Introduction to Gnuplot                                                                

                                                                         Plotting Functions and Data                                                                          

              ██ Gnuplot                                                                                                                                                      

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              ██ What is Gnuplot?                                                                                                                                             

              Gnuplot is a command-driven plotting program used throughout science and engineering.                                                                           

                 •  Runs interactively or from scripts                                                                                                                        

                 •  Plots mathematical functions and data files                                                                                                               

                 •  Produces publication-quality output (PNG, PDF, SVG, and more)                                                                                             

                 •  Available on Linux, macOS, and Windows                                                                                                                    

              Unlike GUI tools (Excel, Origin), gnuplot is driven by commands — which means you can automate and reproduce your plots exactly.                                

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              ██ Starting Gnuplot                                                                                                                                             

              At the terminal:                                                                                                                                                

                                                                $ gnuplot                                                                                                     

              You'll see the gnuplot prompt:                                                                                                                                  

                                                                        G N U P L O T                                                                                         

                                                                        ...                                                                                                   

                                                                gnuplot>                                                                                                      

              Type commands at the gnuplot> prompt. Type quit or press Ctrl-D to exit.                                                                                        

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              ██ Plotting Functions                                                                                                                                           

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              ██ The plot Command                                                                                                                                             

              The simplest gnuplot command:                                                                                                                                   

                                                                gnuplot> plot sin(x)                                                                                          

              This opens a window with a plot of sin(x) over the default x range.                                                                                             

              More examples:                                                                                                                                                  

                                                                gnuplot> plot cos(x)                                                                                          

                                                                gnuplot> plot x**2                                                                                            

                                                                gnuplot> plot exp(-x**2)                                                                                      

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              ██ Built-in Math Functions                                                                                                                                      

              Gnuplot knows the standard mathematical functions:                                                                                                              

                 •  sin(x), cos(x), tan(x) — trigonometric (angles in radians)                                                                                                

                 •  exp(x) — exponential (e^x)                                                                                                                                

                 •  log(x), log10(x) — natural and base-10 logarithm                                                                                                          

                 •  sqrt(x) — square root                                                                                                                                     

                 •  abs(x) — absolute value                                                                                                                                   

                 •  x**n — exponentiation (x to the nth power)                                                                                                                

                 •  pi — the constant π ≈ 3.14159...                                                                                                                          

              Plot two functions at once by separating them with a comma:                                                                                                     

                                                                gnuplot> plot sin(x), cos(x)                                                                                  

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              ██ Setting the Range                                                                                                                                            

              Control which x values are plotted by adding [min:max] right after plot:                                                                                        

                                                                gnuplot> plot [0:2*pi] sin(x)                                                                                 

                                                                gnuplot> plot [-5:5] x**2                                                                                     

                                                                gnuplot> plot [0:10] exp(-x)                                                                                  

              Works with multiple functions too:                                                                                                                              

                                                               gnuplot> plot [0:2*pi] sin(x), cos(x), sin(2*x)                                                                

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              ██ Demo - Plotting Functions                                                                                                                                    

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              ██ Configuring Your Plot                                                                                                                                        

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              ██ set Commands                                                                                                                                                 

              Gnuplot settings are controlled with set:                                                                                                                       

                                                                gnuplot> set title "My Plot"                                                                                  

                                                                gnuplot> set xlabel "Time (s)"                                                                                

                                                                gnuplot> set ylabel "Position (m)"                                                                            

              After changing settings, run replot to refresh the plot:                                                                                                        

                                                                gnuplot> replot                                                                                               

              Or just issue a new plot command.                                                                                                                               

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              ██ Title and Axis Labels                                                                                                                                        

                                                                gnuplot> set title "Damped Oscillation"                                                                       

                                                                gnuplot> set xlabel "Time (s)"                                                                                

                                                                gnuplot> set ylabel "Amplitude"                                                                               

                                                                gnuplot> plot [0:10] exp(-x/3) * cos(2*pi*x)                                                                  

