Integration of LPdiag tool

.gitignore

@@ -9,6 +9,7 @@ __pycache__
 *.pyc
 *.RData*
 *.tmp
+*.swp
 *#
 *~
 #*
@@ -59,3 +60,7 @@ prof/
 
 # macOS
 .DS_Store
+
+# LPdiag
+message_ix/tests/data/lp_diag/diet_output.txt
+message_ix/tools/lp_diag/data/mps/*

RELEASE_NOTES.rst

@@ -13,6 +13,7 @@ Code that imports from the old locations will continue to work, but will raise :
 All changes
 -----------
 
+- Add the :doc:`LPdiag tool <tools/lpdiag>` to diagnose and analyze numerical issues in linear programming (LP) problems stored in MPS-format files (:pull:`704`).
 - Drop support for Python 3.7, which `reached end-of-life on 2023-06-27 <https://peps.python.org/pep-0537/#lifespan>`__ (:pull:`738`).
   :mod:`message_ix` now requires Python version 3.8 or greater.
 - Rename :mod:`message_ix.report` (:pull:`761`).

doc/tools/lp_diag.rst

@@ -0,0 +1,181 @@
+.. currentmodule:: message_ix.tools.lp_diag
+
+:mod:`.lp_diag`: basic diagnostics of linear program (LP) problems
+******************************************************************
+
+.. contents::
+   :local:
+
+Description
+===========
+
+``LPdiag`` provides basic information about the LP programming problems defined by corresponding MPS-format files.
+The diagnostics focuses on the implied numerical properties of the underlying optimization problem.
+
+In this context, the term ``outlier`` denotes the model entities having values in either lower or upper tail of the corresponding value distribution.
+The tails are defined by the corresponding orders of magnitudes defined as :math:`int(alog(abs(val)))`, where ``val`` stands for the value of the corresponding coefficient.
+The default values of the tails are equal to :math:`(-6, 6)`, respectively; they can be redefined, if desired.
+
+The rule of thumb says: the maximum and minimum orders of magnitudes of the LP matrix coefficients passed to optimization should differ by at most four.
+``LPdiag`` helps to achieve such a goal by providing info on outliers.
+Such info can be used e.g., for:
+
+- reconsideration of measurement units of the corresponding variables and relations,
+- consideration of replacing `small` (in relations to other coefficients in the same row or column) elements by zero,
+- splitting the corresponding rows and/or columns,
+- verification of the coefficients' values.
+
+Features
+--------
+
+The current ``LPdiag`` version provides the following information:
+
+- characteristics of the problem (including numbers of rows, columns, non-zero coefficients and distributions of their values),
+- distributions of diverse values characterizing the LP matrix,
+- location (row and column) of each outlier,
+- ranges of values of other coefficients in each such row or column, as well as the corresponding bounds (LHS, RHS for rows, lower and upper bounds for columns).
+
+The functionality of ``LPdiag`` will be gradually enhanced to meet actual needs of the ``message_ix`` modelers.
+
+Usage
+=====
+
+The tool analyzes provided MPS-format files.
+We provide several small MPS files for testing local installations in :file:`message_ix/tests/data/lp_diag/`, as well as becoming familiar with ``LPdiag``.
+The small MPS files are structured as follows:
+
+- :file:`aez.mps`: agro-ecological zones, medium size.
+- :file:`diet.mps`: classical small LP.
+- :file:`jg_korh.mps`: tiny testing problem.
+- :file:`lotfi.mps`: classical medium size.
+- :file:`error_{*}.mps`: various MPS-specs testing error-handling logic in the code.
+
+Hints on generating MPS files are provided below.
+Feel free to store arbitrary large MPS files in :file:`message_ix/tools/lp_diag/data/mps/`, but note that these should not be committed to GitHub.
+
+We suggest the following steps for becoming familiar with ``LPdiag`` and then use it for analysis of actual MPS files:
+
+- becoming familiar with ``LPdiag``,
+- prepare MPS file,
+- actual analysis.
+
+We outline each of these steps below.
+
+Becoming familiar with ``LPdiag``
+---------------------------------
+
+Note that ``LPdiag`` should be run at the terminal prompt.
+
+- Navigate to the folder ``message_ix/tools/lp_diag``.
+- For initial testing run the following command, which will run analysis of the default (pre-specified) MPS provided in the test_mps folder.
+  Other provided MPS example can be run by using the ``--mps`` option explained below.::
+
+	message-ix lp-diag
+
+- To display the available ``LPdiag`` options run::
+
+    $ message-ix lp-diag --help
+    Usage: message-ix lp-diag [OPTIONS]
+
+      Diagnostics of basic properties of LP problems stored in the MPS format.
+
+      Examples:
+        message-ix lp-diag
+        message-ix lp-diag --help
+        message-ix lp-diag --mps aez.mps --outp foo.txt
+
+    Options:
+      --wdir PATH            Working directory.
+      --mps PATH             MPS file name or path.
+      -L, --lo-tail INTEGER  Magnitude order of the lower tail (default: -7).
