Lecture-6A-Fortran-and-C.ipynb

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  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Using Fortran and C code with Python"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "J.R. Johansson (robert@riken.jp) http://dml.riken.jp/~rob/\n",
      "\n",
      "The latest version of this [IPython notebook](http://ipython.org/notebook.html) lecture is available at [http://github.com/jrjohansson/scientific-python-lectures](http://github.com/jrjohansson/scientific-python-lectures).\n",
      "\n",
      "The other notebooks in this lecture series are indexed at [http://jrjohansson.github.com](http://jrjohansson.github.com)."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%pylab inline\n",
      "from IPython.display import Image"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Populating the interactive namespace from numpy and matplotlib\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The advantage of Python is that it is flexible and easy to program. The time it takes to setup a new calulation is therefore short. But for certain types of calculations Python (and any other interpreted language) can be very slow. It is particularly iterations over large arrays that is difficult to do efficiently.\n",
      "\n",
      "Such calculations may be implemented in a compiled language such as C or Fortran. In Python it is relatively easy to call out to libraries with compiled C or Fortran code. In this lecture we will look at how to do that.\n",
      "\n",
      "But before we go ahead and work on optimizing anything, it is always worthwhile to ask.... "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "Image(filename='images/optimizing-what.png')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "png": 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dEWOMMWZQXANURgcPHgQRoVOnTi9m8gMAdetK/YAA4D//Aa5dM2w8jDHGmIFx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\n",
       "prompt_number": 2,
       "text": [
        "<IPython.core.display.Image at 0x7f70a37df110>"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Fortran"
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "F2PY"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "F2PY is a program that (almost) automatically wraps fortran code for use in Python: By using the `f2py` program we can compile fortran code into a module that we can import in a Python program.\n",
      "\n",
      "F2PY is a part of NumPy, but you will also need to have a fortran compiler to run the examples below."
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 0: scalar input, no output"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%file hellofortran.f\n",
      "C File  hellofortran.f\n",
      "        subroutine hellofortran (n)\n",
      "        integer n\n",
      "       \n",
      "        do 100 i=0, n\n",
      "            print *, \"Fortran says hello\"\n",
      "100     continue\n",
      "        end"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Overwriting hellofortran.f\n"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Generate a python module using `f2py`:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "!f2py -c -m hellofortran hellofortran.f"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\u001b[39mrunning build\u001b[0m\r\n",
        "\u001b[39mrunning config_cc\u001b[0m\r\n",
        "\u001b[39munifing config_cc, config, build_clib, build_ext, build commands --compiler options\u001b[0m\r\n",
        "\u001b[39mrunning config_fc\u001b[0m\r\n",
        "\u001b[39munifing config_fc, config, build_clib, build_ext, build commands --fcompiler options\u001b[0m\r\n",
        "\u001b[39mrunning build_src\u001b[0m\r\n",
        "\u001b[39mbuild_src\u001b[0m\r\n",
        "\u001b[39mbuilding extension \"hellofortran\" sources\u001b[0m\r\n",
        "\u001b[39mf2py options: []\u001b[0m\r\n",
        "\u001b[39mf2py:> /tmp/tmpz2IPjB/src.linux-x86_64-2.7/hellofortranmodule.c\u001b[0m\r\n",
        "\u001b[39mcreating /tmp/tmpz2IPjB/src.linux-x86_64-2.7\u001b[0m\r\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Reading fortran codes...\r\n",
        "\tReading file 'hellofortran.f' (format:fix,strict)\r\n",
        "Post-processing...\r\n",
        "\tBlock: hellofortran\r\n",
        "\t\t\tBlock: hellofortran\r\n",
        "Post-processing (stage 2)...\r\n",
        "Building modules...\r\n",
        "\tBuilding module \"hellofortran\"...\r\n",
        "\t\tConstructing wrapper function \"hellofortran\"...\r\n",
        "\t\t  hellofortran(n)\r\n",
        "\tWrote C/API module \"hellofortran\" to file \"/tmp/tmpz2IPjB/src.linux-x86_64-2.7/hellofortranmodule.c\"\r\n",
        "\u001b[39m  adding '/tmp/tmpz2IPjB/src.linux-x86_64-2.7/fortranobject.c' to sources.\u001b[0m\r\n",
        "\u001b[39m  adding '/tmp/tmpz2IPjB/src.linux-x86_64-2.7' to include_dirs.\u001b[0m\r\n",
        "\u001b[39mcopying /usr/lib/python2.7/dist-packages/numpy/f2py/src/fortranobject.c -> /tmp/tmpz2IPjB/src.linux-x86_64-2.7\u001b[0m\r\n",
        "\u001b[39mcopying /usr/lib/python2.7/dist-packages/numpy/f2py/src/fortranobject.h -> /tmp/tmpz2IPjB/src.linux-x86_64-2.7\u001b[0m\r\n",
        "\u001b[39mbuild_src: building npy-pkg config files\u001b[0m\r\n",
        "\u001b[39mrunning build_ext\u001b[0m\r\n",
        "\u001b[39mcustomize UnixCCompiler\u001b[0m\r\n",
        "\u001b[39mcustomize UnixCCompiler using build_ext\u001b[0m\r\n",
        "\u001b[39mcustomize Gnu95FCompiler\u001b[0m\r\n",
        "\u001b[39mFound executable /usr/bin/gfortran\u001b[0m\r\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\u001b[39mcustomize Gnu95FCompiler\u001b[0m\r\n",
        "\u001b[39mcustomize Gnu95FCompiler using build_ext\u001b[0m\r\n",
        "\u001b[39mbuilding 'hellofortran' extension\u001b[0m\r\n",
        "\u001b[39mcompiling C sources\u001b[0m\r\n",
        "\u001b[39mC compiler: x86_64-linux-gnu-gcc -pthread -fno-strict-aliasing -DNDEBUG -g -fwrapv -O2 -Wall -Wstrict-prototypes -fPIC\r\n",
        "\u001b[0m\r\n",
        "\u001b[39mcreating /tmp/tmpz2IPjB/tmp\u001b[0m\r\n",
        "\u001b[39mcreating /tmp/tmpz2IPjB/tmp/tmpz2IPjB\u001b[0m\r\n",
        "\u001b[39mcreating /tmp/tmpz2IPjB/tmp/tmpz2IPjB/src.linux-x86_64-2.7\u001b[0m\r\n",
