2016-06-02-cython-filtering.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "%pylab inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%load_ext cython"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def naive_parallel_filter(x,result,coeff,history):\n",
    "    nsamp = x.shape[1]\n",
    "    nstreams = x.shape[0]\n",
    "    ntaps = coeff.shape[0]\n",
    "    for istream in range(nstreams):\n",
    "        for itap in range(ntaps):\n",
    "            icoeff = 0\n",
    "            for ihistory in range(itap,ntaps):\n",
    "                result[istream,itap] += coeff[icoeff]*history[istream,ihistory]\n",
    "                icoeff += 1\n",
    "            for isamp in range(0,itap):\n",
    "                result[istream,itap] += coeff[icoeff]*x[istream,isamp]\n",
    "                icoeff += 1\n",
    "                \n",
    "        for iresult in range(ntaps,nsamp):\n",
    "            for icoeff in range(ntaps):\n",
    "                result[istream,iresult] += coeff[icoeff]*x[istream,iresult-ntaps+icoeff]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "ntaps = 32\n",
    "x = np.zeros((16,2**10),dtype=np.complex64)\n",
    "coeff = np.ones((ntaps,),dtype=np.float32)\n",
    "history = x[:,:ntaps].copy()\n",
    "result = np.zeros_like(x)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 loop, best of 3: 1.63 s per loop\n"
     ]
    }
   ],
   "source": [
    "%timeit naive_parallel_filter(x,result,coeff,history)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%%cython --cplus\n",
    "\n",
    "def cython1_parallel_filter(x,result,coeff,history):\n",
    "    nsamp = x.shape[1]\n",
    "    nstreams = x.shape[0]\n",
    "    ntaps = coeff.shape[0]\n",
    "    for istream in range(nstreams):\n",
    "        for itap in range(ntaps):\n",
    "            icoeff = 0\n",
    "            for ihistory in range(itap,ntaps):\n",
    "                result[istream,itap] += coeff[icoeff]*history[istream,ihistory]\n",
    "                icoeff += 1\n",
    "            for isamp in range(0,itap):\n",
    "                result[istream,itap] += coeff[icoeff]*x[istream,isamp]\n",
    "                icoeff += 1\n",
    "                \n",
    "        for iresult in range(ntaps,nsamp):\n",
    "            for icoeff in range(ntaps):\n",
    "                result[istream,iresult] += coeff[icoeff]*x[istream,iresult-ntaps+icoeff]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 loop, best of 3: 1.67 s per loop\n"
     ]
    }
   ],
   "source": [
    "%timeit cython1_parallel_filter(x,result,coeff,history)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%%cython --cplus\n",
    "\n",
    "cimport numpy as np\n",
    "def cython2_parallel_filter(np.ndarray x, np.ndarray result,np.ndarray coeff,np.ndarray history):\n",
    "    cdef int nsamp = x.shape[1]\n",
    "    cdef int nstreams = x.shape[0]\n",
    "    cdef int ntaps = coeff.shape[0]\n",
    "    cdef int icoeff = 0\n",
    "    for istream in range(nstreams):\n",
    "        for itap in range(ntaps):\n",
    "            icoeff = 0\n",
    "            for ihistory in range(itap,ntaps):\n",
    "                result[istream,itap] += coeff[icoeff]*history[istream,ihistory]\n",
    "                icoeff += 1\n",
    "            for isamp in range(0,itap):\n",
    "                result[istream,itap] += coeff[icoeff]*x[istream,isamp]\n",
    "                icoeff += 1\n",
    "                \n",
    "        for iresult in range(ntaps,nsamp):\n",
