use b-splines to calculate moments; add spline keyword

[lstagner]

This is more accurate for higher mode numbers. default is to use trapz since splines are 5-10x slower.

import MillerExtendedHarmonic
using MXHEquilibrium
using PyPlot
using EFIT
g = readg("/home/lstagner/.julia/dev/MXHEquilibrium/test/g150219.03200")

M = efit(g,clockwise_phi=false)
bdry = plasma_boundary(M)

fig,ax = plt.subplots(ncols=5)
fig.set_size_inches(12,5)
for (i,N) in enumerate(2:2:10)
    @time mxh1 = MillerExtendedHarmonic.MXH(bdry.r,bdry.z,N; spline=false);
    @time mxh2 = MillerExtendedHarmonic.MXH(bdry.r,bdry.z,N; spline=true);
    ax[i].plot(bdry.r,bdry.z,color="black")

    x1,y1 = mxh1(100)
    ax[i].plot(x1,y1,color="b",ls="--",label="trapz")
    x2,y2 = mxh2(100)
    ax[i].plot(x2,y2,color="r",ls="--",label="spline")
    ax[i].legend(title="N=$N")
    ax[i].set_aspect("equal")
end
fig.tight_layout()

[orso82]

Should we make spline=true the default? @lstagner do you have a sense of how the spline approach affects performance?

[lstagner]

its a somewhat significant slowdown.

N = 2 spline = false:  0.000039 seconds (25 allocations: 12.375 KiB)
N = 2 spline = true:   0.000336 seconds (115 allocations: 347.688 KiB)
N = 4 spline = false:  0.000073 seconds (25 allocations: 12.406 KiB)
N = 4 spline = true:   0.000438 seconds (187 allocations: 615.969 KiB)
N = 6 spline = false:  0.000051 seconds (25 allocations: 12.438 KiB)
N = 6 spline = true:   0.000759 seconds (259 allocations: 884.250 KiB)
N = 8 spline = false:  0.000067 seconds (25 allocations: 12.469 KiB)
N = 8 spline = true:   0.000908 seconds (331 allocations: 1.126 MiB)
N = 10 spline = false:  0.000065 seconds (25 allocations: 12.500 KiB)
N = 10 spline = true:   0.000979 seconds (403 allocations: 1.388 MiB)

[orso82]

Thank you for taking the time to do the benchmark @lstagner