              Give each curve a name in the legend using title in the plot command:                                                                                           

                                                     gnuplot> plot sin(x) title "sine wave", cos(x) title "cosine wave"                                                       

              To suppress the legend entry for a curve:                                                                                                                       

                                                                gnuplot> plot sin(x) notitle                                                                                  

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              ██ Axis Ranges                                                                                                                                                  

              Set axis ranges persistently with set xrange and set yrange:                                                                                                    

                                                                gnuplot> set xrange [0:10]                                                                                    

                                                                gnuplot> set yrange [-1.5:1.5]                                                                                

                                                                gnuplot> replot                                                                                               

              Reset back to auto-scaling:                                                                                                                                     

                                                                gnuplot> set xrange [*:*]                                                                                     

                                                                gnuplot> set yrange [*:*]                                                                                     

              Or remove the setting entirely:                                                                                                                                 

                                                                gnuplot> unset xrange                                                                                         

                                                                gnuplot> unset yrange                                                                                         

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              ██ The Legend (key)                                                                                                                                             

              By default, gnuplot shows a legend (called the "key") in the upper right.                                                                                       

              Move it:                                                                                                                                                        

                                                                gnuplot> set key top left                                                                                     

                                                                gnuplot> set key bottom right                                                                                 

                                                                gnuplot> set key outside right                                                                                

              Hide it entirely:                                                                                                                                               

                                                                gnuplot> unset key                                                                                            

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              ██ Demo - Settings                                                                                                                                              

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              ██ Plotting Data                                                                                                                                                

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              ██ Data File Format                                                                                                                                             

              Gnuplot reads plain text data files:                                                                                                                            

                                                                # time(s)  position(m)  velocity(m/s)                                                                         

                                                                0.0         0.000        1.000                                                                                

                                                                0.5         0.479        0.878                                                                                

                                                                1.0         0.841        0.540                                                                                

                                                                1.5         0.997        0.071                                                                                

                                                                2.0         0.909       -0.416                                                                                

                 •  Lines starting with # are comments (ignored)                                                                                                              

                 •  Columns separated by whitespace (spaces or tabs)                                                                                                          

                 •  One data point per line                                                                                                                                   

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              ██ Plotting a Data File                                                                                                                                         

                                                                gnuplot> plot "data.txt"                                                                                      

              By default, this plots column 2 vs. column 1.                                                                                                                   

              Choose the plot style with with:                                                                                                                                

                                                                gnuplot> plot "data.txt" with lines                                                                           

                                                                gnuplot> plot "data.txt" with points                                                                          

                                                                gnuplot> plot "data.txt" with linespoints                                                                     

              Shorthand (w for with, l/p/lp for style):                                                                                                                       

                                                                gnuplot> plot "data.txt" w lp                                                                                 

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              ██ The using Option                                                                                                                                             

              Select which columns to plot with using xcol:ycol:                                                                                                              

                                                         gnuplot> plot "data.txt" using 1:2       # time vs position                                                          

                                                         gnuplot> plot "data.txt" using 1:3       # time vs velocity                                                          

              Short form is u:                                                                                                                                                

                                                            gnuplot> plot "data.txt" u 1:2 w lp title "position"                                                              

                                                            gnuplot> plot "data.txt" u 1:3 w l  title "velocity"                                                              

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              ██ Column Arithmetic                                                                                                                                            

              using can do math on columns — wrap expressions in parentheses and use $N for column N:                                                                         

                                                         # Column 2 is in meters, convert to centimeters                                                                      

                                                         gnuplot> plot "data.txt" using 1:($2 * 100)                                                                          

                                                         # Column 2 is temperature in Celsius, convert to Fahrenheit                                                          

                                                         gnuplot> plot "data.txt" using 1:($2 * 9/5 + 32)                                                                     

                                                         # Compute kinetic energy: mass in col 2, velocity in col 3                                                           

                                                         gnuplot> plot "data.txt" using 1:(0.5 * $2 * $3**2)                                                                  

