X-Git-Url: https://scm.cri.ensmp.fr/git/linpy.git/blobdiff_plain/7b93cea1daf2889e9ee10ca9c22a1b5124404937..997e3c68590b274c372a6785cda5a69887683891:/doc/examples.rst diff --git a/doc/examples.rst b/doc/examples.rst index a4b0f5a..13c59fc 100644 --- a/doc/examples.rst +++ b/doc/examples.rst @@ -1,9 +1,9 @@ LinPy Examples ============== -Creating a Polyhedron ------------------ - To create any polyhedron, first define the symbols used. Then use the polyhedron functions to define the constraints for the polyhedron. This example creates a square. +Basic Examples +------------- + To create any polyhedron, first define the symbols used. Then use the polyhedron functions to define the constraints. The following is a simple running example illustrating some different operations and properties that can be performed by LinPy with two squares. >>> from linpy import * >>> x, y = symbols('x y') @@ -11,25 +11,38 @@ Creating a Polyhedron >>> square1 = Le(0, x) & Le(x, 2) & Le(0, y) & Le(y, 2) >>> print(square1) And(Ge(x, 0), Ge(-x + 2, 0), Ge(y, 0), Ge(-y + 2, 0)) - -Urnary Operations ------------------ - + + Binary operations and properties examples: + + >>> square2 = Le(2, x) & Le(x, 4) & Le(2, y) & Le(y, 4) + >>> #test equality + >>> square1 == square2 + False + >>> # compute the union of two polygons + >>> square1 | square2 + Or(And(Ge(x, 0), Ge(-x + 2, 0), Ge(y, 0), Ge(-y + 2, 0)), And(Ge(x - 2, 0), Ge(-x + 4, 0), Ge(y - 2, 0), Ge(-y + 4, 0))) + >>> # check if square1 and square2 are disjoint + >>> square1.disjoint(square2) + False + >>> # compute the intersection of two polygons + >>> square1 & square2 + And(Eq(y - 2, 0), Eq(x - 2, 0)) + >>> # compute the convex union of two polygons + >>> Polyhedron(square1 | sqaure2) + And(Ge(x, 0), Ge(-x + 4, 0), Ge(y, 0), Ge(-y + 4, 0), Ge(x - y + 2, 0), Ge(-x + y + 2, 0)) + + Unary operation and properties examples: + >>> square1.isempty() False - >>> square1.isbounded() - True - -Binary Operations ------------------ - - >>> square2 = Le(2, x) & Le(x, 4) & Le(2, y) & Le(y, 4) - >>> square1 + square2 - Or(And(Ge(x, 0), Ge(-x + 2, 0), Ge(y, 0), Ge(-y + 2, 0)), And(Ge(x - 2, 0), Ge(-x + 4, 0), Ge(y - 2, 0), Ge(-y + 4, 0))) - >>> # check if square1 and square2 are disjoint - >>> square1.disjoint(square2) - False - + >>> square1.symbols() + (x, y) + >>> square1.inequalities + (x, -x + 2, y, -y + 2) + >>> # project out the variable x + >>> square1.project([x]) + And(Ge(-y + 2, 0), Ge(y, 0)) + Plot Examples ------------- @@ -51,17 +64,33 @@ Plot Examples .. figure:: images/cube.jpg :align: center - The user can also inspect a polygon's vertices and the integer points included in the polygon. + LinPy can also inspect a polygon's vertices and the integer points included in the polygon. >>> diamond = Ge(y, x - 1) & Le(y, x + 1) & Ge(y, -x - 1) & Le(y, -x + 1) >>> diamond.vertices() [Point({x: Fraction(0, 1), y: Fraction(1, 1)}), Point({x: Fraction(-1, 1), y: Fraction(0, 1)}), Point({x: Fraction(1, 1), y: Fraction(0, 1)}), Point({x: Fraction(0, 1), y: Fraction(-1, 1)})] >>> diamond.points() [Point({x: -1, y: 0}), Point({x: 0, y: -1}), Point({x: 0, y: 0}), Point({x: 0, y: 1}), Point({x: 1, y: 0})] - - - - - - + + The user also can pass another plot to the :meth:`plot` method. This can be useful to compare two polyhedrons on the same axis. This example illustrates the union of two squares. + + >>> from linpy import * + >>> import matplotlib.pyplot as plt + >>> from matplotlib import pylab + >>> x, y = symbols('x y') + >>> square1 = Le(0, x) & Le(x, 2) & Le(0, y) & Le(y, 2) + >>> square2 = Le(1, x) & Le(x, 3) & Le(1, y) & Le(y, 3) + >>> fig = plt.figure() + >>> plot = fig.add_subplot(1, 1, 1, aspect='equal') + >>> square1.plot(plot, facecolor='red', alpha=0.3) + >>> square2.plot(plot, facecolor='blue', alpha=0.3) + >>> squares = Polyhedron(square1 + square2) + >>> squares.plot(plot, facecolor='blue', alpha=0.3) + >>> pylab.show() + + .. figure:: images/union.jpg + :align: center + + +