scalability/Dft_scale.ipynb

{
 "metadata": {
  "name": "",
  "signature": "sha256:e659769ed2587c9dd8c7d3f98fcc727b89961930a449e9f09945794f1f16dd51"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Setting"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "dt=0.001\n",
      "nt=10000\n",
      "tmax=nt*dt\n",
      "time=np.linspace(0,tmax,nt)\n",
      "\n",
      "df=1./tmax\n",
      "fmax=100.\n",
      "nf=int(fmax/df)\n",
      "freq=np.linspace(0,fmax,nf)\n",
      "\n",
      "print tmax,fmax"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "10.0 100.0\n"
       ]
      }
     ],
     "prompt_number": 85
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from scipy import signal\n",
      "ricker=signal.ricker(nt,20.0)\n",
      "plot(time,ricker,'k-')\n",
      "xlabel(\"Time (s)\",fontsize='large')\n",
      "ylabel(\"Amplitude\",fontsize='large')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 86,
       "text": [
        "<matplotlib.text.Text at 0x110fc5290>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x110f7e2d0>"
       ]
      }
     ],
     "prompt_number": 86
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Python, Numpy"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def dft_py(w,dt,nf,df):\n",
      "    fw=np.zeros(nf,dtype=np.complex64)\n",
      "    t=np.linspace(0,w.shape[0]*dt,w.shape[0])\n",
      "    for ifreq in xrange(nf):\n",
      "        omega=2.*np.pi*ifreq*df\n",
      "        fw[ifreq]=0.0j\n",
      "        for it in xrange(w.shape[0]):\n",
      "            fw[ifreq]+=w[it]*np.exp(-1.0j*omega*t[it])\n",
      "        fw[ifreq]*=dt\n",
      "    return fw\n",
      "\n",
      "def dft_np(w,dt,nf,df):\n",
      "    fw=np.zeros(nf,dtype=np.complex128)\n",
      "    t=np.linspace(0,w.shape[0]*dt,w.shape[0])\n",
      "    for ifreq in xrange(nf):\n",
      "        omega=2.*np.pi*ifreq*df\n",
      "        fw[ifreq]=np.dot(w,np.exp(-1.0j*omega*t))*dt\n",
      "    return fw"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 87
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fricker=dft_np(ricker,dt,nf,df)\n",
      "plot(freq,abs(fricker),'k-')\n",
      "xlabel('Frequency (Hz)',fontsize='large')\n",
      "ylabel('Amplitude',fontsize='large')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 88,
       "text": [
        "<matplotlib.text.Text at 0x1113d9e10>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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EJEG5mVyKgUpgB3AKeBa4PqzMNCD4jbYK6AlkRqlbAXzYnsCUXM5122238cIL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\niIiIiIiIiIiIiIiIiIiISKz8H7XgUwZ8Gxh7AAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1113e18d0>"
       ]
      }
     ],
     "prompt_number": 88
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ncut=100\n",
      "%timeit -r 3 -n 3 dft_np(ricker[:ncut],dt,nf,df)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "3 loops, best of 3: 9.38 ms per loop\n"
       ]
      }
     ],
     "prompt_number": 90
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ncut=1000\n",
      "%timeit -r 3 -n 3 dft_np(ricker[:ncut],dt,nf,df)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "3 loops, best of 3: 33.7 ms per loop\n"
       ]
      }
     ],
     "prompt_number": 91
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%timeit -r 3 -n 3 dft_np(ricker,dt,nf,df)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "3 loops, best of 3: 285 ms per loop\n"
       ]
      }
     ],
     "prompt_number": 92
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ncut=100\n",
      "%timeit -r 3 -n 3 dft_py(ricker[:ncut],dt,nf,df)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "3 loops, best of 3: 784 ms per loop\n"
       ]
      }
     ],
     "prompt_number": 93
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ncut=1000\n",
      "%timeit -r 3 -n 3 dft_py(ricker[:ncut],dt,nf,df)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "3 loops, best of 3: 7.84 s per loop\n"
       ]
      }
     ],
     "prompt_number": 94
