Appendix_02_PETSc4Py.ipynb

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      "# Introducing Python\n",
      "# Python in HPC\n",
      "\n",
      "## Supercomputing 2012\n",
      "\n",
      "Presenters: \n",
      "\n",
      "Andy R. Terrel, PhD  \n",
      "Texas Advanced Computing Center  \n",
      "University of Texas at Austin  \n",
      "\n",
      "Travis Oliphant, PhD  \n",
      "Continuum Analytics \n",
      "\n",
      "Aron Ahmadia, PhD  \n",
      "Supercomputing Laboratory  \n",
      "King Abdullah University of Science and Technoglogy \n",
      "\n",
      "Originally written by: Yaakoub El Khamra, TACC\n",
      "\n",
      "[![Creative Commons License](/files/figures/creative_commons_logo.png)](http://creativecommons.org/licenses/by/3.0/deed.en_US)  \n",
      "\n",
      "![TACC Logo](/files/figures/TACC_logo.png)\n",
      "![Continuum Logo](/files/figures/continuum.png)\n",
      "![KAUST Logo](/files/figures/kaust.png)\n",
      "\n",
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      "---\n",
      "\n",
      "## Interacting with the Tutorial Slides\n",
      "<!--====-->\n",
      "\n",
      "This tutorial is an interactive worksheet designed to encourage you to try out the lessons during the demonstration.  If you are looking at the pdf version, we encourage you to download the updated version (see previous slide) and try the interactive version.\n",
      "\n",
      "To run the interactive version, you need a good Python environment including: \n",
      "\n",
      "* IPython version >= 13.0\n",
      "* Numpy version >= 1.5\n",
      "* Scipy\n",
      "* Matplotlib\n",
      "\n",
      "Move to the directory containing the tarball and execute:\n",
      "\n",
      "    $ ipython notebook --pylab=inline\n",
      "\n",
      "We heartily endorse the [Anaconda distribution](https://store.continuum.io/cshop/anaconda) and the [Free Enthought Python Distribution](http://www.enthought.com/products/epd_free.php). "
     ]
    },
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      "---\n",
      "## Presentation mode\n",
      "<!--====-->\n",
      "The slide show mode is only supported by an IPython development branch version. To get it I recommend cloning from the official branch, adding Matthias Carreau's remote, fetching and using his branch slideshow_extension2.  Here are the commands:\n",
      "\n",
      "    git clone git://github.com/ipython/ipython.git # Official clone\n",
      "    cd ipython\n",
      "    git remote add carreau git://github.com/Carreau/ipython.git # Matthias' branch\n",
      "    git fetch carreau # Fetch the branches\n",
      "    git checkout carreau/slideshow_extension2 # Checkout the slideshow extension\n",
      "    python setup.py develop # Install the development version\n",
      "    ipython notebook # Check out the slideshows.\n"
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      "            IPython.ptoolbar = ptoolbar;\n",
      "            ptoolbar.addButtonsGroup([{label:'Stop', icon:'ui-icon-stop', callback:function(){that.stop()}}])\n",
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      "---\n",
      "\n",
      "Acknowledgements\n",
      "-------------------------------------\n",
      "<!--====-->\n",
      "\n",
      "* petsc4py examples developed by [Lisandro Dalcin](http://www.bu.edu/pasi/people/lisandro-dalcin/)\n",
      "* [petsc4py](http://code.google.com/p/petsc4py/) petsc4py are Python bindings for [PETSc](http://www.mcs.anl.gov/petsc/), the Portable, Extensible Toolkit for Scientific Computation. "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "---\n",
      "\n",
      "What is PETSc\n",
      "-------------------------------------\n",
      "<!--====-->\n",
      "\n",
      "\u201cPETSc\u2026is a suite of data structures and routines for the scalable (parallel) solution of scientific applications modeled by partial differential equations. It supports MPI,\u00a0shared memory pthreads, and\u00a0NVIDIA GPUs, as well as hybrid MPI-shared memory pthreads or MPI-GPU parallelism\u201d\n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "---\n",
      "\n",
      "PETSc's Role\n",
      "-------------------------------------\n",
      "<!--====-->\n",
      "\n",
