{
    "info": {
        "author": "Cristovao D. Sousa",
        "author_email": "crisjss@gmail.com",
        "bugtrack_url": null,
        "classifiers": [
            "Development Status :: 4 - Beta",
            "Intended Audience :: Developers",
            "Intended Audience :: Education",
            "Intended Audience :: Manufacturing",
            "Intended Audience :: Science/Research",
            "License :: OSI Approved :: BSD License",
            "Operating System :: OS Independent",
            "Programming Language :: Python",
            "Programming Language :: Python :: 2",
            "Programming Language :: Python :: 3"
        ],
        "description": "PyLMI-SDP\r\n        =========\r\n        \r\n        *Symbolic linear matrix inequalities (LMI) and semi-definite programming\r\n        (SDP) tools for Python*\r\n        \r\n        | This package includes a set of classes to represent and manipulate\r\n        LMIs symbolically using `SymPy <http://sympy.org>`__.\r\n        | It also includes tools to export LMIs to\r\n        `CVXOPT <http://abel.ee.ucla.edu/cvxopt/userguide/coneprog.html#semidefinite-programming>`__\r\n        SDP input and to the `SDPA <http://sdpa.sourceforge.net/>`__ format.\r\n        \r\n        | Depends on `SymPy <http://sympy.org>`__ 0.7.3 and\r\n        `NumPy <http://www.numpy.org/>`__ 1.7.1, and optionally on\r\n        `CVXOPT <http://cvxopt.org/>`__.\r\n        | Single codebase supporting both Python 2.7 and Python 3.3.\r\n        | PyLMI-SDP is tested in these versions but it may work in others.\r\n        \r\n        |Build Status|\r\n        \r\n        LMI Definition\r\n        --------------\r\n        \r\n        Examples\r\n        ~~~~~~~~\r\n        \r\n        .. code:: Python\r\n        \r\n            >>> from sympy import symbols, Matrix\r\n            >>> from lmi_sdp import LMI_PD, LMI_NSD\r\n            >>> variables = symbols('x y z')\r\n            >>> x, y, z = variables\r\n            >>> lmi = LMI_PD(Matrix([[x+1, y+2], [y+2, z+x]]))\r\n            >>> lmi\r\n            Matrix([\r\n            [x + 1, y + 2],\r\n            [y + 2, x + z]]) > 0\r\n        \r\n        .. code:: Python\r\n        \r\n            >>> from lmi_sdp import init_lmi_latex_printing\r\n            >>> from sympy import latex\r\n            >>> init_lmi_latex_printing()\r\n            >>> print(latex(lmi))\r\n            \\left[\\begin{smallmatrix}{}x + 1 & y + 2\\\\y + 2 & x + z\\end{smallmatrix}\\right] \\succ 0\r\n        \r\n        |equation|\r\n        \r\n        .. code:: Python\r\n        \r\n            >>> print(latex(lmi.expanded(variables)))\r\n            \\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\r\n        \r\n        |equation|\r\n        \r\n        .. code:: Python\r\n        \r\n            >>> lmi_2 = LMI_NSD( Matrix([[-x, -y], [-y, -z-x]]), Matrix([[1, 2], [2, 0]]))\r\n            >>> lmi_2\r\n            Matrix([\r\n            [-x,     -y],\r\n            [-y, -x - z]]) <= Matrix([\r\n            [1, 2],\r\n            [2, 0]])\r\n            >>> lmi_2.canonical()\r\n            Matrix([\r\n            [x + 1, y + 2],\r\n            [y + 2, x + z]]) >= 0\r\n        \r\n        .. code:: Python\r\n        \r\n            >>> print(latex(lmi_2))\r\n            \\left[\\begin{smallmatrix}{}- x & - y\\\\- y & - x - z\\end{smallmatrix}\\right] \\preceq \\left[\\begin{smallmatrix}{}1 & 2\\\\2 & 0\\end{smallmatrix}\\right]\r\n        \r\n        |equation|\r\n        \r\n        Convertion to CVXOPT SDP\r\n        ------------------------\r\n        \r\n        Example\r\n        ~~~~~~~\r\n        \r\n        (from CVXOPT `SDP\r\n        example <http://abel.ee.ucla.edu/cvxopt/userguide/coneprog.html#semidefinite-programming>`__)\r\n        \r\n        .. code:: Python\r\n        \r\n            >>> from sympy import symbols, Matrix\r\n            >>> from lmi_sdp import LMI_NSD, init_lmi_latex_printing\r\n            >>>\r\n            >>> init_lmi_latex_printing()\r\n            >>>\r\n            >>> variables = symbols('x1 x2 x3')\r\n            >>> x1, x2, x3 = variables\r\n            >>>\r\n            >>> min_obj = x1 - x2 + x3\r\n            >>>\r\n            >>> LMI_1 = LMI_NSD(\r\n            ...     x1*Matrix([[-7, -11], [-11, 3]]) +\r\n            ...     