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| == Octave == | | == Octave == |
| GNU Octave is software featuring a high-level programming language, primarily intended for numerical computations. Octave helps in solving linear and nonlinear problems numerically, and for performing other numerical experiments using a language that is mostly compatible with MATLAB.<ref>Gnu Octave. (2022, February, 10). In ''Wikipedia''. https://en.wikipedia.org/wiki/GNU_Octave</ref> | | GNU Octave is a high-level programming language, primarily intended for numerical computations. Octave helps to solve linear and nonlinear problems numerically, and to perform other numerical experiments using a language that is mostly compatible with MATLAB.<ref>Gnu Octave. (2022, February, 10). In ''Wikipedia''. https://en.wikipedia.org/wiki/GNU_Octave</ref> |
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| == Preparation ==
| | {{MerlinMultipageExperienceSubpages |
| In this exercise, you'll be generating graphic files by using Octave. In order to view these files, you'll save them in a special directory called "~www" which must be created in your home directory. The following instructions will instruct you on how to create this directory.
| | |Pages=Preparation;Graphing;Sombrero;Histograms;Storage |
| {{Prepare WWW Directory}}
| | }} |
| == Graphing ==
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| Octave may be started by typing 'octave' in the shell. It's easiest to perform this in your '''www''' directory so the files that you create will be saved there.
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| {{ConsoleLine|liang-xue@codermerlin:~$|cd ~/www}}
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| {{ConsoleLine|liang-xue@codermerlin:~$|octave}}
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| You'll know you're in Octave when you see the Octave prompt.
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| {{ConsoleLine|octave:1>|}} | |
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| In order to enable graphics plotting, execute the following command:
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| {{ConsoleLine|octave:1>|graphics_toolkit("gnuplot")}}
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| We'll begin with a 3-D example to demonstrate the power of Octave and the ease with which complex graphs can be created.
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| == Examples == | |
| === 3-D Sombrero Plot ===
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| {{ConsoleLine|octave:2>|tx {{Equal}} ty {{Equal}} linspace (-8, 8, 41);}}
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| {{ConsoleLine|octave:3>|[xx, yy] {{Equal}} meshgrid (tx, ty);}}
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| {{ConsoleLine|octave:4>|r {{Equal}} sqrt (xx .^ 2 + yy .^ 2) + eps;}}
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| {{ConsoleLine|octave:5>|tz {{Equal}} sin (r) ./ r;}}
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| {{ConsoleLine|octave:6>|mesh (tx, ty, tz);}}
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| {{ConsoleLine|octave:7>|xlabel ("tx");}}
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| {{ConsoleLine|octave:8>|ylabel ("ty");}}
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| {{ConsoleLine|octave:9>|zlabel ("tz");}}
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| {{ConsoleLine|octave:10>|title ("3-D Sombrero Plot");}}
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| We can now print the plot to a file with:
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| {{ConsoleLine|octave:11>|print -dpng sombrero.png}}
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| It may take a few seconds to produce the file; be patient.
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| It's necessary to adjust the file's permissions to enable web server access. This may easily be performed from within octave using the following command:
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| {{ConsoleLine|octave:12>|system("chmod -R a+rX ~/www")}}
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| When the prompt returns, the file may be viewed in a browser. Every user has a personal URL. Your file may be viewed here: {{PersonalURL|path=sombrero.png}}
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| === Random Numbers ===
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| We can produce results similar to those of throwing a six-sided die by using the '''rand''' function which returns a random value in the interval (0, 1).
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| {{ConsoleLine|octave:13>|rand}}
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| Try executing this command several times and observe the results. In order to obtain integer values in the range from 1 to 6 we'll multiply the result of '''rand''' by 6, add 1, and then take the '''floor''' of this result.
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| {{ConsoleLine|octave:16>|floor(6*rand + 1)}}
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| Try executing this command several times and observe the results.
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| === Array of Random Numbers ===
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| An array of 10 random throws of a six-sided die can be produced as follows.
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| {{ConsoleLine|octave:17>|A {{Equal}} floor(6 * rand(10, 1) + 1)}}
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| === Plotting a Histogram ===
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| Histograms can easily be plotted from the array. The second argument [1 2 3 4 5 6] provides the midpoints of the 'bins' for our histogram.
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| {{ConsoleLine|octave:18>|hist(A, [1 2 3 4 5 6]);}}
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| === Plotting Multiple Histograms on Same Graph ===
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| <syntaxhighlight lang="matlab">
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| # Plots three histograms of random data from six-sided die
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| # Histograms vary in their population
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| graphics_toolkit("gnuplot")
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| # Generate three random data sets of six-sided die throws
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| A = floor(6 * rand(10000, 1) + 1)
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| B = floor(6 * rand(100, 1) + 1)
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| C = floor(6 * rand(10, 1) + 1)
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| # Plot data as histograms
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| hold on
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| hist(A, [1, 2, 3, 4, 5, 6], "facecolor", "cyan");
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| hist(B, [1, 2, 3, 4, 5, 6], "facecolor", "magenta");
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| hist(C, [1, 2, 3, 4, 5, 6], "facecolor", "green");
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| colormap( summer(64));
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| # Use a logarithmic scale
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| set(gca, 'yscale', 'log');
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| # Add Titles and Legends
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| grid on
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| title("Histogram Plots: Six-sided Die Simulations");
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| xlabel("Six-sided Die Roll")
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| ylabel("Frequency of Occurrence (log scale)")
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| legend ("10 thousand samples", "100 samples", "10 samples", "location", "northeastoutside");
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| # Print to a file
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| print -dpng histogram.png
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| </syntaxhighlight>
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| === Reading from a Remote URL ===
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| We can read the contents of a remote URL using the following command:
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| {{ConsoleLine|octave:17>|s {{Equal}} urlread ("<nowiki>https://www.codermerlin.com/users/john-williams/sample.csv</nowiki>");}}
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| === Reading from a String ===
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| We can read the contents of a string using the following command, interpreting each value read as a Double:
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| {{ConsoleLine|octave:18>|A {{Equal}} strread(s, "%n");}}
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| === Appending from a String ===
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| We can append the contents of a string to an existing array using the following command:
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| {{ConsoleLine|octave:18>|A {{Equal}} [A; strread(s, "%n")];}}
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| == References == | | == References == |
| <references/> | | <references/> |
