WAM7 Dynamic Parameter Identification.ipynb

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     "metadata": {},
     "source": [
      "Experimental Identification of Physically Feasible Dynamic Parameters of the 7-link WAM\u2122 Robot using LMI\u2013SDP Techniques\n",
      "=======================================================================================================================\n",
      "\n",
      "[![DOI](https://zenodo.org/badge/920/cdsousa/wam7_dyn_ident.png)](http://dx.doi.org/10.5281/zenodo.10537)\n",
      "\n",
      "*Experimental code and data associated with the paper:*\n",
      "\n",
      "**Crist\u00f3v\u00e3o D. Sousa and Rui Cortes\u00e3o, \"Physical feasibility of robot base inertial parameter identification: A linear matrix inequality approach,\" The International Journal of Robotics Research, vol. 33, no. 6, pp. 931\u2013944, May. 2014, doi: [10.1177/0278364913514870](http://dx.doi.org/10.1177/0278364913514870)**\n",
      "\n",
      "[Postprint availabe from ResearchGate](http://www.researchgate.net/publication/262483999_Physical_feasibility_of_robot_base_inertial_parameter_identification_A_linear_matrix_inequality_approach)",
      "\n",
      "\n",
      "------------------------\n",
      "\n",
      "\n",
      "Authors\n",
      "-------\n",
      "\n",
      "- Crist\u00f3v\u00e3o D. Sousa, [crisjss@gmail.com](mailto:crisjss@gmail.com)\n",
      "- Rui Cortes\u00e3o, [cortesao@isr.uc.pt](mailto:cortesao@isr.uc.pt)\n",
      "\n",
      "------------------------\n",
      "\n",
      "\n",
      "Research Notebook\n",
      "-----------------\n",
      "\n",
      "The research is done in [Python](http://www.python.org/) within an [IPython notebook](http://ipython.org/notebook.html) (the *WAM7 Dynamic Parameter Identification.ipynb* file).\n",
      "Data is in *data* folder. Additional Python support code is in *support_funcs* folder.\n",
      "\n",
      "The file *WAM7 Dynamic Parameter Identification.html* is a **preview** of the notebook. **It can be seen online at:**\n",
      "\n",
      "**[Experimental WAM Robot Dynamic Identification with LMI](http://goo.gl/dOPj8j)**\n",
      "\n",
      "\n",
      "\n",
      "How to run the code\n",
      "-------------------\n",
      "\n",
      "- clone the git repository (it contains code and data) from https://github.com/cdsousa/wam7_dyn_ident\n",
      "- open the *WAM7 Dynamic Parameter Identification.ipynb* notebook with [IPython](http://ipython.org/)\n",
      "- edit and run the code\n",
      "\n",
      "Dependencies:\n",
      "\n",
      "- [Python](http://www.python.org/)\n",
      "- [IPython](http://ipython.org/)\n",
      "- [SymPy](http://sympy.org/)\n",
      "- [Numpy](http://www.numpy.org/)\n",
      "- [SciPy](http://www.scipy.org/)\n",
      "- [SymPyBotics](https://github.com/cdsousa/SymPyBotics)\n",
      "- [PyLMI-SDP](https://github.com/cdsousa/PyLMI-SDP)\n",
      "\n",
      "------------------------\n",
      "\n",
      "\n",
      "Questions & Feedback\n",
      "--------------------\n",
      "\n",
      "Feel free to contact the authors at [crisjss@gmail.com](mailto:crisjss@gmail.com)\n",
      "\n",
      "------------------------\n",
      "\n",
      "\n",
      "License\n",
      "-------\n",
      "\n",
      "Copyright (c) 2013, Crist\u00f3v\u00e3o Duarte Sousa, Rui Cortes\u00e3o\n",
      "\n",
      "All rights reserved.\n",
      "\n",
      "[![Creative Commons License](http://i.creativecommons.org/l/by-nc-sa/4.0/88x31.png)](http://creativecommons.org/licenses/by-nc-sa/4.0/)\n",
      "This work is licensed under a [Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License](http://creativecommons.org/licenses/by-nc-sa/4.0/)\n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "---------------\n",
      "\n",
      "---------------\n",
      "\n",
      "---------------\n",
      "\n",
      "---------------"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Initializations"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "datafolder = 'data/'\n",
      "tmpfolder = 'tmp/'"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from sympy import init_printing\n",
      "init_printing()\n",
      "\n",
      "%pylab inline"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Populating the interactive namespace from numpy and matplotlib\n"
       ]
      }
     ],
     "prompt_number": 274
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "1 - Robot Model\n",
      "==============="
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import sympybotics"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 26
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "#### Robot Definition"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "rbtdef = sympybotics.RobotDef(\"WAM Arm 7 DOF\",\n",
      "            [(\"-pi/2\", 0, 0, \"q\"),\n",
      "             (\"pi/2\", 0, 0, \"q\"),\n",
      "             (\"-pi/2\", 0.045, 0.55, \"q\"),\n",
      "             (\"pi/2\", -0.045, 0, \"q\"),\n",
      "             (\"-pi/2\", 0, 0.3, \"q\"),\n",
      "             (\"pi/2\", 0, 0, \"q\"),\n",
      "             (0, 0, 0.06, \"q\")],\n",
      "            dh_convention=\"standard\")\n",
      "\n",
      "rbtdef.frictionmodel = {'Coulomb', 'viscous', 'offset'}\n",
      "rbtdef.driveinertiamodel = 'simplified'"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 27
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "#### Model Generation"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%time rbt = sympybotics.RobotDynCode(rbtdef)\n",
      "%time rbt.calc_base_parms()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "CPU times: user 30.4 s, sys: 153 ms, total: 30.6 s\n",
        "Wall time: 30.4 s\n",
        "CPU times: user 25 s, sys: 153 ms, total: 25.2 s"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Wall time: 25.1 s\n"
       ]
      }
     ],
     "prompt_number": 28
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import pickle\n",
      "with open(tmpfolder + 'robotmodels/wam7_model.pkl', 'wb') as file:\n",
      "    pickle.dump( rbt, file )"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 29
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Base Dynamic Parameters"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import pickle\n",
      "with open(tmpfolder +  'robotmodels/wam7_model.pkl', 'rb' ) as file:\n",
      "          rbt = pickle.load( file )"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 30
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "rbt.dyn.n_dynparms, rbt.dyn.n_base"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 31,
       "text": [
        "(98, 69)"
       ]
      }
     ],
     "prompt_number": 31
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "rbt.dyn.baseparms.n()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$\\left[\\begin{smallmatrix}{}Ia_{1} + L_{1yy} + L_{2zz}\\\\fv_{1}\\\\fc_{1}\\\\fo_{1}\\\\L_{2xx} - L_{2zz} + L_{3zz} - 1.1 l_{3y} + 0.300475 m_{3} + 0.300475 m_{4} + 0.300475 m_{5} + 0.300475 m_{6} + 0.300475 m_{7}\\\\L_{2xy}\\\\L_{2xz}\\\\Ia_{2} + L_{2yy} + L_{3zz} - 1.1 l_{3y} + 0.300475 m_{3} + 0.300475 m_{4} + 0.300475 m_{5} + 0.300475 m_{6} + 0.300475 m_{7}\\\\L_{2yz}\\\\l_{2x}\\\\l_{2z} - l_{3y} + 0.55 m_{3} + 0.55 m_{4} + 0.55 m_{5} + 0.55 m_{6} + 0.55 m_{7}\\\\fv_{2}\\\\fc_{2}\\\\fo_{2}\\\\L_{3xx} - L_{3zz} + L_{4zz} + 0.002025 m_{3}\\\\L_{3xy} - 0.045 l_{3y}\\\\L_{3xz}\\\\L_{3yy} + L_{4zz} - 0.002025 m_{3} - 0.00405 m_{4} - 0.00405 m_{5} - 0.00405 m_{6} - 0.00405 m_{7}\\\\L_{3yz}\\\\l_{3x} + 0.045 m_{3} + 0.045 m_{4} + 0.045 m_{5} + 0.045 m_{6} + 0.045 m_{7}\\\\l_{3z} + l_{4y}\\\\Ia_{3}\\\\fv_{3}\\\\fc_{3}\\\\fo_{3}\\\\L_{4xx} - L_{4zz} + L_{5zz} - 0.6 l_{5y} + 0.002025 m_{4} + 0.092025 m_{5} + 0.092025 m_{6} + 0.092025 m_{7}\\\\L_{4xy} + 0.045 l_{4y}\\\\L_{4xz}\\\\L_{4yy} + L_{5zz} - 0.6 l_{5y} - 0.002025 m_{4} + 0.087975 m_{5} + 0.087975 m_{6} + 0.087975 m_{7}\\\\L_{4yz}\\\\l_{4x} - 0.045 m_{4} - 0.045 m_{5} - 0.045 m_{6} - 0.045 m_{7}\\\\l_{4z} - l_{5y} + 0.3 m_{5} + 0.3 m_{6} + 0.3 m_{7}\\\\Ia_{4}\\\\fv_{4}\\\\fc_{4}\\\\fo_{4}\\\\L_{5xx} - L_{5zz} + L_{6zz}\\\\L_{5xy}\\\\L_{5xz}\\\\L_{5yy} + L_{6zz}\\\\L_{5yz}\\\\l_{5x}\\\\l_{5z} + l_{6y}\\\\Ia_{5}\\\\fv_{5}\\\\fc_{5}\\\\fo_{5}\\\\L_{6xx} - L_{6zz} + L_{7yy} + 0.12 l_{7z} + 0.0036 m_{7}\\\\L_{6xy}\\\\L_{6xz}\\\\L_{6yy} + L_{7yy} + 0.12 l_{7z} + 0.0036 m_{7}\\\\L_{6yz}\\\\l_{6x}\\\\l_{6z} + l_{7z} + 0.06 m_{7}\\\\Ia_{6}\\\\fv_{6}\\\\fc_{6}\\\\fo_{6}\\\\L_{7xx} - L_{7yy}\\\\L_{7xy}\\\\L_{7xz}\\\\L_{7yz}\\\\L_{7zz}\\\\l_{7x}\\\\l_{7y}\\\\Ia_{7}\\\\fv_{7}\\\\fc_{7}\\\\fo_{7}\\end{smallmatrix}\\right]$$"
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7nT25uy99wk/Zaz4NLEtLLaU7z5ImD+yFdnjjoqYZRUUemmtPvH/Qj9AlT4ND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\nRK5CYII=\n",
       "prompt_number": 275,
       "text": [
        "\u23a1                                         Ia\u2081 + L_1yy + L_2zz                 \n",
        "\u23a2                                                                             \n",
        "\u23a2                                                 fv\u2081                         \n",
        "\u23a2                                                                             \n",
        "\u23a2                                                 fc\u2081                         \n",
        "\u23a2                                                                             \n",
        "\u23a2                                                 fo\u2081                         \n",
        "\u23a2                                                                             \n",
        "\u23a2L\u2082\u2093\u2093 - L_2zz + L_3zz - 1.1\u22c5l_3y + 0.300475\u22c5m\u2083 + 0.300475\u22c5m\u2084 + 0.300475\u22c5m\u2085 + 0\n",
        "\u23a2                                                                             \n",
        "\u23a2                                                L_2xy                        \n",
        "\u23a2                                                                             \n",
        "\u23a2                                                L_2xz                        \n",
        "\u23a2                                                                             \n",
        "\u23a2Ia\u2082 + L_2yy + L_3zz - 1.1\u22c5l_3y + 0.300475\u22c5m\u2083 + 0.300475\u22c5m\u2084 + 0.300475\u22c5m\u2085 + 0.\n",
        "\u23a2                                                                             \n",
        "\u23a2                                                L_2yz                        \n",
        "\u23a2                                                                             \n",
        "\u23a2                                                 l\u2082\u2093                         \n",
        "\u23a2                                                                             \n",
        "\u23a2                    l_2z - l_3y + 0.55\u22c5m\u2083 + 0.55\u22c5m\u2084 + 0.55\u22c5m\u2085 + 0.55\u22c5m\u2086 + 0.5\n",
        "\u23a2                                                                             \n",
        "\u23a2                                                 fv\u2082                         \n",
        "\u23a2                                                                             \n",
        "\u23a2                                                 fc\u2082                         \n",
        "\u23a2                                                                             \n",
        "\u23a2                                                 fo\u2082                         \n",
        "\u23a2                                                                             \n",
        "\u23a2                                 L\u2083\u2093\u2093 - L_3zz + L_4zz + 0.002025\u22c5m\u2083          \n",
        "\u23a2                                                                             \n",
        "\u23a2                                         L_3xy - 0.045\u22c5l_3y                  \n",
        "\u23a2                                                                             \n",
        "\u23a2                                                L_3xz                        \n",
        "\u23a2                                                                             \n",
        "\u23a2           L_3yy + L_4zz - 0.002025\u22c5m\u2083 - 0.00405\u22c5m\u2084 - 0.00405\u22c5m\u2085 - 0.00405\u22c5m\u2086\n",
        "\u23a2                                                                             \n",
        "\u23a2                                                L_3yz                        \n",
        "\u23a2                                                                             \n",
        "\u23a2                     l\u2083\u2093 + 0.045\u22c5m\u2083 + 0.045\u22c5m\u2084 + 0.045\u22c5m\u2085 + 0.045\u22c5m\u2086 + 0.045\u22c5\n",
        "\u23a2                                                                             \n",
        "\u23a2                                             l_3z + l_4y                     \n",
        "\u23a2                                                                             \n",
        "\u23a2                                                 Ia\u2083                         \n",
        "\u23a2                                                                             \n",
        "\u23a2                                                 fv\u2083                         \n",
        "\u23a2                                                                             \n",
        "\u23a2                                                 fc\u2083                         \n",
        "\u23a2                                                                             \n",
        "\u23a2                                                 fo\u2083                         \n",
        "\u23a2                                                                             \n",
        "\u23a2       L\u2084\u2093\u2093 - L_4zz + L_5zz - 0.6\u22c5l_5y + 0.002025\u22c5m\u2084 + 0.092025\u22c5m\u2085 + 0.092025\n",
        "\u23a2                                                                             \n",
        "\u23a2                                         L_4xy + 0.045\u22c5l_4y                  \n",
        "\u23a2                                                                             \n",
        "\u23a2                                                L_4xz                        \n",
        "\u23a2                                                                             \n",
        "\u23a2          L_4yy + L_5zz - 0.6\u22c5l_5y - 0.002025\u22c5m\u2084 + 0.087975\u22c5m\u2085 + 0.087975\u22c5m\u2086 \n",
        "\u23a2                                                                             \n",
        "\u23a2                                                L_4yz                        \n",
        "\u23a2                                                                             \n",
        "\u23a2                           l\u2084\u2093 - 0.045\u22c5m\u2084 - 0.045\u22c5m\u2085 - 0.045\u22c5m\u2086 - 0.045\u22c5m\u2087   \n",
        "\u23a2                                                                             \n",
        "\u23a2                               l_4z - l_5y + 0.3\u22c5m\u2085 + 0.3\u22c5m\u2086 + 0.3\u22c5m\u2087        \n",
        "\u23a2                                                                             \n",
        "\u23a2                                                 Ia\u2084                         \n",
        "\u23a2                                                                             \n",
        "\u23a2                                                 fv\u2084                         \n",
        "\u23a2                                                                             \n",
        "\u23a2                                                 fc\u2084                         \n",
        "\u23a2                                                                             \n",
        "\u23a2                                                 fo\u2084                         \n",
        "\u23a2                                                                             \n",
        "\u23a2                                        L\u2085\u2093\u2093 - L_5zz + L_6zz                 \n",
        "\u23a2                                                                             \n",
        "\u23a2                                                L_5xy                        \n",
        "\u23a2                                                                             \n",
        "\u23a2                                                L_5xz                        \n",
        "\u23a2                                                                             \n",
        "\u23a2                                            L_5yy + L_6zz                    \n",
        "\u23a2                                                                             \n",
        "\u23a2                                                L_5yz                        \n",
        "\u23a2                                                                             \n",
        "\u23a2                                                 l\u2085\u2093                         \n",
        "\u23a2                                                                             \n",
        "\u23a2                                             l_5z + l_6y                     \n",
        "\u23a2                                                                             \n",
        "\u23a2                                                 Ia\u2085                         \n",
        "\u23a2                                                                             \n",
        "\u23a2                                                 fv\u2085                         \n",
        "\u23a2                                                                             \n",
        "\u23a2                                                 fc\u2085                         \n",
        "\u23a2                                                                             \n",
        "\u23a2                                                 fo\u2085                         \n",
        "\u23a2                                                                             \n",
        "\u23a2                            L\u2086\u2093\u2093 - L_6zz + L_7yy + 0.12\u22c5l_7z + 0.0036\u22c5m\u2087     \n",
        "\u23a2                                                                             \n",
        "\u23a2                                                L_6xy                        \n",
        "\u23a2                                                                             \n",
        "\u23a2                                                L_6xz                        \n",
        "\u23a2                                                                             \n",
        "\u23a2                                L_6yy + L_7yy + 0.12\u22c5l_7z + 0.0036\u22c5m\u2087        \n",
        "\u23a2                                                                             \n",
        "\u23a2                                                L_6yz                        \n",