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              ██ Plotting Multiple Datasets                                                                                                                                   

              Plot multiple columns from the same file by separating plots with a comma:                                                                                      

                                                             gnuplot> plot "data.txt" u 1:2 title "position", \                                                               

                                                                           "data.txt" u 1:3 title "velocity"                                                                  

              The \ continues the command on the next line.                                                                                                                   

              Or from different files:                                                                                                                                        

                                                               gnuplot> plot "run1.txt" u 1:2 title "run 1", \                                                                

                                                                             "run2.txt" u 1:2 title "run 2"                                                                   

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              ██ Demo - Plotting Data                                                                                                                                         

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              ██ Saving Your Plots                                                                                                                                            

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              ██ Output to a File                                                                                                                                             

              By default, gnuplot plots to the screen. To save to a file:                                                                                                     

                                                          gnuplot> set terminal pngcairo                                                                                      

                                                          gnuplot> set output "plot.png"                                                                                      

                                                          gnuplot> plot "data.txt" u 1:2 title "position"                                                                     

                                                          gnuplot> set output        # close/flush the output file                                                            

              Other terminals:                                                                                                                                                

                                                           gnuplot> set terminal pdf                                                                                          

                                                           gnuplot> set terminal svg                                                                                          

                                                           gnuplot> set terminal pdfcairo    # higher quality PDF                                                             

              To go back to plotting on screen:                                                                                                                               

                                                                gnuplot> set terminal qt                                                                                      

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              ██ Gnuplot Scripts                                                                                                                                              

              Save your commands in a .gp file instead of typing interactively:                                                                                               

                                                         # plot_position.gp                                                                                                   

                                                         set title "Position vs Time"                                                                                         

                                                         set xlabel "Time (s)"                                                                                                

                                                         set ylabel "Position (m)"                                                                                            

                                                         set terminal pngcairo                                                                                                

                                                         set output "position.png"                                                                                            

                                                         plot "data.txt" using 1:2 with linespoints title "position"                                                          

                                                         set output                                                                                                           

              Run it from the terminal:                                                                                                                                       

                                                                $ gnuplot plot_position.gp                                                                                    

              This is how you make reproducible plots. The script is the record of exactly what you did — just like a shell script for commands.                              

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              ██ Practice                                                                                                                                                     

              Replicate these plots                                                                                                                                           

               Note: This plot was created using the data in Ocular_Transmission_Human.csv (in the sandbox). Column 1 is wavelength, column 6 is total                26 / 31 

              transmission.                                                                                                                                                   

              ██ Summary                                                                                                                                                      

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              ██ What We Covered                                                                                                                                              

                 •  plot f(x) — plot a mathematical function                                                                                                                  

                 •  plot [min:max] f(x) — set the x range inline                                                                                                              

                 •  plot f(x), g(x) — plot multiple functions at once                                                                                                         

                 •  set title, set xlabel, set ylabel — label your plot                                                                                                       

                 •  set xrange, set yrange — control axis ranges                                                                                                              

                 •  set key / unset key — move or hide the legend                                                                                                             

                 •  title "name" / notitle — label individual curves                                                                                                          

                 •  plot "file.txt" — plot data from a file                                                                                                                   

                 •  with lines / with points / with linespoints — plot styles                                                                                                 

                 •  using 1:2 — select which columns to plot                                                                                                                  

                 •  using 1:($2 * factor) — arithmetic on columns                                                                                                             

                 •  set terminal, set output — save plots to files                                                                                                            

                 •  Gnuplot scripts — reproducible, automated plots                                                                                                           

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              ██ Next Time                                                                                                                                                    

              In the next module, we'll cover function fitting:                                                                                                               

                 •  Defining a model function with adjustable parameters                                                                                                      

                 •  Fitting a model to data with fit                                                                                                                          

                 •  Interpreting fit results and uncertainties                                                                                                                

                 •  Plotting the fit alongside the data                                                                                                                       

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              ██ Last Slide                                                                                                                                                   

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