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Julia_Course/day-3/main.jl
2024-05-15 02:54:36 +02:00

1928 lines
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Julia

### A Pluto.jl notebook ###
# v0.19.42
using Markdown
using InteractiveUtils
# ╔═╡ bf144049-5a44-422c-bd7f-8086b6b37c7b
using DataFrames
# ╔═╡ a967839e-cb9f-4190-89ed-a718c3f37656
# We will use automatic units and error handling
using Measurements, Unitful
# ╔═╡ 4b75e1b4-d80b-41ff-946b-baf5da054047
# Package to deal with CSV files
using CSV
# ╔═╡ ea7dbc26-99b1-4cf9-bdd6-01635293f891
# Builtin package with useful statistical functions
using Statistics
# ╔═╡ 847f91c8-a669-4f7a-956a-be16b3df2746
using Plots
# ╔═╡ 7f72e417-0add-413e-9c17-20b4884532e8
# Imported to use a normal distribution.
# This package does also provide many other statistical distributions!
using Distributions
# ╔═╡ c985a351-cbc7-4385-b5f7-b709eee47092
# Package for fitting
using LsqFit
# ╔═╡ 32f4633c-af89-11ec-0059-5392abfd3bc3
# Oh, no, you found my secret! 😱
# Don't change this hidden cell!
begin
using PlutoUI
TableOfContents()
end
# ╔═╡ 3c6ca7d3-ea57-4c35-bbad-dcb12be76785
md"""
# Dataframes
When analyzing data, you usually deal with big tables.
To work with tables, dataframes are very useful in Julia.
"""
# ╔═╡ fd410d39-834a-4ac7-8602-c4177482a43b
# Define a dataframe with two columns
df1 = DataFrame(
U=[12.0 ± 0.32, 11.78 ± 0.15, 12.56 ± 0.63, 12.34 ± 0.12, 12.01 ± 0.20, 11.94 ± 0.17] .* u"V",
I=([110, 98, 102, 124, 105, 95] 10) .* u"mA",
)
# ╔═╡ 8700d89e-2f37-4500-aa63-978d100bf5b7
# Access one of their two columns
df1.U
# ╔═╡ 785134f4-41b5-4f0f-8db4-24b12747c526
# Access the other column
df1.I
# ╔═╡ c1ba6576-f243-4172-a2c5-fb814d96defd
# Get the names of the columns
names(df1)
# ╔═╡ 64e81e0f-7eb3-43ea-ae39-049aeb9c9d81
# Add a new column
df1.R = uconvert.(u"", df1.U ./ df1.I)
# ╔═╡ 915ca905-09b0-4ab8-8b21-ec8211ecfaa0
# View the dataframe
df1
# ╔═╡ b919df49-c61a-4381-b824-9b8f61ef86fa
# Show summary describing the dataframe and its columns
describe(df1)
# ╔═╡ fcde27d3-1f12-464f-a4f2-b8f3ee656d36
# Get one of the columns
df1[!, [:U]]
# ╔═╡ 1e5ff62e-0c5f-4cae-b41d-fd39a0ff34fd
# Get one of the columns as a copy (colon instead of an exclamation mark)
df1[:, [:U]]
# ╔═╡ 07f716ab-eb96-4a86-af0a-4716c8fe618e
# Describe only a taken column
describe(df1[!, [:U]])
# ╔═╡ 38c48c76-af39-44b8-953a-ad8010d21182
# Define a new dataframe with more rows
df2 = DataFrame(A=1:100, B=rand(100))
# ╔═╡ 5e2292f6-24bf-4d64-a85c-157f3229486d
describe(df2)
# ╔═╡ 3abed7d9-e934-4c8c-bfab-fadb2dcb1c9b
# Show the first 5 rows
first(df2, 5)
# ╔═╡ e26c2737-ce08-4d84-ac72-6c3b160ba3f0
# Show the last 5 rows
last(df2, 5)
# ╔═╡ fd81eac5-a7bb-4103-bb61-015302c5ec2d
# Show the elements with index between 10 and 20
df2[10:20, :]
# ╔═╡ faf38ad2-8cf3-41d8-94b0-54625bdc5112
# Masking (don't forget the points)
df2[0.15 .< df2.B .< 0.2, :]
