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toolbox.jl
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toolbox.jl
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"""
environment
"""
using Pkg
Pkg.activate("reduce_daemensionality_julia")
#----------------------------------------------------------------------
#time stamp for saving analysis results
#----------------------------------------------------------------------
using Dates
function init_logging()
weekno = week(unix2datetime(time()))
datestring = string("KW_2_",lpad(weekno,2,"0"),"/")
workdir = "/net/home/lschulz/logs/"
dir = workdir*datestring
if isdir(dir)==false
mkdir(dir)
end
return dir
end
dir = init_logging()
"""
read in modes
"""
using FileIO
using JLD2
function read_modes_single_file(method,W,vari,spot)
"""
# Define an inner function create_file_list which takes in parameters outdir,method,W,vari,preproc
"""
function create_file_list(outdir,method,W,vari,preproc)
# Read the directory specified by outdir
allfiles = readdir(outdir)
# Split the names of the files in the directory using "_" as the delimiter
filenamesplit = split.(allfiles,"_")
# Find the indices of the files that match the specified method, W, vari, and preproc
method_inds = findall(x->( x[1]==method && x[2] == "$W" && x[4] == "$vari" && x[end][1:4] == preproc),[filenamesplit[i] for i in 1:length(filenamesplit)])
# Concatenate the outdir with the matched files
files = outdir .* allfiles[method_inds]
# Return the list of matched files
return files
end
"""
# Define an inner function read_single_file which takes in parameters filename,yearsamples,N,k
"""
function read_single_file(filename,yearsamples,N=11322,k = 48)
# Load the file specified by filename
File = load(filename)
# Extract the "lambda" variable from the loaded file
lambda = File["lambda"]
# Extract the "EOF" variable from the loaded file
EOF = File["EOF"]
# Extract the "signal" variable from the loaded file
signal = File["signal"]
# Return the extracted variables
return lambda,EOF,signal
end
# Create a name variable by concatenating spot, method, W, and vari
name = "$(spot)_$(method)_$(W)_$(vari)"
# Set N and k to default values
N = 5478
k = 48
# Set yearsamples to 365.25
yearsamples=365.25
# Set preproc to "raw."
preproc="raw."
# Concatenate the savedir with the name variable
savedir = "/net/scratch/lschulz/modes/"*"name"
#data
outdir="/net/scratch/lschulz/fluxfullset/"
# Use the create_file_list function to find the filename that matches the input parameters
filename = create_file_list(outdir,method,W,vari,preproc)[spot]
# Use the read_single_file function to extract the variables lambda, EOF, and signal from the filename
lambda,EOF,signal = read_single_file(filename,yearsamples,N,k)
# Save the extracted variables to a JLD file at the specified savedir
jldsave(savedir,lambda=lambda,modes=EOF,signal=signal)
end
#----------------------------------------------------------------------
#data tools
#----------------------------------------------------------------------
using Statistics
using StatsBase
using MultivariateStats
using Random
using CSV
using DataFrames
using FFTW
using LinearAlgebra
#using Plots
using ManifoldLearning
using Peaks
using NPZ
using FourierAnalysis
#using Plots
using FFTW
using EmpiricalModeDecomposition
using ProgressMeter
using JLD2
using ProfileSVG
using LsqFit
using CairoMakie
using MathTeXEngine
using FileIO
using ImageIO
using NearestNeighbors