        "\u001b[39mcompile options: '-I/tmp/tmpz2IPjB/src.linux-x86_64-2.7 -I/usr/lib/python2.7/dist-packages/numpy/core/include -I/usr/include/python2.7 -c'\u001b[0m\r\n",
        "\u001b[39mx86_64-linux-gnu-gcc: /tmp/tmpz2IPjB/src.linux-x86_64-2.7/hellofortranmodule.c\u001b[0m\r\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "In file included from /usr/lib/python2.7/dist-packages/numpy/core/include/numpy/ndarraytypes.h:1761:0,\r\n",
        "                 from /usr/lib/python2.7/dist-packages/numpy/core/include/numpy/ndarrayobject.h:17,\r\n",
        "                 from /usr/lib/python2.7/dist-packages/numpy/core/include/numpy/arrayobject.h:4,\r\n",
        "                 from /tmp/tmpz2IPjB/src.linux-x86_64-2.7/fortranobject.h:13,\r\n",
        "                 from /tmp/tmpz2IPjB/src.linux-x86_64-2.7/hellofortranmodule.c:17:\r\n",
        "/usr/lib/python2.7/dist-packages/numpy/core/include/numpy/npy_1_7_deprecated_api.h:15:2: warning: #warning \"Using deprecated NumPy API, disable it by \" \"#defining NPY_NO_DEPRECATED_API NPY_1_7_API_VERSION\" [-Wcpp]\r\n",
        " #warning \"Using deprecated NumPy API, disable it by \" \\\r\n",
        "  ^\r\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\u001b[39mx86_64-linux-gnu-gcc: /tmp/tmpz2IPjB/src.linux-x86_64-2.7/fortranobject.c\u001b[0m\r\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "In file included from /usr/lib/python2.7/dist-packages/numpy/core/include/numpy/ndarraytypes.h:1761:0,\r\n",
        "                 from /usr/lib/python2.7/dist-packages/numpy/core/include/numpy/ndarrayobject.h:17,\r\n",
        "                 from /usr/lib/python2.7/dist-packages/numpy/core/include/numpy/arrayobject.h:4,\r\n",
        "                 from /tmp/tmpz2IPjB/src.linux-x86_64-2.7/fortranobject.h:13,\r\n",
        "                 from /tmp/tmpz2IPjB/src.linux-x86_64-2.7/fortranobject.c:2:\r\n",
        "/usr/lib/python2.7/dist-packages/numpy/core/include/numpy/npy_1_7_deprecated_api.h:15:2: warning: #warning \"Using deprecated NumPy API, disable it by \" \"#defining NPY_NO_DEPRECATED_API NPY_1_7_API_VERSION\" [-Wcpp]\r\n",
        " #warning \"Using deprecated NumPy API, disable it by \" \\\r\n",
        "  ^\r\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\u001b[39mcompiling Fortran sources\u001b[0m\r\n",
        "\u001b[39mFortran f77 compiler: /usr/bin/gfortran -Wall -ffixed-form -fno-second-underscore -fPIC -O3 -funroll-loops\r\n",
        "Fortran f90 compiler: /usr/bin/gfortran -Wall -fno-second-underscore -fPIC -O3 -funroll-loops\r\n",
        "Fortran fix compiler: /usr/bin/gfortran -Wall -ffixed-form -fno-second-underscore -Wall -fno-second-underscore -fPIC -O3 -funroll-loops\u001b[0m\r\n",
        "\u001b[39mcompile options: '-I/tmp/tmpz2IPjB/src.linux-x86_64-2.7 -I/usr/lib/python2.7/dist-packages/numpy/core/include -I/usr/include/python2.7 -c'\u001b[0m\r\n",
        "\u001b[39mgfortran:f77: hellofortran.f\u001b[0m\r\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\u001b[39m/usr/bin/gfortran -Wall -Wall -shared /tmp/tmpz2IPjB/tmp/tmpz2IPjB/src.linux-x86_64-2.7/hellofortranmodule.o /tmp/tmpz2IPjB/tmp/tmpz2IPjB/src.linux-x86_64-2.7/fortranobject.o /tmp/tmpz2IPjB/hellofortran.o -lgfortran -o ./hellofortran.so\u001b[0m\r\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Removing build directory /tmp/tmpz2IPjB\r\n"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Example of a python script that use the module:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%file hello.py\n",
      "import hellofortran\n",
      "\n",
      "hellofortran.hellofortran(5)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Overwriting hello.py\n"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# run the script\n",
      "!python hello.py"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " Fortran says hello\r\n",
        " Fortran says hello\r\n",
        " Fortran says hello\r\n",
        " Fortran says hello\r\n",
        " Fortran says hello\r\n",
        " Fortran says hello\r\n"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 1: vector input and scalar output"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%file dprod.f\n",
      "\n",
      "       subroutine dprod(x, y, n)\n",
      "    \n",
      "       double precision x(n), y\n",
      "       y = 1.0\n",
      "    \n",
      "       do 100 i=1, n\n",
      "           y = y * x(i)\n",
      "100    continue\n",
      "       end"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Overwriting dprod.f\n"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "!rm -f dprod.pyf\n",
      "!f2py -m dprod -h dprod.pyf dprod.f"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Reading fortran codes...\r\n",
        "\tReading file 'dprod.f' (format:fix,strict)\r\n",
        "Post-processing...\r\n",
        "\tBlock: dprod\r\n",
        "{}\r\n",
        "In: :dprod:dprod.f:dprod\r\n",
        "vars2fortran: No typespec for argument \"n\".\r\n",
        "\t\t\tBlock: dprod\r\n",
        "Post-processing (stage 2)...\r\n",
        "Saving signatures to file \"./dprod.pyf\"\r\n"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The `f2py` program generated a module declaration file called `dsum.pyf`. Let's look what's in it:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": true,
     "input": [
      "!cat dprod.pyf"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "!    -*- f90 -*-\r\n",
        "! Note: the context of this file is case sensitive.\r\n",
        "\r\n",
        "python module dprod ! in \r\n",
        "    interface  ! in :dprod\r\n",
        "        subroutine dprod(x,y,n) ! in :dprod:dprod.f\r\n",
        "            double precision dimension(n) :: x\r\n",
        "            double precision :: y\r\n",
        "            integer, optional,check(len(x)>=n),depend(x) :: n=len(x)\r\n",
        "        end subroutine dprod\r\n",
        "    end interface \r\n",
        "end python module dprod\r\n",
        "\r\n",
        "! This file was auto-generated with f2py (version:2).\r\n",
        "! See http://cens.ioc.ee/projects/f2py2e/\r\n"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The module does not know what Fortran subroutine arguments is input and output, so we need to manually edit the module declaration files and mark output variables with `intent(out)` and input variable with `intent(in)`:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%file dprod.pyf\n",