    "            for icoeff in range(ntaps):\n",
    "                result[istream,iresult] += coeff[icoeff]*x[istream,iresult-ntaps+icoeff]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 loop, best of 3: 1.68 s per loop\n"
     ]
    }
   ],
   "source": [
    "%timeit cython2_parallel_filter(x,result,coeff,history)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%%cython --cplus\n",
    "\n",
    "cimport numpy as np\n",
    "def cython3_parallel_filter(np.ndarray[np.complex64_t, ndim=2] x, np.ndarray[np.complex64_t, ndim=2] result,np.ndarray[np.float32_t, ndim=1] coeff,np.ndarray[np.complex64_t, ndim=2] history):\n",
    "    cdef int nsamp = x.shape[1]\n",
    "    cdef int nstreams = x.shape[0]\n",
    "    cdef int ntaps = coeff.shape[0]\n",
    "    cdef int icoeff = 0\n",
    "    for istream in range(nstreams):\n",
    "        for itap in range(ntaps):\n",
    "            icoeff = 0\n",
    "            for ihistory in range(itap,ntaps):\n",
    "                result[istream,itap] += coeff[icoeff]*history[istream,ihistory]\n",
    "                icoeff += 1\n",
    "            for isamp in range(0,itap):\n",
    "                result[istream,itap] += coeff[icoeff]*x[istream,isamp]\n",
    "                icoeff += 1\n",
    "                \n",
    "        for iresult in range(ntaps,nsamp):\n",
    "            for icoeff in range(ntaps):\n",
    "                result[istream,iresult] += coeff[icoeff]*x[istream,iresult-ntaps+icoeff]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 loop, best of 3: 3.13 s per loop\n"
     ]
    }
   ],
   "source": [
    "%timeit cython3_parallel_filter(x,result,coeff,history)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
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       "<pre class=\"cython line score-11\" onclick='toggleDiv(this)'>+<span class=\"\">02</span>: <span class=\"k\">cimport</span> <span class=\"nn\">numpy</span> <span class=\"k\">as</span> <span class=\"nn\">np</span></pre>\n",
       "<pre class='cython code score-11 '>  __pyx_t_1 = <span class='py_c_api'>PyDict_New</span>(); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 2, __pyx_L1_error)\n",
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       "</pre><pre class=\"cython line score-0\">&#xA0;<span class=\"\">03</span>: <span class=\"k\">cimport</span> <span class=\"nn\">cython</span></pre>\n",
       "<pre class=\"cython line score-0\">&#xA0;<span class=\"\">04</span>: <span class=\"nd\">@cython</span><span class=\"o\">.</span><span class=\"n\">boundscheck</span><span class=\"p\">(</span><span class=\"bp\">False</span><span class=\"p\">)</span></pre>\n",
       "<pre class=\"cython line score-0\">&#xA0;<span class=\"\">05</span>: <span class=\"nd\">@cython</span><span class=\"o\">.</span><span class=\"n\">wraparound</span><span class=\"p\">(</span><span class=\"bp\">False</span><span class=\"p\">)</span></pre>\n",
       "<pre class=\"cython line score-98\" onclick='toggleDiv(this)'>+<span class=\"\">06</span>: <span class=\"k\">def</span> <span class=\"nf\">cython4_parallel_filter</span><span class=\"p\">(</span><span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">ndarray</span><span class=\"p\">[</span><span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">complex64_t</span><span class=\"p\">,</span> <span class=\"n\">ndim</span><span class=\"o\">=</span><span class=\"mf\">2</span><span class=\"p\">]</span> <span class=\"n\">x</span><span