e-5 6.513e-6]
```
"""
function chebyshev_weights_extrema(y::Array{T,N}, poly::NTuple{N,Array{T,2}}, order::Union{NTuple{N,S},Array{S,1}}) where {T<:AbstractFloat,N,S<:Integer}

Expand Down Expand Up @@ -1205,7 +1287,7 @@ element-type of ```poly```.
Signature
=========
w = chebyshev_weights_extended(y,nodes,order,domain)
w = chebyshev_weights_extended(y,poly,order)
Example
=======
Expand All @@ -1221,6 +1303,7 @@ julia> weights = chebyshev_weights_extended(y,(poly1.poly,poly2.poly),ord)
0.263837 0.0948909 -0.00378841 0.000439284
-0.0249247 -0.00896435 0.000357891 -4.14991e-5
0.00379791 0.00136595 -5.45338e-5 6.32345e-6]
```
"""
function chebyshev_weights_extended(y::Array{T,N}, poly::NTuple{N,Array{T,2}}, order::Union{NTuple{N,S},Array{S,1}}) where {T<:AbstractFloat,N,S<:Integer}

Expand Down Expand Up @@ -1283,6 +1366,7 @@ julia> weights = chebyshev_weights(y,(nodes1,nodes2),ord,dom)
0.26378 0.0948592 -0.00375743 0.0
-0.0246176 -0.00885287 0.0 0.0
0.00372291 0.0 0.0 0.0]
```
"""
function chebyshev_weights(y::Array{T,N}, nodes::NTuple{N,Array{T,1}}, order::S, domain=[ones(T, 1, N); -ones(T, 1, N)]) where {T<:AbstractFloat,N,S<:Integer}

Expand Down Expand Up @@ -1345,6 +1429,7 @@ julia> weights = chebyshev_weights_extrema(y,(nodes1,nodes2),ord,dom)
0.263786 0.0948622 -0.00375987 0.0
-0.024647 -0.0088635 0.0 0.0
0.00386243 0.0 0.0 0.0]
```
"""
function chebyshev_weights_extrema(y::Array{T,N}, nodes::NTuple{N,Array{T,1}}, order::S, domain=[ones(T, 1, N); -ones(T, 1, N)]) where {T<:AbstractFloat,N,S<:Integer}

Expand Down Expand Up @@ -1417,6 +1502,7 @@ julia> weights = chebyshev_weights_extended(y,(nodes1,nodes2),ord,dom)
0.263837 0.0948909 -0.00378841 0.0
-0.0249247 -0.00896435 0.0 0.0
0.00379791 0.0 0.0 0.0]
```
"""
function chebyshev_weights_extended(y::Array{T,N}, nodes::NTuple{N,Array{T,1}}, order::S, domain=[ones(T, 1, N); -ones(T, 1, N)]) where {T<:AbstractFloat,N,S<:Integer}

Expand Down Expand Up @@ -1474,7 +1560,7 @@ element-type of ```poly```.
Signature
=========
w = chebyshev_weights(y,nodes,order,domain)
w = chebyshev_weights(y,poly,order)
Example
=======
Expand All @@ -1490,6 +1576,7 @@ julia> weights = chebyshev_weights(y,(poly1.poly,poly2.poly),ord)
0.26378 0.0948592 -0.00375743 0.0
-0.0246176 -0.00885287 0.0 0.0
0.00372291 0.0 0.0 0.0]
```
"""
function chebyshev_weights(y::Array{T,N}, poly::NTuple{N,Array{T,2}}, order::S) where {T<:AbstractFloat,N,S<:Integer}

Expand Down Expand Up @@ -1536,7 +1623,7 @@ element-type of ```poly```.
Signature
=========
w = chebyshev_weights_extrema(y,nodes,order,domain)
w = chebyshev_weights_extrema(y,poly,order)
Example
=======
Expand All @@ -1552,6 +1639,7 @@ julia> weights = chebyshev_weights_extrema(y,(poly1.poly,poly2.poly),ord)
0.263786 0.0948622 -0.00375987 0.0
-0.024647 -0.0088635 0.0 0.0
0.00386243 0.0 0.0 0.0]
```
"""
function chebyshev_weights_extrema(y::Array{T,N}, poly::NTuple{N,Array{T,2}}, order::S) where {T<:AbstractFloat,N,S<:Integer}

Expand Down Expand Up @@ -1608,7 +1696,7 @@ by the element-type of ```poly```.
Signature
=========
w = chebyshev_weights_extended(y,nodes,order,domain)
w = chebyshev_weights_extended(y,poly,order)
Example
=======
Expand All @@ -1624,6 +1712,7 @@ julia> weights = chebyshev_weights_extended(y,(poly1.poly,poly2.poly),ord)
0.263837 0.0948909 -0.00378841 0.0
-0.0249247 -0.00896435 0.0 0.0
0.00379791 0.0 0.0 0.0]
```
"""
function chebyshev_weights_extended(y::Array{T,N}, poly::NTuple{N,Array{T,2}}, order::S) where {T<:AbstractFloat,N,S<:Integer}

