.. _mathematica:

===========
Mathematica
===========

.. contents:: In this section:
   :local:
   :depth: 2

Description
===========

According to the `page of Mathematica <http://www.wolfram.com/mathematica/>`_, Mathematica defines the state of the art in technical computing, providing the leading computation environment for millions of innovators, educators, and students worldwide.

Available Versions
==================

* mathematica/9.0
* mathematica/10.4 (default)

Serial Job Submission
=====================

.. code-block:: bash
   :caption: submit_mathematica_serial.sh

   #!/bin/bash
   #SBATCH -J mathematica_serial
   #SBATCH -N 1
   #SBATCH -n 1
   #SBATCH -t 05:00:00
   #SBATCH --mem=8G

   export INPUT="script.m"
   export OUTPUT="script.out"

   module load mathematica

   job-nanny math -script script.m > script.out

Job Submission with MathKernel
==============================

.. code-block:: bash
   :caption: submit_mathematica_kernel.sh

   #!/bin/bash
   #SBATCH -J mathematica_kernel
   #SBATCH -N 1
   #SBATCH -n 1
   #SBATCH -t 12:00:00
   #SBATCH --mem=16G

   export INPUT="calculation.m"
   export OUTPUT="calculation.out"

   module load mathematica

   # Start kernel and execute
   job-nanny math -noprompt -run "<<calculation.m" > calculation.out

Job Submission with Parallelism
===============================

.. code-block:: bash
   :caption: submit_mathematica_parallel.sh

   #!/bin/bash
   #SBATCH -J mathematica_parallel
   #SBATCH -N 1
   #SBATCH -c 8
   #SBATCH -t 24:00:00
   #SBATCH --mem=32G

   export INPUT="parallel.m"
   export OUTPUT="parallel.out"

   module load mathematica

   # Create script with parallel configuration
   cat > run_parallel.m << EOF
   LaunchKernels[$SLURM_CPUS_PER_TASK]
   Get["parallel.m"]
   CloseKernels[]
   EOF

   job-nanny math -noprompt -run "<<run_parallel.m" > parallel.out

Mathematica Script Example
==========================

.. code-block:: mathematica
   :caption: calculation.m

   (* Intensive numerical calculation *)
   n = 1000;
   matrix = RandomReal[{0,1}, {n, n}];
   eigenvalues = Eigenvalues[matrix];
   Print["Largest eigenvalue: ", Max[eigenvalues]];
   Print["Smallest eigenvalue: ", Min[eigenvalues]];

   (* Numerical integration *)
   f[x_] := Sin[x]^2 * Exp[-x/10];
   integral = NIntegrate[f[x], {x, 0, 100}];
   Print["Integral: ", integral];

   (* Curve fitting *)
   data = Table[{x, 2*Sin[x] + RandomReal[{-0.1,0.1}]}, {x, 0, 2Pi, 0.1}];
   fit = NonlinearModelFit[data, a*Sin[b*x + c], {a, b, c}, x];
   Print["Fit parameters: ", fit["BestFitParameters"]];

   Export["results.txt", {eigenvalues[[1;;10]], integral, fit["BestFit"]}];

Job Array for Multiple Parameters
=================================

.. code-block:: bash
   :caption: submit_mathematica_array.sh

   #!/bin/bash
   #SBATCH -J mathematica_array
   #SBATCH --array=1-10
   #SBATCH -N 1
   #SBATCH -n 1
   #SBATCH -t 12:00:00
   #SBATCH --mem=8G

   PARAM=$SLURM_ARRAY_TASK_ID
   export INPUT="template.m"
   export OUTPUT="run_${PARAM}/"

   module load mathematica

   mkdir -p run_${PARAM}
   cd run_${PARAM}

   # Create script with specific parameter
   cat > run.m << EOF
   parameter = $PARAM;
   Print["Running with parameter = ", parameter];

   (* Parameter-dependent calculation *)
   result = NIntegrate[Sin[parameter*x]^2, {x, 0, 10}];
   Print["Result: ", result];

   Export["result_${PARAM}.txt", {parameter, result}];
   EOF

   job-nanny math -noprompt -run "<<run.m" > output_${PARAM}.log

Batch Data Processing
=====================

.. code-block:: bash
   :caption: submit_mathematica_batch.sh

   #!/bin/bash
   #SBATCH -J mathematica_batch
   #SBATCH -N 1
   #SBATCH -c 4
   #SBATCH -t 24:00:00
   #SBATCH --mem=16G

   export INPUT="data_*.csv"
   export OUTPUT="analysis/"

   module load mathematica

   mkdir -p analysis

   # Create script to process all files
   cat > batch_process.m << EOF
   files = FileNames["data_*.csv"];
   results = {};

   Do[
      Print["Processing ", file];
      data = Import[file, "CSV"];
      
      (* Analysis *)
      means = Mean[data];
      stds = StandardDeviation[data];
      
      AppendTo[results, {file, means, stds}];
      
      (* Save individual results *)
      Export["analysis/" <> FileBaseName[file] <> "_stats.txt", 
             {means, stds}, "Table"],
   {file, files}];

   (* General summary *)
   Export["analysis/summary.txt", results, "Table"];
   EOF

   job-nanny math -noprompt -run "<<batch_process.m"

Data Visualization
==================

.. code-block:: bash
   :caption: submit_mathematica_plot.sh

   #!/bin/bash
   #SBATCH -J mathematica_plot
   #SBATCH -N 1
   #SBATCH -n 1
   #SBATCH -t 02:00:00
   #SBATCH --mem=4G

   export INPUT="data.txt"
   export OUTPUT="plot.pdf"

   module load mathematica

   cat > plot.m << EOF
   data = Import["data.txt", "Table"];
   
   (* 2D plot *)
   plot1 = ListPlot[data, PlotStyle -> PointSize[0.015], 
                    AxesLabel -> {"X", "Y"}, 
                    PlotLabel -> "Experimental data"];
   
   (* Histogram *)
   plot2 = Histogram[Flatten[data], 30, 
                     AxesLabel -> {"Value", "Frequency"}];
   
   (* Export *)
   Export["plot.pdf", GraphicsGrid[{{plot1}, {plot2}}]];
   EOF

   job-nanny math -noprompt -run "<<plot.m"

References
==========

- Documentation: https://reference.wolfram.com/language/
- Tutorials: https://www.wolfram.com/support/learn/
- Resources Center: https://www.wolfram.com/support/

.. seealso::

   - :ref:`matlab` - Numerical computing environment
   - :ref:`R` - Statistical computing
   - :ref:`running_simulations` - How to submit jobs