class=\"p\">,</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">ndarray</span><span class=\"p\">[</span><span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">complex64_t</span><span class=\"p\">,</span> <span class=\"n\">ndim</span><span class=\"o\">=</span><span class=\"mf\">2</span><span class=\"p\">]</span> <span class=\"n\">result</span><span class=\"p\">,</span><span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">ndarray</span><span class=\"p\">[</span><span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">float32_t</span><span class=\"p\">,</span> <span class=\"n\">ndim</span><span class=\"o\">=</span><span class=\"mf\">1</span><span class=\"p\">]</span> <span class=\"n\">coeff</span><span class=\"p\">,</span><span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">ndarray</span><span class=\"p\">[</span><span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">complex64_t</span><span class=\"p\">,</span> <span class=\"n\">ndim</span><span class=\"o\">=</span><span class=\"mf\">2</span><span class=\"p\">]</span> <span class=\"n\">history</span><span class=\"p\">):</span></pre>\n",
       "<pre class='cython code score-98 '>/* Python wrapper */\n",
       "static PyObject *__pyx_pw_46_cython_magic_1244b7f71a88bf2503cd245b8a20ee30_1cython4_parallel_filter(PyObject *__pyx_self, PyObject *__pyx_args, PyObject *__pyx_kwds); /*proto*/\n",
       "static PyMethodDef __pyx_mdef_46_cython_magic_1244b7f71a88bf2503cd245b8a20ee30_1cython4_parallel_filter = {\"cython4_parallel_filter\", (PyCFunction)__pyx_pw_46_cython_magic_1244b7f71a88bf2503cd245b8a20ee30_1cython4_parallel_filter, METH_VARARGS|METH_KEYWORDS, 0};\n",
       "static PyObject *__pyx_pw_46_cython_magic_1244b7f71a88bf2503cd245b8a20ee30_1cython4_parallel_filter(PyObject *__pyx_self, PyObject *__pyx_args, PyObject *__pyx_kwds) {\n",
       "  PyArrayObject *__pyx_v_x = 0;\n",
       "  PyArrayObject *__pyx_v_result = 0;\n",
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       "    PyObject* values[4] = {0,0,0,0};\n",
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       "      switch (pos_args) {\n",
       "        case  4: values[3] = <span class='py_macro_api'>PyTuple_GET_ITEM</span>(__pyx_args, 3);\n",
       "        case  3: values[2] = <span class='py_macro_api'>PyTuple_GET_ITEM</span>(__pyx_args, 2);\n",
       "        case  2: values[1] = <span class='py_macro_api'>PyTuple_GET_ITEM</span>(__pyx_args, 1);\n",
       "        case  1: values[0] = <span class='py_macro_api'>PyTuple_GET_ITEM</span>(__pyx_args, 0);\n",
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       "        default: goto __pyx_L5_argtuple_error;\n",
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       "      kw_args = <span class='py_c_api'>PyDict_Size</span>(__pyx_kwds);\n",
       "      switch (pos_args) {\n",
       "        case  0:\n",
       "        if (likely((values[0] = <span class='py_c_api'>PyDict_GetItem</span>(__pyx_kwds, __pyx_n_s_x)) != 0)) kw_args--;\n",
       "        else goto __pyx_L5_argtuple_error;\n",
       "        case  1:\n",
       "        if (likely((values[1] = <span class='py_c_api'>PyDict_GetItem</span>(__pyx_kwds, __pyx_n_s_result)) != 0)) kw_args--;\n",
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       "          <span class='pyx_c_api'>__Pyx_RaiseArgtupleInvalid</span>(\"cython4_parallel_filter\", 1, 4, 4, 1); __PYX_ERR(0, 6, __pyx_L3_error)\n",
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       "        case  2:\n",