x2*Matrix([[7, -18], [-18, 8]]) +\r\n            ...     x3*Matrix([[-2, -8], [-8, 1]]),\r\n            ...     Matrix([[33, -9], [-9, 26]]))\r\n            >>>\r\n            >>> LMI_2 = LMI_NSD(\r\n            ...     x1*Matrix([[-21, -11, 0], [-11, 10, 8], [0, 8, 5]]) +\r\n            ...     x2*Matrix([[0, 10, 16], [10, -10, -10], [16, -10, 3]]) +\r\n            ...     x3*Matrix([[-5, 2, -17], [2, -6, 8], [-17, 8, 6]]),\r\n            ...     Matrix([[14, 9, 40], [9, 91, 10], [40, 10, 15]]))\r\n            >>>\r\n            >>> min_obj\r\n            x1 - x2 + x3\r\n        \r\n        |equation|\r\n        \r\n        .. code:: Python\r\n        \r\n            >>> LMI_1.expanded(variables)\r\n            Matrix([\r\n            [ -7.0, -11.0],\r\n            [-11.0,   3.0]])*x1 + Matrix([\r\n            [  7.0, -18.0],\r\n            [-18.0,   8.0]])*x2 + Matrix([\r\n            [-2.0, -8.0],\r\n            [-8.0,  1.0]])*x3 <= Matrix([\r\n            [33, -9],\r\n            [-9, 26]])\r\n        \r\n        |equation|\r\n        \r\n        .. code:: Python\r\n        \r\n            >>> LMI_2.expanded(variables)\r\n            Matrix([\r\n            [-21.0, -11.0, 0.0],\r\n            [-11.0,  10.0, 8.0],\r\n            [  0.0,   8.0, 5.0]])*x1 + Matrix([\r\n            [ 0.0,  10.0,  16.0],\r\n            [10.0, -10.0, -10.0],\r\n            [16.0, -10.0,   3.0]])*x2 + Matrix([\r\n            [ -5.0,  2.0, -17.0],\r\n            [  2.0, -6.0,   8.0],\r\n            [-17.0,  8.0,   6.0]])*x3 <= Matrix([\r\n            [14,  9, 40],\r\n            [ 9, 91, 10],\r\n            [40, 10, 15]])\r\n        \r\n        |equation|\r\n        \r\n        .. code:: Python\r\n        \r\n            >>> from cvxopt import solvers\r\n            >>> from lmi_sdp import to_cvxopt\r\n            >>>\r\n            >>> solvers.options['show_progress'] = False\r\n            >>>\r\n            >>> c, Gs, hs = to_cvxopt(min_obj, [LMI_1, LMI_2], variables)\r\n            >>>\r\n            >>> sol = solvers.sdp(c, Gs=Gs, hs=hs)\r\n            >>> print(sol['x'])\r\n            [-3.68e-01]\r\n            [ 1.90e+00]\r\n            [-8.88e-01]\r\n            <BLANKLINE>\r\n        \r\n        Export to SDPA Format\r\n        ---------------------\r\n        \r\n        Example\r\n        ~~~~~~~\r\n        \r\n        .. code:: Python\r\n        \r\n            >>> from sympy import symbols, Matrix\r\n            >>> from lmi_sdp import LMI_PSD, to_sdpa_sparse\r\n            >>>\r\n            >>> variables = x1, x2 = symbols('x1 x2')\r\n            >>>\r\n            >>> min_obj = 10*x1 + 20*x2\r\n            >>> lmi_1 = LMI_PSD(\r\n            ...     -Matrix([[1, 0, 0, 0], [0, 2, 0, 0], [0, 0, 3, 0], [0, 0, 0, 4]]) +\r\n            ...     Matrix([[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]])*x1 +\r\n            ...     Matrix([[0, 0, 0, 0], [0, 1, 0, 0], [0, 0, 5, 2], [0, 0, 2, 6]])*x2)\r\n            >>> lmi_1\r\n            Matrix([\r\n            [x1 - 1,           0,        0,        0],\r\n            [     0, x1 + x2 - 2,        0,        0],\r\n            [     0,           0, 5*x2 - 3,     2*x2],\r\n            [     0,           0,     2*x2, 6*x2 - 4]]) >= 0\r\n            >>>\r\n            >>> dat = to_sdpa_sparse(min_obj, lmi_1, variables, comment='test sparse')\r\n            >>> print(dat)\r\n            \"test sparse\"\r\n            2 = ndim\r\n            3 = nblocks\r\n            1 1 2 = blockstruct\r\n            10.0, 20.0 = objcoeffs\r\n            0 1 1 1 1.0\r\n            0 2 1 1 2.0\r\n            0 3 1 1 3.0\r\n            0 3 2 2 4.0\r\n            1 1 1 1 1.0\r\n            1 2 1 1 1.0\r\n            2 2 1 1 1.0\r\n            2 3 1 1 5.0\r\n            2 3 1 2 2.0\r\n            2 3 2 2 6.0\r\n            <BLANKLINE>\r\n        \r\n        Author\r\n        ------\r\n        \r\n        `Crist\u00f3v\u00e3o Duarte Sousa <https://github.com/cdsousa>`__\r\n        \r\n        Install\r\n        -------\r\n        \r\n        From git source:\r\n        \r\n        ::\r\n        \r\n            git clone git@github.com:cdsousa/PyLMI-SDP.git\r\n            cd PyLMI-SDP\r\n            python setup.py install\r\n        \r\n        License\r\n        -------\r\n        \r\n        Simplified BSD License. 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