# ╔═╡ 0ebe0800-4e4c-4b2d-9b22-c58430b94a55
# Masking with boolean operators (don't forget the points)
df2[(0.15 .< df2.B .< 0.2) .|| (df2.B .> 0.97), :]
# ╔═╡ 403e40d1-87ba-4847-951f-be7bca058573
# Replace all table entries having the value 100 with 42
replace!(df2.A, 100 => 42)
# ╔═╡ 44dd5cb6-0ad9-443a-ba48-fa551d8971b4
# Show the last three rows to verify that the replacement did work
last(df2, 3)
# ╔═╡ 53c09851-b6a8-4e1e-abfb-9b1b7bc991e1
# More flexibility using `replace!`
replace!(df2.A) do x
# Anonymous function
if isodd(x)
return 2 * x
else
return x
end
end
# ╔═╡ f4a324f1-be90-46c3-9940-956a892519f3
df2
# ╔═╡ d8bfb76a-0b74-4d93-b938-743725e71038
md"""
# CSV
CSV stands for "Comma Separated Values".
CSV files are usually used to store tables. We will use the package `CSV` to read and write CSV files.
"""
# ╔═╡ a6574629-3b59-408a-819a-6888ee208050
# Write our dataframe into a CSV file
# Check the file on your system!
CSV.write("resources/df2.csv", df2)
# ╔═╡ 60b4781e-af85-44bd-bbbe-6fc050395a52
# Read the file that was just written above and store its table to a new dataframe
# Only for demonstrating reading CSV files.
df3 = CSV.read("resources/df2.csv", DataFrame)
# ╔═╡ 5c989c10-724d-47b1-a224-03b77b654551
# Verify that both dataframes have equal values
df2 == df3
# ╔═╡ c34f0f01-dbe4-4222-9b31-ed20ca4be712
md"""
Sometimes, you have to read some CSV files that don't match the defaults the function `CSV.read` expects. Therefore, you have to assign some arguments to help the function reading the table correctly.
"""
# ╔═╡ 0a7e3820-1313-481c-a48f-5505e65a1699
# Take a look at the file first
df_I_B = CSV.read(
"resources/I_B.csv", DataFrame;
delim="\t", # Delimiter. "\t" stands for a tab
skipto=3, # Line where the data starts
header=1, # Line where the header is
drop=[:B_up], # Drop the the third column
)
# ╔═╡ 22a5a0a9-c9d9-4f57-bc9a-e6185542e0a4
md"""
Sometimes, you need even more options for strange CSV files. Take a look at the documentation of the function `CSV.read` to see all possible arguments 📚️
"""
# ╔═╡ c5e2d4a2-0f91-42c8-b9a0-a07bc7b15be3
md"""
# Statistics
Julia does provide some statistical functions.
Below, there of these functions are showed.
"""
# ╔═╡ eb9ca755-34f9-494f-a667-f92b683e60ad
# Mean
mean(df_I_B.I)
# ╔═╡ 811e7fad-faa4-41bb-9454-ada3d3d110ed
# Standard deviation
std(df_I_B.I)
# ╔═╡ dbf48fe9-6687-4e1c-901a-5532f8fde1cf
# Variance
var(df_I_B.I)
# ╔═╡ c14ad542-0536-4495-8b98-25393438f858
md"""
More functions in the documentation of the builtin package `Statistics`:
https://docs.julialang.org/en/v1/stdlib/Statistics/
If you are looking for even more statistical functions, take a look at the package `StatsBase`:
https://github.com/JuliaStats/StatsBase.jl
"""
# ╔═╡ 9f228904-7a85-4845-9d56-de6f62e74517
md"""
# Plotting continued
Now, we will learn about plotting measured data (with error bars).