       "        if (likely((values[2] = <span class='py_c_api'>PyDict_GetItem</span>(__pyx_kwds, __pyx_n_s_coeff)) != 0)) kw_args--;\n",
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       "          <span class='pyx_c_api'>__Pyx_RaiseArgtupleInvalid</span>(\"cython4_parallel_filter\", 1, 4, 4, 2); __PYX_ERR(0, 6, __pyx_L3_error)\n",
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       "        if (likely((values[3] = <span class='py_c_api'>PyDict_GetItem</span>(__pyx_kwds, __pyx_n_s_history)) != 0)) kw_args--;\n",
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       "          <span class='pyx_c_api'>__Pyx_RaiseArgtupleInvalid</span>(\"cython4_parallel_filter\", 1, 4, 4, 3); __PYX_ERR(0, 6, __pyx_L3_error)\n",
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       "      if (unlikely(kw_args &gt; 0)) {\n",
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       "      values[1] = <span class='py_macro_api'>PyTuple_GET_ITEM</span>(__pyx_args, 1);\n",
       "      values[2] = <span class='py_macro_api'>PyTuple_GET_ITEM</span>(__pyx_args, 2);\n",
       "      values[3] = <span class='py_macro_api'>PyTuple_GET_ITEM</span>(__pyx_args, 3);\n",
       "    }\n",
       "    __pyx_v_x = ((PyArrayObject *)values[0]);\n",
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       "    __pyx_v_coeff = ((PyArrayObject *)values[2]);\n",
       "    __pyx_v_history = ((PyArrayObject *)values[3]);\n",
       "  }\n",
       "  goto __pyx_L4_argument_unpacking_done;\n",
       "  __pyx_L5_argtuple_error:;\n",
       "  <span class='pyx_c_api'>__Pyx_RaiseArgtupleInvalid</span>(\"cython4_parallel_filter\", 1, 4, 4, <span class='py_macro_api'>PyTuple_GET_SIZE</span>(__pyx_args)); __PYX_ERR(0, 6, __pyx_L3_error)\n",
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       "  if (unlikely(!<span class='pyx_c_api'>__Pyx_ArgTypeTest</span>(((PyObject *)__pyx_v_history), __pyx_ptype_5numpy_ndarray, 1, \"history\", 0))) __PYX_ERR(0, 6, __pyx_L1_error)\n",
       "  __pyx_r = __pyx_pf_46_cython_magic_1244b7f71a88bf2503cd245b8a20ee30_cython4_parallel_filter(__pyx_self, __pyx_v_x, __pyx_v_result, __pyx_v_coeff, __pyx_v_history);\n",
       "\n",
       "  /* function exit code */\n",
       "  goto __pyx_L0;\n",
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       "  __pyx_L0:;\n",
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       "}\n",
       "\n",
       "static PyObject *__pyx_pf_46_cython_magic_1244b7f71a88bf2503cd245b8a20ee30_cython4_parallel_filter(CYTHON_UNUSED PyObject *__pyx_self, PyArrayObject *__pyx_v_x, PyArrayObject *__pyx_v_result, PyArrayObject *__pyx_v_coeff, PyArrayObject *__pyx_v_history) {\n",
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       "  int __pyx_v_ntaps;\n",
       "  int __pyx_v_icoeff;\n",
       "  int __pyx_v_iresult;\n",
       "  int __pyx_v_istream;\n",
       "  int __pyx_v_itap;\n",
       "  int __pyx_v_ihistory;\n",
       "  int __pyx_v_isamp;\n",
       "  __Pyx_LocalBuf_ND __pyx_pybuffernd_coeff;\n",
       "  __Pyx_Buffer __pyx_pybuffer_coeff;\n",
       "  __Pyx_LocalBuf_ND __pyx_pybuffernd_history;\n",
       "  __Pyx_Buffer __pyx_pybuffer_history;\n",
       "  __Pyx_LocalBuf_ND __pyx_pybuffernd_result;\n",
       "  __Pyx_Buffer __pyx_pybuffer_result;\n",
       "  __Pyx_LocalBuf_ND __pyx_pybuffernd_x;\n",
       "  __Pyx_Buffer __pyx_pybuffer_x;\n",
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       "  <span class='refnanny'>__Pyx_RefNannyDeclarations</span>\n",
