PR to update Julia folder

Languages/Julia/Example1/README.md

@@ -1,15 +1,13 @@
 ### Purpose:
-
-This example illustrates the use of Julia on the Harvard University FAS cluster. Specifically, it evaluates PI via a Monte-Carlo method.
+This example illustrates the use of Julia on the Harvard University
+FAS cluster. Specifically, it evaluates PI via a Monte-Carlo method.
 
 
 ### Contents:
-
 * <code>pi\_monte\_carlo.jl</code>: Julia source code
 * <code>run.sbatch</code>: Batch-job submission script
 
 ### Julia code:
-
 ```julia
 #+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 # Program: pi_monte_carlo.jl
@@ -39,7 +37,6 @@ end
 ```
 
 ### Example Batch-Job Submission Script:
-
 ```bash
 #!/bin/bash
 #SBATCH -J pi_monte_carlo
@@ -51,21 +48,16 @@ end
 #SBATCH -t 0-00:30
 #SBATCH --mem=2G
 
-# Set up Julia and run the program
-export PATH=$PATH:/n/holylabs/LABS/jharvard_lab/Users/jharvard/software/julia-1.9.3/bin
-srun -n 1 -c 1 julia pi_monte_carlo.jl
+# Run the program using Julia
+julia pi_monte_carlo.jl
 ```
 
-**NOTE:** Please remember to point the `PATH` environmental variable to the actual location of your Julia installation.
-
 ### Example Usage:
-
 ```bash
 sbatch run.sbatch
 ```
 
 ### Example Output:
-
 ```bash
 $ cat pi_monte_carlo.out 
 N = 1000: PI = 3.228

Languages/Julia/Example1/pi_monte_carlo.jl

@@ -18,7 +18,8 @@ function montepi(n::Int)
 end
 
 # Main program
-for n in 10 .^(3: 8)
+for i in 3: 8
+ n = 10^i
  p = montepi(n)
  println("N = $n: PI = $p")
 end

Languages/Julia/Example1/run.sbatch

@@ -8,7 +8,5 @@
 #SBATCH -t 0-00:30
 #SBATCH --mem=2G
 
-# Set up Julia and run the program
-export PATH=$PATH:/n/holylabs/LABS/jharvard_lab/Users/jharvard/software/julia-1.9.3/bin
-srun -n 1 -c 1 julia pi_monte_carlo.jl
-
+# Run the program using Julia
+julia pi_monte_carlo.jl

Languages/Julia/Example2/README.md

@@ -1,18 +1,18 @@
 ### Purpose:
-
-This example illustrates solving differential equations numerically in Julia. Specifically, it solves an ODE after an example taken from [this](https://sam-dolan.sites.sheffield.ac.uk/mas212-course/sample-notebooks/ode_example) Python notebook, using [DifferentialEquations.jl](https://docs.sciml.ai/DiffEqDocs/stable/)
+This example illustrates solving differential equations numerically in
+Julia. Specifically, it solves an ODE after an example taken from
+[this](https://sam-dolan.sites.sheffield.ac.uk/mas212-course/sample-notebooks/ode_example)
+Python notebook, using
+[DifferentialEquations.jl](https://docs.sciml.ai/DiffEqDocs/stable/)
 
 
 ### Contents:
-
 * <code>ode\_test.jl</code>: Julia source code
+* <code>figure.py</code>: Python script for generating the figure
 * <code>run.sbatch</code>: Batch-job submission script
-* <code>results.dat</code>: Numeric results
 * <code>figure.png</code>: Figure of ODE's solution
-* <code>figure.py</code>: Python script for generating the figure
 
 ### Julia code:
-
 ```julia
 #++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 # Program: ode_test.jl 
@@ -22,6 +22,7 @@ using SimpleDiffEq
 using Printf
 using Plots
 using Plots.PlotMeasures
+using PyCall
 
 # --- Define the problem ---
 f(u, p, t) = t - u
@@ -52,17 +53,41 @@ for i = 1: size(sol.t)[1]
  @printf(fo, "%8.4f %10.6f %10.6f\n", x, y, y_exact)
 end
 close(fo)
+
+pyimport("numpy")
+
+# --- Run the Python script to plot the result ---
+@pyinclude("figure.py")
 ```
 
-> **Note:** You may need to install the `DifferentialEquations`, `SimpleDiffEq` and `Plots` packages. Use the following command inside the Julia REPL:
+> **Note:** You may need to install the `DifferentialEquations`,
+ `SimpleDiffEq`, `Plots`, `PyCall`, `Conda`, and `matplotlib`
+ packages. Use the following command inside Julia's full-featured
+ interactive command-line REPL (read-eval-print loop) to adding these packages.
 
 ```julia
 julia> using Pkg
 julia> Pkg.add("DifferentialEquations")
 julia> Pkg.add("SimpleDiffEq")
 julia> Pkg.add("Plots")
+julia> Pkg.add("Conda")
+julia> ENV["PYTHON"]=""
+julia> Pkg.build("PyCall")
+julia> using Conda
+julia> Conda.add("matplotlib")
 ```
 
+> **Note:** The `PYTHON` environmental variable above has been set to
+ `blank` prior to building the `PyCall` package. This is to
+ override the default behavior of `PyCall`, which is to use the
+ system's default Python environment in Linux, and instead install
+ Julia's "private" version of Python. You can find more details on
+ how to install `PyCall` at a desired location and call Python
+ functions from a Julia program on
+ [Github](https://github.com/JuliaPy/PyCall.jl) and
+ [Stackoverflow](
+ https://stackoverflow.com/questions/66648841/how-to-call-a-python-function-from-a-julia-program)
+
 ### Example Batch-Job Submission Script:
 