"""
# ╔═╡ c8b3d618-38b7-405a-b677-dac99b30812b
md"""
## Scatter
Scatter plots show points.
"""
# ╔═╡ d829f596-2565-4574-9980-86c4931647b1
# Reminder of df_I_B
df_I_B
# ╔═╡ 1357bb1f-8e8f-482d-bccf-3659a448c846
scatter(
df_I_B.I, df_I_B.B_down,
xlabel="I",
ylabel="B",
label="B(I)",
)
# ╔═╡ 9e9540e7-0531-4faa-99e6-882102e305f2
scatter(
df_I_B.I, df_I_B.B_down,
xlabel="I",
ylabel="B",
label="B(I)",
markershape=:diamond, # Change marker shape
markersize=3, # Change marker size
)
# ╔═╡ 78aa1434-23ec-40a0-b88f-fca4a9533bf6
md"""
## Error bars
In physics, all measurements have errors. To display errors in a scatter plot, error bars are used.
If you are using the package `Measurements.jl`, then these error bars are created automatically.
"""
# ╔═╡ aef17bac-46e0-4035-999d-1bf6a3aa8356
begin
# Create a new dataframe with relative errors
df_I_B_with_err = DataFrame()
# You can use the macro @. to add a point everywhere for broadcasting
# Make sure you add the macro AFTER the equal sign, otherwise `=` will get `.=`
df_I_B_with_err.I = @. df_I_B.I * (1 ± 0.015)u"mA"
df_I_B_with_err.B = @. df_I_B.B_down * (1 ± 0.06)u"Gauss"
end
# ╔═╡ 0a3c905d-d044-4476-bf98-1bce9a1e257f
scatter(
df_I_B_with_err.I,
df_I_B_with_err.B,
xlabel="I",
ylabel="B",
label="B(I)",
markershape=:diamond, # Change marker shape
markersize=3, # Change marker size
)
# ╔═╡ 11c18a71-1758-48f1-b83c-2eced049a20c
md"""
## Histogram
"""
# ╔═╡ fb076919-0a0e-464d-a449-b1e7ff86fdb1
hist_values = rand(Normal(0, 1), 1000) # Random values following a normal distribution
# ╔═╡ 9ec48a21-b33f-4034-83d8-d4f9e49712f5
histogram(hist_values)
# ╔═╡ 90fedbd2-b530-4b30-bd58-07dc76e7551b
md"""
Make sure you choose a good number of bins or use the default value.
"""
# ╔═╡ 28fc5d04-8274-4f63-a015-c50f54b5ab3d
histogram(
hist_values,
xlabel="x",
ylabel="#",
label="Normal(0, 1)",
bins=35, # Too many bins
)
# ╔═╡ 6ab56f2d-759d-44ac-8427-55f85942615e
histogram(
hist_values,
xlabel="x",
ylabel="#",
label="Normal(0, 1)",
bins=10, # Too few bins
)
# ╔═╡ 1d524a9b-84e9-4ffd-b104-331055c78845
md"""
## Export
To save / export a figure, you can use the function `savefig`.
"""
# ╔═╡ 1e14de84-7d87-4df4-8c88-2307cb2262ba
# The last figure will be saved to the assigned path
savefig("resources/test_figure_export.pdf")
# ╔═╡ f44cf458-4ec1-4e2b-b839-f3981683a151
md"""
# Data fitting
Using data fitting, you can determine a model that does describe your measurements.
It is best explained using an example!