        "\u23a2                                                                             \n",
        "\u23a2                                                 l\u2086\u2093                         \n",
        "\u23a2                                                                             \n",
        "\u23a2                                        l_6z + l_7z + 0.06\u22c5m\u2087                \n",
        "\u23a2                                                                             \n",
        "\u23a2                                                 Ia\u2086                         \n",
        "\u23a2                                                                             \n",
        "\u23a2                                                 fv\u2086                         \n",
        "\u23a2                                                                             \n",
        "\u23a2                                                 fc\u2086                         \n",
        "\u23a2                                                                             \n",
        "\u23a2                                                 fo\u2086                         \n",
        "\u23a2                                                                             \n",
        "\u23a2                                            L\u2087\u2093\u2093 - L_7yy                     \n",
        "\u23a2                                                                             \n",
        "\u23a2                                                L_7xy                        \n",
        "\u23a2                                                                             \n",
        "\u23a2                                                L_7xz                        \n",
        "\u23a2                                                                             \n",
        "\u23a2                                                L_7yz                        \n",
        "\u23a2                                                                             \n",
        "\u23a2                                                L_7zz                        \n",
        "\u23a2                                                                             \n",
        "\u23a2                                                 l\u2087\u2093                         \n",
        "\u23a2                                                                             \n",
        "\u23a2                                                l_7y                         \n",
        "\u23a2                                                                             \n",
        "\u23a2                                                 Ia\u2087                         \n",
        "\u23a2                                                                             \n",
        "\u23a2                                                 fv\u2087                         \n",
        "\u23a2                                                                             \n",
        "\u23a2                                                 fc\u2087                         \n",
        "\u23a2                                                                             \n",
        "\u23a3                                                 fo\u2087                         \n",
        "\n",
        "                        \u23a4\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        ".300475\u22c5m\u2086 + 0.300475\u22c5m\u2087\u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "300475\u22c5m\u2086 + 0.300475\u22c5m\u2087 \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "5\u22c5m\u2087                    \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        " - 0.00405\u22c5m\u2087           \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "m\u2087                      \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "\u22c5m\u2086 + 0.092025\u22c5m\u2087       \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "+ 0.087975\u22c5m\u2087           \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a5\n",
        "                        \u23a6"
       ]
      }
     ],
     "prompt_number": 275
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "2 - Trajectories and Recorded Data\n",
      "=================================="
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import pickle\n",
      "import sympybotics\n",
      "import numpy"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 52
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "with open(tmpfolder +  'robotmodels/wam7_model.pkl', 'rb' ) as file:\n",
      "          rbt = pickle.load( file )"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 53
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Plots"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "parms_traj = 'traj1'\n",
      "\n",
      "with open(datafolder +  'trajectories/%s_shwfl_abq0.pkl'%parms_traj, 'rb' ) as file:\n",
      "          s_h_wf_l, a_b_q0 = pickle.load(file)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 276
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "h = 0.001\n",
      "decimate = 10\n",
      "h_plot = h*decimate\n",
      "\n",
      "with open(datafolder +  'trajectories/%s.dat'%parms_traj, 'r' ) as file:\n",
      "          q_ref_orig = numpy.loadtxt(file)\n",
      "s = q_ref_orig.shape[0] / decimate\n",
      "\n",
      "q_ref = numpy.zeros((s, rbt.dof))\n",
      "for i in range(s):\n",
      "    q_ref[i, :] = q_ref_orig[i*decimate, :]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 277
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "si = 1/h_plot\n",
      "sf = si + 20/h_plot\n",
      "t = numpy.arange(sf-si) * h_plot"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 278
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from matplotlib import pyplot as plt\n",
      "plt.close()\n",
      "\n",
      "for i in range(rbt.dof):\n",
      "    plt.plot(t,q_ref[si:sf,i], label=\"$q_%d$\"%(i+1))\n",
      "plt.legend()\n",
      "\n",
      "plt.xlabel(\"Time (s)\")\n",
      "plt.ylabel(\"Joint positions (rad)\")\n",
      "\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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fXysSZP9JH6t2osu5uXL335yIxWI6dOgQzZ8/v7VFIfL2JoqKIvrmm0aLGhgY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\n",
       "text": [
        "<matplotlib.figure.Figure at 0xc31f9d0>"
       ]
      }
     ],
     "prompt_number": 279
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "3 - Regression Data Processing\n",
      "=============================="
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import os\n",
      "import pickle\n",
      "import math\n",
      "import sympy\n",
      "import numpy\n",
      "import sympybotics"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "with open(tmpfolder +  'robotmodels/wam7_model.pkl', 'rb' ) as file:\n",
      "          rbt = pickle.load( file )"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Data Load"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "parms_traj = 'traj1'"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 281
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from support_funcs.regr_data_proc import read_data\n",
      "t_raw, q_raw, tau_raw, t_ref, q_ref = read_data( rbt.dof, 0.001,\n",
      "                                                datafolder + 'recdata/rbtlog_%s.dat'%parms_traj,\n",
      "                                                datafolder + 'trajectories/traj1.dat')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 282
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Some Plots"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from matplotlib import pyplot as plt\n",
      "plt.close()\n",
      "\n",
      "for i in range(q_raw.shape[1]):\n",
      "    plt.plot(t_raw,q_raw[:,i])\n",
      "\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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R3R3ZMgcq1Gr6Yti8BpdB5v549ll44AGQy0GtPopSuSCfLSsrQxgfp2+Ja394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\nAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0xe558450>"
       ]
      }
     ],
     "prompt_number": 283
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from matplotlib import pyplot as plt\n",
      "plt.close()\n",
      "\n",
      "joint = 7\n",
      "plt.plot(t_ref+0.20,q_ref[:,joint-1])\n",
      "plt.plot(t_raw,q_raw[:,joint-1])\n",
      "\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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6u2ecZMuaTX9UdrTot2zKnck3Dr2X9bS6SdrKSOw9Sf0OJ/ma8gmZLqURysoq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\ni1BzKPqBANgNbuLZ7quduCRhUdFAZQu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HKsWQyKfwXaMcmknjhhH92Rkjuqq3b9u+9WQW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\nhQZCEX0FBQWFBkIRfQUFBYUG4v8D1J/SIYnnuGEAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0xc335ed0>"
       ]
      }
     ],
     "prompt_number": 284
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "del t_raw, q_raw, tau_raw, t_ref, q_ref"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Parameter Load"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "with open(datafolder +  'trajectories/%s_shwfl_abq0.pkl'%parms_traj, 'rb' ) as file:\n",
      "          s_h_wf_l, a_b_q0 = pickle.load(file)\n",
      "\n",
      "print(dict(zip(('S', 'h', 'wf', 'L'), s_h_wf_l)))\n",
      "print('\\n')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "{'h': 0.040000000000000001, 'S': 500.0, 'L': 5.0, 'wf': 0.31415926535897931}\n",
        "\n",
        "\n"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Filter Cut-off Frequency Definition"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fc_mult = 10"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 14
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "wf = float(s_h_wf_l[2])\n",
      "L = float(s_h_wf_l[3])\n",
      "fc = fc_mult * ( wf / (2*math.pi) * L )\n",
      "fc"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 15,
       "text": [
        "2.5"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fc_q = fc\n",
      "fc_dq = fc\n",
      "fc_ddq = fc\n",
      "\n",
      "fc_tau = float('Inf')  # fc\n",
      "\n",
      "si = int(3/0.001)\n",
      "sf = -int(1/0.001)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 16
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Data Filtering, Differentiation and Regression Data Generation"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "rec_h = 0.001"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 24
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from support_funcs.regr_data_proc import read_data, diff_and_filt_data, gen_regr_matrices\n",
      "\n",
      "def process_regression_data(traj_name):\n",
      "    t_raw, q_raw, tau_raw, t_ref, q_ref = read_data(dof=rbt.dof, h=rec_h,\n",
      "                                                    rbtlogfile=datafolder + 'recdata/rbtlog_%s.dat'%traj_name,\n",
      "                                                    trajreffile=datafolder + 'trajectories/%s.dat'%traj_name)\n",
      "    \n",
      "    q, dq, ddq, tau = diff_and_filt_data(dof=rbt.dof, h=rec_h,  q_raw=q_raw, tau_raw=tau_raw,\n",
      "                                   fc_q=fc_q, fc_dq=fc_dq, fc_ddq=fc_ddq, fc_tau=fc_tau)\n",
      "    \n",
      "    t_raw = t_raw[si:sf]; q_raw = q_raw[si:sf]; tau_raw = tau_raw[si:sf]\n",
      "    q = q[si:sf]; dq = dq[si:sf]; ddq = ddq[si:sf]; tau = tau[si:sf]\n",
      "    \n",
      "    t_raw = t_raw - t_raw[0]\n",
      "    \n",
      "    t = numpy.array(range(q.shape[0])) * rec_h\n",
      "    \n",
      "    W, omega, Q1, R1, rho1 = gen_regr_matrices(rbt, q, dq, ddq, tau)\n",
      "    \n",
      "    return t_raw, q_raw, tau_raw, t, q, dq, ddq, tau, W, omega, Q1, R1, rho1"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 22
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from support_funcs.utils import _fprint\n",
      "\n",
      "for traj in ['traj1', 'traj2', 'traj3', 'traj4']:\n",
      "    _fprint('>>>>>>>> %s proc <<<<<<<<<'%traj)\n",
      "    %time t_raw, q_raw, tau_raw, t, q, dq, ddq, tau, W, omega, Q1, R1, rho1 = process_regression_data(traj)\n",
      "    \n",
      "    _fprint(' (cond=%f)'%numpy.linalg.cond(W))\n",
      "    \n",
      "    _fprint('%s save'%traj)\n",
      "    \n",
      "    %time \\\n",
      "    numpy.savez_compressed(tmpfolder + 'procdata/' + traj + '_raw', t=t_raw, q=q_raw, tau=tau_raw);\\\n",
      "    numpy.savez_compressed(tmpfolder + 'procdata/' + traj + '_proc', t=t, q=q, dq=dq, ddq=ddq, tau=tau); \\\n",
      "    numpy.savez_compressed(tmpfolder + 'procdata/' + traj + '_regr', W=W, omega=omega, Q1=Q1, R1=R1, rho1=rho1)\n",
      "    \n",
      "    del t_raw, q_raw, tau_raw, t, q, dq, ddq, tau, W, omega, Q1, R1, rho1"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        ">>>>>>>> traj1 proc <<<<<<<<<\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "CPU times: user 1min 26s, sys: 1.17 s, total: 1min 27s\n",
        "Wall time: 1min 41s\n",
        " (cond=99.403409)"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "traj1 save\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "CPU times: user 17.2 s, sys: 1.03 s, total: 18.2 s\n",
        "Wall time: 38.7 s\n",
        ">>>>>>>> traj2 proc <<<<<<<<<"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "CPU times: user 1min 27s, sys: 1.05 s, total: 1min 28s\n",
        "Wall time: 1min 57s\n",
        " (cond=93.618890)"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "traj2 save\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "CPU times: user 16.6 s, sys: 973 ms, total: 17.6 s\n",
        "Wall time: 21.1 s\n",
        ">>>>>>>> traj3 proc <<<<<<<<<"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "CPU times: user 1min 28s, sys: 840 ms, total: 1min 28s\n",
        "Wall time: 1min 30s\n",
        " (cond=105.647955)"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "traj3 save\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "CPU times: user 17.1 s, sys: 867 ms, total: 17.9 s\n",
        "Wall time: 19 s\n",
        ">>>>>>>> traj4 proc <<<<<<<<<"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "CPU times: user 1min 27s, sys: 873 ms, total: 1min 28s\n",
        "Wall time: 1min 30s\n",
        " (cond=101.282987)"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "traj4 save\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "CPU times: user 16.2 s, sys: 813 ms, total: 17 s\n",
        "Wall time: 21.3 s\n"
       ]
      }
     ],
     "prompt_number": 34
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Plot"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "raw = numpy.load(tmpfolder + 'procdata/traj1_raw.npz')\n",
      "tau_raw = raw['tau']\n",
      "q_raw = raw['q']\n",
      "del raw\n",
      "proc = numpy.load(tmpfolder + 'procdata/traj1_proc.npz')\n",
      "t = proc['t']\n",
      "tau = proc['tau']\n",
      "q = proc['q']\n",
      "dq = proc['dq']\n",
      "del proc"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 285
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from matplotlib import pyplot as plt\n",
      "plt.close()\n",
      "\n",
      "joint = 1\n",
      "firsts = 20000\n",
      "plt.plot(t[:firsts],q_raw[:,joint-1][:firsts])\n",
      "#plt.plot(t[:firsts],q[:,joint-1][:firsts])\n",
      "#plt.plot(t[:firsts],dq[:,joint-1][:firsts])\n",
      "plt.plot(t[:firsts],tau_raw[:,joint-1][:firsts])\n",
      "\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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6dbI8ls8fnFxO0hyzsoDx4wFHhJpPPzjN+zlLKEogX12sSZKalcr7NZyJ9/e8\nDwDoXc+2mxpT6i82fGezeCm9EOoXavfxUmsM41LOPKcwx6ZO5VLm9GmgVy/g559J7rg1GD1wWawM\ni08v5nz9EiWAv/4C/v0XmDWL8+lEwXAxXExZ126/dWM1rnVQa8x61fYPvJFfI9Zja5WvBQCsHeMv\nl36x2R4hWBK/BH/dsH+hn2+Ghg8FAGy/we8Tpb1QZy5BzpwBevQgs2Nb6q/SXqYBAD7Yy4+sQtmy\nwK5dwOrVwMaNvJzSoRiWZTtqAVSj0RjVPJjSjTFFdZ/qqFGuhs3X/Oa1b1iPlclkODf6HGqWr2l9\nsIQYGj5U60ClQCVvsvbQa5NxdpkYUGcuMVJSyOLj6tVAVxaZYbp57KvOreLdnsqVgb//BiZMIOmL\nQjG6yWibH/+t4anQL4V1hE7L87znOJFyAk1WGUsLsHkysDcurKvpsq7nOqvjTUkfSJ0iTZEkewFI\nRajMpZx5ripX0kJb1sjNJTHyiROJQ7dGj7o9MDB0oPa1UNrTYWHkKaFPHyA5WZBLwLeUL5pWacrr\nOcXQ6YlYGYG2P7U1+R6bpimbr23G7fTbNl9Xt6x8aGPpzF75ROzGHaYY3ng49twRR4vKEJdy5nvv\n7LUowi9lNBqilVK3LjCVRX2RZoYG2wds19OfFjKM0K0b8PHH5L+ZttWesKJQXch7Oz0xdO2TMpPM\nvse2SfKOWzvsuva7Td9Fq8BWdh3rDPAhtMU37au3R1SNKLHNAOBizvxFwQtsuLRBbDPsYv584NYt\nomhoiwqsbvs0XWSx/DdkmDiRZNX06QMU8NyZr7CoUJKP0HzCrGlYw9785RXdV+DkyJN2HesM8J1n\nzgcVvCrAW+ktthkAXMyZlytZDtPbTRfbDJv55x9gyRJg2zail8IXQmRvLFwIlC4NjBnDb8qiEDNz\nXRzRoQaAxcKnK/9dYXUOocr57WFK6ymSmXlKMcxSSlkKuSoHVtdZwKWceVDZIJQtUVZsM2zi+nVg\n+HBSph8YyO+5j98/jm03tvF6ToUC+O03Ivj19df8nVeomXlkQCR+6PaDw5yApevsSWQXW21fvT1f\n5nCmmk81ychKC6koyZb8fDLpeu89Uo09fLAXjv+bg0aNgC5dgGXLgOfPxbHNpZy51DsNGZKZSRY6\n584lHYL4pv269oJUPXp7Azt3ksYXv/CQgpz2Mg15qjxBZub/jvoXY5qN0TpZtqEOe7EkFnbg7gFW\n5+hWh10nMaa9AAAgAElEQVROOhu+fe1bTscvP7Mc95/f58kabogpgZuXB3z5JVCtGlEYrVkTmD4d\n+G5BKdSum4tffwVGjSIV2zVrAp9+CjxzrOKyaznzfHW+5FQTzaFWAwMHkrv5iBHczjW6yWh+jLKB\nypVJeGjSJOAgR20zv2/88POlnx0y69p6Y6ug5+dDX4bPCYmftx/GNhtr9/EVS1XkzRauiBVmOXQI\naNQIuHSJCN4dPgx89BGR12gY4gW1PBdhYWQtaeNGICEBSEsDQkJI0Z+jcC1nrsp3mpn5J58AhYXA\nt9wmTgCABpUacD+JHTRsSMJDAwYAB9hNOgEAIUtDTJZC8y0nqtEA584Bn38OVD27GgAwdWYa6tQB\nwsPJjfTbb4HHPDZZ50PGl28HGlM/xu5jZ706S5SsIFM4OpslO5tMtIYNI2tFf/5J+uvq4qX00mre\nMFSvTupEDh8ms/n33ye/daGRxv8lnshT5bFqxio2v/xCSuU3bQI8eJho6M5WXq/9OvcT2kD79uRv\neestgE3r1/2J+3H72W1cT7sOgBTZMBxM4ke+ODUVmDcPCA0lssFqNfB+DJFzHTAsC//8Q/qjjh5N\n2u3Vr09ExS7aJ2mth62a4aboFsJfmMVeNBrg6VMgP7M86pSrj6wsoEg8NQQAjp2Z378PtGlDPoer\nV4E33jA9rqRHSbPp0I0akWruu3fJLJ7PSYMpODvzPXv2oF69eqhTpw7mzeOm2c0VZwiznDwJfPgh\nsH074MtTi8Ve9YrLiQ0r+xyRNtW2Lfl7hgwh1aKWuPzfZQBAShZJv+NTJvbyZbIG0agRcOcO8MMP\nQGIiMGcO8FaMDwBg5ZX5CAkBGjcmBVpr15JCqIgI4PXXSa5/erp912fT/OL3y79bfN9T4cnrhEQG\nGeumHM+fA99/T7SAKlYE6tQB3n6rBO4kFSAgAKhQgcSFU0RSfnVUauK1a0CrVsDgweT7UcZC7Zmh\nmJsh5coBO3YAHTuS9oxCVlFzcuZqtRrjx4/Hnj17cO3aNfz++++4fv06X7bZRJGmSPIz85s3iZzt\nhg1k1sgXAWUDtNtlPPW/eS8LHdM2qFUrEkMfNQrYaiEs/fmhzwEAw7cPhyxWhuyCbM7Xvn+fPAp3\n6kRmQKmp5DG3bdvinH1LoQIfHxIDvXmT/HDDw20LGzFsvGJdwGbawWlm39NoNChQF/AaSqjgVcFq\ng+LsbFKoVrMmcPQoMHYsmY1mZADxJ0pAXe42XrwgmVeVK5Mb3/Lljp+pF6qFr0W4c4fczObOJW0U\nrdV8lPAoYbVQUS4HZs4kN8qePYF9+/izV+86XA6Oj49HcHAwatSoAaVSiQEDBmD7dnEUxB5kPQDg\n+D6PbHn8mIhmzZlDYrVC0bFWR1weexln3jkj3EXM0Lw5sHs3cQabN5seY5iTq5tto1vNyob0dOKE\nIyKAoCDg9m1S2GQqV59Nx3UfH+C770iDjiFDSDzdllz69FzrU/rCIvPBUyaMwFeMurpPdXQO7mzx\nfAcOkCeZJ09ImGnjRvLEUvn/fVV0/6YqVUg66vHjJFTYoQMJITgKobPV7t8nE4Lp08msnA2eCk8U\nqAtYPf288QaZ6Lz9NhGw4xtO35rU1FQEBRW3MAsMDERqqjia0V4ePFbb8MyLF0Q0a/hw8k8IFncm\nsreRAZEI9QtFs6rNED8qXpiLWaBJEzLzeP99YOlSfWe48uxKo/HP84tj5jfeu8HqGjk55KZYrx7p\nV3rlCvDVV0TlkQ+io4kE8fr1wLhxgIplR770HOvO3JIGdoG6wEgcjAsBZQMgk5kOsxQUkL9t5Egy\nY1y/ntwQDQnxDTHaV68ecehvvAG0aEEapziCPFUevJTC/M4fPSKhkA8+IGspbJHL5FDIFazbNr7y\nCglFDh9O2jTyCacAFJvZDgDMnDlTux0VFYUoc73POKAqUsHf25/383KlsJAswjVrBnzxhXDXGR85\n3iirJcgnSJTPJCyMPK6//TbJR1+7lnQuOnLviMXj/EtbtlWlIrPm2FiSl3/iBEn/spVFpxbhw1Yf\nWhxTrRpxWH36kMXdX38FlFae8BMzEm03RocCdQGvYQQmvhxYVr8a7dkz8neVKUPWGSzdBBkVUo1G\no/d7VyjIU1HHjuT7ffYssGABCSkIhVAz87Q0MiMfPpw4c1vxVHgiX53POjzWogVJGujVi/w+Wvy/\nFWtcXBzi4uJsN+D/cHLmAQEBSNFZDUlJSUGgiTJGXWcuFIVFwpaD24NGQ+7yHh5k9mOL5oqtyGVy\ndKql345IKVdafKwXkjp1iLOdPZvM1hcvBjQe9tX/Z2WRfN0lS8hN4a+/gMhI+21jW9FYtiyZRb35\nJnF+f/5J+qSag2uI72XhS