what does "argmax().I" mean in Julia - julia

Here is the great example from StatWithJuliaBook (please find the following)
It demos how to smooth a plot of stary sky stars.png
My question is about argmax().I. According to the author, "Note the use of the trailing “.I” at the end of each argmax, which extracts the values of the co-ordinates in column-major."
What does it mean? Is there other parameter? I can't find any description in the document.
According to author, it seems to be the position of column-wise maxmum value, yet when I tried argmax(gImg, dims=2), the result is different.
#julia> yOriginal, xOriginal = argmax(gImg).I
#(192, 168)
#julia> yy, xx = argmax(gImg, dims = 2)
#400×1 Matrix{CartesianIndex{2}}:
# CartesianIndex(1, 187)
# CartesianIndex(2, 229)
⋮
# CartesianIndex(399, 207)
# CartesianIndex(400, 285)
#julia> yy, xx
#(CartesianIndex(1, 187), CartesianIndex(2, 229))
Please advise.
using Plots, Images; pyplot()
img = load("stars.png")
gImg = red.(img)*0.299 + green.(img)*0.587 + blue.(img)*0.114
rows, cols = size(img)
println("Highest intensity pixel: ", findmax(gImg))
function boxBlur(image,x,y,d)
if x<=d || y<=d || x>=cols-d || y>=rows-d
return image[x,y]
else
total = 0.0
for xi = x-d:x+d
for yi = y-d:y+d
total += image[xi,yi]
end
end
return total/((2d+1)^2)
end
end
blurImg = [boxBlur(gImg,x,y,5) for x in 1:cols, y in 1:rows]
yOriginal, xOriginal = argmax(gImg).I
yBoxBlur, xBoxBlur = argmax(blurImg).I
p1 = heatmap(gImg, c=:Greys, yflip=true)
p1 = scatter!((xOriginal, yOriginal), ms=60, ma=0, msw=4, msc=:red)
p2 = heatmap(blurImg, c=:Greys, yflip=true)
p2 = scatter!((xBoxBlur, yBoxBlur), ms=60, ma=0, msw=4, msc=:red)
plot(p1, p2, size=(800, 400), ratio=:equal, xlims=(0,cols), ylims=(0,rows),
colorbar_entry=false, border=:none, legend=:none)

I is a field in an object of type CartesianIndex which is returned by argmax when its argument has more than 1 dimension.
If in doubt always try using dump.
Please consider the code below:
julia> arr = rand(4,4)
4×4 Matrix{Float64}:
0.971271 0.0350186 0.20805 0.284678
0.348161 0.19649 0.30343 0.291894
0.385583 0.990593 0.216894 0.814146
0.283823 0.750008 0.266643 0.473104
julia> el = argmax(arr)
CartesianIndex(3, 2)
julia> dump(el)
CartesianIndex{2}
I: Tuple{Int64, Int64}
1: Int64 3
2: Int64 2
However, getting CartesianIndex object data via its internal structure is not very elegant. The nice Julian way to do it is to use the appropriate method:
julia> Tuple(el)
(3, 2)
Or just access the indices directly:
julia> el[1], el[2]
(3, 2)

Related

How to draw a 'proportion graph' in Julia?

Here is an example of what I am looking for:
I've looked at all of the examples in the documentation and could not find a similar graph. Any help would be appreciated.
Here's a way:
using Plots
#userplot StackedArea
# a simple "recipe" for Plots.jl to get stacked area plots
# usage: stackedarea(xvector, datamatrix, plotsoptions)
#recipe function f(pc::StackedArea)
x, y = pc.args
n = length(x)
y = cumsum(y, dims=2)
seriestype := :shape
# create a filled polygon for each item
for c=1:size(y,2)
sx = vcat(x, reverse(x))
sy = vcat(y[:,c], c==1 ? zeros(n) : reverse(y[:,c-1]))
#series (sx, sy)
end
end
a = [1,1,1,1.5,2,3]
b = [0.5,0.6,0.4,0.3,0.3,0.2]
c = [2,1.8,2.2,3.3,2.5,1.8]
sNames = ["a","b","c"]
source: https://discourse.julialang.org/t/how-to-plot-a-simple-stacked-area-chart/21351/2
Following #sanidhya-singh's link also gives a built-in solution:
julia> areaplot(1:3, [1 2 3; 7 8 9; 4 5 6], seriescolor = [:red :green :blue], fillalpha = [0.2 0.3 0.4])
which gives
Maybe worth adding to the docs though!
[EDIT] This example has been added to the Plots.jl docs

Is it possible to convert an Array{Num,1} to Array{Float64,1} in Julia?