      "python module dprod ! in \n",
      "    interface  ! in :dprod\n",
      "        subroutine dprod(x,y,n) ! in :dprod:dprod.f\n",
      "            double precision dimension(n), intent(in) :: x\n",
      "            double precision, intent(out) :: y\n",
      "            integer, optional,check(len(x)>=n),depend(x),intent(in) :: n=len(x)\n",
      "        end subroutine dprod\n",
      "    end interface \n",
      "end python module dprod"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Overwriting dprod.pyf\n"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Compile the fortran code into a module that can be included in python:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "!f2py -c dprod.pyf dprod.f"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\u001b[39mrunning build\u001b[0m\r\n",
        "\u001b[39mrunning config_cc\u001b[0m\r\n",
        "\u001b[39munifing config_cc, config, build_clib, build_ext, build commands --compiler options\u001b[0m\r\n",
        "\u001b[39mrunning config_fc\u001b[0m\r\n",
        "\u001b[39munifing config_fc, config, build_clib, build_ext, build commands --fcompiler options\u001b[0m\r\n",
        "\u001b[39mrunning build_src\u001b[0m\r\n",
        "\u001b[39mbuild_src\u001b[0m\r\n",
        "\u001b[39mbuilding extension \"dprod\" sources\u001b[0m\r\n",
        "\u001b[39mcreating /tmp/tmpWyCvx1/src.linux-x86_64-2.7\u001b[0m\r\n",
        "\u001b[39mf2py options: []\u001b[0m\r\n",
        "\u001b[39mf2py: dprod.pyf\u001b[0m\r\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Reading fortran codes...\r\n",
        "\tReading file 'dprod.pyf' (format:free)\r\n",
        "Post-processing...\r\n",
        "\tBlock: dprod\r\n",
        "\t\t\tBlock: dprod\r\n",
        "Post-processing (stage 2)...\r\n",
        "Building modules...\r\n",
        "\tBuilding module \"dprod\"...\r\n",
        "\t\tConstructing wrapper function \"dprod\"...\r\n",
        "\t\t  y = dprod(x,[n])\r\n",
        "\tWrote C/API module \"dprod\" to file \"/tmp/tmpWyCvx1/src.linux-x86_64-2.7/dprodmodule.c\"\r\n",
        "\u001b[39m  adding '/tmp/tmpWyCvx1/src.linux-x86_64-2.7/fortranobject.c' to sources.\u001b[0m\r\n",
        "\u001b[39m  adding '/tmp/tmpWyCvx1/src.linux-x86_64-2.7' to include_dirs.\u001b[0m\r\n",
        "\u001b[39mcopying /usr/lib/python2.7/dist-packages/numpy/f2py/src/fortranobject.c -> /tmp/tmpWyCvx1/src.linux-x86_64-2.7\u001b[0m\r\n",
        "\u001b[39mcopying /usr/lib/python2.7/dist-packages/numpy/f2py/src/fortranobject.h -> /tmp/tmpWyCvx1/src.linux-x86_64-2.7\u001b[0m\r\n",
        "\u001b[39mbuild_src: building npy-pkg config files\u001b[0m\r\n",
        "\u001b[39mrunning build_ext\u001b[0m\r\n",
        "\u001b[39mcustomize UnixCCompiler\u001b[0m\r\n",
        "\u001b[39mcustomize UnixCCompiler using build_ext\u001b[0m\r\n",
        "\u001b[39mcustomize Gnu95FCompiler\u001b[0m\r\n",
        "\u001b[39mFound executable /usr/bin/gfortran\u001b[0m\r\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\u001b[39mcustomize Gnu95FCompiler\u001b[0m\r\n",
        "\u001b[39mcustomize Gnu95FCompiler using build_ext\u001b[0m\r\n",
        "\u001b[39mbuilding 'dprod' extension\u001b[0m\r\n",
        "\u001b[39mcompiling C sources\u001b[0m\r\n",
        "\u001b[39mC compiler: x86_64-linux-gnu-gcc -pthread -fno-strict-aliasing -DNDEBUG -g -fwrapv -O2 -Wall -Wstrict-prototypes -fPIC\r\n",
        "\u001b[0m\r\n",
        "\u001b[39mcreating /tmp/tmpWyCvx1/tmp\u001b[0m\r\n",
        "\u001b[39mcreating /tmp/tmpWyCvx1/tmp/tmpWyCvx1\u001b[0m\r\n",
        "\u001b[39mcreating /tmp/tmpWyCvx1/tmp/tmpWyCvx1/src.linux-x86_64-2.7\u001b[0m\r\n",
        "\u001b[39mcompile options: '-I/tmp/tmpWyCvx1/src.linux-x86_64-2.7 -I/usr/lib/python2.7/dist-packages/numpy/core/include -I/usr/include/python2.7 -c'\u001b[0m\r\n",
        "\u001b[39mx86_64-linux-gnu-gcc: /tmp/tmpWyCvx1/src.linux-x86_64-2.7/dprodmodule.c\u001b[0m\r\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "In file included from /usr/lib/python2.7/dist-packages/numpy/core/include/numpy/ndarraytypes.h:1761:0,\r\n",
        "                 from /usr/lib/python2.7/dist-packages/numpy/core/include/numpy/ndarrayobject.h:17,\r\n",
        "                 from /usr/lib/python2.7/dist-packages/numpy/core/include/numpy/arrayobject.h:4,\r\n",
        "                 from /tmp/tmpWyCvx1/src.linux-x86_64-2.7/fortranobject.h:13,\r\n",
        "                 from /tmp/tmpWyCvx1/src.linux-x86_64-2.7/dprodmodule.c:18:\r\n",
        "/usr/lib/python2.7/dist-packages/numpy/core/include/numpy/npy_1_7_deprecated_api.h:15:2: warning: #warning \"Using deprecated NumPy API, disable it by \" \"#defining NPY_NO_DEPRECATED_API NPY_1_7_API_VERSION\" [-Wcpp]\r\n",
        " #warning \"Using deprecated NumPy API, disable it by \" \\\r\n",
        "  ^\r\n",
        "/tmp/tmpWyCvx1/src.linux-x86_64-2.7/dprodmodule.c:111:12: warning: \u2018f2py_size\u2019 defined but not used [-Wunused-function]\r\n",
        " static int f2py_size(PyArrayObject* var, ...)\r\n",
        "            ^\r\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\u001b[39mx86_64-linux-gnu-gcc: /tmp/tmpWyCvx1/src.linux-x86_64-2.7/fortranobject.c\u001b[0m\r\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "In file included from /usr/lib/python2.7/dist-packages/numpy/core/include/numpy/ndarraytypes.h:1761:0,\r\n",
        "                 from /usr/lib/python2.7/dist-packages/numpy/core/include/numpy/ndarrayobject.h:17,\r\n",
        "                 from /usr/lib/python2.7/dist-packages/numpy/core/include/numpy/arrayobject.h:4,\r\n",
        "                 from /tmp/tmpWyCvx1/src.linux-x86_64-2.7/fortranobject.h:13,\r\n",
        "                 from /tmp/tmpWyCvx1/src.linux-x86_64-2.7/fortranobject.c:2:\r\n",
        "/usr/lib/python2.7/dist-packages/numpy/core/include/numpy/npy_1_7_deprecated_api.h:15:2: warning: #warning \"Using deprecated NumPy API, disable it by \" \"#defining NPY_NO_DEPRECATED_API NPY_1_7_API_VERSION\" [-Wcpp]\r\n",
        " #warning \"Using deprecated NumPy API, disable it by \" \\\r\n",
        "  ^\r\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\u001b[39mcompiling Fortran sources\u001b[0m\r\n",
        "\u001b[39mFortran f77 compiler: /usr/bin/gfortran -Wall -ffixed-form -fno-second-underscore -fPIC -O3 -funroll-loops\r\n",