70nFS6seWMNGvmThhV1K9bVe69VKzKrnjePOGVLyGVyeMg9zKYFRkQU\n6++PHEm0hayd016EUEXNyCAx8t69SaGPPZRQkLi5rnKlNV55hSiR9uxJUhjr1zee6MbGxtpkB6f7\naLNmzXD79m0kJyejoKAAmzZtQo8ePbic0m4K1AXauLkU0GiAadPIyjhfKYi2wvwIxcLDg8Qfd+4k\n3Yo2XrWtw8WVKyQUUKMGKdZYtYoUKHFx5ACw7Mwy1mNLlgS2bCEzzrffttwTVc4xOWzrdf4KmkY2\nGYnIAOMPSp5bCWPGAN98w97pKuVKi/K95cuTtNSUFJLiKVROdZ4qj9dw6osXZP0qKoqE6exFqbBv\n0tStG3ma6dwZeMhDBzpO3z4PDw8sW7YMr7/+Oho0aID+/fujfv363K2yg4FbBlof5EBiY4kT++cf\nUv4uBkqFUhKd1Zs3B84nWE99uHCBzOZ/+IHkr7/+OuDvT5z6H3+QfUI+3ZhDqSQLg8+eWRYYW3th\nLafrWEpx44v5gXcwaZJtx+Sqcq06K0biITsb6NuXaJjwiapIhSJNEW+pibm55OmkcWNSEMTle8Us\ngtrD4MHkO9W9O/nsuMA5wtWlSxfcvHkTd+7cwbRp5tOuhObDlpZjoI4kNpZkcxw6RPJ1xULsmbku\nOaoXVscMGwZMmUIWHydMIPnfM2YAVasKbp5VSpYkAktXr7LTm7eHS08uCXJe3WKVyePtWyU+eu+o\n1TElS5IQmKcnCR/k8igmyFR3s12ns0RREclWqlqVn/Cnp8KT06Rp2jQSihwwgP1iuylcpgK0lLIU\netQVJ8Sjy5dfklnkoUOAn5+4tnjIPVBYVMi6aEQI/n3wL2SxMqOSZ1NcuECKqtatI7M7awuOjqZ0\nafKk9fffRB2Pb/66zn+z4qwsflJh2caDPT1JdouvL5n55lj/386KXFUubyGWL74g2Ss//cTPgi2z\nAGovMhmwYgXJMJo40X5paZdx5kkZSXa12+KTr78mj+OHDpHwgNgw+cW3n4n3uaw5vwYAkPpCnJRV\nXT5q9RHnc1SoQHKEZ88mVa8M3rPZx9LMpTB6e/Ibj1OpyOItky1hL40rN7apBsDDgxTGValCFkb5\nmKHzlcmybh35jW7dCpTgqb5QKecezlQqydP80aPAokX2ncNlnPmkfZNw/ak41acAWeD79VfpOHJd\n1EWO6UpvCuax+Eyq5SImRwikMRICXKlVizjyUaOA+P+n8pt78mhTrY3RvguPL5gc+9/L/3ixDyCz\nuwkTyKxv2TJg0et2egjY56wUCuI4K1fmx6Hz4czj4kjrw3/+ASpV4maPLp4KT16yxnx8iG0LF5Jw\nla24jDOf2noqrzrQbNFoSMYG48iZyjkpIUZjY4bV54la4bhd4yyO2/s2zxUUJvigpR1JxGZo3pzk\nz/fsSfRfzGGY4w2wqxTlynffkTx5JpOqfMnydp/L3gU+hYIUI1WsSJ4QuGS55BbmcioYunUL6N+f\nNFYxVD7kilJhOdvHFqpVI1ouY8bYfqxDnPk//wh/jVLKUkYiU0Kj0RAp2+3byV2/ShWHXp4VNcvV\ndIom10xxipC0DGzJ6/neeIPEXy3FpD9v+znSpqTpta3r/2d/Xu0wZPt2knq4c2dxQdDg8MF48KF9\nqbtcZp4KBQm5yGRk0dFSaqcl0nLScPPpTfuOTSMV2LNmkSInvuG6AGpIkybkqcZWHOLMhw0jGQpC\nkqvKdYhDYCgqIiXrBw9KY7HTHCU8SvA2axASMRdpuTBuHCk4MYdCrkDFUhXxex/H1LwnJJDwz7Zt\nRFebQS6T6wmy2QKX1DuAxIP/+IPov4wda/sC35X/rmDz1c123VByckiYp39/8rkIgbU8fHvoZkeQ\nwSHOfP16UroqpKBiTmGOw5x5YSG5QV28SJw5X1K2QsB1pZ1inanTM8y+xzTV5lNzxRypqSTss3w5\nCQPxxeHkw6ybUZujZEnyxHDxIknttMWhN1rRCD+c+8Hmz7CggEgNhITw26/WEK43O75wiDPv2pWU\nDnfuDNy7J8w1lsYvxYqzK4Q5uQ5ZWeTx+tkzUvXm4yP4JTnBlBpLHanr0FviowPmq3CYJw7GqQtF\nVhaZzY0bR+LTfFKgLsDJlJOcz1OmDFHV3LOHhDzY8Cy3uJGmLQ5TrSYFOQoFkRgQstiMrwVQrjhs\nAbR08y24P0KGpmOX4b5A/WG7BAuoLQsiShQZCdSuTR5jSzkuqmM3Ys4abGk80civkYCWFMP0S+XT\nueap8sy+V82nGgAguEIwb9czhBFza9mSZGvwzdhmY9GxJj/B5goViKrmhg2kJsPaDP3Oszs2X6Oo\niLR7e/aMhHeErlfgcwGUCw5x5jtv7UTfzX0BAOktJqBDB/67lbQOai1YyzSNhsi5vvoqEeNZvlwc\nrRV7KOFhuROKkDzOZt8ni4/KPjaMakICp0+yn/B2TnNpiXM6ztFmElXzqYa4oXG8XZNBowHefZc4\nrGXLhJmBHrl3BL9c/oW381WpAhw7RtLvPvjAcpOLE/dPaLd3Dtxp9dyFhURD5/59EtYp6YCWwHwv\ngNqLQ5z5G7/rN9AbP54I2z/gURfrZMpJbUsyPnnyhDy+/vwzqU4cMoT3SwiKmGEWKcxWDGGUDfls\nP2Zu8Tblvr5nbVq1KW/XJNclkwumqYRQE4xraddw+gG/GQz+/iQD7Nw5sv5kLm0x1C8UdX3r4uCQ\ng1Z7o2ZkkDWDFy9IYZejnpyFWAC1B1HyzD/8kKxqd+hAFm34gu9y/h07iMRnkyZEAKpOHV5P7xDE\nDLOYC2VE1YhyrCE6PHrxiPdz3kw3nTK34Wf9HHRbJFLZ8NVXRFpgzx4iNeBslCtHQi5PnxJRNVPK\ngZuvbcbN9Jt4tearFs91+DBp91erFpnxm+o2JRR8xsw1Gg22Xt+KlOe2hy5EKxqaPJloffPh0Bkx\nKV8vftJKHj0iMciPPiIznq+/lp5OCFu239yO9RfXi22GHnV9ib62GFo6jJgVnzFzc2sDXaJLoksX\n4qz4Zt48UgBz8KDwYm7h/uGCnbtUKXJDiooik6atW/Xj6AqZwqKUQH4+EWcbNIiobS5b5vjfKp8z\nc7VGjZg/YlDtu2o2HytqBeiUKUTQPiqK9G+0F+YuxrWllEZDVr7Dw0k608WLQLt2nE4pOqF+oSZ1\nrR3BnONzjPaNaTpGG5ZY13Odgy0q1j9Ra/iROPjlkvlY8riYcPTrR9ZaDNeIzCkkWlto1GiAzz4D\nfvyROHJHSEeMbTZWu3AsBAoFqaL+80/yt3XqRGo3ioqAH879gMy8TKNjNBrSvzQykjRhvniRZM2J\ngVRi5qIv4338MXncatOGNImNjrb9HPNPzAfArQ/o1avAe++RIoMDB0jrM1egdWBr3p5YbCUuOc5o\n3w/df8CYv0mtMlMX4IgcbIYJkRMwcc9E3vRqBm813/m3ffX2aP81yeBo1YrMpBkSnyUixDcE43eN\nx5oea5CaRR5PBzUaZPZ8+fmkzPv6dRL241NfxBJKhRIFRcKH6tq0AS5dIjIJkyeTbBSMAAKVYdi1\nizj9vDzg5k3SMOT5cyKRPGCAODr3DHxms5x/dN7uYyWhzTJmDEkhGjyYdES3tLptih/O/QDAvoyI\nhw+L4/d9+wKnTrmOIweKZXClxOTWk7G0y1KtqqO1eCifyGQyVPOpxtvM3Nq1ZDLimFauBAbq9E8Z\nsWMEEp8l4seEH5GVn6UV32pfo73Jc92/T2b4WVlk1uooRw44dubp4UHCrwkJZM0KAEo+bYmlS4lv\nWLOGJE7MmEEmYAMHiuvIAX7XpSbttbFziA6iz8wZ2rcnJf8DB5KZ8fr17ErkN1/dbNf10tKIfsWa\nNSQn9fp1aVdy2ouUGlQwhPiGIMQ3RDs7Zpy6o1DIFLzEzG1xcN26kToF36XkdWZeJnIKiAPouKEj\nWgYQ3RjDhs4qFemfOmcOCUtOmSJs02RTiJWtEdIgF9gG7PrsI9SR8G+TzwXQEyknrA8ygyRm5gw1\nahA934gIIDSUNPC1prT25p+2lbvdv09yW+vWJbOcS5dIHz5XdOSAdFrHmYJx4gqZQB2ALVyXjzAL\nowjJlgoV9F/3eZM4yLMPz2r7klbyJlPuvDyixNmsGclWOX2ahCQd7cgB8Socl59ZDgCoWErEdl0s\ncOvUREsolUT4/8ABorbYsCEp0sk0XgPRI21Kmtn31Gryg+jZk9woFArSV3LFCtLt3ZURY2Y+/fB0\nvQyPSqVMxwRkMhlaBbZCz7o9HWUaAJJrzkeY5WXBS07HT/nY2EF2bF8SzZuTp9L164GZM0n6XrBw\nBaRWEavCcfrh6QCA8l72y/c6AqksgHJy5lOmTEH9+vURHh6OmJgYPH/+nNVxx+4dszomLAzYu5d0\nZD92jMzahwwhxQAZJnSNDO/eKhXRc54wgTjszz8nTVPv3yexNyn0lXQESrnSyJnnFubi/d3vC3bN\nr45+hZ8SftK+rlzavMj7yZEnMbLJSMFsMQVfYRZ71mhqla+l3Q4NM3YA8+eT9Lp794gT79VLGjFh\nMZxVbFSsw69pDy5Rzv/aa6/h6tWruHjxIkJCQjBnjnEqmikSMyyo+RsQFUVyve/cIZ20FywgAu7K\nycGoMmwyAKBTUjxiYogA1uuvk3TCihVJdoq/P7kZnD0LvPMO6SLuTphaAB26bSiWxi91WGUokw7o\nyIVOS/AVZjly74jZ96a1Md3cvE6F4sqzVzcYfx6vvELavJWX0GRUjMKzfFU+ph4QqHM2z0hFaIvT\nAmi0Th5hixYtsGXLFlbH2fPYX7EiMGkSMHZCLjRFCnjPTcTjsgsBADEdg+DvTZrJMv8aNJCuxrgj\nUSqUyC/Qd9qbr5FF4xcFLxyiVli7fG2cfnAaY5uNFfxabOArzLLzlnmtEHMphoteX4QG3zfgfG1H\nopQrHe6sSs5ygKgKT7hczHzt2rXoyjJrP7fQvoaAMw7PQKnZpeA9V98BDe5fGjExJIzy2mtkNk8d\nOWHVuVUmi3cAoNKCShi2bZhF1T9bYb7Uc0/M1e77vtv3AEz3wxSDS08u2d21hg2aGRo09Gto8r16\nFXnuWeYAHD0zn3Os+Pv6btN3HXZde5HKzNyqM4+OjkajRo2M/v3999/aMbNmzYKnpyfeeust0yc5\nrPMvCXh/j33x2i+Pfmlyv7fSzWInNnDvub6A/PYb2/Ver7+4Hl6z+BOyMNXEoGwJ0rtMSt2ERuwY\nYfexkasj8fCFCSERFshkMlT3qW59oIRwdEz400Ofarffi3zPYde1F74+n7m/zNX3lTZiNcyyf/9+\ni++vW7cOu3btwsGDB80P6mCzXUZYiu86Sj7VGZnTcQ5+v1LcsqzXpl4mxxWqC6FUcBe1sJQzzrfQ\nFBfMyday4czDM3hri+mJCxtHHVM/BotOL7L7+o6GzwXQxGeJqFW+ltnfbMKjBL3XoX6hvFxXSPh6\ncpmWOE3fV5pfkjEJpzDLnj17sGDBAmzfvh0lWQgHDwgdYPe1vj/zvd3HujN+3n5Izky2Os7za35K\n6mUw/SPVzNBotb2dGebpgktoqntId77McQh8xYSfZD9B8NJgvPWXmSd4AE1WFTdlL/xC/NAFG1wi\nNXHChAnIzs5GdHQ0IiIiMG7cOIvjR0bYn4I2aR8pc13ZfSUA4KeeP+Gztp9hYouJdp/THbjw+AKy\n8rMAEF1qS/ARBtFAOqEUIZh3Yh4AbkJdplQAV3VfhcyPrRRTiARfMeF3/n4HALDxykarY2+Ov8mr\n5ryQSGUBlNOnddsGqcP8z/N5EVQa3XQ0RjcVTsHN1RgcNhhH7x0FAKTnpFsc+zz/uUW5UTaM2G5/\nLNoZuPjkIgCYTW1kU+DSpEoTo33vNH2Hm2ECwldM+O9bxetspsJ6W69v1W6H+IZwvp6jcJoFUD7Q\nzNDY7ciz8rN4zbZwN3R/MH9c/cPi2O6/cX/8T3icYH2QE8OEkcytDUTXskP2U+IIEUZgwnp3nt3R\nLprH/BEDALg67iqv1xIaPm52ic/Y196YQ9LPMTtv7TRqOUexDaacPz41Xqv/YQ4uIj/mcLVMI2bh\nzlw4ydyagTPDxwKfqZ6rC08txOR9pPCvedXm2v0NKjlXHj4fN7uXhdykIQCJO3PqyLnDVIC2WNNC\nlOszmuVSYnq76YIpNQaWDWQ9tnVQa5xMOSmIHXzCR9EQs26jC+PIAZIh5KzwETMfs3MMZzsk7cwN\nOTjEQvojxSSmtFkAIGliEjwVnihfsjxKzRbO4Tar2kywc9uLXCa3W5uFmXmbWyxmmxf9Y48fUb9i\nfbRe29ouOxwJHzNztp+3ZobzLaDzETPno2G2ZJ35xN3GWSpM70gKe+QyOe5m3DXaX6NcDe123md5\ngpVPS1HxTi6T260kyYRZzDkntjP+ERFkofjx5MfYemOrldHiopAroNFooC5SQyG3T66Y6QbmiriE\n0BYXuv/WHbJYGd7dabpcd0n8EqN9AWVdXK9WAB5nP7Y6Rkh9Fkc3nmCDXCa3O7VQOzPnKQXTv7Q/\n3m3m2iXrGo0Gay+stTrOkoy1lOH65MJXc3GH/9JaBpKOKv/c/gcAsPLcSovjL71ruvEthR3NA5pb\nHyQgUswVVsjtl8BljjMVZtF92nE1uDQ5Sckq7mbtU8LH6P2i6UXQzNBIvgmFObgsgN5Ov43j948b\n7bdHYdThztxUI4I/r/2p9/pF/gvtdiP/RoLb5MqYcqaW4pLPcp/xen259Pqf2B0zz1Pl4dfLv2q3\nDUmamMTZNqnCZfap+1lv7mfc5tHZ5Ti4LIDG/BGD9uuM+74GlQ2y+VwO/6WZWr3vt7mf3usVZ1cA\nAALKFIdVmMpPirBwkU0wFdLpH9qfizmCYK+eeenZxdoyt5+xL5hzBXQzWm48vYEHWQ8sjpfFyrTK\nlLpPMYYFU6mTUnm21PFwCUGZC0PaE550uDPXddC6/HX9LwDAkeQj+PjAxwCA2xPID0YzQ0OrPjkQ\nGRCp3bb2KPvF4S/suka+Kh9Vvq1itP+12q/ZdT4hkcvkSM+1XA1rCj400J0V3Zl5/eX1EbTI+syx\n3nIi96u7vuBbylfvCaZqGedv+cVlAfTSE+MwcmRAJPo16GditGUc7szHNjfdoKDPH33w6MUjRK2P\n0u7zUvInzerOMF+0SS0n4fuupmfe/Rtym0Fn5klTV8QUGy5uwPqL68U2w6ngEheuvaS23usa5Wqg\naHoRiqbzs/AnNnxXyP476l90qdPF5uNEnZkb3n3arWvnaHPcgguPLwAAvn39W/RraPqOP6nVJEea\nJCqPsh/pvT6Vcspi2CW7IBtPc54KbZaksWX2qRs2NZePL5PJnD5WzqCQkc5V6iI1kjKSIIsV5+9y\nuDOv4FVBux3iG4K1PYpTlu48u6PdVsjsy2el2IctlYum2Je4jydLhMew5L712tbYc2eP2fFl5pRB\npQWVhDZL0tgSF9ZNaDh2v7h5+9TWztHT01ZkMpn28wn/IVw0OxzuzHXvxqObjsbwiOE4Ptw4NcdZ\ntIxdBcPY5fL45doZPRteFLywPkgi6H4HmUwLrvFwV1+gZzI2bA0n/PfyP+329PbT+TZLMijlJHWT\n+R2wqe/gG1HzxqqUJgtmr1R7RW//ks5LXOYRzBmZfWw2xu8ej4iVEayPSXtZXPDBpJ/qLrxKldXn\nVgPgLpDlrDnSbGEWQA1DVIZc/U9f8XDS3uLwnSOah4uFYermNye/cbgNojhzuUyOsiXKmm1T5gx9\n/5yJ32J+YzWuQw3Ss+qzQ5/ZfI2/bvyl3f6jH5HafSvUfEcZMdF13Gk55CbEdfLg5+3aHcTZFg2F\nrtBv86ZbMCTFAjK+MAxD2SsFzWVSIYozV09X4/knz/X26XZZkWIJuDMzsNFAVgJG/qX9jfaxyceW\nxcr0UqyY/3/BFYJtsNJx6DpupqUe1+9cm2ptOB0vdZiZp6pIhRrlanDSt3FFDBeISyisP4WYWhwu\nmmF/ho9kbpU+JY3LfCmOxcvDOBX0Wto1m6tw5TI51NPVTnFTZm5CrqhDzidM0dChpENIzkxGKWUp\n5Kvy4eEpGRciKobpiYeSDlk95t7ze7zaIKlfm2aGxiklMF2F95obh7eY7i/myFflG+2Ty+SSduS6\njRB8S/kCcP6ScqFhZuZMxllOYQ6e5+s/XecW5ophmiQwLOnPVxv/Lgxh0wvVFjj/4r799lvI5XI8\ne8avpgfF8ZjqTWntB8pHhxRHM7vjbG2PSUspiZRimJlnm2pt0Dm4MwDg/vP7emOsLY66MkzMPKpG\nFOtjph2cxqsNnJx5SkoK9u/fj+rVq/NlD0VEZDIZzo8+r7cv9YVl7YzsgmwhTRIEhUxhtpiFYhom\nJpxbmKttBfj10a9xJvUMFp5aCEB/feWX3r/oHS/FjlN8ovv52MuHLT/kZAMnZz5p0iTMn++6ovPu\nSHhl24oeqn/nfDdyUxK4SRn2KR5OajkJTz4y7m/pajBhlVxVrlZmIzkzGZFrIrXt35bGL9WOHxQ2\nSO94U7UkrgQThuLSfP7rV7/mZIPdznz79u0IDAxEWFgYJwMo0kIukyN7WrbdPz5n0J83JYE7btc4\no+Kv8J0AAA6CSURBVHEpz1O02S7m8FJ6uXxaIgBsu7EN7+16D7mFufDy8EK3Ot3wfov3te8v/Xep\ntkBo58CdRsdHVGFfs+CMMGGoXFUuxjQdg061Otl8Dq5PLxaXoqOjo/H4sXEl06xZszBnzhzs21dc\nwm3psXXmzJna7aioKERFRdluKcVheHt6GxVyscUZ9Oet6ZnXWVoH4f7h2HJ9C1Z0W2HxXL5evnyb\nJ0kiAyJRv2J9MjP38EJQ2SC91MT397yP8iVJi8DXg18Xy0zRYBZA81R5qFW+FjLyMgCQNRmFTIHo\n2tFWzxEXF4e4uDi7bbDozPfv329y/5UrV5CUlITwcPJI/uDBAzRt2hTx8fHw8zOepeg6cwpFbKw5\n8zvP7mjDLvNOzLN4rgktJvBqm1TpGtwVao0auYW5KOlR0mRbR8aBGeoqPZ3i+iJlzAJobmEudt/Z\njbjkOGzquwldfiXqh9ay9E6MOIHWQa31JrqxsbE22WBXmCU0NBRPnjxBUlISkpKSEBgYiPPnz5t0\n5BSK1LCl05C1qkdXrmrUxdvTGy8LXmpj5l3rdEWver1MjmXSPJmiMV1xPVdFuwCqykXbam21+9mm\n6PKxQMzLN5Hm6FKcCUvOnMnI4Kths6tQSlkKOYU5kMvkqFiqIjzkHth7Z6/FY66/dx2Xn1x2C//A\nxMzzVHnoVKsT9t8lUQ22k4b6FetztoEXZ3737l0+TkOhOAS5TG426yCnMAcAfx3TXQVvpTdeFr6E\nh9wDXkov7Li5w+oxHnIPl1/4ZFDKlUjPTYeqSAVvpbfJYjoAmLBrAoo0RVjebbl236PJj3gRIZNu\nmR5FdKJrkUWbo/eOAiDNnnU1WOxtlSU2cpkcGXkZOP3gtNF7Lda0EMEi6ePtSZw5swBK0cdT4Ylb\n6bcAkJtYwuMEo6SQkKUhWHZmGb4/q9/tq3LpyrzYQJ05xSxMqTvTk9V3vq+e+P7y+OV645d1WeY4\n4zjAxDENNaeP3juK60+v6+2zVjTlLjBhFiZmztzoPRWeIlsmDZRyJTQaDer61sWNpzcA6Jf0X0u7\nJngTcOrMKWYZ0XgEAODm05smW2EZNkV2Fulixpkbzpzar2svhjlOgbeSLICefXgWcpkcs16dhTKe\nZVCgLkDt8rWtn8DF8VR4IjM/E96e3mgeQLR/dDunnUo5pTf+QdYD3m2gzpxiFka/hEk5Yzh2j7QC\nm3VslsNt4gPGmbMRQ6IQmJn5rfRbWH1+NcqWKKstlhocNlg7rkfdHmKZKCqeCk9k5GbAW+mN6j6k\nKjo9p3iy8/etv/XGBy0K4t0G6swpZqnkbbrvZbt17RCXHKe3L+PjDJNjpQjjzKnsLXuYmDlAJAxy\nVblIzEgEAPRp0Ec7zlX7fFpDqVAiIy8D3p7eUMhJnn3U+ijt+4YKk0JAnTnFLJYaU3RY30G7vbX/\nVpQrWc4RJvGC1pm7QcocXzBhlkZ+jVDNpxpKe5bWvhfqV9xdqFVQKzHMEx3dmTlg3CDdcPLDUMaz\nDG82UGdOMYvuD9YS9uhQiAlfWuuGP1hXhgmz5KvzUdKjpNkuUlLWsRcSpVyJzLxM7W+GbUycz8/L\nPcrXKHbhqjNXw3Jze3GnMA0TZklPT3fpxsz24qnwJGGW/8/M2fJJm094s4E6cwpn2M7gpYK5bBZ7\nz+MOlPQoqS20ysrPMnr/l96/oH0N980GUiqUyC7Ihrenbc6cESfjA/f5NlIo/4dZoOJa5elOzlz3\nbzVVej4obJBbhZ0MYfLtDWfm3UO6O8wG9/k2Uij/h3FMunnA9tC1Tlc+zHE6lAql2CZIDqWcfCaG\nM3PdfrOm4DOUSZ05xW2ZHjed0/GTW03myRKKs8PMzJlqaYaRESMtHlfSoyRvNlBnTnF7bF3IrFex\nHjnORReI2ZI+NR23Jwhbou4sMJpFjMwBQ0DZAL2w1Iz2M/Te79egH282UGdOscgrQfZ1HJI63ep0\n027b6pSr+VTj2xynpIJXBbMpiu4G06xjSuspAEhh1dhmYwEAR4cf1Y4zjKnzGbKizpxiEcOZxMV3\nL+q95rPowZH8c/sf7bYtM/OIyhHa7B13Sk2kWGZii4kAgLScNADAt69/i++7EXVESw1M+FxEp86c\nYhHD3oVh/voNvK+9d82R5ohO1TJVtdvuFma5+O5F3HjvhthmSJKBoQMBAFE1oozes1QdTZ05RRQ+\nbPkhAGBzv83afXzmyYrF0PChdh3nbjPzMP8w1K1YV2wzJEmLwBZY2mUp/L39Tb6/5c0t+L3P74JK\nBtOiIQor6lWsh4WvLwQAVCxVUbufz9V4sbBFV6Zx5cYYEDoAf13/S0CLKM7I+MjxZt+LqR8DAMhX\n5aNVUCs0r9oc6y6s4/X6nGbmS5cuRf369REaGoqPP/7Y+gEUp+XY8GPabd0ZKVOA48x83u5z1mO/\n6vCVVljK3cIsFO6U8CiByIBIyGQyDI8Yzuu57Z6ZHz58GDt27MClS5egVCqRlpbGp10UCaGZoV/2\n7mpOrLwX+1CR7t/ubmEWirSxe2a+YsUKTJs2DUolSa2pVMm09jXF9SihoEJLuwft1lsMpVDExm5n\nfvv2bRw9ehQtW7ZEVFQUzp49y6ddFAkTGRAJwL0rIDsHd3a5JxSKc2MxzBIdHY3Hjx8b7Z81axZU\nKhUyMjJw+vRpnDlzBm+++Sbu3r0rmKEU6SCTyYxCL65OzXI1oSpSiW0GhWIWi858//79Zt9bsWIF\nYmLICm3z5s0hl8uRnp4OX19fo7EzZ87UbkdFRSEqKso+aykUkbgy7gpnlUUKxRJxcXGIi4uz+3iZ\nxk5R55UrV+Lhw4eIjY3FrVu30KlTJ9y/f9/4AjIZZ91oCoVvGn7fENfSSMGTZoYGsljLIRN3exKh\niI+tvtPumPmIESNw9+5dNGrUCAMHDsSGDRvsPRWF4nC61zGtM83kA1MozobdqYlKpRI///wzn7ZQ\nKA7D3OLllje3aGfpYf5hWjU8CkXq0HJ+ilvCRhODScEcFTFKaHMoFM7Qcn6KW2JY8DO6yWgj3ZGh\n4UNx5uEZ1Cpfy5GmUSh2QWfmFAqAlW+sxKRWkwAAP3T7AQDQpU4XMU2iUGyCOnMKxYABoQMAgM7I\nKU4FdeYUt8RS9aZPSR+9VETawJjiDNCYOYVigX9H/WvUkINCkSLUmVPcGsOejIYwOjQUitShYRaK\nW1LXl2Su7Bq0S2RLKBR+oM6c4pa8HfY2AFCpCYrLQJ05xS1hFkCpeBbFVaDOnOLWaEBn5hTXgDpz\nittS3ac66lWsJ7YZFAov2C2By/oCVAKXQqFQbMZhErgUCoVCkQ7UmVMoFIoLQJ05hUKhuADUmVMo\nFIoLQJ05hUKhuADUmVMoFIoLYLczj4+PR2RkJCIiItC8eXOcOXOGT7soFAqFYgN2O/OpU6fiq6++\nQkJCAr788ktMnTqVT7soZoiLixPbBJeCfp78QT9LcbHbmVepUgXPnz8HAGRmZiIgIIA3oyjmoT8Y\nfqGfJ3/Qz1Jc7NYznzt3Ltq0aYOPPvoIRUVFOHXqFJ92USgUCsUGLDrz6OhoPH782Gj/rFmzsGTJ\nEixZsgS9e/fG5s2bMWLECOzfv18wQykUCoViHru1WcqWLYusrCwARBO6XLly2rCLLsHBwUhMTORm\nJYVCobgZtWvXxp07d1iPtzvMEhwcjCNHjqB9+/Y4dOgQQkJCTI6zxRgKhUKh2IfdznzVqlV47733\nkJ+fDy8vL6xatYpPuygUCoViA4JL4FIoFApFeAStAN2zZw/q1auHOnXqYN68eUJeyi2oUaMGwsLC\nEBERgchI2jXeFkaMGAF/f380atRIu+/Zs2eIjo5GSEgIXnvtNWRmZopooXNh6vOcOXMmAgMDERER\ngYiICOzZs0dEC52HlJQUdOjQAQ0bNkRoaCiWLFkCwPbvp2DOXK1WY/z48dizZw+uXbuG33//Hdev\nXxfqcm6BTCZDXFwcEhISEB8fL7Y5TsXw4cONnMvcuXMRHR2NW7duoWPHjpg7d65I1jkfpj5PmUyG\nSZMmISEhAQkJCejcubNI1jkXSqUSixYtwtWrV3H69GksX74c169ft/n7KZgzj4+PR3BwMGrUqAGl\nUokBAwZg+/btQl3ObaBRMfto27Ytypcvr7dvx44dGDp0KABg6NCh2LZtmximOSWmPk+Afj/toXLl\nymjcuDEAoHTp0qhfvz5SU1Nt/n4K5sxTU1MRFBSkfR0YGIjU1FShLucWyGQydOrUCc2aNcPq1avF\nNsfpefLkCfz9/QEA/v7+ePLkicgWOT9Lly5FeHg4Ro4cScNWdpCcnIyEhAS0aNHC5u+nYM5cJpMJ\ndWq35cSJE0hISMDu3buxfPlyHDt2TGyTXAaZTEa/sxwZO3YskpKScOHCBVSpUgWTJ08W2ySnIjs7\nG3369MHixYtRpkwZvffYfD8Fc+YBAQFISUnRvk5JSUFgYKBQl3MLqlSpAgCoVKkSevfuTePmHPH3\n99dWOD969Ah+fn4iW+Tc+Pn5aZ3OqFGj6PfTBgoLC9GnTx8MHjwYvXr1AmD791MwZ96sWTPcvn0b\nycnJKCgowKZNm9CjRw+hLufy5OTk4MWLFwCAly9fYt++fXqZBBTb6dGjB9avXw8AWL9+vfZHRLGP\nR48eabe3bt1Kv58s0Wg0GDlyJBo0aIAPPvhAu9/m76dGQHbt2qUJCQnR1K5dWzN79mwhL+Xy3L17\nVxMeHq4JDw/XNGzYkH6eNjJgwABNlSpVNEqlUhMYGKhZu3atJj09XdOxY0dNnTp1NNHR0ZqMjAyx\nzXQaDD/PH3/8UTN48GBNo0aNNGFhYZqePXtqHj9+LLaZTsGxY8c0MplMEx4ermncuLGmcePGmt27\nd9v8/aRFQxQKheIC0LZxFAqF4gJQZ06hUCguAHXmFAqF4gJQZ06hUCguAHXmFAqF4gJQZ06hUCgu\nAHXmFAqF4gJQZ06hUCguwP8AQjBUj8cdLE8AAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0xc30f210>"
       ]
      }
     ],
     "prompt_number": 286
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "del t, q, dq, tau, q_raw, tau_raw"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 287
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "4 - Dynamic Parameter Estimation\n",
      "================================"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import os\n",
      "import pickle\n",
      "import sympy\n",
      "import numpy\n",
      "import time\n",
      "\n",
      "import sympybotics\n",
      "import lmi_sdp\n",
      "\n",
      "from lmi_sdp import init_lmi_latex_printing\n",
      "init_lmi_latex_printing()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 55
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "with open(tmpfolder +  'robotmodels/wam7_model.pkl', 'rb' ) as file:\n",
      "          rbt = pickle.load( file )"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 56
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "epsilon_safemargin = 1e-6\n",
      "epsilon_sdptol = 1e-7"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 85
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## LMI Matrix Definitions"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "dof = rbt.dof\n",
      "\n",
      "delta = rbt.dyn.dynparms\n",
      "n_delta = rbt.dyn.n_dynparms\n",
      "\n",
      "beta = rbt.dyn.baseparms.n()\n",
      "n_beta = rbt.dyn.n_base\n",
      "beta_symbs = sympy.Matrix([sympy.Symbol('beta'+str(i+1),real=True) for i in range(n_beta)])\n",
      "\n",
      "delta_d = (rbt.dyn.Pd.T*delta)\n",
      "n_delta_d = len(delta_d)\n",
      "\n",
      "Pb = rbt.dyn.Pb\n",
      "\n",
      "varchange_dict = dict(zip(Pb.T*delta ,  beta_symbs - ( beta - Pb.T*delta )))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 57
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from support_funcs.utils import skew, mrepl\n",
      "from sympy import BlockMatrix, Matrix, eye, Identity\n",
      "I = Identity\n",
      "S = skew"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 58
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "D_inertia_blocks = []\n",
      "for i in range(dof):\n",
      "    L = rbt.rbtdef.L[i]\n",
      "    l = rbt.rbtdef.l[i]\n",
      "    m = rbt.rbtdef.m[i]\n",
      "    Di = BlockMatrix([[L,    S(l).T],\n",
      "                      [S(l), I(3)*m]])\n",
      "    D_inertia_blocks.append(Di.as_explicit())"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 59
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "D_inertia_blocks[0]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$\\left[\\begin{smallmatrix}{}L_{1xx} & L_{1xy} & L_{1xz} & 0 & l_{1z} & - l_{1y}\\\\L_{1xy} & L_{1yy} & L_{1yz} & - l_{1z} & 0 & l_{1x}\\\\L_{1xz} & L_{1yz} & L_{1zz} & l_{1y} & - l_{1x} & 0\\\\0 & - l_{1z} & l_{1y} & m_{1} & 0 & 0\\\\l_{1z} & 0 & - l_{1x} & 0 & m_{1} & 0\\\\- l_{1y} & l_{1x} & 0 & 0 & 0 & m_{1}\\end{smallmatrix}\\right]$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAQUAAABlCAMAAABzywZNAAAAP1BMVEX///8AAAAAAAAAAAAAAAAA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\nA609zB9+hP9bIvaXOP0PRDCBhIb27XMAAAAASUVORK5CYII=\n",
       "prompt_number": 288,
       "text": [
        "\u23a1L\u2081\u2093\u2093   L_1xy  L_1xz    0    l_1z  -l_1y\u23a4\n",
        "\u23a2                                       \u23a5\n",
        "\u23a2L_1xy  L_1yy  L_1yz  -l_1z   0     l\u2081\u2093 \u23a5\n",
        "\u23a2                                       \u23a5\n",
        "\u23a2L_1xz  L_1yz  L_1zz  l_1y   -l\u2081\u2093    0  \u23a5\n",
        "\u23a2                                       \u23a5\n",
        "\u23a2  0    -l_1z  l_1y    m\u2081     0      0  \u23a5\n",
        "\u23a2                                       \u23a5\n",
        "\u23a2l_1z     0    -l\u2081\u2093     0     m\u2081     0  \u23a5\n",
        "\u23a2                                       \u23a5\n",
        "\u23a3-l_1y   l\u2081\u2093     0      0     0     m\u2081  \u23a6"
       ]
      }
     ],
     "prompt_number": 288
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "D_other_blocks = []\n",
      "for i in range(dof):\n",
      "    if rbt.rbtdef.driveinertiamodel == 'simplified':\n",
      "        D_other_blocks.append( Matrix([rbt.rbtdef.Ia[i]]) )\n",
      "    if 'viscous' in rbt.rbtdef.frictionmodel:\n",
      "        D_other_blocks.append( Matrix([rbt.rbtdef.fv[i]]) )\n",
      "    if 'Coulomb' in rbt.rbtdef.frictionmodel:\n",
      "        D_other_blocks.append( Matrix([rbt.rbtdef.fc[i]]) )"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 61
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "D_blocks = D_inertia_blocks + D_other_blocks"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 62