I have the following function that uses symbolics in Julia. Everything works fine until the moment of plotting
using Distributions
using Plots
using Symbolics
using SymbolicUtils
function BinomialMeasure(iter::Int64, p::Float64, current_level = nothing)
#variables m0 m1
if current_level == nothing
current_level = [1]
end
next_level = []
for item in current_level
append!(next_level, m0*item)
append!(next_level, m1*item)
end
If iter != 0
current_level = next_level
return BinomialMeasure(iter - 1, p , current_level)
else
return [substitute(i, Dict([m0 => p, m1 => 1 - p])) for i in next_level]
end
end
y = BinomialMeasure(10, 0.4)
x = [( i + 1 ) / length(y) for i = 1:length(y) ]
append!(x, 0)
append!(y,0)
plot(x,y)
Then it returns the following:
MethodError: no method matching AbstractFloat(::Num)
Closest candidates are:
AbstractFloat(::Real, !Matched::RoundingMode) where T<:AbstractFloat at rounding.jl:200
AbstractFloat(::T) where T<:Number at boot.jl:716
AbstractFloat(!Matched::Bool) at float.jl:258
y is an Array{Num,1} and x is an Array{Float64,1}.
I tried map(float, y), convert(float,y) and float(y), but I think it not possible to convert a type Num to a Float64 or at least I don't know how to do it.
you can access the field val without using string and parse
y_val = [i.val for i in y]
this will of course have way better performance than parsing a string

ST-HOSVD in Julia

I am trying to implement ST-HOSVD algorithm in Julia because I could not found library which contains ST-HOSVD.
See this paper in Algorithm 1 in page7.
https://people.cs.kuleuven.be/~nick.vannieuwenhoven/papers/01-STHOSVD.pdf
I cannot reproduce input (4,4,4,4) tensor by approximated tensor whose tucker rank is (2,2,2,2).
I think I have some mistake in indexes of matrix or tensor elements, but I could not locate it.
How to fix it?
If you know library of ST-HOSVD, let me know.
ST-HOSVD is really common way to reduce information. I hope the question helps many Julia user.
using TensorToolbox
function STHOSVD(A, reqrank)
N = ndims(A)
S = copy(A)
Sk = undef
Uk = []
for k = 1:N
if k == 1
Sk = tenmat(S, k)
end
Sk_svd = svd(Sk)
U1 = Sk_svd.U[ :, 1:reqrank[k] ]
V1t = Sk_svd.V[1:reqrank[k], : ]
Sigma1 = diagm( Sk_svd.S[1:reqrank[k]] )
Sk = Sigma1 * V1t
push!(Uk, U1)
end
X = ttm(Sk, Uk[1], 1)
for k=2:N
X = ttm(X, Uk[k], k)
end
return X
end
A = rand(4,4,4,4)
X = X_STHOSVD(A, [2,2,2,2])
EDIT
Here, Sk = tenmat(S, k) is mode n matricization of tensor S.
S∈R^{I_1×I_2×…×I_N}, S_k∈R^{I_k×(Π_{m≠k}^{N} I_m)}
The function is contained in TensorToolbox.jl. See "Basis" in Readme.
The definition of mode-k Matricization can be seen the paper in page 460.
It works.
I have seen 26 page in this slide
using TensorToolbox
using LinearAlgebra
using Arpack
function STHOSVD(T, reqrank)
N = ndims(T)
tensor_shape = size(T)
for i = 1 : N
T_i = tenmat(T, i)
if reqrank[i] == tensor_shape[i]
USV = svd(T_i)
else
USV = svds(T_i; nsv=reqrank[i] )[1]
end
T = ttm( T, USV.U * USV.U', i)
end
return T
end