using SharedArrays
""" signal stuff"""
#----------------------------------------------------------------------
#centralize
#embed lag
#reconstructor
#----------------------------------------------------------------------
#centralize
function centralizer(data::Vector{Float32})
m = mean(data)
cv = std(data)
return (data.-m)./cv
end
#embed lag
function embed_lag(data::Vector{Float32},W::Int64)
Y = []
for i=1:length(data)-W+1
Y = append!(Y,data[i:i+W-1])
end
return reshape(float.(Y),W,length(data)-W+1)::Matrix{Float32}
end
#reconstruction ssa
function reconstructor(A,rho,N,M)
P = N-M+1
#A is the k_th PC (projection) of length P
#rho is the k_th eigenvector (EOF) of length M
#M is window length W
R(t,M_t,L_t,U_t) = M_t*sum([A[t-j+1]*rho[j] for j in L_t:U_t])
function choicer(t)
if 1<=t<=M-1
return 1/t,1,t
elseif M<=t<=P
return 1/M,1,M
elseif P+1<=t<=N
return 1/(N-t+1),t-N+M,M
end
end
return [R(t,choicer(t)...) for t in 1:N]
end
""" proto stuff"""
#----------------------------------------------------------------------
# protophase signal , num_it
# protofrequency signal, year=samples per year
# count sign flips
# count maxima
#iterated hilbert
#----------------------------------------------------------------------
#count sign flips
count_sign_flip(signal) = sum([(sign.(signal[i])!=sign.(signal[i+1])) ? 1 : 0 for i in 1:length(signal)-1])
#count maxima
count_maxima(signal) = length(findmaxima(signal)[1])
function iterated_hilbert(mode::Vector,l)
ll = Int64[]
for i = 1:l
HilbertT = hilbert_transform(Float64.(mode))
protophases = atan.(imag(HilbertT),real(HilbertT))
s = count_sign_flip(protophases)
#println(s)
ll = append!(ll,s)
mode = protophases
end
return median(ll),var(ll)/sqrt(l)
end
#function that spits out the indeces of the modes according to the domains in all locations as a matrix of lists [bandxloc]
function protofrequency(signal::Vector{Float32},yearsamples,Nit)
zeros = []
for i in 1:Nit
HilbertT = hilbert_transform(Float64.(signal))
protophases = atan.(imag(HilbertT),real(HilbertT))
zeros = append!(zeros,count_sign_flip(protophases))
signal = protophases
end
T = 2 * length(signal) / median(zeros)
return Float32(yearsamples / T )
end
function protophase(signal::Vector{Float32},Nit)
protoph = atan.(imag(hilbert_transform(Float64.(signal))),real(hilbert_transform(Float64.(signal))))
for i=1:Nit-1
protoph = atan.(imag(hilbert_transform(Float64.(protoph))),real(hilbert_transform(Float64.(protoph))))
end
return protoph
end
""" proto stuff"""
#----------------------------------------------------------------------
#entropy signal
#correlation_coefficient signal1 signal2
#rec_phase_complete RC::M, lam::v
#rec_protophase RC::M Num_it <==
#phase_diff_hist mode1,mode2 gives bins,cauchy_weights
#----------------------------------------------------------------------
#entropy
function entropy(signal::Vector{Float32})
signal = abs.(centralizer(signal))
return -sum(signal .* log.(signal))
end
#crosscorrelation coefficient
function correlation_coefficient(x::Vector{Float32},y::Vector{Float32})
#lags = 1:Int(length(x)-1)
#c = crosscor(x,y,lags)
return cov(x,y) / var(x) / var(y)
end
function rec_phase_complete(RC::Matrix{Float32},lam::Vector{Float32})
ph = [protophase(RC[:,i]) for i=1:size(RC)[2]]
pha = hcat(ph...)
phas = vec(sum(pha'.*lam,dims=1))
return centralizer(phas)
end
rec_protophase(RC::Matrix{Float32},Nit) = Float32.(hcat([protophase(RC[:,i],Nit) for i=1:size(RC)[2]]...))
