Metadata-Version: 1.1
Name: PyLMI-SDP
Version: 0.2
Summary: Symbolic linear matrix inequalities (LMI) and semi-definiteprogramming (SDP) tools for Python
Home-page: http://github.com/cdsousa/PyLMI-SDP
Author: Cristovao D. Sousa
Author-email: crisjss@gmail.com
License: BSD
Description: PyLMI-SDP
        =========
        
        *Symbolic linear matrix inequalities (LMI) and semi-definite programming
        (SDP) tools for Python*
        
        | This package includes a set of classes to represent and manipulate
        LMIs symbolically using `SymPy <http://sympy.org>`__.
        | 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.
        
        | Depends on `SymPy <http://sympy.org>`__ 0.7.3 and
        `NumPy <http://www.numpy.org/>`__ 1.7.1, and optionally on
        `CVXOPT <http://cvxopt.org/>`__.
        | Single codebase supporting both Python 2.7 and Python 3.3.
        | PyLMI-SDP is tested in these versions but it may work in others.
        
        |Build Status|
        
        LMI Definition
        --------------
        
        Examples
        ~~~~~~~~
        
        .. code:: Python
        
            >>> from sympy import symbols, Matrix
            >>> from lmi_sdp import LMI_PD, LMI_NSD
            >>> variables = symbols('x y z')
            >>> x, y, z = variables
            >>> lmi = LMI_PD(Matrix([[x+1, y+2], [y+2, z+x]]))
            >>> lmi
            Matrix([
            [x + 1, y + 2],
            [y + 2, x + z]]) > 0
        
        .. code:: Python
        
            >>> from lmi_sdp import init_lmi_latex_printing
            >>> from sympy import latex
            >>> init_lmi_latex_printing()
            >>> print(latex(lmi))
            \left[\begin{smallmatrix}{}x + 1 & y + 2\\y + 2 & x + z\end{smallmatrix}\right] \succ 0
        
        |equation|
        
        .. code:: Python
        
            >>> print(latex(lmi.expanded(variables)))
            \left[\begin{smallmatrix}{}1.0 & 0.0\\0.0 & 1.0\end{smallmatrix}\right] x + \left[\begin{smallmatrix}{}0.0 & 1.0\\1.0 & 0.0\end{smallmatrix}\right] y + \left[\begin{smallmatrix}{}0.0 & 0.0\\0.0 & 1.0\end{smallmatrix}\right] z + \left[\begin{smallmatrix}{}1.0 & 2.0\\2.0 & 0.0\end{smallmatrix}\right] \succ 0
        
        |equation|
        
        .. code:: Python
        
            >>> lmi_2 = LMI_NSD( Matrix([[-x, -y], [-y, -z-x]]), Matrix([[1, 2], [2, 0]]))
            >>> lmi_2
            Matrix([
            [-x,     -y],
            [-y, -x - z]]) <= Matrix([
            [1, 2],
            [2, 0]])
            >>> lmi_2.canonical()
            Matrix([
            [x + 1, y + 2],
            [y + 2, x + z]]) >= 0
        
        .. code:: Python
        
            >>> print(latex(lmi_2))
            \left[\begin{smallmatrix}{}- x & - y\\- y & - x - z\end{smallmatrix}\right] \preceq \left[\begin{smallmatrix}{}1 & 2\\2 & 0\end{smallmatrix}\right]
        
        |equation|
        
        Convertion to CVXOPT SDP
        ------------------------
        
        Example
        ~~~~~~~
        
        (from CVXOPT `SDP
        example <http://abel.ee.ucla.edu/cvxopt/userguide/coneprog.html#semidefinite-programming>`__)
        
        .. code:: Python
        
            >>> from sympy import symbols, Matrix
            >>> from lmi_sdp import LMI_NSD, init_lmi_latex_printing
            >>>
            >>> init_lmi_latex_printing()
            >>>
            >>> variables = symbols('x1 x2 x3')
            >>> x1, x2, x3 = variables
            >>>
            >>> min_obj = x1 - x2 + x3
            >>>
            >>> LMI_1 = LMI_NSD(
            ...     x1*Matrix([[-7, -11], [-11, 3]]) +
            ...     x2*Matrix([[7, -18], [-18, 8]]) +
            ...     x3*Matrix([[-2, -8], [-8, 1]]),
            ...     Matrix([[33, -9], [-9, 26]]))
            >>>
            >>> LMI_2 = LMI_NSD(
            ...     x1*Matrix([[-21, -11, 0], [-11, 10, 8], [0, 8, 5]]) +
            ...     x2*Matrix([[0, 10, 16], [10, -10, -10], [16, -10, 3]]) +
            ...     x3*Matrix([[-5, 2, -17], [2, -6, 8], [-17, 8, 6]]),
            ...     Matrix([[14, 9, 40], [9, 91, 10], [40, 10, 15]]))
            >>>
            >>> min_obj
            x1 - x2 + x3
        