Expand Down Expand Up @@ -1765,6 +1854,7 @@ julia> weights = chebyshev_weights_threaded(y,(nodes1,nodes2),ord,dom)
0.26378 0.0948592 -0.00375743 0.000432628
-0.0246176 -0.00885287 0.000350667 -4.03756e-5
0.00372291 0.00133882 -5.30312e-5 6.10598e-6]
```
"""
function chebyshev_weights_threaded(y::Array{T,N}, nodes::NTuple{N,Array{T,1}}, order::Union{NTuple{N,S},Array{S,1}}, domain=[ones(T, 1, N); -ones(T, 1, N)]) where {T<:AbstractFloat,N,S<:Integer}

Expand Down Expand Up @@ -1821,6 +1911,7 @@ julia> weights = chebyshev_weights_extrema_threaded(y,(nodes1,nodes2),ord,dom)
0.263786 0.0948622 -0.00375987 0.000444808
-0.024647 -0.0088635 0.000351305 -4.15608e-5
0.00386243 0.001389 -5.5053e-5 6.513e-6]
```
"""
function chebyshev_weights_extrema_threaded(y::Array{T,N}, nodes::NTuple{N,Array{T,1}}, order::Union{NTuple{N,S},Array{S,1}}, domain=[ones(T, 1, N); -ones(T, 1, N)]) where {T<:AbstractFloat,N,S<:Integer}

Expand Down Expand Up @@ -1887,6 +1978,7 @@ julia> weights = chebyshev_weights_extended_threaded(y,(nodes1,nodes2),ord,dom)
0.263837 0.0948909 -0.00378841 0.000439284
-0.0249247 -0.00896435 0.000357891 -4.14991e-5
0.00379791 0.00136595 -5.45338e-5 6.32345e-6]
```
"""
function chebyshev_weights_extended_threaded(y::Array{T,N}, nodes::NTuple{N,Array{T,1}}, order::Union{NTuple{N,S},Array{S,1}}, domain=[ones(T, 1, N); -ones(T, 1, N)]) where {T<:AbstractFloat,N,S<:Integer}

Expand Down Expand Up @@ -1937,7 +2029,7 @@ is given by the element-type of ```poly```.
Signature
=========
w = chebyshev_weights_threaded(y,nodes,order,domain)
w = chebyshev_weights_threaded(y,poly,order)
Example
=======
Expand All @@ -1953,6 +2045,7 @@ julia> weights = chebyshev_weights_threaded(y,(poly1.poly,poly2.poly),ord)
0.26378 0.0948592 -0.00375743 0.000432628
-0.0246176 -0.00885287 0.000350667 -4.03756e-5
0.00372291 0.00133882 -5.30312e-5 6.10598e-6]
```
"""
function chebyshev_weights_threaded(y::Array{T,N}, poly::NTuple{N,Array{T,2}}, order::Union{NTuple{N,S},Array{S,1}}) where {T<:AbstractFloat,N,S<:Integer}

Expand Down Expand Up @@ -1992,7 +2085,7 @@ is given by the element-type of ```poly```.
Signature
=========
w = chebyshev_weights_extrema_threaded(y,nodes,order,domain)
w = chebyshev_weights_extrema_threaded(y,poly,order)
Example
=======
Expand All @@ -2008,6 +2101,7 @@ julia> weights = chebyshev_weights_extrema_threaded(y,(poly1.poly,poly2.poly),or
0.263786 0.0948622 -0.00375987 0.000444808
-0.024647 -0.0088635 0.000351305 -4.15608e-5
0.00386243 0.001389 -5.5053e-5 6.513e-6]
```
"""
function chebyshev_weights_extrema_threaded(y::Array{T,N}, poly::NTuple{N,Array{T,2}}, order::Union{NTuple{N,S},Array{S,1}}) where {T<:AbstractFloat,N,S<:Integer}

Expand Down Expand Up @@ -2057,7 +2151,7 @@ weights is given by the element-type of ```poly```.
Signature
=========
w = chebyshev_weights_extended_threaded(y,nodes,order,domain)
w = chebyshev_weights_extended_threaded(y,poly,order)
Example
=======
Expand All @@ -2073,6 +2167,7 @@ julia> weights = chebyshev_weights_extended_threaded(y,(poly1.poly,poly2.poly),o
0.263837 0.0948909 -0.00378841 0.000439284
-0.0249247 -0.00896435 0.000357891 -4.14991e-5
0.00379791 0.00136595 -5.45338e-5 6.32345e-6]
```
"""
function chebyshev_weights_extended_threaded(y::Array{T,N}, poly::NTuple{N,Array{T,2}}, order::Union{NTuple{N,S},Array{S,1}}) where {T<:AbstractFloat,N,S<:Integer}