function phase_diff_hist(mode1::Vector{Float32},mode2::Vector{Float32}) #takes in protophases
bins = (-pi:0.01:pi)
phasediff = mode1 .- mode2
h = fit(Histogram,phasediff,bins)
hist = normalize(h,mode=:pdf).weights
p0 = ones(2)
c = coef(curve_fit(cauchy,Array(bins)[1:end-1],hist,p0))
return bins[1:end-1],hist,c[1],c[2]
end
"""fluxnet simple measures"""
#----------------------------------------------------------------------
#spec entropy
#diff eps
#autocorr
#rec_protophase RC::M Num_it <==
#phase_diff_hist mode1,mode2 gives bins,cauchy_weights
#----------------------------------------------------------------------
#fluxnet entropy based on lambda
function spectral_entropy(datadir,var_ind,loc_ind,rec_m,season_ind)
if rec_m == "ssa"
lambda = load(datadir*"ssa_$(loc_ind)_$(var_ind)_$(season_ind).jld2")["lambda"]
elseif rec_m == "diff"
lambda = load(datadir*"diff_$(loc_ind)_$(var_ind)_$(season_ind).jld2")["lambda"]
end
return entropy(lambda)
end
#diffusion eps
function diff_eps(datadir,var_ind,loc_ind)
season_ind = 1
eps = load(datadir*"diff_$(loc_ind)_$(var_ind)_$(season_ind).jld2")["eps"]
return eps
end
#autocorrelation strength complete reconstructed signal
function autocorr(datadir,var_ind,loc_ind,rec_m)
season_ind = 1
if rec_m == "ssa"
RC = load(datadir*"ssa_$(loc_ind)_$(var_ind)_$(season_ind).jld2")["RC"]
elseif rec_m == "diff"
RC = load(datadir*"diff_$(loc_ind)_$(var_ind)_$(season_ind).jld2")["RC"]
end
return correlation_coefficient(sum(RC,dims=2)[:,1],sum(RC,dims=2)[:,1])
end
#autocorrelation strength raw signal
function autocorr_raw(datadir,var_ind,loc_ind)
season_ind = 1
signal = load(datadir*"diff_$(loc_ind)_$(var_ind)_$(season_ind).jld2")["signal"]
return correlation_coefficient(signal,signal)
end
"""
coupling whole signal
cauchy fits
"""
#readout signal and perform single hilbert transform
function protophase_by_varind_recm(datadir,loc_ind,season_ind,var_ind,rec_m)
if rec_m == "raw"
signal = load(datadir*"ssa_$(loc_ind)_$(var_ind)_$(season_ind).jld2")["signal"]
elseif rec_m == "ssa"
signal = sum(load(datadir*"ssa_$(loc_ind)_$(var_ind)_$(season_ind).jld2")["RC"],dims=2)[:,1]
elseif rec_m == "diff"
signal = sum(load(datadir*"diff_$(loc_ind)_$(var_ind)_$(season_ind).jld2")["RC"],dims=2)[:,1]
end
return atan.(imag(hilbert_transform(Float64.(signal))),real(hilbert_transform(Float64.(signal))))
end
function cauchy(x,p) # fit cauchy / delta to a normalized phase difference
x0 = p[1]
gamma = p[2]
@. return 1/(pi*gamma*(1+((x-x0)/gamma)^2))
end
function fit_cauchy(onebins) # perform the fit to the histogram list
bins = (-pi:0.01:pi)
bin_N = length(bins)-1
p0 = ones(2)
return coef(curve_fit(cauchy,Array(bins)[1:end-1],onebins,p0))
end
#complete signal phase difference histogram between two spots
function varmap(loc_ind_1,loc_ind_2,datadir,season_ind,rec_m,var_ind)
bins = (-pi:0.01:pi)
bin_N = length(bins)-1
phasediff = protophase_by_varind_recm(datadir,loc_ind_1,season_ind,var_ind,rec_m) .- protophase_by_varind_recm(datadir,loc_ind_2,season_ind,var_ind,rec_m)
h = fit(Histogram,phasediff,bins)
h = normalize(h,mode=:pdf).weights
return h
end
#cauchy fit between two spots for complete reconstructior or raw signal