+      -U, --up-tail INTEGER  Magnitude order of the upper tail (default: 5).
+      --outp PATH            Path for file output.
+      --help                 Show this message and exit.
+
+Further details about the optional parameters:
+
+- :program:`--wdir`: specification of the desired work-directory (by default the work-directory is the same, in which ``LPdiag`` is located).
+- :program:`--mps`: name of the MPS file to be analysed; if the file is not located in the work-directory, then the name should include the path to the file (see the example above).
+- :program:`--outp`: name of the file to which the output shall be redirected.
+  By default the output is listed to the stdout, i.e., to the terminal window unless the redirection is included in the command.
+  Optionally, the output can be redirected to a specified file.
+  Such redirection can be specified by either using the ``--outp file_name`` option, as illustrated by the second example shown above (in the output resulting from using the ``-h`` option), or by including the redirection in the corresponding command, e.g.,::
+
+	message-ix lp-diag -h > foo.txt
+
+- :program:`--lo-tail`, :program:`--up-tail`: These are passed to :meth:`.LPdiag.print_statistics`.
+   To obtain the numbers of coefficients at every magnitude in the MPS file, specify equal or overlapping values::
+
+    message-ix lp-diag -L 0 -U 0 --mps file.mps
+
+
+Generation of the MPS file in the :mod:`message_ix` environment
+---------------------------------------------------------------
+
+The MPS-format is the oldest but still widely used for specification of the LP problems.
+Most modeling environments provide various ways of the MPS file generation.
+
+In the ``message_ix`` environment one can generate the MPS file e.g., upon solving a :class:`message_ix.Scenario` by defining in :meth:`message_ix.Scenario.solve` the ``writemps`` option together with the desired name of the MPS file.
+The MPS file will then be generated and deposited in the :file:`message_ix/model/` directory.
+Details are available in the `GAMS-Documentation <https://www.gams.com/latest/docs/S_CPLEX.html#CPLEXwritemps>`__
+
+Example of specification of the corresponding option:
+
+.. code-block:: python
+
+	scenario.solve(solve_options={"writemps": "<file_name>.mps"})
+
+
+Actual analysis
+---------------
+
+For actual analysis one needs to specify the corresponding MPS file in a command run (still in the directory ``message_ix/tools/lp_diag``)::
+
+	message-ix lp-diag --mps loc/name
+
+…where ``loc`` and ``name`` stand for the path to the directory where the MPS-file is located, and ``name`` stands for the corresponding file-name, respectively.
+Other option(s) can be included in the command, as explained above.
+
+If the output redirection is desired (e.g., for results to be shared or composed of many lines), then run::
+
+	message-ix lp-diag --mps loc/name --outp outfile.txt
+
+Extensions in the file names are optional.
+An alternative way of output redirection is explained above.
+
+
+Summary of the provided analysis results
+========================================
+
+The results are composed of the following elements:
+
+- Info on the work-directory.
+- Info during reading the MPS file:
+
+	- Should a syntax error occur during reading the file, then the corresponding exception is thrown with the corresponding details.
+	- Basic info during processing of each MPS section.
+- Basic attributes of the read MPS.
+- Distribution of values of the objective (goal function) coefficients.
+- Distribution of :math:`abs(val)` of the matrix elements.
+- Distribution of values of :math:`int(log10(abs(values)))`.
+- Distribution of values of :math:`int(log10(abs(values)))` sorted by magnitudes of values (magnitudes of zero-occurrences skipped).
+- For each (lower and upper) tail of the matrix coefficient values of the corresponding sub-matrix:
+
+  - Distributions of diverse values (:math:`value, abs(val), log10(abs(val))`) of the matrix elements.
+  - For each order of magnitude: number of elements
+  - Row-wise location of each outlier with:
+
+    1. info on other coefficients in the same row, and
+    2. order of magnitude of the row's LHS and RHS.
+  - Column-wise location of each outlier with:
+
+    1. info on other coefficients in the same column, and
+    2. order of magnitude of the column's lower and upper bounds.
+- The processing start- and end-times.
+
+
+API reference
+=============
+
+.. automodule:: message_ix.tools.lp_diag
+   :members:

message_ix/cli.py

@@ -7,6 +7,7 @@
 
 import message_ix
 import message_ix.tools.add_year.cli
+import message_ix.tools.lp_diag.cli
 
 # Override the docstring of the ixmp CLI so that it masquerades as the
 # message_ix CLI
@@ -154,6 +155,7 @@ def dl(branch, tag, path):
 
 # Add subcommands
 main.add_command(message_ix.tools.add_year.cli.main)
+main.add_command(message_ix.tools.lp_diag.cli.main)
 
 try:
     import message_ix.testing.nightly