"""
# ╔═╡ 25362ad6-5b49-4900-8026-c2d54197ba94
md"""
## Example
"""
# ╔═╡ d6c9be8a-1025-449c-86c8-7d92ad240965
# Defining a model.
# Here, we choose a linear model `f(x) = m * x + c`
@. linear_model(x, p) = p[1] * x + p[2]
# ╔═╡ 9befeddf-24fa-4af8-9b1d-df1a9865a9ff
# Initial guess of the parameters in `p`
p0 = [1.0, 1.0]
# ╔═╡ e4c81d90-8d06-4c38-9886-252aa7285558
# You have to strip units and remove errors
fit = curve_fit(
linear_model, # First argument is the model
ustrip.(Measurements.value.(df_I_B_with_err.I)), # Measured x values
ustrip.(Measurements.value.(df_I_B_with_err.B)), # Measured y values
p0
)
# ╔═╡ ee858e78-6b69-485f-95d5-d735956e26d1
# Our fit parameters
param = fit.param
# ╔═╡ 51a17b24-b71b-4670-9bc5-de7576d6fc75
# The error of the fit parameters
sigma = stderror(fit)
# ╔═╡ 5957fce3-dcbd-4fc5-83b7-6730b6412dbd
begin
scatter(
df_I_B_with_err.I, df_I_B_with_err.B;
label="B(I)",
markershape=:diamond,
markersize=3,
)
x = Measurements.value.(ustrip.(LinRange(
minimum(df_I_B_with_err.I),
maximum(df_I_B_with_err.I),
250
)))
plot!(
x, linear_model(x, param),
label="Linear fit",
linewidth=3, # Change line width
)
end
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TestExt = ["Test", "Random"]
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ConstructionBaseUnitfulExt = "ConstructionBase"
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ConstructionBase = "187b0558-2788-49d3-abe0-74a17ed4e7c9"
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deps = ["LaTeXStrings", "Latexify", "Unitful"]
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git-tree-sha1 = "2f0486047a07670caad3a81a075d2e518acc5c59"
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git-tree-sha1 = "91844873c4085240b95e795f692c4cec4d805f8a"
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git-tree-sha1 = "ac88fb95ae6447c8dda6a5503f3bafd496ae8632"
uuid = "ffd25f8a-64ca-5728-b0f7-c24cf3aae800"
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[[deps.Xorg_libICE_jll]]
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git-tree-sha1 = "326b4fea307b0b39892b3e85fa451692eda8d46c"
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deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libICE_jll"]
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git-tree-sha1 = "afead5aba5aa507ad5a3bf01f58f82c8d1403495"
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git-tree-sha1 = "12e0eb3bc634fa2080c1c37fccf56f7c22989afd"
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git-tree-sha1 = "34d526d318358a859d7de23da945578e8e8727b7"
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[[deps.Xorg_libXext_jll]]
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git-tree-sha1 = "d2d1a5c49fae4ba39983f63de6afcbea47194e85"
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git-tree-sha1 = "0e0dc7431e7a0587559f9294aeec269471c991a4"
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[[deps.Xorg_libXi_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll", "Xorg_libXfixes_jll"]
git-tree-sha1 = "89b52bc2160aadc84d707093930ef0bffa641246"
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[[deps.Xorg_libXinerama_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll"]
git-tree-sha1 = "26be8b1c342929259317d8b9f7b53bf2bb73b123"
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git-tree-sha1 = "34cea83cb726fb58f325887bf0612c6b3fb17631"
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git-tree-sha1 = "47e45cd78224c53109495b3e324df0c37bb61fbe"
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deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "8fdda4c692503d44d04a0603d9ac0982054635f9"
uuid = "14d82f49-176c-5ed1-bb49-ad3f5cbd8c74"
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git-tree-sha1 = "b4bfde5d5b652e22b9c790ad00af08b6d042b97d"
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git-tree-sha1 = "730eeca102434283c50ccf7d1ecdadf521a765a4"