function phase_diff_complete(datadir,loc_ind_1,loc_ind_2,rec_m,var_ind)
season_ind = 1
hist = varmap(loc_ind_1,loc_ind_2,datadir,season_ind,rec_m,var_ind)
cauchypar = fit_cauchy(hist)
x0 = cauchypar[1]
gamma = cauchypar[2]
return x0,gamma
end
"""
coupling index based
cauchy fits
"""
#index based readout signal and perform single hilbert transform
function protophase_by_varind_recm_modeind(datadir,loc_ind,mode_ind,season_ind,var_ind,rec_m)
if rec_m == "ssa"
signal = sum(load(datadir*"ssa_$(loc_ind)_$(var_ind)_$(season_ind).jld2")["RC"][:,mode_ind],dims=2)[:,1]
elseif rec_m == "diff"
signal = sum(load(datadir*"diff_$(loc_ind)_$(var_ind)_$(season_ind).jld2")["RC"][:,mode_ind],dims=2)[:,1]
end
return atan.(imag(hilbert_transform(Float64.(signal))),real(hilbert_transform(Float64.(signal))))
end
#index based signal phase difference histogram between two spots
function varmap_ind(loc_ind_1,loc_ind_2,mode_ind_1,mode_ind_2,datadir,season_ind,rec_m,var_ind)
bins = (-pi:0.01:pi)
bin_N = length(bins)-1
phasediff = protophase_by_varind_recm_modeind(datadir,loc_ind_1,mode_ind_1,season_ind,var_ind,rec_m)
.- protophase_by_varind_recm_modeind(datadir,loc_ind_2,mode_ind_2,season_ind,var_ind,rec_m)
h = fit(Histogram,phasediff,bins)
h = normalize(h,mode=:pdf).weights
return h
end
#index of Tband based protophase difference cauchy fit # needs to be tested not to contain nothing
function phase_diff_ind(datadir,loc_ind_1,loc_ind_2,mode_ind_1,mode_ind_2,rec_m,var_ind)
season_ind = 1
bins = (-pi:0.01:pi)
bin_N = length(bins)-1
hist = varmap_ind(loc_ind_1,loc_ind_2,mode_ind_1,mode_ind_2,datadir,season_ind,rec_m,var_ind)
cauchypar = fit_cauchy(hist)
x0 = cauchypar[1]
gamma = cauchypar[2]
return x0,gamma
end
"""
coupling
crosscorrelation coefficient index based
"""
#index based readout signal
function reconstruction_by_varind_recm_modeind(datadir,loc_ind,mode_ind,season_ind,var_ind,rec_m)
if rec_m == "ssa"
signal = sum(load(datadir*"ssa_$(loc_ind)_$(var_ind)_$(season_ind).jld2")["RC"][:,mode_ind],dims=2)[:,1]
elseif rec_m == "diff"
signal = sum(load(datadir*"diff_$(loc_ind)_$(var_ind)_$(season_ind).jld2")["RC"][:,mode_ind],dims=2)[:,1]
end
return signal
end
#index based correlation crosscorrelation coefficient - can also be used for autocorrelation
function crosscor_ind(loc_ind_1,loc_ind_2,mode_ind_1,mode_ind_2,datadir,season_ind,rec_m,var_ind)
season_ind = 1
signal_1 = reconstruction_by_varind_recm_modeind(datadir,loc_ind_1,mode_ind_1,season_ind,var_ind,rec_m)
signal_2 = reconstruction_by_varind_recm_modeind(datadir,loc_ind_2,mode_ind_2,season_ind,var_ind,rec_m)
return correlation_coefficient(signal_1,signal_2)
end
"""the heavy weights"""
function phase_rec_fluxer(datadir,loc_ind,mode_indices,rec_m,var_ind)
RC = load(datadir*"$(rec_m)_$(loc_ind)_$(var_ind)_$(season_ind).jld2")["RC"][:,mode_indices]
lam = [norm(load(datadir*"$(rec_m)_$(loc_ind)_$(var_ind)_$(season_ind).jld2")["PC"][:,m]) for m=mode_indices]
return rec_phase_complete(RC,lam)
end
function mode_protofrequencies(datadir::String,loc_ind,mode_indices,rec_m,var_ind)
RC = load(datadir*"$(rec_m)_$(loc_ind)_$(var_ind)_$(season_ind).jld2")["RC"][:,mode_indices]