        "Fortran f90 compiler: /usr/bin/gfortran -Wall -fno-second-underscore -fPIC -O3 -funroll-loops\r\n",
        "Fortran fix compiler: /usr/bin/gfortran -Wall -ffixed-form -fno-second-underscore -Wall -fno-second-underscore -fPIC -O3 -funroll-loops\u001b[0m\r\n",
        "\u001b[39mcompile options: '-I/tmp/tmpWyCvx1/src.linux-x86_64-2.7 -I/usr/lib/python2.7/dist-packages/numpy/core/include -I/usr/include/python2.7 -c'\u001b[0m\r\n",
        "\u001b[39mgfortran:f77: dprod.f\u001b[0m\r\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\u001b[39m/usr/bin/gfortran -Wall -Wall -shared /tmp/tmpWyCvx1/tmp/tmpWyCvx1/src.linux-x86_64-2.7/dprodmodule.o /tmp/tmpWyCvx1/tmp/tmpWyCvx1/src.linux-x86_64-2.7/fortranobject.o /tmp/tmpWyCvx1/dprod.o -lgfortran -o ./dprod.so\u001b[0m\r\n",
        "Removing build directory /tmp/tmpWyCvx1\r\n"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "Using the module from Python"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import dprod"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 12
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "help(dprod)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Help on module dprod:\n",
        "\n",
        "NAME\n",
        "    dprod\n",
        "\n",
        "FILE\n",
        "    /home/rob/Desktop/scientific-python-lectures/dprod.so\n",
        "\n",
        "DESCRIPTION\n",
        "    This module 'dprod' is auto-generated with f2py (version:2).\n",
        "    Functions:\n",
        "      y = dprod(x,n=len(x))\n",
        "    .\n",
        "\n",
        "DATA\n",
        "    __version__ = '$Revision: $'\n",
        "    dprod = <fortran object>\n",
        "\n",
        "VERSION\n",
        "\n",
        "\n",
        "\n"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "dprod.dprod(arange(1,50))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 14,
       "text": [
        "6.082818640342675e+62"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# compare to numpy\n",
      "prod(arange(1.0,50.0))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 15,
       "text": [
        "6.0828186403426752e+62"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "dprod.dprod(arange(1,10), 5) # only the 5 first elements"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 16,
       "text": [
        "120.0"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Compare performance:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "xvec = rand(500)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 17
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "timeit dprod.dprod(xvec)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "1000000 loops, best of 3: 882 ns per loop\n"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "timeit xvec.prod()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "100000 loops, best of 3: 4.45 \u00b5s per loop\n"
       ]
      }
     ],
     "prompt_number": 19
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 2: cummulative sum, vector input and vector output"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The cummulative sum function for an array of data is a good example of a loop intense algorithm: Loop through a vector and store the cummulative sum in another vector."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# simple python algorithm: example of a SLOW implementation\n",
      "# Why? Because the loop is implemented in python.\n",
      "def py_dcumsum(a):\n",
      "    b = empty_like(a)\n",
      "    b[0] = a[0]\n",
      "    for n in range(1,len(a)):\n",
      "        b[n] = b[n-1]+a[n]\n",
      "    return b"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 20
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Fortran subroutine for the same thing: here we have added the `intent(in)` and `intent(out)` as comment lines in the original fortran code, so we do not need to manually edit the fortran module declaration file generated by `f2py`. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%file dcumsum.f\n",
      "c File dcumsum.f\n",
      "       subroutine dcumsum(a, b, n)\n",
      "       double precision a(n)\n",
      "       double precision b(n)\n",
      "       integer n\n",
      "cf2py  intent(in) :: a\n",
      "cf2py  intent(out) :: b\n",
      "cf2py  intent(hide) :: n\n",
      "\n",
      "       b(1) = a(1)\n",
      "       do 100 i=2, n\n",
      "           b(i) = b(i-1) + a(i)\n",
      "100    continue\n",
      "       end"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Overwriting dcumsum.f\n"
       ]
      }
     ],
     "prompt_number": 21
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We can directly compile the fortran code to a python module:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "!f2py -c dcumsum.f -m dcumsum"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\u001b[39mrunning build\u001b[0m\r\n",
        "\u001b[39mrunning config_cc\u001b[0m\r\n",
        "\u001b[39munifing config_cc, config, build_clib, build_ext, build commands --compiler options\u001b[0m\r\n",
        "\u001b[39mrunning config_fc\u001b[0m\r\n",
        "\u001b[39munifing config_fc, config, build_clib, build_ext, build commands --fcompiler options\u001b[0m\r\n",
        "\u001b[39mrunning build_src\u001b[0m\r\n",
        "\u001b[39mbuild_src\u001b[0m\r\n",
        "\u001b[39mbuilding extension \"dcumsum\" sources\u001b[0m\r\n",
        "\u001b[39mf2py options: []\u001b[0m\r\n",
        "\u001b[39mf2py:> /tmp/tmpfvrMl6/src.linux-x86_64-2.7/dcumsummodule.c\u001b[0m\r\n",
        "\u001b[39mcreating /tmp/tmpfvrMl6/src.linux-x86_64-2.7\u001b[0m\r\n",
        "Reading fortran codes...\r\n",
        "\tReading file 'dcumsum.f' (format:fix,strict)\r\n",
        "Post-processing...\r\n",
        "\tBlock: dcumsum\r\n",
        "\t\t\tBlock: dcumsum\r\n",
        "Post-processing (stage 2)...\r\n",
        "Building modules...\r\n",
        "\tBuilding module \"dcumsum\"...\r\n",
        "\t\tConstructing wrapper function \"dcumsum\"...\r\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\t\t  b = dcumsum(a)\r\n",
        "\tWrote C/API module \"dcumsum\" to file \"/tmp/tmpfvrMl6/src.linux-x86_64-2.7/dcumsummodule.c\"\r\n",
        "\u001b[39m  adding '/tmp/tmpfvrMl6/src.linux-x86_64-2.7/fortranobject.c' to sources.\u001b[0m\r\n",
