blob(N, Nj)

Makes moving picture of a random blob by superposition of random circles

Arguments

• N number of loops for, and if movie, default = 100
• Nj smoothness, roughly (?)

Outputs

• x
• y

closedcurve_2d(xs, ys)

Generate a closed curve based on (x, y) points given and Euclidean distance

Arguments

• xs x coordinates of the points
• ys y coordinates of the points

Outputs

• xpath x coordinates of the path
• ypath y coordinates of the path

conv(x,y)

Convolves two arrays of the same length using FFT algorithm

Arguments

• x::Array{Number}: first array
• y::Array{Number}: second array

Outputs

• Array containing the real part of the convolution of x and y

degamini(v)

Arguments

• v A vector with repeated entries

Outputs

• dv The same vector with all the repeat sset to 1
• foldi A same-dimensional vector with how many repeats there are
• be A matrix with begin and end indices into the original vector

Example

dv, foldi, be = degamini([1, 2, 2, 3])

answer is dv = [1, 2, 3]; foldi = [1, 2, 1]; be = [1 1; 2 3; 4 4]

dpss_eigval(dpVecs, n, nw, ntapers)

Eigenvalues/concentrations for the Slepian sequences, given the vectors (Percival 390)

Arguments

• dpVecs: (n x ntapers) Matrix in which Slepian eigenvectors are the columns
• n: Integer length of the data
• nw: Float time bandwidth product
• ntapers: Integer number of tapers

Outputs

• eeigvalss: Vector of lengthh ntapers containing the eigenvalues

dpss_tapers(n,w,k,tap_or_egval)

Simply compute discrete prolate spheroidal sequence tapers, eigenvalues

...

Arguments

• n::Int64: Length of the taper

• nw::Float64: Time-bandwidth product

• k::Int64: Number of tapers

• tap_or_egval::Symbol = :tap: Either :tap, :egval, or :both

...

...

Outputs

• vv::Vector{Float64}: The matrix of eigenvalues, if taporegval is set to :tap

• dpss_eigval: Struct conaining the dpss tapers

...

findnst(xs, ys, x0, y0)

Find the nearest 2D point in arrays xs, ys to (x0, y0) Euclidean distance

gamini(data, folding)

Arguments

-data: some data vector -folding: The replication factor for every element of the data; if a scalar thsi applies to all of the elements (default 3), if zero or negative, no replication occurs

Outputs

-bigger

Example usage

a, b = degamini(gamini([1, 2, 3, 1, 4, 5], [1, 2, 3, 2, 4, 2]))

One gets [1, 2, 2, 3, 3, 3, 1, 1, 4, 4, 4, 4, 5, 5] as the intermediate result.

See also

@degamini, @gamini2

get_plan(n)

Obtain an FFT plan

Arguments

• n::Int64: Length of the FFT plan

Outputs

• Tuple containing two ComplexF64 arrays of length n and an FFT plan

getbdypts_2d(mask)

Starting with a matrix of zeros and ones, get the points on the boundary

Arguments

- `mask` a matrix of zeros and ones

Outputs

- `x` x-coordinates of the boundary points
- `y` y-coordinates of the boundary points

gpss(w, k, t, f; <keyword arguments>)

Generalized prolate spheroidal sequences on an unequal grid

...

Arguments

Positional Arguments

• w::Float64: the bandwidth

• k::Int64: number of Slepian tapers, must be <=2bwlength(x)

• t::Vector{Int64}: vector containing the time indices

• f::Float64: frequency at which the tapers are to be computed

Keyword Arguments

• beta::Float64 = 0.5: analysis half-bandwidth (similar to Nyquist rate)

...

...

Outputs

• lambda::Vector{Float64} the concentrations of the generalized prolate spheroidal

sequences

• u::Matrix{Float64} the matrix containing the sequences themselves

• R the Cholesky factor for the generalized eigenvalue problem

...

See also: gpss_orth

gpss_orth(w, k, t, f; <keyword arguments>)

Generalized, orthogonalized prolate spheroidal sequences on an unequal grid

...