      "Developing parallel, nontrivial PDE solvers that deliver high performance is still dif\ufb01cult and requires months (or even years) of concentrated effort. PETSc is a toolkit that can ease these dif\ufb01culties and reduce the development time, but it is not a black-box PDE solver, nor a silver bullet.\n",
      "Barry Smith"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "---\n",
      "\n",
      "What can you use it for?\n",
      "-------------------------------------\n",
      "<!--====-->\n",
      "\n",
      " * Scientific Computations: parallel linear algebra, in particular linear and nonlinear solvers\n",
      " * Toolkit: Contains high level solvers, but also the low level tools to roll your own.\n",
      " * Portable: Available on many platforms, basically anything that has MPI\n",
      "\n",
      "Why use it? It's big, powerful, well supported."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "---\n",
      "\n",
      "A bit more about PETSc\n",
      "-------------------------------------\n",
      "<!--====-->\n",
      "\n",
      "What problems can it tackle:\n",
      "\n",
      " * Serial and Parallel\n",
      " * Linear and nonlinear\n",
      " * Finite difference and finite element\n",
      " * Structured and unstructured\n",
      "\n",
      "What is in PETSc:\n",
      "\n",
      " * Linear system solvers (sparse/dense, iterative/direct)\n",
      " * Nonlinear system solvers\n",
      " * Tools for distributed matrices\n",
      " * Support for profiling, debugging, graphical output\n",
      "\n",
      "And much much more"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "---\n",
      "\n",
      "Where to learn more about PETSc\n",
      "-------------------------------------\n",
      "<!--====-->\n",
      "\n",
      " * PETSc Tutorial at TACC\n",
      " * Regular tutorials by PETSc developers\n",
      " * [The PETSc website](http://www.mcs.anl.gov/petsc/)\n",
      " * [The PETSc documentation](http://www.mcs.anl.gov/petsc/documentation/index.html)\n",
      " * PETSc source code examples in the tarball"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "---\n",
      "\n",
      "PETSc4Py\n",
      "-------------------------------------\n",
      "<!--====-->\n",
      "\n",
      "* Python bindings for PETSc, the Portable Extensible Toolkit for Scientic Computation\n",
      "* Implemented with Cython\n",
      "* A good friend of petsc4py is:\n",
      " - mpi4py: Python bindings for MPI, the Message Passing Interface\n",
      "* Other two projects depend on petsc4py:\n",
      " - slepc4py: Python bindings for SLEPc, the Scalable Library for Eigenvalue Problem Computations\n",
      " - tao4py: Python bindings for TAO, the Toolkit for Advanced Optimization"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "---\n",
      "\n",
      "Python for control and logic C for local computation\n",
      "-------------------------------------\n",
      "<!--====-->\n",
      "\n",
      "* Decouple organization of storage from mathematical operations\n",
      " - Vectors are not arrays\n",
      "* Lots of small arrays\n",
      " - get/setValues() methods\n",
      "* Views into larger arrays\n",
      "* Dense, local computation is cache/bandwidth e\ufb03cient"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "---\n",
      "\n",
      "PETSc4Py Interface\n",
      "-------------------------------------\n",
      "<!--====-->\n",
      "\n",
      "* Using PETSc4Py is very similar to using MPI4Py\n",
      "* Provides ALL PETSc functionality in a Pythonic way\n",
      "* Manages all memory (creation/destruction)\n",
      "* Visualization with matplotlib"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "---\n",
      "\n",
      "PETSc4Py Basic Operations\n",
      "-------------------------------------\n",
      "<!--====-->\n",
      "\n",
      "* Create a sparse matrix, set its size and type:\n",
      " - A = PETSc.Mat()\n",
      " - A.create(PETSc.COMM_WORLD)\n",
      " - A.setSizes([m*n, m*n])\n",
      " - A.setType(\u2018mpiaij')\n",
      "* Create a linear solver and solve:\n",
      " - ksp = PETSc.KSP()\n",
      " - ksp.create(PETSc.COMM_WORLD)\n",
      " - ksp.setOperators(A)\n",
      " - ksp.setFromOptions()\n",
      " - ksp.solve(b, x)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "---\n",
      "\n",
      "PETSc4Py Example\n",
      "-------------------------------------\n",
      "<!--====-->\n",
      "\n",
      "2D Poisson problem: -Laplacian(u) = 1, 0 < x,y < 1\n",
      "\n",