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "D_blocks"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$\\begin{bmatrix}\\left[\\begin{smallmatrix}{}L_{1xx} & L_{1xy} & L_{1xz} & 0 & l_{1z} & - l_{1y}\\\\L_{1xy} & L_{1yy} & L_{1yz} & - l_{1z} & 0 & l_{1x}\\\\L_{1xz} & L_{1yz} & L_{1zz} & l_{1y} & - l_{1x} & 0\\\\0 & - l_{1z} & l_{1y} & m_{1} & 0 & 0\\\\l_{1z} & 0 & - l_{1x} & 0 & m_{1} & 0\\\\- l_{1y} & l_{1x} & 0 & 0 & 0 & m_{1}\\end{smallmatrix}\\right], & \\left[\\begin{smallmatrix}{}L_{2xx} & L_{2xy} & L_{2xz} & 0 & l_{2z} & - l_{2y}\\\\L_{2xy} & L_{2yy} & L_{2yz} & - l_{2z} & 0 & l_{2x}\\\\L_{2xz} & L_{2yz} & L_{2zz} & l_{2y} & - l_{2x} & 0\\\\0 & - l_{2z} & l_{2y} & m_{2} & 0 & 0\\\\l_{2z} & 0 & - l_{2x} & 0 & m_{2} & 0\\\\- l_{2y} & l_{2x} & 0 & 0 & 0 & m_{2}\\end{smallmatrix}\\right], & \\left[\\begin{smallmatrix}{}L_{3xx} & L_{3xy} & L_{3xz} & 0 & l_{3z} & - l_{3y}\\\\L_{3xy} & L_{3yy} & L_{3yz} & - l_{3z} & 0 & l_{3x}\\\\L_{3xz} & L_{3yz} & L_{3zz} & l_{3y} & - l_{3x} & 0\\\\0 & - l_{3z} & l_{3y} & m_{3} & 0 & 0\\\\l_{3z} & 0 & - l_{3x} & 0 & m_{3} & 0\\\\- l_{3y} & l_{3x} & 0 & 0 & 0 & m_{3}\\end{smallmatrix}\\right], & \\left[\\begin{smallmatrix}{}L_{4xx} & L_{4xy} & L_{4xz} & 0 & l_{4z} & - l_{4y}\\\\L_{4xy} & L_{4yy} & L_{4yz} & - l_{4z} & 0 & l_{4x}\\\\L_{4xz} & L_{4yz} & L_{4zz} & l_{4y} & - l_{4x} & 0\\\\0 & - l_{4z} & l_{4y} & m_{4} & 0 & 0\\\\l_{4z} & 0 & - l_{4x} & 0 & m_{4} & 0\\\\- l_{4y} & l_{4x} & 0 & 0 & 0 & m_{4}\\end{smallmatrix}\\right], & \\left[\\begin{smallmatrix}{}L_{5xx} & L_{5xy} & L_{5xz} & 0 & l_{5z} & - l_{5y}\\\\L_{5xy} & L_{5yy} & L_{5yz} & - l_{5z} & 0 & l_{5x}\\\\L_{5xz} & L_{5yz} & L_{5zz} & l_{5y} & - l_{5x} & 0\\\\0 & - l_{5z} & l_{5y} & m_{5} & 0 & 0\\\\l_{5z} & 0 & - l_{5x} & 0 & m_{5} & 0\\\\- l_{5y} & l_{5x} & 0 & 0 & 0 & m_{5}\\end{smallmatrix}\\right], & \\left[\\begin{smallmatrix}{}L_{6xx} & L_{6xy} & L_{6xz} & 0 & l_{6z} & - l_{6y}\\\\L_{6xy} & L_{6yy} & L_{6yz} & - l_{6z} & 0 & l_{6x}\\\\L_{6xz} & L_{6yz} & L_{6zz} & l_{6y} & - l_{6x} & 0\\\\0 & - l_{6z} & l_{6y} & m_{6} & 0 & 0\\\\l_{6z} & 0 & - l_{6x} & 0 & m_{6} & 0\\\\- l_{6y} & l_{6x} & 0 & 0 & 0 & m_{6}\\end{smallmatrix}\\right], & \\left[\\begin{smallmatrix}{}L_{7xx} & L_{7xy} & L_{7xz} & 0 & l_{7z} & - l_{7y}\\\\L_{7xy} & L_{7yy} & L_{7yz} & - l_{7z} & 0 & l_{7x}\\\\L_{7xz} & L_{7yz} & L_{7zz} & l_{7y} & - l_{7x} & 0\\\\0 & - l_{7z} & l_{7y} & m_{7} & 0 & 0\\\\l_{7z} & 0 & - l_{7x} & 0 & m_{7} & 0\\\\- l_{7y} & l_{7x} & 0 & 0 & 0 & m_{7}\\end{smallmatrix}\\right], & \\left[\\begin{smallmatrix}{}Ia_{1}\\end{smallmatrix}\\right], & \\left[\\begin{smallmatrix}{}fv_{1}\\end{smallmatrix}\\right], & \\left[\\begin{smallmatrix}{}fc_{1}\\end{smallmatrix}\\right], & \\left[\\begin{smallmatrix}{}Ia_{2}\\end{smallmatrix}\\right], & \\left[\\begin{smallmatrix}{}fv_{2}\\end{smallmatrix}\\right], & \\left[\\begin{smallmatrix}{}fc_{2}\\end{smallmatrix}\\right], & \\left[\\begin{smallmatrix}{}Ia_{3}\\end{smallmatrix}\\right], & \\left[\\begin{smallmatrix}{}fv_{3}\\end{smallmatrix}\\right], & \\left[\\begin{smallmatrix}{}fc_{3}\\end{smallmatrix}\\right], & \\left[\\begin{smallmatrix}{}Ia_{4}\\end{smallmatrix}\\right], & \\left[\\begin{smallmatrix}{}fv_{4}\\end{smallmatrix}\\right], & \\left[\\begin{smallmatrix}{}fc_{4}\\end{smallmatrix}\\right], & \\left[\\begin{smallmatrix}{}Ia_{5}\\end{smallmatrix}\\right], & \\left[\\begin{smallmatrix}{}fv_{5}\\end{smallmatrix}\\right], & \\left[\\begin{smallmatrix}{}fc_{5}\\end{smallmatrix}\\right], & \\left[\\begin{smallmatrix}{}Ia_{6}\\end{smallmatrix}\\right], & \\left[\\begin{smallmatrix}{}fv_{6}\\end{smallmatrix}\\right], & \\left[\\begin{smallmatrix}{}fc_{6}\\end{smallmatrix}\\right], & \\left[\\begin{smallmatrix}{}Ia_{7}\\end{smallmatrix}\\right], & \\left[\\begin{smallmatrix}{}fv_{7}\\end{smallmatrix}\\right], & \\left[\\begin{smallmatrix}{}fc_{7}\\end{smallmatrix}\\right]\\end{bmatrix}$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 289,
       "text": [
        "\u23a1\u23a1L\u2081\u2093\u2093   L_1xy  L_1xz    0    l_1z  -l_1y\u23a4, \u23a1L\u2082\u2093\u2093   L_2xy  L_2xz    0    l_2z \n",
        "\u23a2\u23a2                                       \u23a5  \u23a2                                 \n",
        "\u23a2\u23a2L_1xy  L_1yy  L_1yz  -l_1z   0     l\u2081\u2093 \u23a5  \u23a2L_2xy  L_2yy  L_2yz  -l_2z   0   \n",
        "\u23a2\u23a2                                       \u23a5  \u23a2                                 \n",
        "\u23a2\u23a2L_1xz  L_1yz  L_1zz  l_1y   -l\u2081\u2093    0  \u23a5  \u23a2L_2xz  L_2yz  L_2zz  l_2y   -l\u2082\u2093 \n",
        "\u23a2\u23a2                                       \u23a5  \u23a2                                 \n",
        "\u23a2\u23a2  0    -l_1z  l_1y    m\u2081     0      0  \u23a5  \u23a2  0    -l_2z  l_2y    m\u2082     0   \n",
        "\u23a2\u23a2                                       \u23a5  \u23a2                                 \n",
        "\u23a2\u23a2l_1z     0    -l\u2081\u2093     0     m\u2081     0  \u23a5  \u23a2l_2z     0    -l\u2082\u2093     0     m\u2082  \n",
        "\u23a2\u23a2                                       \u23a5  \u23a2                                 \n",
        "\u23a3\u23a3-l_1y   l\u2081\u2093     0      0     0     m\u2081  \u23a6  \u23a3-l_2y   l\u2082\u2093     0      0     0   \n",
        "\n",
        " -l_2y\u23a4, \u23a1L\u2083\u2093\u2093   L_3xy  L_3xz    0    l_3z  -l_3y\u23a4, \u23a1L\u2084\u2093\u2093   L_4xy  L_4xz    0 \n",
        "      \u23a5  \u23a2                                       \u23a5  \u23a2                         \n",
        "  l\u2082\u2093 \u23a5  \u23a2L_3xy  L_3yy  L_3yz  -l_3z   0     l\u2083\u2093 \u23a5  \u23a2L_4xy  L_4yy  L_4yz  -l_4\n",
        "      \u23a5  \u23a2                                       \u23a5  \u23a2                         \n",
        "   0  \u23a5  \u23a2L_3xz  L_3yz  L_3zz  l_3y   -l\u2083\u2093    0  \u23a5  \u23a2L_4xz  L_4yz  L_4zz  l_4y\n",
        "      \u23a5  \u23a2                                       \u23a5  \u23a2                         \n",
        "   0  \u23a5  \u23a2  0    -l_3z  l_3y    m\u2083     0      0  \u23a5  \u23a2  0    -l_4z  l_4y    m\u2084 \n",
        "      \u23a5  \u23a2                                       \u23a5  \u23a2                         \n",
        "   0  \u23a5  \u23a2l_3z     0    -l\u2083\u2093     0     m\u2083     0  \u23a5  \u23a2l_4z     0    -l\u2084\u2093     0 \n",
        "      \u23a5  \u23a2                                       \u23a5  \u23a2                         \n",
        "  m\u2082  \u23a6  \u23a3-l_3y   l\u2083\u2093     0      0     0     m\u2083  \u23a6  \u23a3-l_4y   l\u2084\u2093     0      0 \n",
        "\n",
        "   l_4z  -l_4y\u23a4, \u23a1L\u2085\u2093\u2093   L_5xy  L_5xz    0    l_5z  -l_5y\u23a4, \u23a1L\u2086\u2093\u2093   L_6xy  L_6\n",
        "              \u23a5  \u23a2                                       \u23a5  \u23a2                 \n",
        "z   0     l\u2084\u2093 \u23a5  \u23a2L_5xy  L_5yy  L_5yz  -l_5z   0     l\u2085\u2093 \u23a5  \u23a2L_6xy  L_6yy  L_6\n",
        "              \u23a5  \u23a2                                       \u23a5  \u23a2                 \n",
        "   -l\u2084\u2093    0  \u23a5  \u23a2L_5xz  L_5yz  L_5zz  l_5y   -l\u2085\u2093    0  \u23a5  \u23a2L_6xz  L_6yz  L_6\n",
        "              \u23a5  \u23a2                                       \u23a5  \u23a2                 \n",
        "    0      0  \u23a5  \u23a2  0    -l_5z  l_5y    m\u2085     0      0  \u23a5  \u23a2  0    -l_6z  l_6\n",
        "              \u23a5  \u23a2                                       \u23a5  \u23a2                 \n",
        "    m\u2084     0  \u23a5  \u23a2l_5z     0    -l\u2085\u2093     0     m\u2085     0  \u23a5  \u23a2l_6z     0    -l\u2086\n",
        "              \u23a5  \u23a2                                       \u23a5  \u23a2                 \n",
        "    0     m\u2084  \u23a6  \u23a3-l_5y   l\u2085\u2093     0      0     0     m\u2085  \u23a6  \u23a3-l_6y   l\u2086\u2093     0\n",
        "\n",
        "xz    0    l_6z  -l_6y\u23a4, \u23a1L\u2087\u2093\u2093   L_7xy  L_7xz    0    l_7z  -l_7y\u23a4, [Ia\u2081], [fv\n",
        "                      \u23a5  \u23a2                                       \u23a5            \n",
        "yz  -l_6z   0     l\u2086\u2093 \u23a5  \u23a2L_7xy  L_7yy  L_7yz  -l_7z   0     l\u2087\u2093 \u23a5            \n",
        "                      \u23a5  \u23a2                                       \u23a5            \n",
        "zz  l_6y   -l\u2086\u2093    0  \u23a5  \u23a2L_7xz  L_7yz  L_7zz  l_7y   -l\u2087\u2093    0  \u23a5            \n",
        "                      \u23a5  \u23a2                                       \u23a5            \n",
        "y    m\u2086     0      0  \u23a5  \u23a2  0    -l_7z  l_7y    m\u2087     0      0  \u23a5            \n",
        "                      \u23a5  \u23a2                                       \u23a5            \n",
        "\u2093     0     m\u2086     0  \u23a5  \u23a2l_7z     0    -l\u2087\u2093     0     m\u2087     0  \u23a5            \n",
        "                      \u23a5  \u23a2                                       \u23a5            \n",
        "      0     0     m\u2086  \u23a6  \u23a3-l_7y   l\u2087\u2093     0      0     0     m\u2087  \u23a6            \n",
        "\n",
        "\u2081], [fc\u2081], [Ia\u2082], [fv\u2082], [fc\u2082], [Ia\u2083], [fv\u2083], [fc\u2083], [Ia\u2084], [fv\u2084], [fc\u2084], [Ia\u2085\n",
        "                                                                              \n",
        "                                                                              \n",
        "                                                                              \n",
        "                                                                              \n",
        "                                                                              \n",
        "                                                                              \n",
        "                                                                              \n",
        "                                                                              \n",
        "                                                                              \n",
        "                                                                              \n",
        "\n",
        "], [fv\u2085], [fc\u2085], [Ia\u2086], [fv\u2086], [fc\u2086], [Ia\u2087], [fv\u2087], [fc\u2087]\u23a4\n",
        "                                                         \u23a5\n",
        "                                                         \u23a5\n",
        "                                                         \u23a5\n",
        "                                                         \u23a5\n",
        "                                                         \u23a5\n",
        "                                                         \u23a5\n",
        "                                                         \u23a5\n",
        "                                                         \u23a5\n",
        "                                                         \u23a5\n",
        "                                                         \u23a6"
       ]
      }
     ],
     "prompt_number": 289
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Change of Variable Space"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "varchange_dict = dict(zip(Pb.T*delta ,  beta_symbs - ( beta - Pb.T*delta )))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 83
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "DB_blocks = [mrepl(Di, varchange_dict) for Di in D_blocks]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 84
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## LMI Definitions"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from lmi_sdp import LMI_PD, LMI"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 86
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "DB_LMIs = list(map(LMI_PD, DB_blocks))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 87
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "DB_LMIs[0]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$\\left[\\begin{smallmatrix}{}L_{1xx} & L_{1xy} & L_{1xz} & 0 & l_{1z} & - l_{1y}\\\\L_{1xy} & - Ia_{1} - L_{2zz} + \\beta_{1} & L_{1yz} & - l_{1z} & 0 & l_{1x}\\\\L_{1xz} & L_{1yz} & L_{1zz} & l_{1y} & - l_{1x} & 0\\\\0 & - l_{1z} & l_{1y} & m_{1} & 0 & 0\\\\l_{1z} & 0 & - l_{1x} & 0 & m_{1} & 0\\\\- l_{1y} & l_{1x} & 0 & 0 & 0 & m_{1}\\end{smallmatrix}\\right] \\succ 0$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAYEAAABlCAMAAACcJa82AAAAP1BMVEX///8AAAAAAAAAAAAAAAAA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\nAkmQY3QAAAAASUVORK5CYII=\n",
       "prompt_number": 290,
       "text": [
        "\u23a1L\u2081\u2093\u2093         L_1xy        L_1xz    0    l_1z  -l_1y\u23a4 > 0\n",
        "\u23a2                                                   \u23a5    \n",
        "\u23a2L_1xy  -Ia\u2081 - L_2zz + \u03b2\u2081  L_1yz  -l_1z   0     l\u2081\u2093 \u23a5    \n",
        "\u23a2                                                   \u23a5    \n",
        "\u23a2L_1xz        L_1yz        L_1zz  l_1y   -l\u2081\u2093    0  \u23a5    \n",
        "\u23a2                                                   \u23a5    \n",
        "\u23a2  0          -l_1z        l_1y    m\u2081     0      0  \u23a5    \n",
        "\u23a2                                                   \u23a5    \n",
        "\u23a2l_1z           0          -l\u2081\u2093     0     m\u2081     0  \u23a5    \n",
        "\u23a2                                                   \u23a5    \n",
        "\u23a3-l_1y         l\u2081\u2093           0      0     0     m\u2081  \u23a6    "
       ]
      }
     ],
     "prompt_number": 290
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "DB_LMIs_marg = list(map(lambda lm: LMI(lm, epsilon_safemargin*eye(lm.shape[0])) , DB_blocks))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 89
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "DB_LMIs_marg[0]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$\\left[\\begin{smallmatrix}{}L_{1xx} & L_{1xy} & L_{1xz} & 0 & l_{1z} & - l_{1y}\\\\L_{1xy} & - Ia_{1} - L_{2zz} + \\beta_{1} & L_{1yz} & - l_{1z} & 0 & l_{1x}\\\\L_{1xz} & L_{1yz} & L_{1zz} & l_{1y} & - l_{1x} & 0\\\\0 & - l_{1z} & l_{1y} & m_{1} & 0 & 0\\\\l_{1z} & 0 & - l_{1x} & 0 & m_{1} & 0\\\\- l_{1y} & l_{1x} & 0 & 0 & 0 & m_{1}\\end{smallmatrix}\\right] \\succeq \\left[\\begin{smallmatrix}{}1.0 \\cdot 10^{-6} & 0 & 0 & 0 & 0 & 0\\\\0 & 1.0 \\cdot 10^{-6} & 0 & 0 & 0 & 0\\\\0 & 0 & 1.0 \\cdot 10^{-6} & 0 & 0 & 0\\\\0 & 0 & 0 & 1.0 \\cdot 10^{-6} & 0 & 0\\\\0 & 0 & 0 & 0 & 1.0 \\cdot 10^{-6} & 0\\\\0 & 0 & 0 & 0 & 0 & 1.0 \\cdot 10^{-6}\\end{smallmatrix}\\right]$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": 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       "prompt_number": 291,
       "text": [
        "\u23a1L\u2081\u2093\u2093         L_1xy        L_1xz    0    l_1z  -l_1y\u23a4 \u2265 \u23a11.0e-6    0       0  \n",
        "\u23a2                                                   \u23a5   \u23a2                     \n",
        "\u23a2L_1xy  -Ia\u2081 - L_2zz + \u03b2\u2081  L_1yz  -l_1z   0     l\u2081\u2093 \u23a5   \u23a2  0     1.0e-6    0  \n",
        "\u23a2                                                   \u23a5   \u23a2                     \n",
        "\u23a2L_1xz        L_1yz        L_1zz  l_1y   -l\u2081\u2093    0  \u23a5   \u23a2  0       0     1.0e-\n",
        "\u23a2                                                   \u23a5   \u23a2                     \n",
        "\u23a2  0          -l_1z        l_1y    m\u2081     0      0  \u23a5   \u23a2  0       0       0  \n",
        "\u23a2                                                   \u23a5   \u23a2                     \n",
        "\u23a2l_1z           0          -l\u2081\u2093     0     m\u2081     0  \u23a5   \u23a2  0       0       0  \n",
        "\u23a2                                                   \u23a5   \u23a2                     \n",
        "\u23a3-l_1y         l\u2081\u2093           0      0     0     m\u2081  \u23a6   \u23a3  0       0       0  \n",
        "\n",
        "     0       0       0   \u23a4\n",
        "                         \u23a5\n",
        "     0       0       0   \u23a5\n",
        "                         \u23a5\n",
        "6    0       0       0   \u23a5\n",
        "                         \u23a5\n",
        "   1.0e-6    0       0   \u23a5\n",
        "                         \u23a5\n",
        "     0     1.0e-6    0   \u23a5\n",
        "                         \u23a5\n",
        "     0       0     1.0e-6\u23a6"
       ]
      }
     ],
     "prompt_number": 291
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "DB_LMIs_marg[0].canonical()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$\\left[\\begin{smallmatrix}{}L_{1xx} - 1.0 \\cdot 10^{-6} & L_{1xy} & L_{1xz} & 0 & l_{1z} & - l_{1y}\\\\L_{1xy} & - Ia_{1} - L_{2zz} + \\beta_{1} - 1.0 \\cdot 10^{-6} & L_{1yz} & - l_{1z} & 0 & l_{1x}\\\\L_{1xz} & L_{1yz} & L_{1zz} - 1.0 \\cdot 10^{-6} & l_{1y} & - l_{1x} & 0\\\\0 & - l_{1z} & l_{1y} & m_{1} - 1.0 \\cdot 10^{-6} & 0 & 0\\\\l_{1z} & 0 & - l_{1x} & 0 & m_{1} - 1.0 \\cdot 10^{-6} & 0\\\\- l_{1y} & l_{1x} & 0 & 0 & 0 & m_{1} - 1.0 \\cdot 10^{-6}\\end{smallmatrix}\\right] \\succeq 0$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": 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IHKWRbxSp0JnNZA0Egq9d1nDk2SSjCKkC20syeRMjcU52kteQGL/aSBBr5DHpkFGko1Ng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\nAElFTkSuQmCC\n",
       "prompt_number": 292,
       "text": [
        "\u23a1L\u2081\u2093\u2093 - 1.0e-6            L_1xy                 L_1xz            0          l_\n",
        "\u23a2                                                                             \n",
        "\u23a2    L_1xy      -Ia\u2081 - L_2zz + \u03b2\u2081 - 1.0e-6      L_1yz          -l_1z          \n",
        "\u23a2                                                                             \n",
        "\u23a2    L_1xz                L_1yz             L_1zz - 1.0e-6     l_1y         -l\n",
        "\u23a2                                                                             \n",
        "\u23a2      0                  -l_1z                  l_1y       m\u2081 - 1.0e-6       \n",
        "\u23a2                                                                             \n",
        "\u23a2    l_1z                   0                    -l\u2081\u2093            0       m\u2081 - \n",
        "\u23a2                                                                             \n",
        "\u23a3    -l_1y                 l\u2081\u2093                    0              0            \n",
        "\n",
        "1z         -l_1y   \u23a4 \u2265 0\n",
        "                   \u23a5    \n",
        "0           l\u2081\u2093    \u23a5    \n",
        "                   \u23a5    \n",
        "\u2081\u2093           0     \u23a5    \n",
        "                   \u23a5    \n",
        "0            0     \u23a5    \n",
        "                   \u23a5    \n",
        "1.0e-6       0     \u23a5    \n",
        "                   \u23a5    \n",
        "0       m\u2081 - 1.0e-6\u23a6    "
       ]
      }
     ],
     "prompt_number": 292
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## SDP Solver Interfaces"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### [SDPA](http://sdpa.sourceforge.net/)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def sdpa(objf, lmis, variables):\n",
      "    sdpadat = lmi_sdp.to_sdpa_sparse(objf, lmis, variables)\n",
      "    with open(tmpfolder + 'sdpa_dat/sdp.dat-s', 'w') as f:\n",
      "        f.write(sdpadat)\n",
      "    \n",
      "    stdout = !sdpa -ds \"$tmpfolder\"sdpa_dat/sdp.dat-s -o \"$tmpfolder\"sdpa_dat/sdpa.out -p \"$tmpfolder\"sdpa_dat/param.sdpa -pt 2\n",
      "    print('\\n'.join(stdout))\n",
      "\n",
      "    outfile = !cat \"$tmpfolder\"sdpa_dat/sdpa.out\n",