 ```bash
@@ -76,56 +101,15 @@ julia> Pkg.add("Plots")
 #SBATCH -t 0-00:30
 #SBATCH --mem=4G
 
-# Set up Julia and run the program
-export PATH=$PATH:/n/holylabs/LABS/jharvard_lab/Users/jharvard/software/julia-1.9.3/bin
-srun -n 1 -c 1 julia ode_test.jl
+# Run the program using Julia
+julia ode_test.jl
 ```
-**NOTE:** Please remember to point the `PATH` environmental variable to the actual location of your Julia installation.
 
 ### Example Usage:
-
 ```bash
 sbatch run.sbatch
 ```
 
-### Example Output:
-
-```bash
-$ cat results.dat 
- Time Numeric Exact 
- ------------------------------ 
- 0.0000 1.000000 1.000000
- 0.2000 0.837462 0.837462
- 0.4000 0.740639 0.740640
- 0.6000 0.697624 0.697623
- 0.8000 0.698660 0.698658
- 1.0000 0.735763 0.735759
- 1.2000 0.802393 0.802388
- 1.4000 0.893198 0.893194
- 1.6000 1.003802 1.003793
- 1.8000 1.130613 1.130598
- 2.0000 1.270681 1.270671
- 2.2000 1.421625 1.421606
- 2.4000 1.581455 1.581436
- 2.6000 1.748569 1.748547
- 2.8000 1.921645 1.921620
- 3.0000 2.099603 2.099574
- 3.2000 2.281551 2.281524
- 3.4000 2.466785 2.466747
- 3.6000 2.654677 2.654647
- 3.8000 2.844781 2.844742
- 4.0000 3.036672 3.036631
- 4.2000 3.230027 3.229991
- 4.4000 3.424601 3.424555
- 4.6000 3.620150 3.620104
- 4.8000 3.816498 3.816459
- 5.0000 4.013510 4.013476
-```
-
-### Figure of Solution:
-
-<img src="figure.png" alt="solution" width="500"/>
-
 ### Python script for generating the figure:
 
 ```python
@@ -136,7 +120,6 @@ import os
 import numpy as np
 import matplotlib as mpl
 import matplotlib.pyplot as plt
-plt.style.use('seaborn-white')
 from matplotlib.ticker import MultipleLocator, FormatStrFormatter
 
 def rc_params():
@@ -195,6 +178,44 @@ plt.legend(fontsize=15, loc="upper left", shadow=True, fancybox=True)
 plt.savefig(fig_path, format='png', dpi=100, bbox_inches='tight')
 ```
 
+### Example Output:
+```bash
+$ cat results.dat
+ Time Numeric Exact
+ ------------------------------
+ 0.0000 1.000000 1.000000
+ 0.2000 0.837462 0.837462
+ 0.4000 0.740639 0.740640
+ 0.6000 0.697624 0.697623
+ 0.8000 0.698660 0.698658
+ 1.0000 0.735763 0.735759
+ 1.2000 0.802393 0.802388
+ 1.4000 0.893198 0.893194
+ 1.6000 1.003802 1.003793
+ 1.8000 1.130613 1.130598
+ 2.0000 1.270681 1.270671
+ 2.2000 1.421625 1.421606
+ 2.4000 1.581455 1.581436
+ 2.6000 1.748569 1.748547
+ 2.8000 1.921645 1.921620
+ 3.0000 2.099603 2.099574
+ 3.2000 2.281551 2.281524
+ 3.4000 2.466785 2.466747
+ 3.6000 2.654677 2.654647
+ 3.8000 2.844781 2.844742
+ 4.0000 3.036672 3.036631
+ 4.2000 3.230027 3.229991
+ 4.4000 3.424601 3.424555
+ 4.6000 3.620150 3.620104
+ 4.8000 3.816498 3.816459
+ 5.0000 4.013510 4.013476
+```
+
+### Figure of Solution:
+<img src="figure.png" alt="solution" width="500"/>
+
 ### References:
 
-* [Official **DifferentialEquations.jl** Documentation](https://docs.sciml.ai/DiffEqDocs/stable/)
+* [Official **DifferentialEquations.jl** Documentation](https://docs.sciml.ai/DiffEqDocs/stable/)
+* [PyCall](https://github.com/JuliaPy/PyCall.jl)
+* [Pycall to call Python code](https://stackoverflow.com/questions/66648841/how-to-call-a-python-function-from-a-julia-program)

Languages/Julia/Example2/figure.py

@@ -5,7 +5,6 @@
 import numpy as np
 import matplotlib as mpl
 import matplotlib.pyplot as plt
-plt.style.use('seaborn-white')
 from matplotlib.ticker import MultipleLocator, FormatStrFormatter
 
 def rc_params():

Languages/Julia/Example2/ode_test.jl

@@ -6,6 +6,7 @@ using SimpleDiffEq
 using Printf
 using Plots
 using Plots.PlotMeasures
+using PyCall
 
 # --- Define the problem ---
 f(u, p, t) = t - u
@@ -37,3 +38,7 @@ for i = 1: size(sol.t)[1]
 end
 close(fo)
 
+pyimport("numpy")
+
+# --- Run the Python script to plot the result ---
+@pyinclude("figure.py")

Languages/Julia/Example2/run.sbatch

@@ -8,7 +8,5 @@
 #SBATCH -t 0-00:30
 #SBATCH --mem=4G
 
-# Set up Julia and run the program
-#export PATH=$PATH:/n/holylabs/LABS/jharvard_lab/Users/jharvard/software/julia-1.9.3/bin
-export PATH=$PATH:/n/home06/pkrastev/holyscratch01/Work/Julia/julia-1.9.3/bin
-srun -n 1 -c 1 julia ode_test.jl
+# Run the program using Julia
+julia ode_test.jl