        "\u001b[39m  adding '/tmp/tmpfvrMl6/src.linux-x86_64-2.7' to include_dirs.\u001b[0m\r\n",
        "\u001b[39mcopying /usr/lib/python2.7/dist-packages/numpy/f2py/src/fortranobject.c -> /tmp/tmpfvrMl6/src.linux-x86_64-2.7\u001b[0m\r\n",
        "\u001b[39mcopying /usr/lib/python2.7/dist-packages/numpy/f2py/src/fortranobject.h -> /tmp/tmpfvrMl6/src.linux-x86_64-2.7\u001b[0m\r\n",
        "\u001b[39mbuild_src: building npy-pkg config files\u001b[0m\r\n",
        "\u001b[39mrunning build_ext\u001b[0m\r\n",
        "\u001b[39mcustomize UnixCCompiler\u001b[0m\r\n",
        "\u001b[39mcustomize UnixCCompiler using build_ext\u001b[0m\r\n",
        "\u001b[39mcustomize Gnu95FCompiler\u001b[0m\r\n",
        "\u001b[39mFound executable /usr/bin/gfortran\u001b[0m\r\n",
        "\u001b[39mcustomize Gnu95FCompiler\u001b[0m\r\n",
        "\u001b[39mcustomize Gnu95FCompiler using build_ext\u001b[0m\r\n",
        "\u001b[39mbuilding 'dcumsum' extension\u001b[0m\r\n",
        "\u001b[39mcompiling C sources\u001b[0m\r\n",
        "\u001b[39mC compiler: x86_64-linux-gnu-gcc -pthread -fno-strict-aliasing -DNDEBUG -g -fwrapv -O2 -Wall -Wstrict-prototypes -fPIC\r\n",
        "\u001b[0m\r\n",
        "\u001b[39mcreating /tmp/tmpfvrMl6/tmp\u001b[0m\r\n",
        "\u001b[39mcreating /tmp/tmpfvrMl6/tmp/tmpfvrMl6\u001b[0m\r\n",
        "\u001b[39mcreating /tmp/tmpfvrMl6/tmp/tmpfvrMl6/src.linux-x86_64-2.7\u001b[0m\r\n",
        "\u001b[39mcompile options: '-I/tmp/tmpfvrMl6/src.linux-x86_64-2.7 -I/usr/lib/python2.7/dist-packages/numpy/core/include -I/usr/include/python2.7 -c'\u001b[0m\r\n",
        "\u001b[39mx86_64-linux-gnu-gcc: /tmp/tmpfvrMl6/src.linux-x86_64-2.7/dcumsummodule.c\u001b[0m\r\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "In file included from /usr/lib/python2.7/dist-packages/numpy/core/include/numpy/ndarraytypes.h:1761:0,\r\n",
        "                 from /usr/lib/python2.7/dist-packages/numpy/core/include/numpy/ndarrayobject.h:17,\r\n",
        "                 from /usr/lib/python2.7/dist-packages/numpy/core/include/numpy/arrayobject.h:4,\r\n",
        "                 from /tmp/tmpfvrMl6/src.linux-x86_64-2.7/fortranobject.h:13,\r\n",
        "                 from /tmp/tmpfvrMl6/src.linux-x86_64-2.7/dcumsummodule.c:18:\r\n",
        "/usr/lib/python2.7/dist-packages/numpy/core/include/numpy/npy_1_7_deprecated_api.h:15:2: warning: #warning \"Using deprecated NumPy API, disable it by \" \"#defining NPY_NO_DEPRECATED_API NPY_1_7_API_VERSION\" [-Wcpp]\r\n",
        " #warning \"Using deprecated NumPy API, disable it by \" \\\r\n",
        "  ^\r\n",
        "/tmp/tmpfvrMl6/src.linux-x86_64-2.7/dcumsummodule.c:111:12: warning: \u2018f2py_size\u2019 defined but not used [-Wunused-function]\r\n",
        " static int f2py_size(PyArrayObject* var, ...)\r\n",
        "            ^\r\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\u001b[39mx86_64-linux-gnu-gcc: /tmp/tmpfvrMl6/src.linux-x86_64-2.7/fortranobject.c\u001b[0m\r\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "In file included from /usr/lib/python2.7/dist-packages/numpy/core/include/numpy/ndarraytypes.h:1761:0,\r\n",
        "                 from /usr/lib/python2.7/dist-packages/numpy/core/include/numpy/ndarrayobject.h:17,\r\n",
        "                 from /usr/lib/python2.7/dist-packages/numpy/core/include/numpy/arrayobject.h:4,\r\n",
        "                 from /tmp/tmpfvrMl6/src.linux-x86_64-2.7/fortranobject.h:13,\r\n",
        "                 from /tmp/tmpfvrMl6/src.linux-x86_64-2.7/fortranobject.c:2:\r\n",
        "/usr/lib/python2.7/dist-packages/numpy/core/include/numpy/npy_1_7_deprecated_api.h:15:2: warning: #warning \"Using deprecated NumPy API, disable it by \" \"#defining NPY_NO_DEPRECATED_API NPY_1_7_API_VERSION\" [-Wcpp]\r\n",
        " #warning \"Using deprecated NumPy API, disable it by \" \\\r\n",
        "  ^\r\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\u001b[39mcompiling Fortran sources\u001b[0m\r\n",
        "\u001b[39mFortran f77 compiler: /usr/bin/gfortran -Wall -ffixed-form -fno-second-underscore -fPIC -O3 -funroll-loops\r\n",
        "Fortran f90 compiler: /usr/bin/gfortran -Wall -fno-second-underscore -fPIC -O3 -funroll-loops\r\n",
        "Fortran fix compiler: /usr/bin/gfortran -Wall -ffixed-form -fno-second-underscore -Wall -fno-second-underscore -fPIC -O3 -funroll-loops\u001b[0m\r\n",
        "\u001b[39mcompile options: '-I/tmp/tmpfvrMl6/src.linux-x86_64-2.7 -I/usr/lib/python2.7/dist-packages/numpy/core/include -I/usr/include/python2.7 -c'\u001b[0m\r\n",
        "\u001b[39mgfortran:f77: dcumsum.f\u001b[0m\r\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\u001b[39m/usr/bin/gfortran -Wall -Wall -shared /tmp/tmpfvrMl6/tmp/tmpfvrMl6/src.linux-x86_64-2.7/dcumsummodule.o /tmp/tmpfvrMl6/tmp/tmpfvrMl6/src.linux-x86_64-2.7/fortranobject.o /tmp/tmpfvrMl6/dcumsum.o -lgfortran -o ./dcumsum.so\u001b[0m\r\n",
        "Removing build directory /tmp/tmpfvrMl6\r\n"
       ]
      }
     ],
     "prompt_number": 22
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import dcumsum"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 23
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a = array([1.0,2.0,3.0,4.0,5.0,6.0,7.0,8.0])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 24
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "py_dcumsum(a)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 25,
       "text": [
        "array([  1.,   3.,   6.,  10.,  15.,  21.,  28.,  36.])"
       ]
      }
     ],
     "prompt_number": 25
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "dcumsum.dcumsum(a)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 26,
       "text": [
        "array([  1.,   3.,   6.,  10.,  15.,  21.,  28.,  36.])"
       ]
      }
     ],
     "prompt_number": 26
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "cumsum(a)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 27,
       "text": [
        "array([  1.,   3.,   6.,  10.,  15.,  21.,  28.,  36.])"
       ]
      }
     ],
     "prompt_number": 27
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Benchmark the different implementations:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a = rand(10000)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 28