      "    sol = [float(v) for v in outfile[outfile.index('xVec = ') + 1].replace('{', '').replace('}', '').split(',')]\n",
      "    return numpy.matrix(sol).T"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 93
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### [CSDP](https://projects.coin-or.org/Csdp/)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def csdp(objf, lmis, variables):\n",
      "    sdpadat = lmi_sdp.to_sdpa_sparse(objf, lmis, variables)\n",
      "    with open(tmpfolder + 'sdpa_dat/sdp.dat-s', 'w') as f:\n",
      "        f.write(sdpadat)\n",
      "    \n",
      "    stdout = !cd \"$tmpfolder\"sdpa_dat; csdp sdp.dat-s csdp.out\n",
      "    print('\\n'.join(stdout))\n",
      "\n",
      "    outfile = !cat \"$tmpfolder\"sdpa_dat/csdp.out\n",
      "    sol = [float(v) for v in outfile[0].split()]\n",
      "    return numpy.matrix(sol).T"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 77
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### [DSDP5](doi.org/10.1145/1356052.1356057)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def dsdp5(objf, lmis, variables):\n",
      "    sdpadat = lmi_sdp.to_sdpa_sparse(objf, lmis, variables)\n",
      "    with open(tmpfolder + 'sdpa_dat/sdp.dat-s', 'w') as f:\n",
      "        f.write(sdpadat)\n",
      "    \n",
      "    stdout = !cd \"$tmpfolder\"sdpa_dat; dsdp5 sdp.dat-s -save dsdp5.out -gaptol $epsilon_sdptol\n",
      "    print('\\n'.join(stdout))\n",
      "\n",
      "    outfile = !cat \"$tmpfolder\"sdpa_dat/dsdp5.out\n",
      "    sol = [float(v) for v in outfile[0].split()]\n",
      "    return numpy.matrix(sol).T"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 78
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### [DSDP5 through CVXOPT](http://abel.ee.ucla.edu/cvxopt/userguide/coneprog.html#cvxopt.solvers.sdp)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def cvxopt_dsdp5(objf, lmis, variables):\n",
      "    import cvxopt.solvers\n",
      "    c, Gs, hs = lmi_sdp.to_cvxopt(objf, lmis, variables)\n",
      "    cvxopt.solvers.options['DSDP_GapTolerance'] = epsilon_sdptol\n",
      "    tic = time.time()\n",
      "    sdpout = cvxopt.solvers.sdp(c, Gs=Gs, hs=hs, solver='dsdp')\n",
      "    toc = time.time()\n",
      "    print(sdpout['status'], ('ATT!: \\'optimal\\' does not necessarlly means feasible'))\n",
      "    print('Elapsed time: %.2f s'%(toc-tic))\n",
      "    return numpy.matrix(sdpout['x'])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 142
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### [CVXOPT CONELP](http://abel.ee.ucla.edu/cvxopt/userguide/coneprog.html#cvxopt.solvers.sdp)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def cvxopt_conelp(objf, lmis, variables):\n",
      "    import cvxopt.solvers\n",
      "    c, Gs, hs = lmi_sdp.to_cvxopt(objf, lmis, variables)\n",
      "    cvxopt.solvers.options['feastol'] = epsilon_sdptol\n",
      "    tic = time.time()\n",
      "    sdpout = cvxopt.solvers.sdp(c, Gs=Gs, hs=hs)\n",
      "    toc = time.time()\n",
      "    print(sdpout['status'])\n",
      "    print('Elapsed time: %.2f s'%(toc-tic))\n",
      "    return numpy.matrix(sdpout['x'])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 143
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### [Raw SDPA file](http://plato.asu.edu/ftp/sdpa_format.txt)\n",
      "\n",
      "Can be solved online with a *Semidefinite Programming* solver at [NEOS Solvers](http://www.neos-server.org/neos/solvers/index.html)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def sdpa_file(objf, lmis, variables):\n",
      "    sdpadat = lmi_sdp.to_sdpa_sparse(objf, lmis, variables)\n",
      "    with open(tmpfolder + 'sdpa_dat/sdpa_input.dat-s', 'w') as f:\n",
      "        f.write(sdpadat)\n",
      "        \n",
      "    print(\"SDPA file saved at: %ssdpa_dat/sdpa_input.dat-s\"%tmpfolder)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 156
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "--------------"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Setting the default SDP solver:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "solve_sdp = dsdp5"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 153
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## OLS Regression ($\\hat{\\beta}$)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "indentification_traj = 'traj1'"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 122
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "regr_mats = numpy.load(tmpfolder + 'procdata/' + indentification_traj + '_regr.npz')\n",
      "W = numpy.matrix(regr_mats['W'])\n",
      "omega = numpy.matrix(regr_mats['omega'])\n",
      "R1 = numpy.matrix(regr_mats['R1'])\n",
      "rho1 = numpy.matrix(regr_mats['rho1'])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 97
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "omega.shape[0] / rbt.dof"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 125,
       "text": [
        "57656"
       ]
      }
     ],
     "prompt_number": 125
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "W.shape"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 126,
       "text": [
        "(403592, 69)"
       ]
      }
     ],
     "prompt_number": 126
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "numpy.linalg.cond(W)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 127,
       "text": [
        "99.403409432329326"
       ]
      }
     ],
     "prompt_number": 127
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%time beta_ols = (R1.T * R1).I * R1.T * rho1"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "CPU times: user 3.33 ms, sys: 0 ns, total: 3.33 ms\n",
        "Wall time: 2.98 ms\n"
       ]
      }
     ],
     "prompt_number": 130
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "numpy.savetxt(tmpfolder + 'solutions/' + indentification_traj + '_beta_ols.dat', beta_ols)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 131
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "rho2_norm_sqr = numpy.linalg.norm(omega - W * beta_ols)**2"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 132
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Base Parameter Feasibility Test (BPFT) of OLS Solution"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "dict_subs = dict(zip(beta_symbs, beta_ols))\n",
      "lmis_ols_bpft = [ lmi_sdp.LMI_PD(mrepl(lmi.canonical().gts, dict_subs)) for lmi in DB_LMIs ]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 106
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "lmis_ols_bpft[0]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$\\left[\\begin{smallmatrix}{}L_{1xx} & L_{1xy} & L_{1xz} & 0 & l_{1z} & - l_{1y}\\\\L_{1xy} & - Ia_{1} - L_{2zz} + 0.338064863107223 & L_{1yz} & - l_{1z} & 0 & l_{1x}\\\\L_{1xz} & L_{1yz} & L_{1zz} & l_{1y} & - l_{1x} & 0\\\\0 & - l_{1z} & l_{1y} & m_{1} & 0 & 0\\\\l_{1z} & 0 & - l_{1x} & 0 & m_{1} & 0\\\\- l_{1y} & l_{1x} & 0 & 0 & 0 & m_{1}\\end{smallmatrix}\\right] \\succ 0$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": 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MO8Z0bg7zDnf2VCS1SIDjVP7AhkHOiJZvOhqRPWXMNVy3Y0znFmPemYrEf0wimozdTjgw\nqH/vYTcEy8Brk6/Gg2u4aseZzi3GvDMVGV8kwPRyp4IDg5wR3QlAKCx7yphruGbHmc4txrzusZo3\nTFgkIJSp/LodZkTzQb0xQmA6tyzzOG84tmrB1Df1dYcZ0Tf1pEyzSIsTrSzzOvTZFglwevw9UBlI\nZn4Sm1qpMZrDsy0SEAX6S0+8JIlp/yJx38otuCzyL03jB3YbbsZiS0H+PyV6qBJdV9LHAAAAAElF\nTkSuQmCC\n",
       "prompt_number": 293,
       "text": [
        "\u23a1L\u2081\u2093\u2093                L_1xy                L_1xz    0    l_1z  -l_1y\u23a4 > 0\n",
        "\u23a2                                                                  \u23a5    \n",
        "\u23a2L_1xy  -Ia\u2081 - L_2zz + 0.338064863107223  L_1yz  -l_1z   0     l\u2081\u2093 \u23a5    \n",
        "\u23a2                                                                  \u23a5    \n",
        "\u23a2L_1xz               L_1yz                L_1zz  l_1y   -l\u2081\u2093    0  \u23a5    \n",
        "\u23a2                                                                  \u23a5    \n",
        "\u23a2  0                 -l_1z                l_1y    m\u2081     0      0  \u23a5    \n",
        "\u23a2                                                                  \u23a5    \n",
        "\u23a2l_1z                  0                  -l\u2081\u2093     0     m\u2081     0  \u23a5    \n",
        "\u23a2                                                                  \u23a5    \n",
        "\u23a3-l_1y                l\u2081\u2093                   0      0     0     m\u2081  \u23a6    "
       ]
      }
     ],
     "prompt_number": 293
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "variables_ols_bpft = list(delta_d)\n",
      "objf_ols_bpft = 0  # no objective function - \"find\" problem"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 146
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Testing with all solvers\n",
      "\n",
      "**Just one of the following calls is sufficient to show feasibility/infeasibility**"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sol = sdpa_file(objf_ols_bpft, lmis_ols_bpft, variables_ols_bpft) # One can solve the output file at http://www.neos-server.org/neos/solvers/sdp:DSDP/SDPA.html for example."
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "SDPA file saved at: tmp/sdpa_dat/sdpa_input.dat-s\n"
       ]
      }
     ],
     "prompt_number": 314
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sol = dsdp5(objf_ols_bpft, lmis_ols_bpft, variables_ols_bpft)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "sdp.dat-s -save dsdp5.out -gaptol 1e-07 \n",
        "\n",
        "Variables 29 \n",
        "Matrix Blocks: 28, Total Number of Constraints: 63 \n",
        "Nonzeros in Constraints: 225\n",
        "\n",
        "Read Data File into Buffer:      1.577e-03 seconds\n",
        "DSDP Set Data:                   1.400e-04 seconds\n",
        "DSDP Process Data:               9.730e-04 seconds\n",
        "\n",
        "Data Norms: C: 6.29e+00, A: 1.11e+01, b: 0.00e+00\n",
        "Scale C: 1.00e+00\n",
        "\n",
        "Potential Parameter: 5.00\n",
        "Reapply Schur matrix: 10\n",
        "\n",
        "Iter   PP Objective      DD Objective    PInfeas   DInfeas     Nu     StepLength   Pnrm\n",
        "---------------------------------------------------------------------------------------\n",
        "0     1.00000000e+10   -2.92832115e+12   1.0e+00   2.9e+04   2.9e+12  0.00  0.00   0.00 \n",
        "10    1.71998746e+10   -2.50353072e+08   9.6e+01   2.5e+00   5.2e+06  1.00  1.00  29.59 \n",
        "20   -3.13175640e+06   -3.13559113e+06   1.7e+03   3.1e-02   2.6e-01  1.00  1.00  777.35 \n",
        "30   -3.13553533e+06   -3.13553537e+06   3.9e+02   3.1e-02   6.9e-05  1.00  0.05  11.20 \n",
        "31   -3.13553536e+06   -3.13553537e+06   3.9e+02   3.1e-02   1.7e-05  1.00  0.01  43.87 \n",
        "DSDP Converged. \n",
        "DSDP Primal Unbounded, Dual Infeasible\n",
        "\n",
        "P Objective  :  -3.13553540e+06 \n",
        "DSDP Solution:   0.00000000e+00 \n",
        "\n",
        "DSDP Solve Time:                     4.853e-02 seconds\n",
        "DSDP Preparation and Solve Time:     4.950e-02 seconds\n",
        "\n",
        "\n",
        "P Infeasible: 3.30e-04 \n",
        "D Infeasible: 4.30e-03 \n",
        "Minimal P Eigenvalue: 0.00e+00 \n",
        "Minimal D Eigenvalue: 0.00 \n",
        "Relative P - D Objective values: -1.00e+00 \n",
        "Relative X Dot S: 6.29e-07 \n",
        "\n",
        "Max Y: 7.76186874e+06,  Bounded by 1.0e+07\n",
        "Trace X: 1.00000000e+08,   Bounded by Penalty Parameter: 1.0e+08 \n",
        "\n",
        "PERFORMANCE SUMMARY\n",
        "                     Event                      Calls    Time(s)   Time(%)\n",
        "--------------------------------------------------------------------------\n",
        "                                   R Cone        1522   2.7299e-04   0.55\n",
        "                             Bound Y Cone        1522   9.3937e-04   1.89\n",
        "                                 SDP Cone        1554   4.4057e-02  88.64\n",
        "                           Cone Setup 1&2           2   8.8906e-04   1.79\n",
        "                            Cone Invert S         260   7.9303e-03  15.96\n",
        "                                 Cone RHS         229   2.2626e-03   4.55\n",
        "                  Cone Compute Newton Eq.          33   6.9811e-03  14.05\n",
        "                   Cone Max P Step Length          31   1.9808e-03   3.99\n",
        "               Cone Compute and Factor SP          56   6.9070e-04   1.39\n",
        "                   Cone Max D Step Length         269   1.7859e-02  35.93\n",
        "                Cone Compute and Factor S         312   4.8833e-03   9.82\n",
        "                           Cone Potential         304   2.0545e-03   4.13\n",
        "                                Cone View          32   1.4782e-05   0.03\n",
        "                           Cone Compute X           1   2.6393e-04   0.53\n",
        "                            SDP VecMatVec        1749   2.0385e-04   0.41\n",
        "                                  SDP Dot        8712   1.4002e-03   2.82\n",
        "                               SDP SSolve        7938   3.4273e-03   6.90\n",
        "                                SDP X+vv'        6189   1.2157e-03   2.45\n",
        "                        Factor Newton Eq.          33   5.8389e-04   1.17\n",
        "                         Solve Newton Eq.         554   9.4843e-04   1.91\n",
        "                              Primal Step          31   3.5055e-03   7.05\n",
        "                                Dual Step          31   2.7962e-03   5.63\n",
        "                           Corrector Step         229   3.2270e-02  64.93\n",
        "                                 CG Solve         292   2.0711e-03   4.17\n",
        "                               DSDP Solve           1   4.8246e-02  97.07\n",
        "--------------------------------------------------------------------------\n",
        "--- DSDP Finished ---\n",
        "\n"
       ]
      }
     ],
     "prompt_number": 133
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sol = sdpa(objf_ols_bpft, lmis_ols_bpft, variables_ols_bpft)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "SDPA start at [Mon Oct 21 00:31:02 2013]\n",
        "set   is STABLE_BUT_SLOW\n",
        "data  is tmp/sdpa_dat/sdp.dat-s : sparse\n",
        "out   is tmp/sdpa_dat/sdpa.out\n",
        "NumThreads  is set as 1\n",
        "Schur computation : DENSE \n",
        "   mu      thetaP  thetaD  objP      objD      alphaP  alphaD  beta \n",
        " 0 1.0e+08 1.0e+00 1.0e+00 -0.00e+00 -1.22e+05 5.7e-01 6.6e-01 3.00e-01\n",
        " 1 5.7e+07 4.3e-01 3.4e-01 -0.00e+00 -2.06e+05 6.4e-01 7.1e-01 3.00e-01\n",
        " 2 2.8e+07 1.6e-01 9.7e-02 -0.00e+00 -2.90e+05 7.0e-01 7.4e-01 3.00e-01\n",
        " 3 1.2e+07 4.7e-02 2.5e-02 -0.00e+00 -4.02e+05 7.5e-01 7.9e-01 3.00e-01\n",
        " 4 4.3e+06 1.2e-02 5.4e-03 -0.00e+00 -5.74e+05 7.8e-01 7.9e-01 3.00e-01\n",
        " 5 1.4e+06 2.6e-03 1.1e-03 -0.00e+00 -8.19e+05 8.0e-01 8.0e-01 3.00e-01\n",
        " 6 4.3e+05 5.3e-04 2.3e-04 -0.00e+00 -1.13e+06 7.8e-01 8.0e-01 3.00e-01\n",
        " 7 1.5e+05 1.1e-04 4.5e-05 -0.00e+00 -1.37e+06 7.4e-01 8.0e-01 3.00e-01\n",
        " 8 6.1e+04 3.0e-05 9.1e-06 -0.00e+00 -1.23e+06 6.7e-01 8.0e-01 3.00e-01\n",
        " 9 2.8e+04 9.9e-06 1.8e-06 -0.00e+00 -7.79e+05 4.6e-01 8.0e-01 3.00e-01\n",
        "10 1.5e+04 5.4e-06 3.6e-07 -0.00e+00 -3.19e+05 2.5e-01 4.5e-01 3.00e-01\n",
        "pdINF criteria :: line 1192 in sdpa_parts.cpp\n",
        "11 1.2e+04 4.0e-06 2.0e-07 -0.00e+00 +1.66e+05 2.5e-01 4.5e-01 3.00e-01\n",
        "\n",
        "phase.value  = pdINF     \n",
        "   Iteration = 11\n",
        "          mu = +1.2128636218831845e+04\n",
        "relative gap = +2.0000000000000000e+00\n",
        "        gap  = -1.6574670752527865e+05\n",
        "     digits  = -3.0102999566398120e-01\n",
        "objValPrimal = -0.0000000000000000e+00\n",
        "objValDual   = +1.6574670752527865e+05\n",
        "p.feas.error = +4.0191563899952598e-02\n",
        "d.feas.error = +5.9960590591629868e-03\n",
        "total time   = 0.166728\n",
        "  main loop time = 0.165674\n",
        "      total time = 0.166728\n",
        "file  check time = 0.000000\n",
        "file change time = 0.000008\n",
        "file   read time = 0.001046\n",
        "SDPA end at [Mon Oct 21 00:31:02 2013]\n",
        "ALL TIME = 0.167907\n"
       ]
      }
     ],
     "prompt_number": 134
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sol = csdp(objf_ols_bpft, lmis_ols_bpft, variables_ols_bpft)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "This is a pure dual feasibility problem.\n",
        "Iter:  0 Ap: 0.00e+00 Pobj: -3.8296290e+03 Ad: 0.00e+00 Dobj:  0.0000000e+00 \n",
        "Iter:  1 Ap: 8.96e-01 Pobj: -5.2770492e+03 Ad: 8.16e-01 Dobj:  0.0000000e+00 \n",
        "Iter:  2 Ap: 6.30e-01 Pobj: -4.7758728e+03 Ad: 6.04e-01 Dobj:  0.0000000e+00 \n",
        "Iter:  3 Ap: 5.03e-01 Pobj: -4.1867025e+03 Ad: 8.53e-01 Dobj:  0.0000000e+00 \n",
        "Iter:  4 Ap: 8.74e-01 Pobj: -1.5539887e+03 Ad: 4.75e-01 Dobj:  0.0000000e+00 \n",
        "Iter:  5 Ap: 3.90e-01 Pobj:  2.5868012e+00 Ad: 2.09e-01 Dobj:  0.0000000e+00 \n",
        "Iter:  6 Ap: 8.83e-02 Pobj:  2.6946911e+03 Ad: 1.83e-01 Dobj:  0.0000000e+00 \n",
        "Iter:  7 Ap: 3.62e-03 Pobj:  8.0058280e+03 Ad: 1.06e-02 Dobj:  0.0000000e+00 \n",
        "Iter:  8 Ap: 1.61e-02 Pobj:  6.0199514e+04 Ad: 1.30e-02 Dobj:  0.0000000e+00 \n",
        "Iter:  9 Ap: 6.67e-03 Pobj:  2.9195543e+05 Ad: 8.91e-03 Dobj:  0.0000000e+00 \n",
        "Iter: 10 Ap: 4.86e-03 Pobj:  1.5474164e+06 Ad: 7.36e-03 Dobj:  0.0000000e+00 \n",
        "Iter: 11 Ap: 7.92e-04 Pobj:  3.2963353e+06 Ad: 1.12e-02 Dobj:  0.0000000e+00 \n",
        "Iter: 12 Ap: 1.26e-03 Pobj:  2.0726205e+07 Ad: 7.06e-04 Dobj:  0.0000000e+00 \n",
        "Iter: 13 Ap: 1.46e-03 Pobj:  1.5980240e+08 Ad: 2.73e-03 Dobj:  0.0000000e+00 \n",
        "Iter: 14 Ap: 8.50e-05 Pobj:  2.5340103e+08 Ad: 1.18e-03 Dobj:  0.0000000e+00 \n",
        "Iter: 15 Ap: 1.78e-05 Pobj:  2.9154914e+08 Ad: 2.85e-04 Dobj:  0.0000000e+00 \n",
        "Iter: 16 Ap: 2.57e-04 Pobj:  9.5874891e+08 Ad: 6.27e-03 Dobj:  0.0000000e+00 \n",
        "Declaring dual infeasibility.\n",
        "Success: SDP is dual infeasible\n",
        "Certificate of dual infeasibility: tr(CX)=1.00000e+00, ||A(X)||=3.11064e-09\n",
        "Elements time: 0.000348 \n",
        "Factor time: 0.000292 \n",
        "Other time: 0.021691 \n",
        "Total time: 0.022331 \n"
       ]
      }
     ],
     "prompt_number": 135
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sol = cvxopt_conelp(objf_ols_bpft, lmis_ols_bpft, variables_ols_bpft)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "     pcost       dcost       gap    pres   dres   k/t\n",
        " 0:  0.0000e+00 -1.2158e+01  1e+02  2e+00  7e+00  1e+00\n",
        " 1:  0.0000e+00 -2.3016e-01  3e+00  2e-01  6e-01  8e-01"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        " 2:  0.0000e+00 -9.6107e-02  1e+00  6e-02  2e-01  3e-01\n",
        " 3:  0.0000e+00  2.0962e-01  4e+01  3e-01  1e+00  2e+00\n",
