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jenskoberjenskober
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added tests as jupyter notebooks
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‎readme.ipynb

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{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "b5473e6d",
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"metadata": {},
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"source": [
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"PyLMI-SDP\n",
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"=========\n",
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"\n",
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"*Symbolic linear matrix inequalities (LMI) and semi-definite programming (SDP) tools for Python*\n",
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"\n",
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"This package includes a set of classes to represent and manipulate LMIs symbolically using [SymPy](http://sympy.org).\n",
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"It also includes tools to export LMIs to [CVXOPT](http://abel.ee.ucla.edu/cvxopt/userguide/coneprog.html#semidefinite-programming) SDP input and to the [SDPA](http://sdpa.sourceforge.net/) format.\n",
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"\n",
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"Depends on [SymPy](http://sympy.org) and [NumPy](http://www.numpy.org/); and optionally on [CVXOPT](http://cvxopt.org) and on [SciPy](http://www.scipy.org) (for sparse matrices).\n",
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"Single codebase supporting both Python 2.7 and Python 3.x.\n",
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"PyLMI-SDP is tested for various combinations of Python and sympy. See [here](https://github.com/cdsousa/PyLMI-SDP/actions/workflows/ci.yaml).\n",
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"\n",
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"PyLMI-SDP is at [GitHub](https://github.com/cdsousa/PyLMI-SDP).\n",
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"\n",
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"[![Build Status](https://github.com/cdsousa/PyLMI-SDP/actions/workflows/ci.yaml/badge.svg?branch=master)](https://github.com/cdsousa/PyLMI-SDP/actions/workflows/ci.yaml)\n",
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"[![Coverage Status](https://coveralls.io/repos/cdsousa/PyLMI-SDP/badge.png?branch=master)](https://coveralls.io/r/cdsousa/PyLMI-SDP?branch=master)"
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]
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},
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{
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"cell_type": "markdown",
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"id": "0a7fafdf",
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"print(dat)"
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]
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},
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{
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"cell_type": "markdown",
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"id": "b626817a",
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"metadata": {},
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"source": [
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"Author\n",
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"------\n",
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"\n",
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"[Cristóvão Duarte Sousa](https://github.com/cdsousa)\n",
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"\n",
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"Install\n",
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"-------\n",
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"\n",
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"From PyPi:\n",
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"\n",
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" pip install PyLMI-SDP\n",
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"\n",
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"From git source:\n",
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"\n",
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" git clone https://github.com/cdsousa/PyLMI-SDP.git\n",
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" cd PyLMI-SDP\n",
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" python setup.py install\n",
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"\n",
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"License\n",
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"-------\n",
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"\n",
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"Simplified BSD License. See [License File](LICENSE.txt)\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "12742999",
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"id": "80b3b32c",
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"metadata": {},
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"outputs": [],
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"source": []