Expand Down Expand Up @@ -2135,6 +2230,7 @@ julia> weights = chebyshev_weights_threaded(y,(nodes1,nodes2),ord,dom)
0.26378 0.0948592 -0.00375743 0.0
-0.0246176 -0.00885287 0.0 0.0
0.00372291 0.0 0.0 0.0]
```
"""
function chebyshev_weights_threaded(y::Array{T,N}, nodes::NTuple{N,Array{T,1}}, order::S, domain=[ones(T, 1, N); -ones(T, 1, N)]) where {T<:AbstractFloat,N,S<:Integer}

Expand Down Expand Up @@ -2198,6 +2294,7 @@ julia> weights = chebyshev_weights_extrema_threaded(y,(nodes1,nodes2),ord,dom)
0.263786 0.0948622 -0.00375987 0.0
-0.024647 -0.0088635 0.0 0.0
0.00386243 0.0 0.0 0.0]
```
"""
function chebyshev_weights_extrema_threaded(y::Array{T,N}, nodes::NTuple{N,Array{T,1}}, order::S, domain=[ones(T, 1, N); -ones(T, 1, N)]) where {T<:AbstractFloat,N,S<:Integer}

Expand Down Expand Up @@ -2271,6 +2368,7 @@ julia> weights = chebyshev_weights_extended_threaded(y,(nodes1,nodes2),ord,dom)
0.263837 0.0948909 -0.00378841 0.0
-0.0249247 -0.00896435 0.0 0.0
0.00379791 0.0 0.0 0.0]
```
"""
function chebyshev_weights_extended_threaded(y::Array{T,N}, nodes::NTuple{N,Array{T,1}}, order::S, domain=[ones(T, 1, N); -ones(T, 1, N)]) where {T<:AbstractFloat,N,S<:Integer}

Expand Down Expand Up @@ -2328,7 +2426,7 @@ weights is given by the element-type of ```poly```.
Signature
=========
w = chebyshev_weights_threaded(y,nodes,order,domain)
w = chebyshev_weights_threaded(y,poly,order)
Example
=======
Expand All @@ -2344,6 +2442,7 @@ julia> weights = chebyshev_weights_threaded(y,(poly1.poly,poly2.poly),ord)
0.26378 0.0948592 -0.00375743 0.0
-0.0246176 -0.00885287 0.0 0.0
0.00372291 0.0 0.0 0.0]
```
"""
function chebyshev_weights_threaded(y::Array{T,N}, poly::NTuple{N,Array{T,2}}, order::S) where {T<:AbstractFloat,N,S<:Integer}

Expand Down Expand Up @@ -2390,7 +2489,7 @@ weights is given by the element-type of ```poly```.
Signature
=========
w = chebyshev_weights_extrema_threaded(y,nodes,order,domain)
w = chebyshev_weights_extrema_threaded(y,poly,order)
Example
=======
Expand All @@ -2406,6 +2505,7 @@ julia> weights = chebyshev_weights_extrema_threaded(y,(poly1.poly,poly2.poly),or
0.263786 0.0948622 -0.00375987 0.0
-0.024647 -0.0088635 0.0 0.0
0.00386243 0.0 0.0 0.0]
```
"""
function chebyshev_weights_extrema_threaded(y::Array{T,N}, poly::NTuple{N,Array{T,2}}, order::S) where {T<:AbstractFloat,N,S<:Integer}

Expand Down Expand Up @@ -2462,7 +2562,7 @@ Chebyshev weights is given by the element-type of ```poly```.
Signature
=========
w = chebyshev_weights_extended_threaded(y,nodes,order,domain)
w = chebyshev_weights_extended_threaded(y,poly,order)
Example
=======
Expand All @@ -2478,6 +2578,7 @@ julia> weights = chebyshev_weights_extended_threaded(y,(poly1.poly,poly2.poly),o
0.263837 0.0948909 -0.00378841 0.0
-0.0249247 -0.00896435 0.0 0.0
0.00379791 0.0 0.0 0.0]
```
"""
function chebyshev_weights_extended_threaded(y::Array{T,N}, poly::NTuple{N,Array{T,2}}, order::S) where {T<:AbstractFloat,N,S<:Integer}

Expand Down
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