      "with boundary conditions u = 0 for x=0, x=1, y=0, y=1"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "try: range = xrange\n",
      "except: pass\n",
      "\n",
      "import sys, petsc4py\n",
      "petsc4py.init(sys.argv)\n",
      "\n",
      "from petsc4py import PETSc\n",
      "\n",
      "class Poisson2D(object):\n",
      "\n",
      "    def __init__(self, da):\n",
      "        assert da.getDim() == 2\n",
      "        self.da = da\n",
      "        self.localX  = da.createLocalVec()\n",
      "\n",
      "    def formRHS(self, B):\n",
      "        b = self.da.getVecArray(B)\n",
      "        mx, my = self.da.getSizes()\n",
      "        hx, hy = [1.0/m for m in [mx, my]]\n",
      "        (xs, xe), (ys, ye) = self.da.getRanges()\n",
      "        for j in range(ys, ye):\n",
      "            for i in range(xs, xe):\n",
      "                b[i, j] = 1*hx*hy\n",
      "\n",
      "    def mult(self, mat, X, Y):\n",
      "        #\n",
      "        self.da.globalToLocal(X, self.localX)\n",
      "        x = self.da.getVecArray(self.localX)\n",
      "        y = self.da.getVecArray(Y)\n",
      "        #\n",
      "        mx, my = self.da.getSizes()\n",
      "        hx, hy = [1.0/m for m in [mx, my]]\n",
      "        (xs, xe), (ys, ye) = self.da.getRanges()\n",
      "        for j in range(ys, ye):\n",
      "            for i in range(xs, xe):\n",
      "                u = x[i, j] # center\n",
      "                u_e = u_w = u_n = u_s = 0\n",
      "                if i > 0:    u_w = x[i-1, j] # west\n",
      "                if i < mx-1: u_e = x[i+1, j] # east\n",
      "                if j > 0:    u_s = x[i, j-1] # south\n",
      "                if j < ny-1: u_n = x[i, j+1] # north\n",
      "                u_xx = (-u_e + 2*u - u_w)*hy/hx\n",
      "                u_yy = (-u_n + 2*u - u_s)*hx/hy\n",
      "                y[i, j] = u_xx + u_yy\n",
      "\n",
      "OptDB = PETSc.Options()\n",
      "\n",
      "n  = OptDB.getInt('n', 16)\n",
      "nx = OptDB.getInt('nx', n)\n",
      "ny = OptDB.getInt('ny', n)\n",
      "\n",
      "da = PETSc.DA().create([nx, ny], stencil_width=1)\n",
      "pde = Poisson2D(da)\n",
      "\n",
      "x = da.createGlobalVec()\n",
      "b = da.createGlobalVec()\n",
      "# A = da.createMat('python')\n",
      "A = PETSc.Mat().createPython(\n",
      "    [x.getSizes(), b.getSizes()], comm=da.comm)\n",
      "A.setPythonContext(pde)\n",
      "A.setUp()\n",
      "\n",
      "ksp = PETSc.KSP().create()\n",
      "ksp.setOperators(A)\n",
      "ksp.setType('cg')\n",
      "pc = ksp.getPC()\n",
      "pc.setType('none')\n",
      "ksp.setFromOptions()\n",
      "\n",
      "pde.formRHS(b)\n",
      "ksp.solve(b, x)\n",
      "\n",
      "u = da.createNaturalVec()\n",
      "da.globalToNatural(x, u)\n",
      "\n",
      "from matplotlib import pylab\n",
      "from numpy import mgrid\n",
      "\n",
      "X, Y =  mgrid[0:1:1j*nx,0:1:1j*ny]\n",
      "Z = x[...].reshape(nx,ny, order='F')\n",
      "pylab.figure()\n",
      "pylab.contourf(X,Y,Z)\n",
      "pylab.plot(X.ravel(),Y.ravel(),'.k')\n",
      "pylab.axis('equal')\n",
      "pylab.colorbar()\n",
      "pylab.show()    "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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HDsydO1ewTdOWJvSywfTZDiYmxYm2wZRtlXhAWytLIMSSEuy+EVLjlI4Vg2IW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\nYS0mp9j746M1+KrCuLg4pqc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zmD59OuLj9bOEueuuu3i3qBlt7pkVwwtxpP16QsfoKWws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\n"
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "---\n",
      "\n",
      "PETSc4Py and in parallel\n",
      "-------------------------------------\n",
      "<!--====-->"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Some preliminaries to connect to the engines\n",
      "\n",
      "from IPython.parallel import Client\n",
      "c = Client()\n",
      "view = c[:]\n",
      "\n",
      "%load_ext parallelmagic\n",
      "view.activate()\n",
      "view.block = True\n",
      "%autopx"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "%autopx enabled\n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "try: range = xrange\n",
      "except: pass\n",
      "\n",
      "import sys, petsc4py\n",
      "petsc4py.init(sys.argv)\n",
      "\n",
      "from petsc4py import PETSc\n",
