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B-spline evaluation

Spline evalution can be done in two ways. The first one uses the spline constructors in B-spline constructors.

f = BSpline(3)
x = LinRange(-1,5,10)
f.(x)
10-element Array{Float64,1}:
 0.0                 
 0.0                 
 0.006172839506172841
 0.16666666666666657 
 0.5740740740740737  
 0.5740740740740743  
 0.16666666666666852 
 0.006172839506170929
 0.0                 
 0.0

The second one uses the internal function in Internal evaluation functions.

CardinalBSplines.evaluate_BSpline.(Val{3}(), x, Float64)
10-element Array{Float64,1}:
 0.0                 
 0.0                 
 0.006172839506172841
 0.16666666666666657 
 0.5740740740740737  
 0.5740740740740743  
 0.16666666666666852 
 0.006172839506170929
 0.0                 
 0.0

No allocation happens during evaluation

x = LinRange(-1,5,10000);
s = Array{Float64}(undef, 10000);
s .= f.(x);
@time s .= f.(x);
  0.000165 seconds (5 allocations: 208 bytes)

Examples

B-splines

plot(legend=false)
[plot!(x,BSpline(degree).(x)) for degree in 0:10]
/home/travis/.julia/packages/GR/oiZD3/src/../deps/gr/bin/gksqt: error while loading shared libraries: libQt5Widgets.so.5: cannot open shared object file: No such file or directory
connect: Connection refused
GKS: can't connect to GKS socket application
Did you start 'gksqt'?

GKS: Open failed in routine OPEN_WS
GKS: GKS not in proper state. GKS must be either in the state WSOP or WSAC in routine ACTIVATE_WS

Centered B-splines

plot(legend=false)
[plot!(x,CenteredBSpline(degree).(x)) for degree in 0:10]
/home/travis/.julia/packages/GR/oiZD3/src/../deps/gr/bin/gksqt: error while loading shared libraries: libQt5Widgets.so.5: cannot open shared object file: No such file or directory
connect: Connection refused
GKS: can't connect to GKS socket application
Did you start 'gksqt'?

GKS: Open failed in routine OPEN_WS
GKS: GKS not in proper state. GKS must be either in the state WSOP or WSAC in routine ACTIVATE_WS

Periodic B-splines

plot(legend=false)
[plot!(x,PeriodicBSpline(degree, 3).(x)) for degree in 0:10]
/home/travis/.julia/packages/GR/oiZD3/src/../deps/gr/bin/gksqt: error while loading shared libraries: libQt5Widgets.so.5: cannot open shared object file: No such file or directory
connect: Connection refused
GKS: can't connect to GKS socket application
Did you start 'gksqt'?

GKS: Open failed in routine OPEN_WS
GKS: GKS not in proper state. GKS must be either in the state WSOP or WSAC in routine ACTIVATE_WS

Derivatives of B-Splines

plot(legend=false)
[plot!(x,BSplineDiff(4,diff).(x)) for diff in 0:4]
/home/travis/.julia/packages/GR/oiZD3/src/../deps/gr/bin/gksqt: error while loading shared libraries: libQt5Widgets.so.5: cannot open shared object file: No such file or directory
connect: Connection refused
GKS: can't connect to GKS socket application
Did you start 'gksqt'?

GKS: Open failed in routine OPEN_WS
GKS: GKS not in proper state. GKS must be either in the state WSOP or WSAC in routine ACTIVATE_WS

B-spline constructors

CardinalBSplines.CenteredBSpline — Method
CenteredBSpline(m, T=Float64)

Construct a centered B-spline of order m and type T

The support of the centered B-spline is s $\left[-\tfrac{m+1}{2},\tfrac{m+1}{2}\right]$.

source

Internal evaluation functions