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%timeit -r 3 -n 3 dft_py(ricker,dt,nf,df)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "3 loops, best of 3: 1min 18s per loop\n"
       ]
      }
     ],
     "prompt_number": 95
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Numba"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numba\n",
      "\n",
      "dft_nb=numba.autojit(dft_py)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 96
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ncut=100\n",
      "%timeit -r 3 -n 3 dft_nb(ricker[:ncut],dt,nf,df)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "3 loops, best of 3: 786 ms per loop\n"
       ]
      }
     ],
     "prompt_number": 99
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ncut=1000\n",
      "%timeit -r 3 -n 3 dft_nb(ricker[:ncut],dt,nf,df)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "3 loops, best of 3: 7.87 s per loop\n"
       ]
      }
     ],
     "prompt_number": 100
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%timeit -r 3 -n 3 dft_nb(ricker,dt,nf,df)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "3 loops, best of 3: 1min 18s per loop\n"
       ]
      }
     ],
     "prompt_number": 101
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Cython"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%load_ext cythonmagic"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%cython\n",
      "import cython\n",
      "import numpy as np\n",
      "cimport numpy as np\n",
      "import cmath\n",
      "\n",
      "ctypedef np.double_t DTYPE_t\n",
      "ctypedef np.complex128_t DTYPEC_t\n",
      "\n",
      "@cython.boundscheck(False)\n",
      "@cython.wraparound(False)\n",
      "@cython.nonecheck(False)\n",
      "def dft_cy(np.ndarray[double] w,double dt,int nf,double df):\n",
      "    cdef np.ndarray[np.complex128_t] fw=np.zeros(nf,dtype=np.complex128)\n",
      "    cdef np.ndarray[double,ndim=1] t=np.linspace(0.,w.shape[0]*dt,w.shape[0])\n",
      "    cdef int ifreq,it\n",
      "    cdef double pi=np.pi\n",
      "    cdef DTYPE_t omega\n",
      "    for ifreq in xrange(nf):\n",
      "        omega=2.*pi*ifreq*df\n",
      "        fw[ifreq]=0.0j\n",
      "        for it in xrange(w.shape[0]):\n",
      "            fw[ifreq]=fw[ifreq]+w[it]*cmath.exp(-1.0j*omega*t[it])\n",
      "        fw[ifreq]=fw[ifreq]*dt\n",
      "    return fw"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ncut=100\n",
      "%timeit -r 3 -n 3 dft_cy(ricker[:ncut],dt,nf,df)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "3 loops, best of 3: 29.3 ms per loop\n"
       ]
      }
     ],
     "prompt_number": 105
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ncut=1000\n",
      "%timeit -r 3 -n 3 dft_cy(ricker[:ncut],dt,nf,df)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "3 loops, best of 3: 284 ms per loop\n"
       ]
      }
     ],
     "prompt_number": 106
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%timeit -r 3 -n 3 dft_cy(ricker,dt,nf,df)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "3 loops, best of 3: 2.86 s per loop\n"
       ]
      }
     ],
     "prompt_number": 107
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Fortran"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%file dft_f.f90\n",
      "\n",
      "subroutine dft_fv(fw,w,nt,dt,nf,df)\n",
      "integer,intent(in):: nt,nf\n",
      "real(kind=8),intent(in):: dt,df\n",
      "real(kind=8),intent(in):: w(nt)\n",
      "complex(kind=8),intent(out):: fw(nf)\n",
      "integer it,ifreq\n",
      "real(kind=8),parameter:: pi=3.141592654d0\n",
      "real(kind=8):: omega,t(nt)\n",
      "do it=1,nt\n",
      "    t(it)=(it-1)*dt\n",
      "enddo\n",
      "do ifreq=1,nf\n",
      "    omega=2.d0*pi*(ifreq-1)*df\n",
      "    fw(ifreq)=dcmplx(0.d0,0.d0)\n",
      "    do it=1,nt\n",
      "        fw(ifreq)=fw(ifreq)+w(it)*cdexp(-dcmplx(0.d0,1.d0)*omega*t(it))\n",
      "    enddo\n",
      "    fw(ifreq)=fw(ifreq)*dt\n",
      "enddo\n",
      "end subroutine\n",