        " 4:  0.0000e+00  7.3312e-01  3e+01  1e-01  5e-01  2e+00"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        " 5:  0.0000e+00  4.7892e-01  2e+01  7e-02  3e-01  1e+00\n",
        " 6:  0.0000e+00  3.4714e+00  1e+02  6e-02  2e-01  4e+00\n",
        " 7:  0.0000e+00  1.1664e+01  3e+02  6e-02  2e-01  1e+01\n",
        " 8:  0.0000e+00  1.0313e+02  2e+03  5e-02  2e-01  1e+02\n",
        " 9:  0.0000e+00  1.7208e+03  4e+04  5e-02  2e-01  2e+03\n",
        "10:  0.0000e+00  1.3030e+04  3e+05  5e-02  2e-01  1e+04\n",
        "11:  0.0000e+00  9.8979e+04  2e+06  5e-02  2e-01  1e+05\n",
        "12:  0.0000e+00  3.6891e+05  8e+06  5e-02  2e-01  4e+05"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "13:  0.0000e+00  9.4734e+05  2e+07  5e-02  2e-01  9e+05\n",
        "14:  0.0000e+00  1.0511e+06  3e+07  5e-02  2e-01  1e+06\n",
        "15:  0.0000e+00  1.0467e+07  3e+08  5e-02  2e-01  1e+07\n",
        "Certificate of primal infeasibility found.\n",
        "primal infeasible\n",
        "Elapsed time: 3.98 s\n"
       ]
      }
     ],
     "prompt_number": 144
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Base Parameter Feasibility Correction (BPFC)     ($\\beta^\\prime$)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "u = sympy.Symbol('u')\n",
      "U_beta = BlockMatrix([[Matrix([u]),            (beta_ols - beta_symbs).T],\n",
      "                 [beta_ols - beta_symbs,                 I(n_beta)]])\n",
      "U_beta = U_beta.as_explicit()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 155
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "lmis_ols_bpfc = [LMI(U_beta)] + DB_LMIs_marg"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 148
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "lmis_ols_bpfc[1]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 151,
       "text": [
        "Matrix([\n",
        "[L_1xx,                 L_1xy, L_1xz,     0,  l_1z, -l_1y],\n",
        "[L_1xy, -Ia_1 - L_2zz + beta1, L_1yz, -l_1z,     0,  l_1x],\n",
        "[L_1xz,                 L_1yz, L_1zz,  l_1y, -l_1x,     0],\n",
        "[    0,                 -l_1z,  l_1y,   m_1,     0,     0],\n",
        "[ l_1z,                     0, -l_1x,     0,   m_1,     0],\n",
        "[-l_1y,                  l_1x,     0,     0,     0,   m_1]]) >= Matrix([\n",
        "[1.0e-6,      0,      0,      0,      0,      0],\n",
        "[     0, 1.0e-6,      0,      0,      0,      0],\n",
        "[     0,      0, 1.0e-6,      0,      0,      0],\n",
        "[     0,      0,      0, 1.0e-6,      0,      0],\n",
        "[     0,      0,      0,      0, 1.0e-6,      0],\n",
        "[     0,      0,      0,      0,      0, 1.0e-6]])"
       ]
      }
     ],
     "prompt_number": 151
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "variables_ols_bpfc = [u] + list(beta_symbs) + list(delta_d)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 158
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "objf_ols_bpfc = u"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 159
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sol_ols_bpfc = solve_sdp(objf_ols_bpfc, lmis_ols_bpfc, variables_ols_bpfc)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "sdp.dat-s -save dsdp5.out -gaptol 1e-07 \n",
        "\n",
        "Variables 99 \n",
        "Matrix Blocks: 29, Total Number of Constraints: 133 \n",
        "Nonzeros in Constraints: 496\n",
        "\n",
        "Read Data File into Buffer:      2.906e-03 seconds\n",
        "DSDP Set Data:                   3.750e-04 seconds\n",
        "DSDP Process Data:               1.300e-02 seconds\n",
        "\n",
        "Data Norms: C: 1.07e+01, A: 1.95e+01, b: 1.00e+00\n",
        "Scale C: 1.00e+00\n",
        "\n",
        "Potential Parameter: 5.00\n",
        "Reapply Schur matrix: 4\n",
        "\n",
        "Iter   PP Objective      DD Objective    PInfeas   DInfeas     Nu     StepLength   Pnrm\n",
        "---------------------------------------------------------------------------------------\n",
        "0     1.00000000e+10   -5.14384241e+12   2.0e+00   5.1e+04   5.1e+12  0.00  0.00   0.00 \n",
        "10    8.94838822e+13   -2.05367041e+13   4.0e+05   2.1e+05   1.7e+11  1.00  1.00   4.27 \n",
        "20    3.96240164e+11   -1.17762893e+11   4.0e+03   1.2e+03   1.2e+09  1.00  1.00   0.87 \n",
        "30    1.06170401e+10   -3.07067071e+09   1.1e+02   3.1e+01   3.2e+07  1.00  1.00   0.85 \n",
        "40    3.77063860e+08   -1.30536934e+07   2.3e+00   3.8e-02   8.0e+05  1.00  1.00   1.29 \n",
        "50    2.85418165e+06   -1.79351721e+05   3.7e-03   0.0e+00   5.7e+03  1.00  1.00   0.75 \n",
        "60    4.66229609e+04   -2.81961727e+03   6.0e-05   0.0e+00   9.2e+01  1.00  1.00   0.76 \n",
        "70    7.59797227e+02   -3.56581951e+01   9.6e-07   0.0e+00   1.4e+00  1.00  1.00   0.79 \n",
        "80    8.46771878e+00   -1.92951934e-01   1.0e-08   0.0e+00   1.3e-02  1.00  1.00   0.67 \n",
        "90    2.93352905e-02   -5.22112404e-03   4.1e-11   0.0e+00   8.1e-05  1.00  1.00   0.36 \n",
        "100  -4.05308004e-03   -4.05373027e-03   7.7e-07   0.0e+00   4.1e-10  1.00  0.22  15.85 \n",
        "102  -4.05370129e-03   -4.05372704e-03   7.7e-07   0.0e+00   1.6e-11  1.00  0.19  10.72 \n",
        "DSDP Converged. \n",
        "\n",
        "P Objective  :  -4.05371809e-03 \n",
        "DSDP Solution:  -4.05372704e-03 \n",
        "\n",
        "DSDP Solve Time:                     3.348e-01 seconds\n",
        "DSDP Preparation and Solve Time:     3.478e-01 seconds\n",
        "\n",
        "\n",
        "P Infeasible: 5.07e-11 \n",
        "D Infeasible: 0.00e+00 \n",
        "Minimal P Eigenvalue: 0.00e+00 \n",
        "Minimal D Eigenvalue: 0.00 \n",
        "Relative P - D Objective values: 8.88e-09 \n",
        "Relative X Dot S: 8.42e-05 \n",
        "\n",
        "Max Y: 7.74596688e+06,  Bounded by 1.0e+07\n",
        "Trace X: 1.31199245e+00,   Bounded by Penalty Parameter: 1.0e+08 \n",
        "\n",
        "PERFORMANCE SUMMARY\n",
        "                     Event                      Calls    Time(s)   Time(%)\n",
        "--------------------------------------------------------------------------\n",
        "                                   R Cone        2983   4.4370e-04   0.13\n",
        "                             Bound Y Cone        2983   5.1186e-03   1.47\n",
        "                                 SDP Cone        2990   2.6234e-01  75.32\n",
        "                           Cone Setup 1&2           2   6.4659e-03   1.86\n",
        "                            Cone Invert S         494   9.4769e-02  27.21\n",
        "                                 Cone RHS         392   8.4302e-03   2.42\n",
        "                  Cone Compute Newton Eq.         103   7.0249e-02  20.17\n",
        "                   Cone Max P Step Length         102   9.1012e-03   2.61\n",
        "               Cone Compute and Factor SP         108   3.3925e-03   0.97\n",
        "                   Cone Max D Step Length         500   4.4077e-02  12.65\n",
        "                Cone Compute and Factor S         544   1.7388e-02   4.99\n",
        "                           Cone Potential         542   7.2529e-03   2.08\n",
        "                                Cone View         103   5.5313e-05   0.02\n",
        "                           Cone Compute X           1   2.8479e-03   0.82\n",
        "                            SDP VecMatVec       20763   2.4064e-02   6.91\n",
        "                                  SDP Dot       22484   5.6109e-03   1.61\n",
        "                               SDP SSolve       49739   1.8926e-02   5.43\n",
        "                                SDP X+vv'       28976   7.2739e-03   2.09\n",
        "                        Factor Newton Eq.         103   4.9710e-02  14.27\n",
        "                         Solve Newton Eq.         638   7.9246e-03   2.28\n",
        "                              Primal Step         102   1.4073e-02   4.04\n",
        "                                Dual Step         102   1.3460e-02   3.86\n",
        "                           Corrector Step         392   1.4484e-01  41.58\n",
        "                                 CG Solve         598   2.3246e-02   6.67\n",
        "                               DSDP Solve           1   3.3189e-01  95.29\n",
        "--------------------------------------------------------------------------\n",
        "--- DSDP Finished ---\n",
        "\n"
       ]
      }
     ],
     "prompt_number": 160
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "u_prime = sol_ols_bpfc[0,0]\n",
      "beta_prime = sol_ols_bpfc[1:1+n_beta]\n",
      "delta_d_prime = sol_ols_bpfc[1+n_beta:]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 161
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "u_prime"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 162,
       "text": [
        "0.0040537274987536539"
       ]
      }
     ],
     "prompt_number": 162
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Solution Double Check"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "dict_subs = dict(zip(beta_symbs, beta_prime.flatten().tolist()[0]))\n",
      "dict_subs.update(dict(zip(delta_d, delta_d_prime.flatten().tolist()[0])))\n",
      "\n",
      "test = 'ok'\n",
      "for i, DBi in enumerate(DB_blocks):\n",
      "        m = numpy.matrix(mrepl(DBi, dict_subs)).astype(float)\n",
      "        for v in numpy.linalg.eigvals( m ):\n",
      "            if v <= 0.0:\n",
      "                print i, v\n",
      "                test = 'fail'\n",
      "print(test)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "ok\n"
       ]
      }
     ],
     "prompt_number": 165
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "numpy.savetxt(tmpfolder + 'solutions/' + indentification_traj + '_beta_prime.dat', beta_prime)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 166
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Feasible Base Parameter Estimation with Ordinary Least Squares (FBPE-OLS)     ($\\beta^\\star$)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "u = sympy.Symbol('u')\n",
      "U_rho = BlockMatrix([[Matrix([u - rho2_norm_sqr]), (rho1 - R1*beta_symbs).T],\n",
      "                     [rho1 - R1*beta_symbs,                       I(n_beta)]])\n",
      "U_rho = U_rho.as_explicit()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 167
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "lmis_fbpe_ols = [LMI(U_rho)] + DB_LMIs_marg"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 168
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "variables_fbpe_ols = [u] + list(beta_symbs) + list(delta_d)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 169
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "objf_fbpe_ols = u"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 170
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sol_fbpe_ols = solve_sdp(objf_fbpe_ols, lmis_fbpe_ols, variables_fbpe_ols)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "sdp.dat-s -save dsdp5.out -gaptol 1e-07 \n",
        "\n",
        "Variables 99 \n",
        "Matrix Blocks: 29, Total Number of Constraints: 133 \n",
        "Nonzeros in Constraints: 2731\n",
        "\n",
        "Read Data File into Buffer:      5.281e-03 seconds\n",
        "DSDP Set Data:                   2.069e-04 seconds\n",
        "DSDP Process Data:               2.709e-02 seconds\n",
        "\n",
        "Data Norms: C: 7.85e+04, A: 1.70e+04, b: 1.00e+00\n",
        "Scale C: 2.16e-01\n",
        "\n",
        "Potential Parameter: 5.00\n",
        "Reapply Schur matrix: 4\n",
        "\n",
        "Iter   PP Objective      DD Objective    PInfeas   DInfeas     Nu     StepLength   Pnrm\n",
        "---------------------------------------------------------------------------------------\n",
        "0     1.00000000e+10   -1.95170612e+17   2.0e+00   2.0e+09   2.0e+17  0.00  0.00   0.00 \n",
        "10    4.79481958e+10   -5.52331104e+09   8.8e+01   5.5e+01   4.5e+07  1.00  1.00   4.50 \n",
        "20    3.80079020e+07   -1.91235465e+06   4.8e-02   0.0e+00   7.6e+04  0.92  1.00   0.46 \n",
        "30    2.26577621e+05   -8.69552142e+04   3.7e-04   0.0e+00   5.3e+02  1.00  1.00   1.13 \n",
        "40   -7.67526149e+04   -7.91085802e+04   6.7e-06   0.0e+00   1.4e+00  0.93  1.00   0.79 \n",
        "49   -7.90832993e+04   -7.90833045e+04   3.9e-06   0.0e+00   3.3e-06  1.00  0.14  22.65 \n",
        "DSDP Converged. \n",
        "\n",
        "P Objective  :  -7.90833028e+04 \n",
        "DSDP Solution:  -7.90833045e+04 \n",
        "\n",
        "DSDP Solve Time:                     1.863e-01 seconds\n",
        "DSDP Preparation and Solve Time:     2.133e-01 seconds\n",
        "\n",
        "\n",
        "P Infeasible: 1.05e-07 \n",
        "D Infeasible: 0.00e+00 \n",
        "Minimal P Eigenvalue: 0.00e+00 \n",
        "Minimal D Eigenvalue: 0.00 \n",
        "Relative P - D Objective values: 1.11e-08 \n",
        "Relative X Dot S: 2.21e-08 \n",
        "\n",
        "Max Y: 7.74598319e+06,  Bounded by 1.0e+07\n",
        "Trace X: 1.35073124e+05,   Bounded by Penalty Parameter: 1.0e+08 \n",
        "\n",
        "PERFORMANCE SUMMARY\n",
        "                     Event                      Calls    Time(s)   Time(%)\n",
        "--------------------------------------------------------------------------\n",
        "                                   R Cone        1446   2.2626e-04   0.11\n",
        "                             Bound Y Cone        1446   2.4633e-03   1.15\n",
        "                                 SDP Cone        1455   1.8423e-01  86.24\n",
        "                           Cone Setup 1&2           2   2.6737e-02  12.52\n",
        "                            Cone Invert S         229   4.2826e-02  20.05\n",
        "                                 Cone RHS         180   4.3845e-03   2.05\n",
        "                  Cone Compute Newton Eq.          51   7.0492e-02  33.00\n",
        "                   Cone Max P Step Length          49   4.6999e-03   2.20\n",
        "               Cone Compute and Factor SP          53   1.9619e-03   0.92\n",
        "                   Cone Max D Step Length         233   2.1428e-02  10.03\n",
        "                Cone Compute and Factor S         283   1.0113e-02   4.73\n",
        "                           Cone Potential         277   3.7549e-03   1.76\n",
        "                                Cone View          50   2.2650e-05   0.01\n",
        "                           Cone Compute X           1   1.3101e-03   0.61\n",
        "                            SDP VecMatVec        8473   2.5526e-02  11.95\n",
        "                                  SDP Dot       11326   5.3620e-03   2.51\n",
        "                               SDP SSolve       24938   2.0281e-02   9.49\n",
        "                                SDP X+vv'       16465   1.1526e-02   5.39\n",
        "                        Factor Newton Eq.          51   1.1742e-02   5.50\n",
        "                         Solve Newton Eq.         515   6.2709e-03   2.94\n",
        "                              Primal Step          49   7.4983e-03   3.51\n",
        "                                Dual Step          49   6.9761e-03   3.27\n",
        "                           Corrector Step         180   7.3392e-02  34.35\n",
        "                                 CG Solve         280   1.1479e-02   5.37\n",
        "                               DSDP Solve           1   1.8492e-01  86.56\n",
        "--------------------------------------------------------------------------\n",
        "--- DSDP Finished ---\n",
        "\n"
       ]
      }
     ],
     "prompt_number": 172
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "u_star = sol_fbpe_ols[0,0]\n",
      "beta_star = numpy.matrix(sol_fbpe_ols[1:1+n_beta])\n",
      "delta_d_star = numpy.matrix(sol_fbpe_ols[1+n_beta:])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 173
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "u_star"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$79083.3047994$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAH8AAAAPBAMAAAA/sQ3hAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nEoVYL6AAAAAASUVORK5CYII=\n",
       "prompt_number": 198,
       "text": [
        "79083.3047994"
       ]
      }
     ],
     "prompt_number": 198
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Solution Double Check"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "dict_subs = dict(zip(beta_symbs, beta_star.flatten().tolist()[0]))\n",
      "dict_subs.update(dict(zip(delta_d, delta_d_star.flatten().tolist()[0])))\n",
      "\n",
      "test = 'ok'\n",
      "for DBi in DB_blocks:\n",
      "        m = numpy.matrix(mrepl(DBi, dict_subs)).astype(float)\n",
      "        for v in numpy.linalg.eigvals( m ):\n",
      "            if v <= 0.0:\n",
      "                print(v)\n",
      "                test = 'fail'\n",
      "print(test)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "ok\n"
       ]
      }
     ],
     "prompt_number": 174
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "numpy.savetxt(tmpfolder + 'solutions/' + indentification_traj + '_beta_star.dat', beta_star)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 175
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Additional Constraints on Centers-of-Mass    ($\\beta^{\\star e}$)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "link_cuboid_hulls = [\n",
      "[[ -0.140 , +0.140 ],[ -0.174 , +0.174 ],[ -0.084 , +0.346 ]],\n",
      "[[ -0.084 , +0.084 ],[ -0.174 , +0.174 ],[ -0.084 , +0.170 ]],\n",
      "[[ -0.090 , +0.040 ],[ -0.550 , +0.040 ],[ -0.045 , +0.045 ]],\n",
      "[[ -0.045 , +0.095 ],[ -0.045 , +0.045 ],[ -0.050 , +0.830 ]],\n",
      "[[ -0.045 , +0.045 ],[ -0.020 , +0.100 ],[ -0.045 , +0.045 ]],\n",
      "[[ -0.045 , +0.045 ],[ -0.060 , +0.045 ],[ -0.020 , +0.060 ]],\n",
      "[[ -0.045 , +0.045 ],[ -0.045 , +0.045 ],[ -0.018 , +0.001 ]],\n",
      "]\n",
      "\n",
      "robotmaxmass = 27.0"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 179
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "#### LMI Matrix Definition"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "D_add_blocks = []\n",
      "for i in range(rbt.dof):\n",
      "    l = rbt.rbtdef.l[i]\n",
      "    m = rbt.rbtdef.m[i]\n",
      "    link_cuboid_hull = link_cuboid_hulls[i]\n",
      "    for j in range(3):\n",
      "        D_add_blocks.append( Matrix( [[  l[j] - m*link_cuboid_hull[j][0] ]] ) )\n",
      "        D_add_blocks.append( Matrix( [[ -l[j] + m*link_cuboid_hull[j][1] ]] ) )\n",
      "\n",
      "D_add_blocks.append(Matrix([robotmaxmass - sum(rbt.rbtdef.m)]))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 180
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "#### Variable Change and LMI Definition"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "DB_add_blocks = [ mrepl(Di, varchange_dict) for Di in D_add_blocks ]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 189
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "DB_add_LMIs = list(map(LMI_PD, DB_add_blocks))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 190
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "DB_add_LMIs_marg = list(map(lambda lm: LMI(lm, epsilon_safemargin*eye(lm.shape[0])) , DB_add_blocks))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 191