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "timeit py_dcumsum(a)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "100 loops, best of 3: 4.83 ms per loop\n"
       ]
      }
     ],
     "prompt_number": 29
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "timeit dcumsum.dcumsum(a)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "100000 loops, best of 3: 12.2 \u00b5s per loop\n"
       ]
      }
     ],
     "prompt_number": 30
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "timeit a.cumsum()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "10000 loops, best of 3: 27.4 \u00b5s per loop\n"
       ]
      }
     ],
     "prompt_number": 31
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Further reading"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "1. http://www.scipy.org/F2py\n",
      "1. http://dsnra.jpl.nasa.gov/software/Python/F2PY_tutorial.pdf\n",
      "1. http://www.shocksolution.com/2009/09/f2py-binding-fortran-python/"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "C"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "ctypes"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "ctypes is a Python library for calling out to C code. It is not as automatic as `f2py`, and we manually need to load the library and set properties such as the functions return and argument types. On the otherhand we do not need to touch the C code at all. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%file functions.c\n",
      "\n",
      "#include <stdio.h>\n",
      "\n",
      "void hello(int n);\n",
      "\n",
      "double dprod(double *x, int n);\n",
      "\n",
      "void dcumsum(double *a, double *b, int n);\n",
      "\n",
      "void\n",
      "hello(int n)\n",
      "{\n",
      "    int i;\n",
      "    \n",
      "    for (i = 0; i < n; i++)\n",
      "    {\n",
      "        printf(\"C says hello\\n\");\n",
      "    }\n",
      "}\n",
      "\n",
      "\n",
      "double \n",
      "dprod(double *x, int n)\n",
      "{\n",
      "    int i;\n",
      "    double y = 1.0;\n",
      "    \n",
      "    for (i = 0; i < n; i++)\n",
      "    {\n",
      "        y *= x[i];\n",
      "    }\n",
      "\n",
      "    return y;\n",
      "}\n",
      "\n",
      "void\n",
      "dcumsum(double *a, double *b, int n)\n",
      "{\n",
      "    int i;\n",
      "    \n",
      "    b[0] = a[0];\n",
      "    for (i = 1; i < n; i++)\n",
      "    {\n",
      "        b[i] = a[i] + b[i-1];\n",
      "    }\n",
      "}"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Overwriting functions.c\n"
       ]
      }
     ],
     "prompt_number": 32
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Compile the C file into a shared library:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "!gcc -c -Wall -O2 -Wall -ansi -pedantic -fPIC -o functions.o functions.c\n",
      "!gcc -o libfunctions.so -shared functions.o"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 33
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The result is a compiled shared library `libfunctions.so`:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "!file libfunctions.so"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "libfunctions.so: ELF 64-bit LSB  shared object, x86-64, version 1 (SYSV), dynamically linked, BuildID[sha1]=d68173ae6a804f703472af96f413b81a189db4b8, not stripped\r\n"
       ]
      }
     ],
     "prompt_number": 34
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now we need to write wrapper functions to access the C library: To load the library we use the ctypes package, which included in the Python standard library (with extensions from numpy for passing arrays to C). Then we manually set the types of the argument and return values (no automatic code inspection here!). "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%file functions.py\n",
      "\n",
      "import numpy\n",
      "import ctypes\n",
      "\n",
      "_libfunctions = numpy.ctypeslib.load_library('libfunctions', '.')\n",
      "\n",
      "_libfunctions.hello.argtypes = [ctypes.c_int]\n",
      "_libfunctions.hello.restype  =  ctypes.c_void_p\n",
      "\n",
      "_libfunctions.dprod.argtypes = [numpy.ctypeslib.ndpointer(dtype=numpy.float), ctypes.c_int]\n",
      "_libfunctions.dprod.restype  = ctypes.c_double\n",
      "\n",
      "_libfunctions.dcumsum.argtypes = [numpy.ctypeslib.ndpointer(dtype=numpy.float), numpy.ctypeslib.ndpointer(dtype=numpy.float), ctypes.c_int]\n",
      "_libfunctions.dcumsum.restype  = ctypes.c_void_p\n",
      "\n",
      "def hello(n):\n",
      "    return _libfunctions.hello(int(n))\n",
      "\n",
      "def dprod(x, n=None):\n",
      "    if n is None:\n",
      "        n = len(x)\n",
      "    x = numpy.asarray(x, dtype=numpy.float)\n",
      "    return _libfunctions.dprod(x, int(n))\n",
      "\n",
      "def dcumsum(a, n):\n",
      "    a = numpy.asarray(a, dtype=numpy.float)\n",
      "    b = numpy.empty(len(a), dtype=numpy.float)\n",
      "    _libfunctions.dcumsum(a, b, int(n))\n",
      "    return b"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Overwriting functions.py\n"
       ]
      }
     ],
     "prompt_number": 35
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%file run_hello_c.py\n",
      "\n",
      "import functions\n",
      "\n",
      "functions.hello(3)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Overwriting run_hello_c.py\n"
       ]
      }
     ],
     "prompt_number": 36
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "!python run_hello_c.py"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "C says hello\r\n",
        "C says hello\r\n",
        "C says hello\r\n"
       ]
      }
     ],
     "prompt_number": 37
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import functions"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 38
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Product function:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "functions.dprod([1,2,3,4,5]) "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 39,
       "text": [
        "120.0"
       ]
      }
     ],
     "prompt_number": 39
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Cummulative sum:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a = rand(100000)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 40