lam = [norm(load(datadir*"$(rec_m)_$(loc_ind)_$(var_ind)_$(season_ind).jld2")["PC"][:,m]) for m=mode_indices]
return [protofrequency(RC[:,i]) for i=1:size(RC)[2]],lam
end
function all_mode_protofrequencies(datadir::String,rec_m,var_ind,loc_indices,mode_indices,season_ind)
f = Matrix{Float32}(undef,length(mode_indices),length(loc_indices))
l = Matrix{Float32}(undef,length(mode_indices),length(loc_indices))
for loc_ind in loc_indices
RC = load(datadir*"$(rec_m)_$(loc_ind)_$(var_ind)_$(season_ind).jld2")["RC"][:,mode_indices]
lam = [norm(load(datadir*"$(rec_m)_$(loc_ind)_$(var_ind)_$(season_ind).jld2")["PC"][:,m]) for m=mode_indices]
f[:,loc_ind] = [protofrequency(RC[:,i]) for i=1:size(RC)[2]]
l[:,loc_ind] = lam
end
return f,l
end
function reconstruction_error(datadir,var_ind,loc_ind,rec_m,season_ind)
original = load(datadir*"$(rec_m)_$(loc_ind)_$(var_ind)_3.jld2")["signal"]
deseason = load(datadir*"$(rec_m)_$(loc_ind)_$(var_ind)_$(season_ind).jld2")["signal"]
season = original .- deseason
rec_deseas = vec(sum(load(datadir*"$(rec_m)_$(loc_ind)_$(var_ind)_$(season_ind).jld2")["RC"],dims=2))
return norm(original.-season),norm(deseason .- rec_deseas)
end
function phase_diff_spots_by_modeind(datadir,loc_ind_1,loc_ind_2,mode_indices_1,mode_indices_2,rec_m,var_ind,season_ind)
bins = (-pi:0.01:pi)
bin_N = length(bins)-1
phasediff = phase_rec_fluxer(datadir,loc_ind_1,mode_indices_1,rec_m,var_ind) .- phase_rec_fluxer(datadir,loc_ind_2,mode_indices_2,rec_m,var_ind)
h = fit(Histogram,phasediff,bins)
hist = normalize(h,mode=:pdf).weights
cauchypar = fit_cauchy(hist)
x0 = cauchypar[1]
gamma = cauchypar[2]
return x0,gamma
end
function crosscorr_spots_by_modeind(datadir,loc_ind_1,loc_ind_2,mode_indices_1,mode_indices_2,rec_m,var_ind,season_ind)
if !isempty(mode_indices_1) && !isempty(mode_indices_2)
RC1 = vec(sum(load(datadir*"$(rec_m)_$(loc_ind_1)_$(var_ind)_$(season_ind).jld2")["RC"][:,mode_indices_1],dims=2))
RC2 = vec(sum(load(datadir*"$(rec_m)_$(loc_ind_2)_$(var_ind)_$(season_ind).jld2")["RC"][:,mode_indices_2],dims=2))
return correlation_coefficient(RC1,RC2)
else
return 0.0
end
end
#cauchy
function coupling_strength_cauchy(coupling_inds,mode_inds,datadir,rec_m,var_ind,season_ind)
function strengthperind(inds)
loc_ind_1 = inds[1]
loc_ind_2 = inds[2]
mode_indices_1 = mode_inds[loc_ind_1]
mode_indices_2 = mode_inds[loc_ind_2]
if !isempty(mode_indices_1) && !isempty(mode_indices_2)
return phase_diff_spots_by_modeind(datadir,loc_ind_1,loc_ind_2,mode_indices_1,mode_indices_2,rec_m,var_ind,season_ind)[2]
else
return 0.0
end
end
m = map(strengthperind,coupling_inds)
return m
end
function coupling_phase_cauchy(coupling_inds,mode_inds,datadir,rec_m,var_ind,season_ind)
function strengthperind(inds)
loc_ind_1 = inds[1]
loc_ind_2 = inds[2]
mode_indices_1 = mode_inds[loc_ind_1]
mode_indices_2 = mode_inds[loc_ind_2]
if !isempty(mode_indices_1) && !isempty(mode_indices_2)
return phase_diff_spots_by_modeind(datadir,loc_ind_1,loc_ind_2,mode_indices_1,mode_indices_2,rec_m,var_ind,season_ind)[1]
else
return 0.0
end
end
m = map(strengthperind,coupling_inds)
return m
end
#crosscorr coefficient for coupling strength