        |equation|
        
        .. code:: Python
        
            >>> LMI_1.expanded(variables)
            Matrix([
            [ -7.0, -11.0],
            [-11.0,   3.0]])*x1 + Matrix([
            [  7.0, -18.0],
            [-18.0,   8.0]])*x2 + Matrix([
            [-2.0, -8.0],
            [-8.0,  1.0]])*x3 <= Matrix([
            [33, -9],
            [-9, 26]])
        
        |equation|
        
        .. code:: Python
        
            >>> LMI_2.expanded(variables)
            Matrix([
            [-21.0, -11.0, 0.0],
            [-11.0,  10.0, 8.0],
            [  0.0,   8.0, 5.0]])*x1 + Matrix([
            [ 0.0,  10.0,  16.0],
            [10.0, -10.0, -10.0],
            [16.0, -10.0,   3.0]])*x2 + Matrix([
            [ -5.0,  2.0, -17.0],
            [  2.0, -6.0,   8.0],
            [-17.0,  8.0,   6.0]])*x3 <= Matrix([
            [14,  9, 40],
            [ 9, 91, 10],
            [40, 10, 15]])
        
        |equation|
        
        .. code:: Python
        
            >>> from cvxopt import solvers
            >>> from lmi_sdp import to_cvxopt
            >>>
            >>> solvers.options['show_progress'] = False
            >>>
            >>> c, Gs, hs = to_cvxopt(min_obj, [LMI_1, LMI_2], variables)
            >>>
            >>> sol = solvers.sdp(c, Gs=Gs, hs=hs)
            >>> print(sol['x'])
            [-3.68e-01]
            [ 1.90e+00]
            [-8.88e-01]
            <BLANKLINE>
        
        Export to SDPA Format
        ---------------------
        
        Example
        ~~~~~~~
        
        .. code:: Python
        
            >>> from sympy import symbols, Matrix
            >>> from lmi_sdp import LMI_PSD, to_sdpa_sparse
            >>>
            >>> variables = x1, x2 = symbols('x1 x2')
            >>>
            >>> min_obj = 10*x1 + 20*x2
            >>> lmi_1 = LMI_PSD(
            ...     -Matrix([[1, 0, 0, 0], [0, 2, 0, 0], [0, 0, 3, 0], [0, 0, 0, 4]]) +
            ...     Matrix([[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]])*x1 +
            ...     Matrix([[0, 0, 0, 0], [0, 1, 0, 0], [0, 0, 5, 2], [0, 0, 2, 6]])*x2)
            >>> lmi_1
            Matrix([
            [x1 - 1,           0,        0,        0],
            [     0, x1 + x2 - 2,        0,        0],
            [     0,           0, 5*x2 - 3,     2*x2],
            [     0,           0,     2*x2, 6*x2 - 4]]) >= 0
            >>>
            >>> dat = to_sdpa_sparse(min_obj, lmi_1, variables, comment='test sparse')
            >>> print(dat)
            "test sparse"
            2 = ndim
            3 = nblocks
            1 1 2 = blockstruct
            10.0, 20.0 = objcoeffs
            0 1 1 1 1.0
            0 2 1 1 2.0
            0 3 1 1 3.0
            0 3 2 2 4.0
            1 1 1 1 1.0
            1 2 1 1 1.0
            2 2 1 1 1.0
            2 3 1 1 5.0
            2 3 1 2 2.0
            2 3 2 2 6.0
            <BLANKLINE>
        
        Author
        ------
        
        `Cristóvão Duarte Sousa <https://github.com/cdsousa>`__
        
        Install
        -------
        
        From git source:
        
        ::
        
            git clone git@github.com:cdsousa/PyLMI-SDP.git
            cd PyLMI-SDP
            python setup.py install
        
