Code: mdmultispec(t, x[, y]): Remove type assertions in keyword arguments

[Andy Nowacki]

mdmultispec(t, x, y) and mdmultispec(t, ::Matrix) both have typed keyword arguments. Consider removing or relaxing them.

For instance, is there any reason not to allow an Integer for bw?

julia> mdmultispec(t, x, y, bw=3)
ERROR: TypeError: in keyword argument bw, expected Float64, got a value of type Int64
Stacktrace:
 [1] top-level scope at REPL[8]:1

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[Charlotte Haley]

[This commit}(https://bitbucket.org/clhaley/multitaper.jl/commits/5d141b5d0bfd52496e4594633f9b457efa517d3c) attempts to address this.

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[Andy Nowacki]

I realise that I don’t know what the bw argument actually means, but I feel it probably needs to be in the range 0 < bw < 1. In that case, perhaps the right thing to do is check for this and give the user an informative error message?

My attempt at checking for the update:

julia> let n = 20, t = sort(rand(n)), x = randn(n), y = randn(n)
           mdmultispec(t, x, y, bw=3)
       end
┌ Warning: Adjusting nev from 119 to 19
└ @ Arpack ~/.julia/packages/Arpack/o35I5/src/Arpack.jl:82
ERROR: BoundsError: attempt to access 20×19 Array{Float64,2} at index [1:20, 21]
Stacktrace:
 [1] throw_boundserror(::Array{Float64,2}, ::Tuple{Base.Slice{Base.OneTo{Int64}},Int64}) at ./abstractarray.jl:541
 [2] checkbounds at ./abstractarray.jl:506 [inlined]
 [3] _getindex at ./multidimensional.jl:742 [inlined]
 [4] getindex(::Array{Float64,2}, ::Function, ::Int64) at ./abstractarray.jl:1060
 [5] mdslepian(::Int64, ::Int64, ::Array{Float64,1}) at /Users/nowacki/.julia/dev/Multitaper/src/MDmwps.jl:369
 [6] mdmultispec(::Array{Float64,1}, ::Array{Float64,1}, ::Array{Float64,1}; bw::Int64, k::Int64, dt::Float64, jk::Bool, nz::Float64, Ftest::Bool, lambdau::Nothing) at /Users/nowacki/.julia/dev/Multitaper/src/MDmwps.jl:213
 [7] top-level scope at REPL[24]:2

I didn’t get a sense of what the bandwidth was supposed to be (what are its units, or is it a proportion of the Nyquist frequency, for instance) from the docs, but I am not an expert in this field by any means and it may not be necessary to document this more precisely.

[Charlotte Haley]

Good question. The bandwidth is sometimes given by stating the time-bandwidth product, NW for unit sampling, which is given in units of the Rayleigh resolution (1/N delta t, where N is the number of samples and delta t is the sampling interval). However, in this particular function, bw is actually dependent on the delta-t for the time series, and so is not restricted.