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "res_c = functions.dcumsum(a, len(a)) "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 41
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "res_fortran = dcumsum.dcumsum(a)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 42
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "res_c - res_fortran"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 43,
       "text": [
        "array([ 0.,  0.,  0., ...,  0.,  0.,  0.])"
       ]
      }
     ],
     "prompt_number": 43
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Simple benchmark"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "timeit functions.dcumsum(a, len(a))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "1000 loops, best of 3: 286 \u00b5s per loop\n"
       ]
      }
     ],
     "prompt_number": 44
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "timeit dcumsum.dcumsum(a)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "10000 loops, best of 3: 119 \u00b5s per loop\n"
       ]
      }
     ],
     "prompt_number": 45
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "timeit a.cumsum()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "1000 loops, best of 3: 261 \u00b5s per loop\n"
       ]
      }
     ],
     "prompt_number": 46
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Further reading"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "* http://docs.python.org/2/library/ctypes.html\n",
      "* http://www.scipy.org/Cookbook/Ctypes"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Cython"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "A hybrid between python and C that can be compiled: Basically Python code with type declarations."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%file cy_dcumsum.pyx\n",
      "\n",
      "cimport numpy\n",
      "\n",
      "def dcumsum(numpy.ndarray[numpy.float64_t, ndim=1] a, numpy.ndarray[numpy.float64_t, ndim=1] b):\n",
      "    cdef int i, n = len(a)\n",
      "    b[0] = a[0]\n",
      "    for i from 1 <= i < n:\n",
      "        b[i] = b[i-1] + a[i]\n",
      "    return b"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Overwriting cy_dcumsum.pyx\n"
       ]
      }
     ],
     "prompt_number": 47
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "A build file for generating C code and compiling it into a Python module."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%file setup.py\n",
      "\n",
      "from distutils.core import setup\n",
      "from distutils.extension import Extension\n",
      "from Cython.Distutils import build_ext\n",
      "\n",
      "setup(\n",
      "    cmdclass = {'build_ext': build_ext},\n",
      "    ext_modules = [Extension(\"cy_dcumsum\", [\"cy_dcumsum.pyx\"])]\n",
      ")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Overwriting setup.py\n"
       ]
      }
     ],
     "prompt_number": 48
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "!python setup.py build_ext --inplace"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "running build_ext\r\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "cythoning cy_dcumsum.pyx to cy_dcumsum.c\r\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "warning: /usr/local/lib/python2.7/dist-packages/Cython/Includes/numpy.pxd:869:17: Non-trivial type declarators in shared declaration (e.g. mix of pointers and values). Each pointer declaration should be on its own line.\r\n",
        "warning: /usr/local/lib/python2.7/dist-packages/Cython/Includes/numpy.pxd:869:24: Non-trivial type declarators in shared declaration (e.g. mix of pointers and values). Each pointer declaration should be on its own line.\r\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "building 'cy_dcumsum' extension\r\n",
        "x86_64-linux-gnu-gcc -pthread -fno-strict-aliasing -DNDEBUG -g -fwrapv -O2 -Wall -Wstrict-prototypes -fPIC -I/usr/include/python2.7 -c cy_dcumsum.c -o build/temp.linux-x86_64-2.7/cy_dcumsum.o\r\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "In file included from /usr/include/python2.7/numpy/ndarraytypes.h:1761:0,\r\n",
        "                 from /usr/include/python2.7/numpy/ndarrayobject.h:17,\r\n",
        "                 from /usr/include/python2.7/numpy/arrayobject.h:4,\r\n",
        "                 from cy_dcumsum.c:352:\r\n",
        "/usr/include/python2.7/numpy/npy_1_7_deprecated_api.h:15:2: warning: #warning \"Using deprecated NumPy API, disable it by \" \"#defining NPY_NO_DEPRECATED_API NPY_1_7_API_VERSION\" [-Wcpp]\r\n",
        " #warning \"Using deprecated NumPy API, disable it by \" \\\r\n",
        "  ^\r\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "In file included from /usr/include/python2.7/numpy/ndarrayobject.h:26:0,\r\n",
        "                 from /usr/include/python2.7/numpy/arrayobject.h:4,\r\n",
        "                 from cy_dcumsum.c:352:\r\n",
        "/usr/include/python2.7/numpy/__multiarray_api.h:1629:1: warning: \u2018_import_array\u2019 defined but not used [-Wunused-function]\r\n",
        " _import_array(void)\r\n",
        " ^\r\n",
        "In file included from /usr/include/python2.7/numpy/ufuncobject.h:327:0,\r\n",
        "                 from cy_dcumsum.c:353:\r\n",
        "/usr/include/python2.7/numpy/__ufunc_api.h:241:1: warning: \u2018_import_umath\u2019 defined but not used [-Wunused-function]\r\n",
        " _import_umath(void)\r\n",
        " ^\r\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "x86_64-linux-gnu-gcc -pthread -shared -Wl,-O1 -Wl,-Bsymbolic-functions -Wl,-Bsymbolic-functions -Wl,-z,relro -fno-strict-aliasing -DNDEBUG -g -fwrapv -O2 -Wall -Wstrict-prototypes -D_FORTIFY_SOURCE=2 -g -fstack-protector --param=ssp-buffer-size=4 -Wformat -Werror=format-security build/temp.linux-x86_64-2.7/cy_dcumsum.o -o /home/rob/Desktop/scientific-python-lectures/cy_dcumsum.so\r\n"
       ]
      }
     ],
     "prompt_number": 49
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import cy_dcumsum"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 50
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a = array([1,2,3,4], dtype=float)\n",
      "b = empty_like(a)\n",
      "cy_dcumsum.dcumsum(a,b)\n",
      "b"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 51,
       "text": [
        "array([  1.,   3.,   6.,  10.])"