        License
        -------
        
        Simplified BSD License. See `License File <LICENSE.txt>`__
        
        .. |Build Status| image:: https://travis-ci.org/cdsousa/PyLMI-SDP.png?branch=master
           :target: https://travis-ci.org/cdsousa/PyLMI-SDP
        .. |equation| image:: http://latex.codecogs.com/gif.latex?%5Cleft%5B%5Cbegin%7Bsmallmatrix%7D%7B%7Dx%2B1%26y%2B2%5C%5Cy%2B2%26x%2Bz%5Cend%7Bsmallmatrix%7D%5Cright%5D%5Csucc0
        .. |equation| image:: http://latex.codecogs.com/gif.latex?%5Cleft%5B%5Cbegin%7Bsmallmatrix%7D%7B%7D1.0%260.0%5C%5C0.0%261.0%5Cend%7Bsmallmatrix%7D%5Cright%5Dx%2B%5Cleft%5B%5Cbegin%7Bsmallmatrix%7D%7B%7D0.0%261.0%5C%5C1.0%260.0%5Cend%7Bsmallmatrix%7D%5Cright%5Dy%2B%5Cleft%5B%5Cbegin%7Bsmallmatrix%7D%7B%7D0.0%260.0%5C%5C0.0%261.0%5Cend%7Bsmallmatrix%7D%5Cright%5Dz%2B%5Cleft%5B%5Cbegin%7Bsmallmatrix%7D%7B%7D1.0%262.0%5C%5C2.0%260.0%5Cend%7Bsmallmatrix%7D%5Cright%5D%5Csucc0
        .. |equation| image:: http://latex.codecogs.com/gif.latex?%5Cleft%5B%5Cbegin%7Bsmallmatrix%7D%7B%7D-x%26-y%5C%5C-y%26-x-z%5Cend%7Bsmallmatrix%7D%5Cright%5D%5Cpreceq%5Cleft%5B%5Cbegin%7Bsmallmatrix%7D%7B%7D1%262%5C%5C2%260%5Cend%7Bsmallmatrix%7D%5Cright%5D
        .. |equation| image:: http://latex.codecogs.com/gif.latex?x_%7B1%7D-x_%7B2%7D%2Bx_%7B3%7D
        .. |equation| image:: http://latex.codecogs.com/gif.latex?%5Cleft%5B%5Cbegin%7Bsmallmatrix%7D%7B%7D-7.0%26-11.0%5C%5C-11.0%263.0%5Cend%7Bsmallmatrix%7D%5Cright%5Dx_%7B1%7D%2B%5Cleft%5B%5Cbegin%7Bsmallmatrix%7D%7B%7D7.0%26-18.0%5C%5C-18.0%268.0%5Cend%7Bsmallmatrix%7D%5Cright%5Dx_%7B2%7D%2B%5Cleft%5B%5Cbegin%7Bsmallmatrix%7D%7B%7D-2.0%26-8.0%5C%5C-8.0%261.0%5Cend%7Bsmallmatrix%7D%5Cright%5Dx_%7B3%7D%5Cpreceq%5Cleft%5B%5Cbegin%7Bsmallmatrix%7D%7B%7D33%26-9%5C%5C-9%2626%5Cend%7Bsmallmatrix%7D%5Cright%5D
        .. |equation| image:: http://latex.codecogs.com/gif.latex?%5Cleft%5B%5Cbegin%7Bsmallmatrix%7D%7B%7D-21.0%26-11.0%260.0%5C%5C-11.0%2610.0%268.0%5C%5C0.0%268.0%265.0%5Cend%7Bsmallmatrix%7D%5Cright%5Dx_%7B1%7D%2B%5Cleft%5B%5Cbegin%7Bsmallmatrix%7D%7B%7D0.0%2610.0%2616.0%5C%5C10.0%26-10.0%26-10.0%5C%5C16.0%26-10.0%263.0%5Cend%7Bsmallmatrix%7D%5Cright%5Dx_%7B2%7D%2B%5Cleft%5B%5Cbegin%7Bsmallmatrix%7D%7B%7D-5.0%262.0%26-17.0%5C%5C2.0%26-6.0%268.0%5C%5C-17.0%268.0%266.0%5Cend%7Bsmallmatrix%7D%5Cright%5Dx_%7B3%7D%5Cpreceq%5Cleft%5B%5Cbegin%7Bsmallmatrix%7D%7B%7D14%269%2640%5C%5C9%2691%2610%5C%5C40%2610%2615%5Cend%7Bsmallmatrix%7D%5Cright%5D
        
Keywords: LMI SDP
Platform: UNKNOWN
Classifier: Development Status :: 4 - Beta
Classifier: License :: OSI Approved :: BSD License
Classifier: Operating System :: OS Independent
Classifier: Programming Language :: Python
Classifier: Intended Audience :: Developers
Classifier: Intended Audience :: Education
Classifier: Intended Audience :: Manufacturing
Classifier: Intended Audience :: Science/Research