function coupling_strength_crosscorr(coupling_inds,mode_inds,datadir,rec_m,var_ind,season_ind)
function strengthperind(inds)
loc_ind_1 = inds[1]
loc_ind_2 = inds[2]
mode_indices_1 = mode_inds[loc_ind_1]
mode_indices_2 = mode_inds[loc_ind_2]
return crosscorr_spots_by_modeind(datadir,loc_ind_1,loc_ind_2,mode_indices_1,mode_indices_2,rec_m,var_ind,season_ind)
end
m = map(strengthperind,coupling_inds)
return m
end
"""frequency bands"""
function list_harmonics(hmax)
L = Float32[]
for h=1:hmax
for l=1:hmax
L = append!(L,l/h)
L = append!(L,h/l)
end
end
return sort(unique(L))
end
function list_pure_harmonics(hmax)
L = Float32[]
for h=1:hmax
L = append!(L,1/h)
L = append!(L,h)
end
return sort(unique(L))
end
harmonic_bands(hmax,eps1) = [[i-eps1,i+eps1] for i in list_harmonics(hmax)]
anharmonic_bands(har_bands,eps2) = [[har_bands[i][2]-eps2,har_bands[i+1][1]+eps2] for i = 1:length(har_bands)-1]
simplebands(eps) = [[10^-3,0.375+eps],[0.375-eps,1.25+eps],[1.25-eps,10^3]]
simplebands() = [[10^-3,0.375],[0.375,1.25],[1.25,10^3]]
function Tbands(freq_domains,var_ind,loc_inds,datadir,rec_m,season_ind)
ind = Matrix{Vector{Int64}}(undef,length(freq_domains),length(loc_inds))
lambi = Matrix{Vector{Float32}}(undef,length(freq_domains),length(loc_inds))
for (i,loc_ind) in enumerate(loc_inds), (j,domain) in enumerate(freq_domains)
f_low = domain[1]
f_up = domain[2]
mode_indices=1:48
p_frequencies,lam = mode_protofrequencies(datadir::String,loc_ind,mode_indices,rec_m,var_ind)
#mode_ind = findall(freq->f_up>freq>f_low,p_frequencies)
mode_ind = Array(1:48)[f_low .< p_frequencies .< f_up]
ind[j,i] = vec(mode_ind)
lambi[j,i] = lam[vec(mode_ind)]
end
return ind,lambi
end
function matrix_Tbands(freq_domains,protofrequencies)
ind = Matrix{Vector{Int64}}(undef,length(freq_domains),size(protofrequencies)[2])
for i in 1:size(protofrequencies)[2], (j,domain) in enumerate(freq_domains)
f_low = domain[1]
f_up = domain[2]
p_frequencies = protofrequencies[:,i]
mode_ind = Array(1:48)[f_low .< p_frequencies .< f_up]
ind[j,i] = Int64.(vec(mode_ind))
end
return ind
end
function calculate_bands(datadir,rec_m,var_ind,season_ind)
f,l = all_mode_protofrequencies(datadir,rec_m,var_ind,1:71,1:48,season_ind)
b1 = simplebands(0.02)
b2h = harmonic_bands(8,0.02)
b2a = anharmonic_bands(b2h,0.01)
b2 = vcat(b2h,b2a)
i1 = matrix_Tbands(b1,f)
i2 = matrix_Tbands(b2,f)
B1 = [Int64.(vcat([vcat([Int64(j) for j in i]...) for i in unique(i2[1:43,k])]...)) for k in 1:71]
B2 = [Int64.(vcat([vcat([Int64(j) for j in i]...) for i in unique(i2[44:end,k])]...)) for k in 1:71]
return l,[i1[1,:],i1[2,:],i1[3,:]],[B1,B2]
end
function extract_from_files(filename_list,N=11322,k = 48) #with .jld2 both in files and savename
year=365
L = length(filename_list)
lambda = Array{Float32}(undef,k,L)
protophases = Array{Float32}(undef,N,k,L)
protofreq = Array{Float32}(undef,k,L)
RC = Array{Float32}(undef,N,k,L)
for (i,filename) in enumerate(filename_list)
File = load(filename)
lambda[:,i] = File["lambda"]
RC[:,:,i] = File["RC"]
protophases[:,:,i] = rec_protophase(RC[:,:,i],1)
protofreq[:,i] = hcat([protofrequency(protophases[:,kk,i],year) for kk in 1:k]...)