       ]
      }
     ],
     "prompt_number": 51
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a = array([1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 52
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "b = empty_like(a)\n",
      "cy_dcumsum.dcumsum(a, b)\n",
      "b"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 53,
       "text": [
        "array([  1.,   3.,   6.,  10.,  15.,  21.,  28.,  36.])"
       ]
      }
     ],
     "prompt_number": 53
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "py_dcumsum(a)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 54,
       "text": [
        "array([  1.,   3.,   6.,  10.,  15.,  21.,  28.,  36.])"
       ]
      }
     ],
     "prompt_number": 54
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a = rand(100000)\n",
      "b = empty_like(a)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 55
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "timeit py_dcumsum(a)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "10 loops, best of 3: 50.1 ms per loop\n"
       ]
      }
     ],
     "prompt_number": 56
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "timeit cy_dcumsum.dcumsum(a,b)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "1000 loops, best of 3: 263 \u00b5s per loop\n"
       ]
      }
     ],
     "prompt_number": 57
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Cython in the IPython notebook"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "When working with the IPython (especially in the notebook), there is a more convenient way of compiling and loading Cython code. Using the `%%cython` IPython magic (command to IPython), we can simply type the Cython code in a code cell and let IPython take care of the conversion to C code, compilation and loading of the function. To be able to use the `%%cython` magic, we first need to load the extension `cythonmagic`:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%load_ext cythonmagic"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 58
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%cython\n",
      "\n",
      "cimport numpy\n",
      "\n",
      "def cy_dcumsum2(numpy.ndarray[numpy.float64_t, ndim=1] a, numpy.ndarray[numpy.float64_t, ndim=1] b):\n",
      "    cdef int i, n = len(a)\n",
      "    b[0] = a[0]\n",
      "    for i from 1 <= i < n:\n",
      "        b[i] = b[i-1] + a[i]\n",
      "    return b"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 62
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "timeit cy_dcumsum2(a,b)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "1000 loops, best of 3: 265 \u00b5s per loop\n"
       ]
      }
     ],
     "prompt_number": 63
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Further reading"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "* http://cython.org\n",
      "* http://docs.cython.org/src/userguide/tutorial.html\n",
      "* http://wiki.cython.org/tutorials/numpy"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Versions"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%reload_ext version_information\n",
      "\n",
      "%version_information ctypes, Cython"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<table><tr><th>Software</th><th>Version</th></tr><tr><td>Python</td><td>2.7.6 (default, Mar 22 2014, 22:59:56) [GCC 4.8.2]</td></tr><tr><td>IPython</td><td>1.1.0</td></tr><tr><td>OS</td><td>posix [linux2]</td></tr><tr><td>ctypes</td><td>1.1.0</td></tr><tr><td>Cython</td><td>0.20.2</td></tr><tr><td colspan='2'>Tue Aug 26 23:37:29 2014 JST</td></tr></table>"
       ],
       "json": [
        "{ \"Software versions\" : [{ \"module\" : \"Python\", \"version\" : \"2.7.6 (default, Mar 22 2014, 22:59:56) [GCC 4.8.2]\" }, { \"module\" : \"IPython\", \"version\" : \"1.1.0\" }, { \"module\" : \"OS\", \"version\" : \"posix [linux2]\" }, { \"module\" : \"ctypes\", \"version\" : \"1.1.0\" }, { \"module\" : \"Cython\", \"version\" : \"0.20.2\" } ] }"
       ],
       "latex": [
        "\\begin{table}\n",
        "\\begin{tabular}{|l|l|}\\hline\n",
        "{\\bf Software} & {\\bf Version} \\\\ \\hline\\hline\n",
        "Python & 2.7.6 (default, Mar 22 2014, 22:59:56) [GCC 4.8.2] \\\\ \\hline\n",
        "IPython & 1.1.0 \\\\ \\hline\n",
        "OS & posix [linux2] \\\\ \\hline\n",
        "ctypes & 1.1.0 \\\\ \\hline\n",
        "Cython & 0.20.2 \\\\ \\hline\n",
        "\\hline \\multicolumn{2}{|l|}{Tue Aug 26 23:37:29 2014 JST} \\\\ \\hline\n",
        "\\end{tabular}\n",
        "\\end{table}\n"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 64,
       "text": [
        "Software versions\n",
        "Python 2.7.6 (default, Mar 22 2014, 22:59:56) [GCC 4.8.2]\n",
        "IPython 1.1.0\n",
        "OS posix [linux2]\n",
        "ctypes 1.1.0\n",
        "Cython 0.20.2\n",
        "\n",
        "Tue Aug 26 23:37:29 2014 JST"
       ]
      }
     ],
     "prompt_number": 64
    }
   ],
   "metadata": {}
  }
 ]
}