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "DB_add_LMIs_marg[0]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$\\left[\\begin{smallmatrix}{}l_{1x} + 0.14 m_{1}\\end{smallmatrix}\\right] \\succeq \\left[\\begin{smallmatrix}{}1.0 \\cdot 10^{-6}\\end{smallmatrix}\\right]$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAANIAAAAUBAMAAAAKBn7YAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nyYkplJId6ySU+fJvuj+uDvlgVxcAAAAASUVORK5CYII=\n",
       "prompt_number": 299,
       "text": [
        "[l\u2081\u2093 + 0.14\u22c5m\u2081] \u2265 [1.0e-6]"
       ]
      }
     ],
     "prompt_number": 299
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "DB_add_LMIs_marg[-1]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$\\left[\\begin{smallmatrix}{}- m_{1} - m_{2} - m_{3} - m_{4} - m_{5} - m_{6} - m_{7} + 27.0\\end{smallmatrix}\\right] \\succeq \\left[\\begin{smallmatrix}{}1.0 \\cdot 10^{-6}\\end{smallmatrix}\\right]$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAaAAAAAUBAMAAAA5NPS9AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAdt3NMolEVLsQZpnv\nqyLgemnZAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAD6klEQVRYCc2VX4hUdRTHv3f2ztzuOP8cEKRF\nmNTW9EE3tqce4poIkcbOQpoiyID5ByTaHiopovsQ0dLLraUH2WIH0op8GSMpW4qJ/kiBupEKguAV\nX5TI3YcoNsnpnN+f++fHwGxP3QPzu+d8fue3c757zv0N6o8gk/bhiFGWtc4zSJ+QTu3ugzOBzMLy\nreWUtTszgvJfnsUzx49z0atW8SoE7WBP2gBBzkSb87IhqEWV7MevuN7r+UCx6cyL0mjJ0UfZAEGv\nVkY5MRuCfKpkM8bDK4eOBCTCwxIB0aF8kzxpAwRdkFnZEfQjFlqTeInKmg1xjh7yHXpb1kmrEGT7\nHFsTQicHcjwB96+THu2kOlT8auuwtVpg3iJbDjl1YmVn5RsyX67/nfji4OsBXC50PMAmekhB1oOe\n2JSC7K8bHJ3Ea7RyoMaTBP2BLm8lO1R8vl26as0DV3mHTZPte0IRx+TJNZ4iH/2N88EaCqYUgCLO\n5GGD4MX7DVLu9dqEfIEfAMoBeSSIXCUIzrWH5vbzvuiQ02B3PaqcSEGOxtOdm5v7AosQQ5cUdLuO\namtFEwfVOAKa+IUGnWfT5E1nVILKOw38iTMk9ScJoEmxN28Qp3PTICvu/MbE5yXfAZ5gZzzEt/SQ\nHcJT605/3GIcC3LvoTRJhASp8aTgktugVXXo2FtkAX7BTuQoczOQJqPukkGCfNPhQ1Mo1+wuNgDP\nbkSaFAP6ylROKTSJjb0oj419N/YocIrK2cU1zXr0L9KCPoimORZkLyHXpgwSpMaTgplhj9bUyOF7\nrMaCLQTxHpkmdFSZIvYeDUqe5VcWPbe90SDFTz83yOwrTxsEhTYTnz6FZsHDwxzlWvEt544wEZYW\nVCMmBfF4xpYcucoi9eiTfEJQRKZDdSQihVFFFqhHRb9pIRKkCPC4/h5FZr2SQTAkgE/rtpePBfgZ\nuBVYnfh3qNwSCbwkBNHI1WakIDmeUVKqQ4V5PIbf9yYEaeJG14QmNdxTf+Q5DIWVy8H2XT94aTKE\nqv4elVMFD50wRfC+iHxaL/Z6APVjZ4h9+2ha5Ts0LfbFEguiG63aojzqkBrPOCvZoYjSO5S2mdvN\nNHC79OIYpi8Fje/DNu2qZ9l71yA4IIBvYo7FpXAj3okFke7olpPjGWf1E7T17mScILwtvYZBXoiu\nbb3x3t1Qu/JpT3yTBnBPR2+V3jkqnI4Ok091y0VICuqiMoVh8TsEpws1nlFSauRimgmvn6DKZ//U\n7AvInzlLJXKgxjMuuF+H4t3/1esnaHBBWRc0vZZtPQsRIzdQUdYFJQQsV1BdyE8czIhbHzEKsdZ6\nBukT1kf+BfDMPWL6+vjMAAAAAElFTkSuQmCC\n",
       "prompt_number": 300,
       "text": [
        "[-m\u2081 - m\u2082 - m\u2083 - m\u2084 - m\u2085 - m\u2086 - m\u2087 + 27.0] \u2265 [1.0e-6]"
       ]
      }
     ],
     "prompt_number": 300
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Testing $\\beta^\\star$ solution on new constraints"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "dict_subs = dict(zip(beta_symbs, beta_star))\n",
      "lmis_star_bpft_add = [ lmi_sdp.LMI_PD(mrepl(lmi.canonical().gts, dict_subs)) for lmi in DB_add_LMIs_marg ]\n",
      "variables_star_bpft_add = list(delta_d)\n",
      "objf_star_bpft_add = delta_d[0]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 196
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sol_star_bpft_add = solve_sdp(objf_star_bpft_add, lmis_star_bpft_add, variables_star_bpft_add)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "sdp.dat-s -save dsdp5.out -gaptol 1e-07 \n",
        "\n",
        "Variables 29 \n",
        "Matrix Blocks: 43, Total Number of Constraints: 43 \n",
        "Nonzeros in Constraints: 152\n",
        "\n",
        "Read Data File into Buffer:      3.550e-04 seconds\n",
        "DSDP Set Data:                   1.562e-04 seconds\n",
        "DSDP Process Data:               1.860e-04 seconds\n",
        "\n",
        "Data Norms: C: 2.72e+01, A: 6.32e+00, b: 1.00e+00\n",
        "Scale C: 2.35e-01\n",
        "\n",
        "Potential Parameter: 5.00\n",
        "Reapply Schur matrix: 10\n",
        "\n",
        "Iter   PP Objective      DD Objective    PInfeas   DInfeas     Nu     StepLength   Pnrm\n",
        "---------------------------------------------------------------------------------------\n",
        "0     1.00000000e+10   -1.52142044e+12   2.0e+00   1.5e+04   1.5e+12  0.00  0.00   0.00 \n",
        "10    3.45214200e+11   -1.71045848e+10   2.7e+00   1.7e+02   4.0e+08  1.00  1.00  11.56 \n",
        "20    1.00000036e+07    1.00000000e+07   1.0e+00   0.0e+00   7.2e-03  1.00  0.25   3.81 \n",
        "21    1.00000007e+07    1.00000000e+07   1.0e+00   0.0e+00   1.4e-03  1.00  1.00   0.37 \n",
        "DSDP Converged. \n",
        "DSDP Dual Unbounded, Primal Infeasible\n",
        "\n",
        "P Objective  :   3.09883027e-01 \n",
        "DSDP Solution:   1.00000000e+07 \n",
        "\n",
        "DSDP Solve Time:                     1.372e-02 seconds\n",
        "DSDP Preparation and Solve Time:     1.391e-02 seconds\n",
        "\n",
        "\n",
        "P Infeasible: 5.00e-01 \n",
        "D Infeasible: 0.00e+00 \n",
        "Minimal P Eigenvalue: 0.00e+00 \n",
        "Minimal D Eigenvalue: 0.00 \n",
        "Relative P - D Objective values: -1.00e+00 \n",
        "Relative X Dot S: 3.10e-08 \n",
        "\n",
        "Max Y: 1.00000000e+07,  Bounded by 1.0e+07\n",
        "Trace X: 1.00131520e+01,   Bounded by Penalty Parameter: 1.0e+08 \n",
        "\n",
        "PERFORMANCE SUMMARY\n",
        "                     Event                      Calls    Time(s)   Time(%)\n",
        "--------------------------------------------------------------------------\n",
        "                                   R Cone        1171   1.1897e-04   0.84\n",
        "                             Bound Y Cone        1172   5.8627e-04   4.15\n",
        "                                 SDP Cone        1175   1.0917e-02  77.26\n",
        "                           Cone Setup 1&2           2   1.1396e-04   0.81\n",
        "                            Cone Invert S         201   1.3900e-04   0.98\n",
        "                                 Cone RHS         180   2.0082e-03  14.21\n",
        "                  Cone Compute Newton Eq.          21   2.0275e-03  14.35\n",
        "                   Cone Max P Step Length          21   4.4680e-04   3.16\n",
        "               Cone Compute and Factor SP          24   1.6379e-04   1.16\n",
        "                   Cone Max D Step Length         204   4.2412e-03  30.01\n",
        "                Cone Compute and Factor S         240   1.5836e-03  11.21\n",
        "                           Cone Potential         238   1.1387e-03   8.06\n",
        "                                Cone View          22   9.0599e-06   0.06\n",
        "                           Cone Compute X           1   8.7023e-05   0.62\n",
        "                                  SDP Dot       10803   1.4775e-03  10.46\n",
        "                               SDP SSolve        3080   1.4615e-04   1.03\n",
        "                                SDP X+vv'        3080   4.8733e-04   3.45\n",
        "                        Factor Newton Eq.          21   5.0306e-04   3.56\n",
        "                         Solve Newton Eq.         272   3.9077e-04   2.77\n",
        "                              Primal Step          21   7.7152e-04   5.46\n",
        "                                Dual Step          21   7.1764e-04   5.08\n",
        "                           Corrector Step         180   9.1679e-03  64.88\n",
        "                                 CG Solve         223   7.7915e-04   5.51\n",
        "                               DSDP Solve           1   1.3623e-02  96.40\n",
        "--------------------------------------------------------------------------\n",
        "--- DSDP Finished ---\n",
        "\n"
       ]
      }
     ],
     "prompt_number": 197
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Finding new solution"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "lmis_fbpe_ols_add = [LMI(U_rho)] + DB_LMIs_marg + DB_add_LMIs_marg"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 198
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "variables_fbpe_ols_add = [u] + list(beta_symbs) + list(delta_d)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 199
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "objf_fbpe_ols_add = u"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 200
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sol_fbpe_ols_add = solve_sdp(objf_fbpe_ols_add, lmis_fbpe_ols_add, variables_fbpe_ols_add)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "sdp.dat-s -save dsdp5.out -gaptol 1e-07 \n",
        "\n",
        "Variables 99 \n",
        "Matrix Blocks: 72, Total Number of Constraints: 176 \n",
        "Nonzeros in Constraints: 2907\n",
        "\n",
        "Read Data File into Buffer:      5.550e-03 seconds\n",
        "DSDP Set Data:                   2.770e-04 seconds\n",
        "DSDP Process Data:               2.512e-02 seconds\n",
        "\n",
        "Data Norms: C: 7.85e+04, A: 1.70e+04, b: 1.00e+00\n",
        "Scale C: 2.16e-01\n",
        "\n",
        "Potential Parameter: 5.00\n",
        "Reapply Schur matrix: 4\n",
        "\n",
        "Iter   PP Objective      DD Objective    PInfeas   DInfeas     Nu     StepLength   Pnrm\n",
        "---------------------------------------------------------------------------------------\n",
        "0     1.00000000e+10   -2.20525078e+17   2.0e+00   2.2e+09   2.2e+17  0.00  0.00   0.00 \n",
        "10    6.42274529e+10   -1.26844261e+10   7.1e+01   1.3e+02   5.4e+07  1.00  1.00  25.19 \n",
        "20    1.66393991e+07   -7.71143772e+05   8.2e-03   4.8e-04   2.8e+04  1.00  1.00   0.91 \n",
        "30    7.89224941e+04   -8.39443551e+04   7.6e-05   2.6e-06   2.5e+02  1.00  1.00   0.90 \n",
        "40   -7.87767914e+04   -7.93188073e+04   2.6e-07   0.0e+00   8.6e-01  1.00  1.00   0.58 \n",
        "49   -7.92968411e+04   -7.92968452e+04   2.0e-12   0.0e+00   2.5e-06  1.00  0.09  35.10 \n",
        "DSDP Converged. \n",
        "\n",
        "P Objective  :  -7.92968434e+04 \n",
        "DSDP Solution:  -7.92968452e+04 \n",
        "\n",
        "DSDP Solve Time:                     2.141e-01 seconds\n",
        "DSDP Preparation and Solve Time:     2.392e-01 seconds\n",
        "\n",
        "\n",
        "P Infeasible: 6.60e-07 \n",
        "D Infeasible: 0.00e+00 \n",
        "Minimal P Eigenvalue: 0.00e+00 \n",
        "Minimal D Eigenvalue: 0.00 \n",
        "Relative P - D Objective values: 1.16e-08 \n",
        "Relative X Dot S: 1.40e-08 \n",
        "\n",
        "Max Y: 5.77350269e+06,  Bounded by 1.0e+07\n",
        "Trace X: 1.56254795e+05,   Bounded by Penalty Parameter: 1.0e+08 \n",
        "\n",
        "PERFORMANCE SUMMARY\n",
        "                     Event                      Calls    Time(s)   Time(%)\n",
        "--------------------------------------------------------------------------\n",
        "                                   R Cone        1503   3.4451e-04   0.14\n",
        "                             Bound Y Cone        1503   2.5673e-03   1.07\n",
        "                                 SDP Cone        1511   2.0890e-01  87.21\n",
        "                           Cone Setup 1&2           2   2.4807e-02  10.36\n",
        "                            Cone Invert S         232   4.7350e-02  19.77\n",
        "                                 Cone RHS         183   6.6803e-03   2.79\n",
        "                  Cone Compute Newton Eq.          49   7.6302e-02  31.85\n",
        "                   Cone Max P Step Length          49   6.4700e-03   2.70\n",
        "               Cone Compute and Factor SP          52   2.5373e-03   1.06\n",
        "                   Cone Max D Step Length         235   2.8568e-02  11.93\n",
        "                Cone Compute and Factor S         308   1.3522e-02   5.64\n",
        "                           Cone Potential         302   5.0220e-03   2.10\n",
        "                                Cone View          50   2.2173e-05   0.01\n",
        "                           Cone Compute X           1   1.4482e-03   0.60\n",
        "                            SDP VecMatVec       10227   2.5274e-02  10.55\n",
        "                                  SDP Dot       27501   7.9923e-03   3.34\n",
        "                               SDP SSolve       34566   2.0879e-02   8.72\n",
        "                                SDP X+vv'       24339   1.2524e-02   5.23\n",
        "                        Factor Newton Eq.          49   1.2095e-02   5.05\n",
        "                         Solve Newton Eq.         517   6.6221e-03   2.76\n",
        "                              Primal Step          49   9.9127e-03   4.14\n",
        "                                Dual Step          49   9.3367e-03   3.90\n",
        "                           Corrector Step         183   8.9437e-02  37.34\n",
        "                                 CG Solve         283   1.1377e-02   4.75\n",
        "                               DSDP Solve           1   2.1258e-01  88.75\n",
        "--------------------------------------------------------------------------\n",
        "--- DSDP Finished ---\n",
        "\n"
       ]
      }
     ],
     "prompt_number": 201
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "u_starextra = sol_fbpe_ols_add[0,0]\n",
      "beta_starextra = numpy.matrix(sol_fbpe_ols_add[1:1+n_beta])\n",
      "delta_d_starextra = numpy.matrix(sol_fbpe_ols_add[1+n_beta:])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 202
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "u_starextra"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 203,
       "text": [
        "79296.845571512735"
       ]
      }
     ],
     "prompt_number": 203
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Solution Double Check"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "dict_subs = dict(zip(beta_symbs, beta_starextra.flatten().tolist()[0]))\n",
      "dict_subs.update(dict(zip(delta_d, delta_d_starextra.flatten().tolist()[0])))\n",
      "\n",
      "test = 'ok'\n",
      "for DBi in (DB_blocks + DB_add_blocks):\n",
      "        m = numpy.matrix(mrepl(DBi, dict_subs)).astype(float)\n",
      "        for v in numpy.linalg.eigvals( m ):\n",
      "            if v <= 0.0: test = 'fail'\n",
      "print(test)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "ok\n"
       ]
      }
     ],
     "prompt_number": 204
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "numpy.savetxt(tmpfolder + 'solutions/' + indentification_traj + '_beta_starextra.dat', beta_starextra)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 205
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Inertia Matrix Definiteness Tests"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def test_mass_matrix_psd(beta_solution):\n",
      "    K = rbt.dyn.Pb.T + rbt.dyn.Kd * rbt.dyn.Pd.T\n",
      "    A = numpy.matrix(K).astype(float)\n",
      "    b = numpy.matrix(beta_solution).astype(float)\n",
      "    x = numpy.linalg.pinv(A) * b\n",
      "    d_test = x\n",
      "    \n",
      "    M_func_def = sympybotics.robotcodegen.robot_code_to_func( 'python', rbt.M_code, 'M', 'M_func', rbt.rbtdef)\n",
      "    exec(M_func_def, globals())\n",
      "    global sin, cos\n",
      "    from math import sin, cos\n",
      "    \n",
      "    ntests = 10000\n",
      "    \n",
      "    ok = 0\n",
      "    nok = 0\n",
      "    for i in range(ntests):\n",
      "        q_test = numpy.random.rand(rbt.dof)\n",
      "        M_out = M_func( numpy.array(d_test).flatten().tolist(), q_test)\n",
      "        M = numpy.matrix(M_out).reshape((rbt.dof,rbt.dof))\n",
      "        try:\n",
      "            c = numpy.linalg.cholesky(M)\n",
      "        except:\n",
      "            nok += 1\n",
      "            continue\n",
      "        ok += 1\n",
      "        \n",
      "    print 'ok     %8i  %3i%%'%(ok, 100.0*ok/ntests) \n",
      "    print 'not ok %8i  %3i%%'%(nok, 100.0*nok/ntests)\n",
      "    if nok > 0 :\n",
      "        print('\\nNot PSD -> Not feasible!')\n",
      "    else:\n",
      "        print('\\nSeems feasible.')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 221
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "beta_ols = numpy.matrix(numpy.loadtxt(tmpfolder + 'solutions/traj1_beta_ols.dat')).T\n",
      "test_mass_matrix_psd(beta_ols)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "ok         4416   44%\n",
        "not ok     5584   55%\n",
        "\n",
        "Not PSD -> Not feasible!\n"
       ]
      }
     ],
     "prompt_number": 222
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "beta_starextra = numpy.matrix(numpy.loadtxt(tmpfolder + 'solutions/traj1_beta_starextra.dat')).T\n",
      "test_mass_matrix_psd(beta_starextra)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "ok        10000  100%\n",
        "not ok        0    0%\n",
        "\n",
        "Seems feasible.\n"
       ]
      }
     ],
     "prompt_number": 223
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "5 - Regression Model Validation\n",
      "===================================================="
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "import sympybotics\n",
      "import pickle\n",
      "\n",
      "from collections import OrderedDict\n",
      "from support_funcs.utils import ListTable"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 224
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "with open(tmpfolder +  'robotmodels/wam7_model.pkl', 'rb' ) as file:\n",
      "          rbt = pickle.load( file )"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 225
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def analyse(W, omega, R1, beta):\n",
      "    from numpy import matrix, mean\n",
      "    from numpy.linalg import cond, norm\n",
      "    \n",
      "    p = dict()\n",
      "    \n",
      "    n = W.shape[0]\n",
      "    \n",
      "    omega_norm = norm(omega)\n",
      "    omega_mean = mean(omega)\n",
      "    \n",
      "    p['err'] = norm(omega - W * beta)\n",
      "    p['merr'] = p['err'] / n\n",
      "    \n",
      "    p['se'] = p['err']**2\n",
      "    p['mse'] = p['se']/(n-W.shape[1])\n",
      "    p['rmse'] = p['mse']**0.5\n",
      "    \n",
      "    C = p['mse'] * (R1.T * R1).I\n",
      "    p['sd'] = np.sqrt(C.diagonal()).T\n",
      "    p['sd%'] = 100. * p['sd'] / np.abs(beta)\n",
      "    \n",
      "    p['relerr'] = p['err']/ omega_norm\n",
      "    p['relerr%'] = p['relerr']*100.\n",
      "    \n",
      "    p['1-r2'] = p['err']**2 / norm(omega - omega_mean)**2\n",
      "    p['r2'] = 1 - p['1-r2']\n",
      "\n",
      "    return p\n",
      "    "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 226
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "trajs = OrderedDict([('id', 'traj1'),\n",
      "                     ('vA', 'traj2'),\n",
      "                     ('vB', 'traj3'),\n",
      "                     ('vC', 'traj4')])\n",
      "\n",
      "\n",
      "betas = OrderedDict([('beta_ols', 'B^'),\n",
      "                     ('beta_prime', 'B\\''),\n",
      "                     ('beta_star', 'B*'),\n",
      "                     ('beta_starextra', 'B*e')])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 227