Arguments

Positional Arguments

• w::Float64: the bandwidth

• k::Int64: number of Slepian tapers, must be <=2bwlength(x)

• t::Vector{Int64}: vector containing the time indices

• f::Float64: frequency at which the tapers are to be computed

Keyword Arguments

• beta::Float64 = 0.5: analysis half-bandwidth (similar to Nyquist rate)

...

...

Outputs

• lambda::Vector{Float64} the concentrations of the generalized prolate spheroidal

sequences

• u::Matrix{Float64} the matrix containing the sequences themselves, equivalent to

u*R for the ordinary gpss routine.

...

See also: gpss

interp1()

1D data interpolation, linear https://www.mathworks.com/help/matlab/ref/interp1.html?stid=docta

Arguments

• Vector x contains the sample points, and
• v contains the corresponding values, v(x).
• Vector xq contains the coordinates of the query points.

Outputs

• interpolated values of a 1-D function at specific query points using linear interpolation

Example usage

interp1(LinRange(0, 1, 10), log10.(LinRange(0, 1, 10)), [0.5, 0.9], :linear)

interp2(z, xy, z0)

Arguments

• z::Vector vector of z's
• yx::Matrix y, x coordinates at each of the z's
• z0<:Number level at which to interpolate z0

Outputs

• zyx coordinates corresponding to level z0

interpcontour(z, z0, thph, N)

Arguments

• z::Vector the two z-values between which the level z0 falls.
• z0<:Number the z-level of the desired contour
• thph::Matrix the zyx coordinates (first N are at level z[1] second are at level z[2])
• N::Int64 number of points for each contour

matranges(ranges)

Makes an index vector with monotonically increasing indices between pairs of numbers supplied as input. From slepian_alpha

Arguments

• ranges

  Outputs

Example

matranges([1, 4, 1, 2, -1, 2])
# answer is [1, 2, 3, 4, 1, 2, -1, 0, 1, 2]

mdslepian(w, k, t)

Generalized prolate spheroidal sequences for the 1D missing data problem

...

Arguments

Positional Arguments

• w::Float64: the bandwidth

• k::Int64: number of Slepian tapers, must be <=2bwlength(x)

• t::Vector{Int64}: vector containing the time indices

...

...

Outputs

• lambda,u::Tuple{Vector{Float64}, Vector{Float64}}: tuple containing the

concentrations and the tapers

...

See also: mdmultispec, gpss

phicurve(thph, th)

Adapted from slepian_alpha; finds the longitude crossings and thus integration domains of a closed curve parameterized in colatitude/longitude space at certian query points of colatitude.

Arguments

• thph:: Colatitude/longitude of the closed curve (degrees)
• th:: Colatitude at which crossings are required (degrees)

Outputs

• phint A matrix with crossings/intervals and zeros of dimensions MxN where M = length(th) and N can be anything depending on the oscillations of the curve
• thp Colatitude matrix for hatched plotting, if possible
• php Longitude matrix for hatched plotting, if possible
• forreal Indices of the ones that are real (could be at zero)

Depends on: @sub2ind, @interp1, @degamini, @matranges, and possibly @blob (demo2)

quadpts(qx, Nqx, qy, forreal, xints, wqx, wqy)

Scale the quaduature points and weights

Arguments

• qx
• Nqx
• qy
• forreal
• xints
• wqx
• wqy

Outputs

• QX Quadrature points in x
• QY Quadrature points in y
• w Quadrature weights
• Nrun Number of horizontal line segments in the domain

randcirc(xm, ym, r,dr, N)

Arguments

• xm horizontal positon of the center
• ym vertical position of the center
• r radius
• dr size of random perturbations around the radius
• N number of random spike points

Outputs

• x x-coordinate
• y y-coordinate

Related

@blob

sub2ind(A, row, col)

Convert to linear indices https://www.mathworks.com/help/matlab/ref/sub2ind.html