‎test_lm.ipynb

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{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": 1,
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"id": "795391a0",
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"metadata": {},
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"outputs": [],
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"source": [
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"from sympy import Matrix, zeros, MatAdd, MatMul\n",
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"from sympy.abc import x, y, z\n",
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"import numpy as np\n",
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"from lmi_sdp import NonLinearExpressionError, NonLinearMatrixError, \\\n",
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" lin_expr_coeffs, lm_sym_to_coeffs, lm_coeffs_to_sym, lm_sym_expanded"
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]
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},
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{
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"cell_type": "markdown",
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"id": "e0453e3a",
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"metadata": {},
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"source": [
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"### test_lin_expr_coeffs()"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"id": "f88d087f",
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"metadata": {},
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"outputs": [],
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"source": [
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"e = 1.2 + 3*x - 4.5*y + z\n",
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"coeffs, const = lin_expr_coeffs(e, [x, y, z])\n",
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"assert coeffs == [3.0, -4.5, 1.0]\n",
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"assert const == 1.2"
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]
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},
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{
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"cell_type": "markdown",
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"id": "30cdc900",
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"metadata": {},
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"source": [
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"### test_lin_expr_coeffs_exceptions()"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"id": "b1a4daa5",
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"metadata": {},
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"outputs": [],
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"source": [
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"except_ok = False\n",
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"try:\n",
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" lin_expr_coeffs(1.2 + x + y*z, [x, y, z])\n",
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"except NonLinearExpressionError:\n",
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" except_ok = True\n",
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"assert except_ok\n",
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"\n",
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"except_ok = False\n",
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"try:\n",
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" lin_expr_coeffs(1.2 + x*y, [x])\n",
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"except NonLinearExpressionError:\n",
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" except_ok = True\n",
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"assert except_ok"
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]
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},
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{
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"cell_type": "markdown",
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"id": "34e44ff5",
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"metadata": {},
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"source": [
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"### test_lm_sym_to_coeffs()"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 4,
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"id": "b37d52a5",
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"metadata": {},
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"outputs": [],
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"source": [
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"m = Matrix([[1.2, x], [3.4*y, 1.2 + 3*x - 4.5*y + z]])\n",
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"coeffs = lm_sym_to_coeffs(m, [x, y, z])\n",
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"assert len(coeffs) == 2\n",
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"assert len(coeffs[0]) == 3\n",
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"assert (coeffs[0][0] == np.array([[0.0, 1.0], [0.0, 3.0]])).all()\n",
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"assert (coeffs[0][1] == np.array([[0.0, 0.0], [3.4, -4.5]])).all()\n",
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"assert (coeffs[0][2] == np.array([[0.0, 0.0], [0.0, 1.0]])).all()\n",
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"assert (coeffs[1] == np.array([[1.2, 0.0], [0.0, 1.2]])).all()\n",
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"\n",
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"assert lm_sym_to_coeffs(Matrix([0.0]), [x, y, z]) == \\\n",
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" ([np.array([[0.0]]), np.array([[0.0]]), np.array([[0.0]])],\n",
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" np.array([[0.0]]))"
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]
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},
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{
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"cell_type": "markdown",
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"id": "5cfb7bbf",
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"metadata": {},
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"source": [
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"### test_lm_sym_to_coeffs_sparse()"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 5,
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"id": "ca9cbbd7",
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"metadata": {},
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"outputs": [],
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"source": [
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"try:\n",
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" import scipy\n",
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"except ImportError: # pragma: no cover\n",
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" pass\n",
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"else:\n",
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" m = Matrix([[1.2, x], [3.4*y, 1.2 + 3*x - 4.5*y + z]])\n",
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" coeffs = lm_sym_to_coeffs(m, [x, y, z], sparse=True)\n",
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" assert len(coeffs) == 2\n",
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" assert len(coeffs[0]) == 3\n",
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" assert (coeffs[0][0].toarray() ==\n",
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" np.array([[0.0, 1.0], [0.0, 3.0]])).all()\n",
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" assert (coeffs[0][1].toarray() ==\n",
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" np.array([[0.0, 0.0], [3.4, -4.5]])).all()\n",
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" assert (coeffs[0][2].toarray() ==\n",
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" np.array([[0.0, 0.0], [0.0, 1.0]])).all()\n",
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" assert (coeffs[1].toarray() == np.array([[1.2, 0.0], [0.0, 1.2]])).all()"
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]
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},
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{
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"cell_type": "markdown",
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"id": "8e7c6bcd",
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"metadata": {},
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"source": [
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"### test_lm_sym_to_coeffs_exceptions()"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 6,
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"id": "d04b79b5",
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"metadata": {},
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"outputs": [],
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"source": [
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"except_ok = False\n",
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"try:\n",
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" lm_sym_to_coeffs(Matrix([1.2 + x + y*z]), [x, y, z])\n",
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"except NonLinearMatrixError:\n",
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" except_ok = True\n",
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"assert except_ok\n",
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"\n",
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"except_ok = False\n",
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"try:\n",
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" lm_sym_to_coeffs(Matrix([1.2 + x*y]), [x])\n",
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"except NonLinearMatrixError:\n",
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" except_ok = True\n",
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"assert except_ok"
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]
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},
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{
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"cell_type": "markdown",
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"id": "771ff882",
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"metadata": {},
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"source": [
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"### test_lm_coeffs_to_sym()"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 7,
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"id": "d2a2bb3a",
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"metadata": {},
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"outputs": [],
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"source": [
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"var_coeffs = [None]*3\n",
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"var_coeffs[0] = np.array([[0.0, 1.0], [0.0, 3.0]])\n",
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"var_coeffs[1] = np.array([[0.0, 0.0], [3.4, -4.5]])\n",
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"var_coeffs[2] = np.array([[0.0, 0.0], [0.0, 1.0]])\n",
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"consts = np.array([[1.2, 0.0], [0.0, 1.2]])\n",
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"coeffs = (var_coeffs, consts)\n",
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"m = Matrix([[1.2, x], [3.4*y, 1.2 + 3*x - 4.5*y + z]])\n",
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"assert lm_coeffs_to_sym(coeffs, [x, y, z]) - m == zeros(2)"
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]
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},
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{
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"cell_type": "markdown",
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"id": "f9a1d7a3",
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"metadata": {},
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"source": [
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"### test_lm_sym_expanded()"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 8,
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"id": "dcba0418",
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"metadata": {},
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"outputs": [],
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"source": [
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"m = Matrix([[0, x], [3.4*y, 3*x - 4.5*y + z]])\n",
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"c = Matrix([[1.2, 0], [0, 1.2]])\n",
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"cx = MatMul(Matrix([[0.0, 1.0], [0.0, 3.0]]), x)\n",
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"cy = MatMul(Matrix([[0.0, 0.0], [3.4, -4.5]]), y)\n",
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"cz = MatMul(Matrix([[0.0, 0.0], [0.0, 1.0]]), z)\n",
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"cc = Matrix([[1.2, 0.0], [0.0, 1.2]])\n",
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"assert MatAdd(cx, cy, cz, cc) == lm_sym_expanded(m+c, [x, y, z])\n",
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"assert MatAdd(cx, cy, cz) == lm_sym_expanded(m, [x, y, z])\n",
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"assert cc == lm_sym_expanded(c, [x, y, z])"
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]
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "py38",
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"language": "python",
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"name": "py38"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.8.12"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 5
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}

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