      "\n",
      "class Poisson2D(object):\n",
      "\n",
      "    def __init__(self, da):\n",
      "        assert da.getDim() == 2\n",
      "        self.da = da\n",
      "        self.localX  = da.createLocalVec()\n",
      "\n",
      "    def formRHS(self, B):\n",
      "        b = self.da.getVecArray(B)\n",
      "        mx, my = self.da.getSizes()\n",
      "        hx, hy = [1.0/m for m in [mx, my]]\n",
      "        (xs, xe), (ys, ye) = self.da.getRanges()\n",
      "        for j in range(ys, ye):\n",
      "            for i in range(xs, xe):\n",
      "                b[i, j] = 1*hx*hy\n",
      "\n",
      "    def mult(self, mat, X, Y):\n",
      "        #\n",
      "        self.da.globalToLocal(X, self.localX)\n",
      "        x = self.da.getVecArray(self.localX)\n",
      "        y = self.da.getVecArray(Y)\n",
      "        #\n",
      "        mx, my = self.da.getSizes()\n",
      "        hx, hy = [1.0/m for m in [mx, my]]\n",
      "        (xs, xe), (ys, ye) = self.da.getRanges()\n",
      "        for j in range(ys, ye):\n",
      "            for i in range(xs, xe):\n",
      "                u = x[i, j] # center\n",
      "                u_e = u_w = u_n = u_s = 0\n",
      "                if i > 0:    u_w = x[i-1, j] # west\n",
      "                if i < mx-1: u_e = x[i+1, j] # east\n",
      "                if j > 0:    u_s = x[i, j-1] # south\n",
      "                if j < ny-1: u_n = x[i, j+1] # north\n",
      "                u_xx = (-u_e + 2*u - u_w)*hy/hx\n",
      "                u_yy = (-u_n + 2*u - u_s)*hx/hy\n",
      "                y[i, j] = u_xx + u_yy\n",
      "\n",
      "OptDB = PETSc.Options()\n",
      "\n",
      "# change nx and ny if you want\n",
      "n  = OptDB.getInt('n', 16)\n",
      "nx = OptDB.getInt('nx', n)\n",
      "ny = OptDB.getInt('ny', n)\n",
      "\n",
      "da = PETSc.DA().create([nx, ny], stencil_width=1)\n",
      "pde = Poisson2D(da)\n",
      "\n",
      "x = da.createGlobalVec()\n",
      "b = da.createGlobalVec()\n",
      "# A = da.createMat('python')\n",
      "A = PETSc.Mat().createPython(\n",
      "    [x.getSizes(), b.getSizes()], comm=da.comm)\n",
      "A.setPythonContext(pde)\n",
      "A.setUp()\n",
      "\n",
      "ksp = PETSc.KSP().create()\n",
      "ksp.setOperators(A)\n",
      "ksp.setType('cg')\n",
      "pc = ksp.getPC()\n",
      "pc.setType('none')\n",
      "ksp.setFromOptions()\n",
      "\n",
      "pde.formRHS(b)\n",
      "ksp.solve(b, x)\n",
      "\n",
      "u = da.createNaturalVec()\n",
      "da.globalToNatural(x, u)\n",
      "x.getSizes()\n",
      "\n",
      "engine_arrays = u.array\n",
      "rank=da.comm.rank\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# now disable the parallel run to get the d\n",
      "%autopx"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "%autopx disabled\n"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# view the engine arrays and ranks\n",
      "arrays = view['engine_arrays']\n",
      "ranks = view['rank']\n",
      "# Sort the arrays based on rank\n",
      "arrays_and_ranks = zip(ranks, arrays)\n",
      "arrays_and_ranks.sort()\n",
      "sorted_ranks,sorted_arrays = zip(*arrays_and_ranks)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Create a list to use with concatenate\n",
      "list_arrays=list(sorted_arrays)\n",
      "# Concatenate the ordered list of arrays into one flat array\n",
      "u_flat = concatenate(list_arrays, axis=0)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Get the global sizes nx and ny\n",
      "nx=view['nx'][0]\n",
      "ny=view['ny'][0]\n",
      "\n",
      "# create a mesh grid\n",
      "X, Y =  mgrid[0:1:1j*nx,0:1:1j*ny]\n",
      "# reshape the solution, orderering is Fortran based\n",
      "u = u_flat[...].reshape(nx,ny, order='F')\n",
      "\n",
      "# Let's plot\n",
      "pylab.figure()\n",
      "pylab.contourf(X,Y,u)\n",
      "pylab.plot(X.ravel(),Y.ravel(),'.k')\n",
      "pylab.axis('equal')\n",
      "pylab.colorbar()\n",
      "pylab.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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HDsydO1ewTdOWJvSywfTZDiYmxYm2wZRtlXhAWytLIMSSEuy+EVLjlI4Vg2IW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\nYS0mp9j746M1+KrCuLg4pqc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      }
     ],
     "prompt_number": 7
    }
   ],
   "metadata": {}
  }
 ]
}