      "\n",
      "subroutine dft_fvec(fw,w,nt,dt,nf,df)\n",
      "integer,intent(in):: nt,nf\n",
      "real(kind=8),intent(in):: dt,df\n",
      "real(kind=8),intent(in):: w(nt)\n",
      "complex(kind=8),intent(out):: fw(nf)\n",
      "integer it,ifreq\n",
      "real(kind=8),parameter:: pi=3.141592654d0\n",
      "real(kind=8):: omega,t(nt)\n",
      "do it=1,nt\n",
      "    t(it)=(it-1)*dt\n",
      "enddo\n",
      "do ifreq=1,nf\n",
      "    omega=2.d0*pi*(ifreq-1)*df\n",
      "    fw(ifreq)=dot_product(w(:),cdexp(-dcmplx(0.d0,1.d0)*omega*t(:)))*dt\n",
      "enddo\n",
      "end subroutine"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Overwriting dft_f.f90\n"
       ]
      }
     ],
     "prompt_number": 109
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "!f2py -c -m dft_fortran dft_f.f90 --f90exec=/opt/local/bin/gfortran-mp-4.9 > log.txt"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 110
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import dft_fortran\n",
      "print dft_fortran.__doc__"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "This module 'dft_fortran' is auto-generated with f2py (version:2).\n",
        "Functions:\n",
        "  fw = dft_fv(w,dt,nf,df,nt=len(w))\n",
        "  fw = dft_fvec(w,dt,nf,df,nt=len(w))\n",
        ".\n"
       ]
      }
     ],
     "prompt_number": 111
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fw=dft_fortran.dft_fv(ricker,dt,nf,df)\n",
      "plot(freq,abs(fw))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 112,
       "text": [
        "[<matplotlib.lines.Line2D at 0x1115216d0>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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MzLapmy7v9wj169XMqdSFJCJ+YNd9BPCc9Uq1OO39nAzqphvsIIYu2b4dbr8933vpmtGj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\niIiIiIiIAPw/OISdYkQnqogAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x111403690>"
       ]
      }
     ],
     "prompt_number": 112
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fw=dft_fortran.dft_fvec(ricker,dt,nf,df)\n",
      "plot(freq,abs(fw))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 113,
       "text": [
        "[<matplotlib.lines.Line2D at 0x1115ac050>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x111527110>"
       ]
      }
     ],
     "prompt_number": 113
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ncut=100\n",
      "%timeit -r 3 -n 3 dft_fortran.dft_fv(ricker[:ncut],dt,nf,df)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "3 loops, best of 3: 2.09 ms per loop\n"
       ]
      }
     ],
     "prompt_number": 114
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ncut=1000\n",
      "%timeit -r 3 -n 3 dft_fortran.dft_fv(ricker[:ncut],dt,nf,df)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "3 loops, best of 3: 21.4 ms per loop\n"
       ]
      }
     ],
     "prompt_number": 115
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%timeit -r 3 -n 3 dft_fortran.dft_fv(ricker,dt,nf,df)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "3 loops, best of 3: 218 ms per loop\n"
       ]
      }
     ],
     "prompt_number": 116
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 116
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ncut=100\n",
      "%timeit -r 3 -n 3 dft_fortran.dft_fvec(ricker[:ncut],dt,nf,df)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "3 loops, best of 3: 2.24 ms per loop\n"
       ]
      }
     ],
     "prompt_number": 117
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ncut=1000\n",
      "%timeit -r 3 -n 3 dft_fortran.dft_fvec(ricker[:ncut],dt,nf,df)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "3 loops, best of 3: 21.2 ms per loop\n"
       ]
      }
     ],
     "prompt_number": 118
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%timeit -r 3 -n 3 dft_fortran.dft_fvec(ricker,dt,nf,df)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "3 loops, best of 3: 216 ms per loop\n"
       ]
      }
     ],
     "prompt_number": 119
    }
   ],
   "metadata": {}
  }
 ]
}