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git-tree-sha1 = "04341cb870f29dcd5e39055f895c39d016e18ccd"
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git-tree-sha1 = "0fab0a40349ba1cba2c1da699243396ff8e94b97"
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deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxcb_jll"]
git-tree-sha1 = "e7fd7b2881fa2eaa72717420894d3938177862d1"
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deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "d1151e2c45a544f32441a567d1690e701ec89b00"
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git-tree-sha1 = "dfd7a8f38d4613b6a575253b3174dd991ca6183e"
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deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "e78d10aab01a4a154142c5006ed44fd9e8e31b67"
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[[deps.Xorg_xkbcomp_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libxkbfile_jll"]
git-tree-sha1 = "330f955bc41bb8f5270a369c473fc4a5a4e4d3cb"
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deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_xkbcomp_jll"]
git-tree-sha1 = "691634e5453ad362044e2ad653e79f3ee3bb98c3"
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git-tree-sha1 = "e92a1a012a10506618f10b7047e478403a046c77"
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[[deps.Zstd_jll]]
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git-tree-sha1 = "e678132f07ddb5bfa46857f0d7620fb9be675d3b"
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git-tree-sha1 = "431b678a28ebb559d224c0b6b6d01afce87c51ba"
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git-tree-sha1 = "a68c9655fbe6dfcab3d972808f1aafec151ce3f8"
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git-tree-sha1 = "3516a5630f741c9eecb3720b1ec9d8edc3ecc033"
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git-tree-sha1 = "3a2ea60308f0996d26f1e5354e10c24e9ef905d4"
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git-tree-sha1 = "5982a94fcba20f02f42ace44b9894ee2b140fe47"
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git-tree-sha1 = "141fe65dc3efabb0b1d5ba74e91f6ad26f84cc22"
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git-tree-sha1 = "daacc84a041563f965be61859a36e17c4e4fcd55"
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git-tree-sha1 = "ad50e5b90f222cfe78aa3d5183a20a12de1322ce"
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git-tree-sha1 = "b910cb81ef3fe6e78bf6acee440bda86fd6ae00c"
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git-tree-sha1 = "814e154bdb7be91d78b6802843f76b6ece642f11"
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[[deps.x264_jll]]
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git-tree-sha1 = "4fea590b89e6ec504593146bf8b988b2c00922b2"
uuid = "1270edf5-f2f9-52d2-97e9-ab00b5d0237a"
version = "2021.5.5+0"
[[deps.x265_jll]]
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git-tree-sha1 = "ee567a171cce03570d77ad3a43e90218e38937a9"
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[[deps.xkbcommon_jll]]
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git-tree-sha1 = "9c304562909ab2bab0262639bd4f444d7bc2be37"
uuid = "d8fb68d0-12a3-5cfd-a85a-d49703b185fd"
version = "1.4.1+1"
"""
# ╔═╡ Cell order:
# ╟─3c6ca7d3-ea57-4c35-bbad-dcb12be76785
# ╠═bf144049-5a44-422c-bd7f-8086b6b37c7b
# ╠═a967839e-cb9f-4190-89ed-a718c3f37656
# ╠═fd410d39-834a-4ac7-8602-c4177482a43b
# ╠═8700d89e-2f37-4500-aa63-978d100bf5b7
# ╠═785134f4-41b5-4f0f-8db4-24b12747c526
# ╠═c1ba6576-f243-4172-a2c5-fb814d96defd
# ╠═64e81e0f-7eb3-43ea-ae39-049aeb9c9d81
# ╠═915ca905-09b0-4ab8-8b21-ec8211ecfaa0
# ╠═b919df49-c61a-4381-b824-9b8f61ef86fa
# ╠═fcde27d3-1f12-464f-a4f2-b8f3ee656d36
# ╠═1e5ff62e-0c5f-4cae-b41d-fd39a0ff34fd
# ╠═07f716ab-eb96-4a86-af0a-4716c8fe618e
# ╠═38c48c76-af39-44b8-953a-ad8010d21182
# ╠═5e2292f6-24bf-4d64-a85c-157f3229486d
# ╠═3abed7d9-e934-4c8c-bfab-fadb2dcb1c9b
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