end
return lambda,protofreq,RC
end #return lambda(k,L),protophases(N,k,L),protofreq(k,L),RC(N,k,L)
function extract_from_single_file(filename,yearsamples,N=11322,k = 48)
File = load(filename)
lambda = File["lambda"]
EOF = File["EOF"]
RC = File["RC"]
protophases = rec_protophase(RC,1)
protofreq = hcat([protofrequency(EOF[:,kk],yearsamples,1) for kk in 1:k]...)
return lambda,protofreq,RC
end
function create_file_list(outdir,method,W,vari,preproc) #at the moment this does diffusion
allfiles = readdir(outdir)
filenamesplit = split.(allfiles,"_")
method_inds = findall(x->( x[1]==method && x[2] == "$W" && x[4] == "$vari" && x[end][1:4] == preproc),[filenamesplit[i] for i in 1:length(filenamesplit)])
files = outdir .* allfiles[method_inds]
return files
end #return files
"""
analyze the phase-coupling of two modes
"""
function phase_synchronization(mode1::Vector{Float32},mode2::Vector{Float32}) #takes in protophases
bins = (-pi:0.01:pi)
phasediff = mode1 .- mode2
h = fit(Histogram,phasediff,bins)
hist = normalize(h,mode=:pdf).weights
p0 = ones(2)
c = coef(curve_fit(cauchy,Array(bins)[1:end-1],hist,p0))
return Float32.([max(min(c[1],10),-10),c[2]])
end #return x0,gamma
"""
analyze phase coupling along mode_indices inside a file where the bands are already put together
"""
function cauchy_by_modes(protobands)
T,spots,bands = size(protobands)
gamma = ones(Float32,spots,spots,bands,bands)
x0 = ones(Float32,spots,spots,bands,bands)
for band1 in 1:bands, spot1 in 1:spots, band2 in 1:bands, spot2 in 1:spots
if spot1 == spot2
g,x = 0,0
else
g,x = phase_synchronization(protobands[:,spot1,band1],protobands[:,spot2,band2])
end
gamma[spot1,spot2,band1,band2] = g
x0[spot1,spot2,band1,band2] = x
end
#gamma[findall(x->x>10,gamma)] = 10
#x0[findall(x->x>10,x0)] = 10
return Float32.(gamma), Float32.(x0)
end #return gamma(L,L,bands,bands) , x0(L,L,bands,bands)
"""
put the modes together by band
"""
function band_indices(freq_domains,protofrequencies) #read in a matrix of the frequencies
#need some feeding of locking up all the protofrequencies of all the spots we want
#should be easily done
n_bands = length(freq_domains)
n_spots =size(protofrequencies)[2]
ind = Matrix{Vector{Int64}}(undef,n_bands,n_spots)
for i in 1:n_spots, (j,domain) in enumerate(freq_domains)
f_low = domain[1]
f_up = domain[2]
p_frequencies = protofrequencies[:,i]
mode_ind = Array(1:48)[f_low .< p_frequencies .< f_up]
ind[j,i] = Int64.(vec(mode_ind))
end
return ind
end #return ind (bands, L) vec
function combine_by_bands(indices,RC,lambdas)
T, n_comp, n_spots = size(RC)
n_bands = size(indices)[1]
#then we iterate over all of them getting to know the modes we want to have
#then one large file of the modes! which is only N bands spots shoudl be possible for all data size, this is great!
protobands = Array{Float32}(undef,T,n_spots,n_bands)
lambda_bands = Array{Float32}(undef,n_spots,n_bands)
for band in 1:n_bands, spot in 1:n_spots
mode_indices = indices[band,spot]
protobands[:,spot,band] = Float32.(10^-5 .+ protophase(sum(RC[:,mode_indices,spot],dims=2)[:],1))
lambda_bands[spot,band] = Float32.(sum(10^-5 .+ lambdas[mode_indices,spot]))
if isempty(mode_indices)
protobands[:,spot,band] = ones(Float32,T)*10^-5
end
end
return protobands,lambda_bands
end #return protobands(N,L,bands),lambda_bands(N,L,bands)
#----------------------------------------------------------------------
# modelling stuff
#----------------------------------------------------------------------