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "solutions_beta = {betaname:np.matrix(np.loadtxt(tmpfolder + 'solutions/%s_%s.dat'%(trajs['id'], betaname))).T for betaname in betas}"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 229
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "analysis = dict()\n",
      "\n",
      "for traj in trajs:\n",
      "    from numpy.linalg import cond\n",
      "    \n",
      "    print(traj)\n",
      "    \n",
      "    analysis[traj] = dict()\n",
      "    \n",
      "    regr_mats = np.load(tmpfolder + 'procdata/' + trajs[traj] + '_regr.npz')\n",
      "    W = np.matrix(regr_mats['W'])\n",
      "    omega = np.matrix(regr_mats['omega'])\n",
      "    R1 = np.matrix(regr_mats['R1'])\n",
      "    \n",
      "    analysis[traj]['cond'] = cond(W)\n",
      "    \n",
      "    analysis[traj]['betas'] = dict()\n",
      "    \n",
      "    for betaname in betas:\n",
      "        beta = solutions_beta[betaname]\n",
      "        analysis[traj]['betas'][betaname] = analyse(W, omega, R1, beta)\n",
      "    \n",
      "    del W, omega, R1"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "id\n",
        "vA"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "vB"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "vC"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      }
     ],
     "prompt_number": 232
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "prop = lambda x: x['relerr%']\n",
      "form = '%.2f'\n",
      "\n",
      "table = ListTable()\n",
      "table.append([''] + ['cond'] + betas.values())\n",
      "for (traj, trajname) in zip(trajs, ['identification', 'validation A', 'validation B', 'validation C']):\n",
      "    row = [traj] + ['%.0f'%analysis[traj]['cond']] + [ form%prop(analysis[traj]['betas'][b]) for b in betas]\n",
      "    table.append(row)\n",
      "table"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<table><tr><td></td><td>cond</td><td>B^</td><td>B'</td><td>B*</td><td>B*e</td></tr><tr><td>id</td><td>99</td><td>6.60</td><td>6.68</td><td>6.64</td><td>6.65</td></tr><tr><td>vA</td><td>94</td><td>7.16</td><td>7.14</td><td>7.01</td><td>6.98</td></tr><tr><td>vB</td><td>106</td><td>8.47</td><td>8.49</td><td>8.44</td><td>8.40</td></tr><tr><td>vC</td><td>101</td><td>6.81</td><td>6.79</td><td>6.76</td><td>6.74</td></tr></table>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 233,
       "text": [
        "[['', 'cond', 'B^', \"B'\", 'B*', 'B*e'],\n",
        " ['id', '99', '6.60', '6.68', '6.64', '6.65'],\n",
        " ['vA', '94', '7.16', '7.14', '7.01', '6.98'],\n",
        " ['vB', '106', '8.47', '8.49', '8.44', '8.40'],\n",
        " ['vC', '101', '6.81', '6.79', '6.76', '6.74']]"
       ]
      }
     ],
     "prompt_number": 233
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import yaml, sympy\n",
      "with open(datafolder + 'robotparams/wam7_cad.yml', 'r') as f:\n",
      "    wam7_cad = yaml.load(f)\n",
      "delta_cad = sympy.Matrix([wam7_cad.get(str(d), d) for d in rbt.dyn.dynparms])\n",
      "beta_cad = (rbt.dyn.Pb.T + rbt.dyn.Kd * rbt.dyn.Pd.T) * delta_cad"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 234
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "form = '%.4g'\n",
      "\n",
      "import sympy\n",
      "\n",
      "table = ListTable()\n",
      "header = ['', 'Bcad', 'B^', '% std dev B^', 'B*e']\n",
      "table.append(header)\n",
      "for i, b in enumerate(rbt.dyn.baseparms):\n",
      "    if beta_cad[i].is_Number:\n",
      "        cad_v = sympy.N(beta_cad[i], 4)\n",
      "    elif beta_cad[i].is_Symbol:\n",
      "        cad_v = '---'\n",
      "    else:\n",
      "        cad_v = sympy.N(beta_cad[i], 4)\n",
      "    row = ['%.7s ...'%b if len(str(b)) > 7 else str(b), cad_v]\n",
      "    row += [form%solutions_beta['beta_ols'][i,0], '%.2g'%analysis['id']['betas']['beta_ols']['sd%'][i,0]]\n",
      "    row += [form%solutions_beta['beta_starextra'][i,0]]\n",
      "    table.append(row)\n",
      "table"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<table><tr><td></td><td>Bcad</td><td>B^</td><td>% std dev B^</td><td>B*e</td></tr><tr><td>Ia_1 +  ...</td><td>Ia_1 + 0.1328</td><td>0.3381</td><td>0.53</td><td>0.3049</td></tr><tr><td>fv_1</td><td>---</td><td>1.63</td><td>0.28</td><td>1.648</td></tr><tr><td>fc_1</td><td>---</td><td>1.601</td><td>0.26</td><td>1.605</td></tr><tr><td>fo_1</td><td>---</td><td>0.01037</td><td>18</td><td>0.007658</td></tr><tr><td>L_2xx - ...</td><td>1.181</td><td>1.017</td><td>0.29</td><td>1.04</td></tr><tr><td>L_2xy</td><td>1.347e-5</td><td>-0.0505</td><td>3.2</td><td>-0.05561</td></tr><tr><td>L_2xz</td><td>0.0001170</td><td>-0.02539</td><td>4.8</td><td>-0.02304</td></tr><tr><td>Ia_2 +  ...</td><td>Ia_2 + 1.189</td><td>1.451</td><td>0.23</td><td>1.446</td></tr><tr><td>L_2yz</td><td>-3.659e-5</td><td>-0.03322</td><td>4.3</td><td>-0.038</td></tr><tr><td>l_2x</td><td>-0.009183</td><td>0.08154</td><td>1.7</td><td>0.08391</td></tr><tr><td>l_2z -  ...</td><td>2.333</td><td>2.358</td><td>0.027</td><td>2.36</td></tr><tr><td>fv_2</td><td>---</td><td>2.372</td><td>0.21</td><td>2.364</td></tr><tr><td>fc_2</td><td>---</td><td>0.533</td><td>0.71</td><td>0.5332</td></tr><tr><td>fo_2</td><td>---</td><td>0.898</td><td>1.2</td><td>0.9296</td></tr><tr><td>L_3xx - ...</td><td>0.003856</td><td>-0.01168</td><td>20</td><td>0.0183</td></tr><tr><td>L_3xy - ...</td><td>-2.509e-5</td><td>0.03663</td><td>2.9</td><td>0.02517</td></tr><tr><td>L_3xz</td><td>-5.098e-6</td><td>0.002625</td><td>45</td><td>-0.00827</td></tr><tr><td>L_3yy + ...</td><td>-0.006954</td><td>-0.06614</td><td>2.2</td><td>0.001251</td></tr><tr><td>L_3yz</td><td>5.295e-6</td><td>-0.04278</td><td>2.5</td><td>-0.03598</td></tr><tr><td>l_3x +  ...</td><td>0.1476</td><td>0.1194</td><td>0.44</td><td>0.1255</td></tr><tr><td>l_3z +  ...</td><td>-0.0004910</td><td>-0.002107</td><td>18</td><td>-0.0009105</td></tr><tr><td>Ia_3</td><td>---</td><td>0.1139</td><td>1.3</td><td>0.06988</td></tr><tr><td>fv_3</td><td>---</td><td>0.8554</td><td>0.52</td><td>0.8111</td></tr><tr><td>fc_3</td><td>---</td><td>0.3454</td><td>1.1</td><td>0.3718</td></tr><tr><td>fo_3</td><td>---</td><td>-0.09566</td><td>2.1</td><td>-0.08749</td></tr><tr><td>L_4xx - ...</td><td>0.1149</td><td>0.165</td><td>0.9</td><td>0.1385</td></tr><tr><td>L_4xy + ...</td><td>-3.944e-5</td><td>0.01292</td><td>5.4</td><td>0.009043</td></tr><tr><td>L_4xz</td><td>-8.193e-5</td><td>-0.02431</td><td>2.4</td><td>-0.01386</td></tr><tr><td>L_4yy + ...</td><td>0.1057</td><td>0.1213</td><td>1.1</td><td>0.1239</td></tr><tr><td>L_4yz</td><td>9.417e-5</td><td>-0.01128</td><td>6.2</td><td>-0.005383</td></tr><tr><td>l_4x -  ...</td><td>-0.1235</td><td>-0.1057</td><td>0.35</td><td>-0.101</td></tr><tr><td>l_4z -  ...</td><td>0.5010</td><td>0.5209</td><td>0.088</td><td>0.5174</td></tr><tr><td>Ia_4</td><td>---</td><td>-0.005825</td><td>27</td><td>1.009e-06</td></tr><tr><td>fv_4</td><td>---</td><td>0.6153</td><td>0.8</td><td>0.6005</td></tr><tr><td>fc_4</td><td>---</td><td>0.6291</td><td>0.57</td><td>0.6417</td></tr><tr><td>fo_4</td><td>---</td><td>0.05353</td><td>5.4</td><td>0.03402</td></tr><tr><td>L_5xx - ...</td><td>0.0005648</td><td>-0.008932</td><td>12</td><td>-0.01554</td></tr><tr><td>L_5xy</td><td>-2.564e-7</td><td>0.005089</td><td>7.4</td><td>-0.002231</td></tr><tr><td>L_5xz</td><td>1.882e-9</td><td>0.0198</td><td>2.4</td><td>0.01646</td></tr><tr><td>L_5yy + ...</td><td>0.0006530</td><td>0.006071</td><td>11</td><td>0.007886</td></tr><tr><td>L_5yz</td><td>8.326e-7</td><td>-0.0092</td><td>4.5</td><td>-0.002773</td></tr><tr><td>l_5x</td><td>1.104e-5</td><td>0.006003</td><td>4.9</td><td>0.006159</td></tr><tr><td>l_5z +  ...</td><td>-0.006580</td><td>-0.01351</td><td>2</td><td>-0.01388</td></tr><tr><td>Ia_5</td><td>---</td><td>-0.0009694</td><td>81</td><td>1.004e-06</td></tr><tr><td>fv_5</td><td>---</td><td>0.1457</td><td>3.3</td><td>0.1387</td></tr><tr><td>fc_5</td><td>---</td><td>0.03597</td><td>7.7</td><td>0.03627</td></tr><tr><td>fo_5</td><td>---</td><td>0.004681</td><td>43</td><td>0.001217</td></tr><tr><td>L_6xx - ...</td><td>0.0006155</td><td>0.003965</td><td>20</td><td>0.009329</td></tr><tr><td>L_6xy</td><td>-1.483e-6</td><td>0.001507</td><td>22</td><td>-0.002418</td></tr><tr><td>L_6xz</td><td>2.005e-6</td><td>-0.01062</td><td>3.4</td><td>-0.003334</td></tr><tr><td>L_6yy + ...</td><td>0.0007576</td><td>0.01942</td><td>3</td><td>0.01731</td></tr><tr><td>L_6yz</td><td>0.0002216</td><td>0.00495</td><td>7.2</td><td>0.004267</td></tr><tr><td>l_6x</td><td>-5.125e-5</td><td>-0.007862</td><td>3.2</td><td>-0.006727</td></tr><tr><td>l_6z +  ...</td><td>0.01421</td><td>0.009031</td><td>2.4</td><td>0.009509</td></tr><tr><td>Ia_6</td><td>---</td><td>-0.008871</td><td>10</td><td>1.003e-06</td></tr><tr><td>fv_6</td><td>---</td><td>0.1437</td><td>3.2</td><td>0.1344</td></tr><tr><td>fc_6</td><td>---</td><td>0.06428</td><td>4.7</td><td>0.07144</td></tr><tr><td>fo_6</td><td>---</td><td>-0.007354</td><td>26</td><td>-0.007547</td></tr><tr><td>L_7xx - ...</td><td>-3.286e-7</td><td>-0.01584</td><td>3.2</td><td>-0.01357</td></tr><tr><td>L_7xy</td><td>1.909e-7</td><td>-0.002082</td><td>12</td><td>-0.0009831</td></tr><tr><td>L_7xz</td><td>-1.771e-8</td><td>0.0002248</td><td>61</td><td>6.76e-05</td></tr><tr><td>L_7yz</td><td>3.623e-8</td><td>0.0002694</td><td>52</td><td>0.0007734</td></tr><tr><td>L_7zz</td><td>7.408e-5</td><td>-0.0005387</td><td>29</td><td>0.0003627</td></tr><tr><td>l_7x</td><td>-5.474e-6</td><td>0.00782</td><td>2.4</td><td>0.007006</td></tr><tr><td>l_7y</td><td>1.120e-5</td><td>-0.0003508</td><td>52</td><td>-0.0003549</td></tr><tr><td>Ia_7</td><td>---</td><td>0.0009977</td><td>27</td><td>0.0001039</td></tr><tr><td>fv_7</td><td>---</td><td>0.05763</td><td>5.6</td><td>0.05625</td></tr><tr><td>fc_7</td><td>---</td><td>0.0118</td><td>27</td><td>0.01253</td></tr><tr><td>fo_7</td><td>---</td><td>-0.002192</td><td>84</td><td>-0.002699</td></tr></table>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 271,
       "text": [
        "[['', 'Bcad', 'B^', '% std dev B^', 'B*e'],\n",
        " ['Ia_1 +  ...', Ia_1 + 0.1328, '0.3381', '0.53', '0.3049'],\n",
        " ['fv_1', '---', '1.63', '0.28', '1.648'],\n",
        " ['fc_1', '---', '1.601', '0.26', '1.605'],\n",
        " ['fo_1', '---', '0.01037', '18', '0.007658'],\n",
        " ['L_2xx - ...', 1.181, '1.017', '0.29', '1.04'],\n",
        " ['L_2xy', 1.347e-5, '-0.0505', '3.2', '-0.05561'],\n",
        " ['L_2xz', 0.0001170, '-0.02539', '4.8', '-0.02304'],\n",
        " ['Ia_2 +  ...', Ia_2 + 1.189, '1.451', '0.23', '1.446'],\n",
        " ['L_2yz', -3.659e-5, '-0.03322', '4.3', '-0.038'],\n",
        " ['l_2x', -0.009183, '0.08154', '1.7', '0.08391'],\n",
        " ['l_2z -  ...', 2.333, '2.358', '0.027', '2.36'],\n",
        " ['fv_2', '---', '2.372', '0.21', '2.364'],\n",
        " ['fc_2', '---', '0.533', '0.71', '0.5332'],\n",
        " ['fo_2', '---', '0.898', '1.2', '0.9296'],\n",
        " ['L_3xx - ...', 0.003856, '-0.01168', '20', '0.0183'],\n",
        " ['L_3xy - ...', -2.509e-5, '0.03663', '2.9', '0.02517'],\n",
        " ['L_3xz', -5.098e-6, '0.002625', '45', '-0.00827'],\n",
        " ['L_3yy + ...', -0.006954, '-0.06614', '2.2', '0.001251'],\n",
        " ['L_3yz', 5.295e-6, '-0.04278', '2.5', '-0.03598'],\n",
        " ['l_3x +  ...', 0.1476, '0.1194', '0.44', '0.1255'],\n",
        " ['l_3z +  ...', -0.0004910, '-0.002107', '18', '-0.0009105'],\n",
        " ['Ia_3', '---', '0.1139', '1.3', '0.06988'],\n",
        " ['fv_3', '---', '0.8554', '0.52', '0.8111'],\n",
        " ['fc_3', '---', '0.3454', '1.1', '0.3718'],\n",
        " ['fo_3', '---', '-0.09566', '2.1', '-0.08749'],\n",
        " ['L_4xx - ...', 0.1149, '0.165', '0.9', '0.1385'],\n",
        " ['L_4xy + ...', -3.944e-5, '0.01292', '5.4', '0.009043'],\n",
        " ['L_4xz', -8.193e-5, '-0.02431', '2.4', '-0.01386'],\n",
        " ['L_4yy + ...', 0.1057, '0.1213', '1.1', '0.1239'],\n",
        " ['L_4yz', 9.417e-5, '-0.01128', '6.2', '-0.005383'],\n",
        " ['l_4x -  ...', -0.1235, '-0.1057', '0.35', '-0.101'],\n",
        " ['l_4z -  ...', 0.5010, '0.5209', '0.088', '0.5174'],\n",
        " ['Ia_4', '---', '-0.005825', '27', '1.009e-06'],\n",
        " ['fv_4', '---', '0.6153', '0.8', '0.6005'],\n",
        " ['fc_4', '---', '0.6291', '0.57', '0.6417'],\n",
        " ['fo_4', '---', '0.05353', '5.4', '0.03402'],\n",
        " ['L_5xx - ...', 0.0005648, '-0.008932', '12', '-0.01554'],\n",
        " ['L_5xy', -2.564e-7, '0.005089', '7.4', '-0.002231'],\n",
        " ['L_5xz', 1.882e-9, '0.0198', '2.4', '0.01646'],\n",
        " ['L_5yy + ...', 0.0006530, '0.006071', '11', '0.007886'],\n",
        " ['L_5yz', 8.326e-7, '-0.0092', '4.5', '-0.002773'],\n",
        " ['l_5x', 1.104e-5, '0.006003', '4.9', '0.006159'],\n",
        " ['l_5z +  ...', -0.006580, '-0.01351', '2', '-0.01388'],\n",
        " ['Ia_5', '---', '-0.0009694', '81', '1.004e-06'],\n",
        " ['fv_5', '---', '0.1457', '3.3', '0.1387'],\n",
        " ['fc_5', '---', '0.03597', '7.7', '0.03627'],\n",
        " ['fo_5', '---', '0.004681', '43', '0.001217'],\n",
        " ['L_6xx - ...', 0.0006155, '0.003965', '20', '0.009329'],\n",
        " ['L_6xy', -1.483e-6, '0.001507', '22', '-0.002418'],\n",
        " ['L_6xz', 2.005e-6, '-0.01062', '3.4', '-0.003334'],\n",
        " ['L_6yy + ...', 0.0007576, '0.01942', '3', '0.01731'],\n",
        " ['L_6yz', 0.0002216, '0.00495', '7.2', '0.004267'],\n",
        " ['l_6x', -5.125e-5, '-0.007862', '3.2', '-0.006727'],\n",
        " ['l_6z +  ...', 0.01421, '0.009031', '2.4', '0.009509'],\n",
        " ['Ia_6', '---', '-0.008871', '10', '1.003e-06'],\n",
        " ['fv_6', '---', '0.1437', '3.2', '0.1344'],\n",
        " ['fc_6', '---', '0.06428', '4.7', '0.07144'],\n",
        " ['fo_6', '---', '-0.007354', '26', '-0.007547'],\n",
        " ['L_7xx - ...', -3.286e-7, '-0.01584', '3.2', '-0.01357'],\n",
        " ['L_7xy', 1.909e-7, '-0.002082', '12', '-0.0009831'],\n",
        " ['L_7xz', -1.771e-8, '0.0002248', '61', '6.76e-05'],\n",
        " ['L_7yz', 3.623e-8, '0.0002694', '52', '0.0007734'],\n",
        " ['L_7zz', 7.408e-5, '-0.0005387', '29', '0.0003627'],\n",
        " ['l_7x', -5.474e-6, '0.00782', '2.4', '0.007006'],\n",
        " ['l_7y', 1.120e-5, '-0.0003508', '52', '-0.0003549'],\n",
        " ['Ia_7', '---', '0.0009977', '27', '0.0001039'],\n",
        " ['fv_7', '---', '0.05763', '5.6', '0.05625'],\n",
        " ['fc_7', '---', '0.0118', '27', '0.01253'],\n",
        " ['fo_7', '---', '-0.002192', '84', '-0.002699']]"
       ]
      }
     ],
     "prompt_number": 271
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Torque Plot"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "traj = 'vA'\n",
      "betaname = 'beta_starextra'"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 301
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "regr_mats = np.load(tmpfolder + 'procdata/' + trajs[traj] + '_regr.npz')\n",
      "W = np.matrix(regr_mats['W'])\n",
      "omega = np.matrix(regr_mats['omega'])\n",
      "\n",
      "regr_mats = np.load(tmpfolder + 'procdata/' + trajs[traj] + '_proc.npz')\n",
      "t = regr_mats['t']\n",
      "tau_proc = np.matrix(regr_mats['tau'])\n",
      "\n",
      "regr_mats = np.load(tmpfolder + 'procdata/' + trajs[traj] + '_raw.npz')\n",
      "tau_raw = np.matrix(regr_mats['tau'])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 302
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "beta_solution = np.matrix(np.loadtxt(tmpfolder + 'solutions/%s_%s.dat'%(trajs['id'], betaname))).T"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 303
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "tau = tau_raw"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 304
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "omega_pred = W * beta_solution\n",
      "tau_pred = omega_pred.reshape( omega_pred.shape[0]/tau.shape[1], tau.shape[1] )\n",
      "err_pred = tau - tau_pred"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 305
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "joint = 7\n",
      "firsts = 20000\n",
      "s=tau_raw.shape[0]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 306
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from matplotlib import pyplot as plt\n",
      "plt.close()\n",
      "\n",
      "plt.figure(figsize=(12,8))\n",
      "\n",
      "axes = []\n",
      "for i in range(tau.shape[1]):\n",
      "    ax = plt.subplot(3, 3, i+1)\n",
      "    ax.plot(t[:firsts],tau_raw[:,i][:firsts], label=\"Measured torque\")\n",
      "    ax.plot(t[:firsts],tau_pred[:,i][:firsts], label=\"Estimated torque\")\n",
      "    ax.plot(t[:firsts],err_pred[:,i][:firsts], label=\"Error\")\n",
      "    ax.set_title( \"Joint %d\"%(i+1) )\n",
      "    plt.xlabel(\"Time (s)\")\n",
      "    plt.ylabel(\"Torque (Nm)\")\n",
      "    axes.append(ax)\n",
      "\n",
      "plt.tight_layout()\n",
      "\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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B3XUweqCUd6jGXI26Co1OQIR37r5161B06oWxnI7Sj2u1NLIkzJtnaAlKQc37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\nBoGQAKGEJEASQgihS0elGooUEUUBuygIFnxRLOC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66DXfz9iLbpKlUplf1/ffNy5sunB8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H3NsTX8krwOMno5/Ju/vetNhHSxUym201eQG0f3sGvvnvbYJKuyspLLly9TVFRERUUFQgiEEFRU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/DYY/Djj4wCRoGYfM+YATNnqjsrIiv4l/vgNUkhIsvmsPHdge/Eqd4I5g9ms1jH5PEE1l8F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\n",
       "text": [
        "<matplotlib.figure.Figure at 0xc078b10>"
       ]
      }
     ],
     "prompt_number": 310
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "---------------------------\n",
      "\n",
      "---------------------------\n",
      "\n",
      "---------------------------\n",
      "\n",
      "---------------------------\n",
      "\n",
      "---------------------------\n",
      "\n",
      "---------------------------\n",
      "\n",
      "---------------------------\n",
      "\n",
      "---------------------------\n",
      "\n",
      "---------------------------\n",
      "\n",
      "### (generate readme and notebook preview)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def save_files(): \n",
      "    from IPython.display import display, Javascript\n",
      "    Javascript('IPython.notebook.save_notebook()')\n",
      "    \n",
      "    import json\n",
      "    with open('WAM7 Dynamic Parameter Identification.ipynb', 'r') as f:\n",
      "        d = json.load(f)\n",
      "    with open('README.md', 'w') as f:\n",
      "        f.write(''.join(d['worksheets'][0]['cells'][0]['source']).encode('UTF-8'))\n",
      "    \n",
      "    !ipython nbconvert \"WAM7 Dynamic Parameter Identification.ipynb\" --to html"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#save_files()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#!git status"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 36
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#!git commit -a -m \"Add automathic README.md file generator\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 37
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#!git push"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 38
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}