IDL two step graph

I'm struggling with setting a y(x) condition that varies with x range. As an example below, the code wants to plot y=x between x=0 and x=5.1; otherwise y=2x.
Upon compilation, the code spits out the following: Expression must be a scalar or 1 element array in this context:
In other words don't know how to assign an array variable 'x' into if statement.
Thank you all for your help in advance.
PRO test
x = findgen(101.0,start=0)/10.0 ; 0.0 start, 10.0 end increment of 0.1
print,x
if x lt 5.1 then begin
y = 1.0 * x ;
endif else begin
y = 2.0* x
endelse
graph1=plot(x,y,thick=2,NAME=first,/CURRENT, $
linestyle = 0, ytitle=' y',xtitle='x' ) ; O
END
The problem is the test in your IF statement. Use WHERE instead to do something like the following.
y = x ;; need to initialize variable
low = WHERE(x lt 5.1,lw,COMPLEMENT=upp,NCOMPLEMENT=up)
IF (lw[0] GT 0) THEN y[low] = x[low] ;; technically don't need this line
IF (up[0] GT 0) THEN y[upp] = 2e0*x[upp]

Implementation of Savitzky Golay in Julia

I have come across an implementation of SG-filter in Julia at this link. When I execute the function apply_filter, an error is returned -
UndefVarError: apply_filter not defined
I think this is an implementation for a previous version of Julia (?). I am executing this in Julia 1.0 as of now. Couldn't find documentation about the defined types, which is where my guess is concerning the error
I would like to forewarn the user about using the function savitzkyGolay in Julia. There is a mismatch with the result from Scipy implementation (which must have undergone several iterations of checking by the community)
#pyimport scipy.signal as ss
x=[1,2,3,4,5,6,7,8,9,10]
savitzkyGolay(x,5,1)
10-element Array{Float64,1}:
1.6000000000000003
2.200000000000001
3.0
4.0
5.000000000000001
6.000000000000001
7.0
8.0
8.8
9.400000000000002
#Python's scipy implementation
ss.savgol_filter(x,5,1)
10-element Array{Float64,1}:
1.0000000000000007
2.0000000000000004
2.9999999999999996
3.999999999999999
4.999999999999999
5.999999999999999
6.999999999999998
7.999999999999998
8.999999999999996
9.999999999999995
If it can help, I have simplified the code.
using Pkg, LinearAlgebra, DSP, Plots
function vandermonde(halfWindow, polyDeg)
x=[1.0*i for i in -halfWindow:halfWindow]
n = polyDeg+1
m = length(x)
V = zeros(m, n)
for i = 1:m
V[i,1] = 1.0
end
for j = 2:n
for i = 1:m
V[i,j] = x[i] * V[i,j-1]
end
end
return V
end
function SG(halfWindow, polyDeg)
V = vandermonde(halfWindow,polyDeg)
Q,R=qr(V)
n = polyDeg+1
m = 2*halfWindow+1
R1 = vcat(R, zeros(m-n,n))
sg = R1\Q'
for i in 1:(polyDeg+1)
sg[i,:] = sg[i,:]*factorial(i-1)
end
return sg'
end
function apply_filter(filter,signal)
halfWindow = round(Int,(length(filter)-1)/2)
padded_signal = [signal[1]*ones(halfWindow);signal;signal[end]*ones(halfWindow)]
filter_cross_signal = conv(filter[end:-1:1], padded_signal)
return filter_cross_signal[2*halfWindow+1:end-2*halfWindow]
end
Here is how I use it :
mean_speed_unfiltered = readdlm("mean_speeds_raw_-2.txt")
sg = SG(500,2); # halt-window, polynomal degree
t = 10*10^(-3)#s #time of the simulation
dt = 0.1/γ; #time step
Nt = convert(Int, round(t/dt)); #number of iteration
#Smooth the mean speed curve:
mean_speeds_smoothed = apply_filter(sg[:,1],mean_speed_unfiltered)
png(plot([j*dt for j=0:Nt] , mean_speeds_smoothed, title = "Smoothed mean speed over
time", xlabel = "t (s)"), "Mean_speed_filtered_SG")
derivative_mean_speeds_smoothed = apply_filter(sg[:,2],mean_speed_unfiltered)
plt1 = plot(mean_speeds_smoothed,derivative_mean_speeds_smoothed, title = "derivative mean speed over speed", xlabel = "<v>(t) (s)", ylabel = "d<v(t)>/dt")
png(plt1, "Force_SG_1D2Lasers")
However it seems to me that the code presented in https://gist.github.com/lnacquaroli/c97fbc9a15488607e236b3472bcdf097#file-savitzkygolay-jl-L34 is faster.

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