       "  <span class='refnanny'>__Pyx_RefNannySetupContext</span>(\"cython4_parallel_filter\", 0);\n",
       "  __pyx_pybuffer_x.pybuffer.buf = NULL;\n",
       "  __pyx_pybuffer_x.refcount = 0;\n",
       "  __pyx_pybuffernd_x.data = NULL;\n",
       "  __pyx_pybuffernd_x.rcbuffer = &amp;__pyx_pybuffer_x;\n",
       "  __pyx_pybuffer_result.pybuffer.buf = NULL;\n",
       "  __pyx_pybuffer_result.refcount = 0;\n",
       "  __pyx_pybuffernd_result.data = NULL;\n",
       "  __pyx_pybuffernd_result.rcbuffer = &amp;__pyx_pybuffer_result;\n",
       "  __pyx_pybuffer_coeff.pybuffer.buf = NULL;\n",
       "  __pyx_pybuffer_coeff.refcount = 0;\n",
       "  __pyx_pybuffernd_coeff.data = NULL;\n",
       "  __pyx_pybuffernd_coeff.rcbuffer = &amp;__pyx_pybuffer_coeff;\n",
       "  __pyx_pybuffer_history.pybuffer.buf = NULL;\n",
       "  __pyx_pybuffer_history.refcount = 0;\n",
       "  __pyx_pybuffernd_history.data = NULL;\n",
       "  __pyx_pybuffernd_history.rcbuffer = &amp;__pyx_pybuffer_history;\n",
       "  {\n",
       "    __Pyx_BufFmt_StackElem __pyx_stack[1];\n",
       "    if (unlikely(<span class='pyx_c_api'>__Pyx_GetBufferAndValidate</span>(&amp;__pyx_pybuffernd_x.rcbuffer-&gt;pybuffer, (PyObject*)__pyx_v_x, &amp;__Pyx_TypeInfo___pyx_t_float_complex, PyBUF_FORMAT| PyBUF_STRIDES, 2, 0, __pyx_stack) == -1)) __PYX_ERR(0, 6, __pyx_L1_error)\n",
       "  }\n",
       "  __pyx_pybuffernd_x.diminfo[0].strides = __pyx_pybuffernd_x.rcbuffer-&gt;pybuffer.strides[0]; __pyx_pybuffernd_x.diminfo[0].shape = __pyx_pybuffernd_x.rcbuffer-&gt;pybuffer.shape[0]; __pyx_pybuffernd_x.diminfo[1].strides = __pyx_pybuffernd_x.rcbuffer-&gt;pybuffer.strides[1]; __pyx_pybuffernd_x.diminfo[1].shape = __pyx_pybuffernd_x.rcbuffer-&gt;pybuffer.shape[1];\n",
       "  {\n",
       "    __Pyx_BufFmt_StackElem __pyx_stack[1];\n",
       "    if (unlikely(<span class='pyx_c_api'>__Pyx_GetBufferAndValidate</span>(&amp;__pyx_pybuffernd_result.rcbuffer-&gt;pybuffer, (PyObject*)__pyx_v_result, &amp;__Pyx_TypeInfo___pyx_t_float_complex, PyBUF_FORMAT| PyBUF_STRIDES| PyBUF_WRITABLE, 2, 0, __pyx_stack) == -1)) __PYX_ERR(0, 6, __pyx_L1_error)\n",
       "  }\n",
       "  __pyx_pybuffernd_result.diminfo[0].strides = __pyx_pybuffernd_result.rcbuffer-&gt;pybuffer.strides[0]; __pyx_pybuffernd_result.diminfo[0].shape = __pyx_pybuffernd_result.rcbuffer-&gt;pybuffer.shape[0]; __pyx_pybuffernd_result.diminfo[1].strides = __pyx_pybuffernd_result.rcbuffer-&gt;pybuffer.strides[1]; __pyx_pybuffernd_result.diminfo[1].shape = __pyx_pybuffernd_result.rcbuffer-&gt;pybuffer.shape[1];\n",
       "  {\n",
       "    __Pyx_BufFmt_StackElem __pyx_stack[1];\n",
       "    if (unlikely(<span class='pyx_c_api'>__Pyx_GetBufferAndValidate</span>(&amp;__pyx_pybuffernd_coeff.rcbuffer-&gt;pybuffer, (PyObject*)__pyx_v_coeff, &amp;__Pyx_TypeInfo_nn___pyx_t_5numpy_float32_t, PyBUF_FORMAT| PyBUF_STRIDES, 1, 0, __pyx_stack) == -1)) __PYX_ERR(0, 6, __pyx_L1_error)\n",
       "  }\n",
       "  __pyx_pybuffernd_coeff.diminfo[0].strides = __pyx_pybuffernd_coeff.rcbuffer-&gt;pybuffer.strides[0]; __pyx_pybuffernd_coeff.diminfo[0].shape = __pyx_pybuffernd_coeff.rcbuffer-&gt;pybuffer.shape[0];\n",
       "  {\n",
       "    __Pyx_BufFmt_StackElem __pyx_stack[1];\n",
       "    if (unlikely(<span class='pyx_c_api'>__Pyx_GetBufferAndValidate</span>(&amp;__pyx_pybuffernd_history.rcbuffer-&gt;pybuffer, (PyObject*)__pyx_v_history, &amp;__Pyx_TypeInfo___pyx_t_float_complex, PyBUF_FORMAT| PyBUF_STRIDES, 2, 0, __pyx_stack) == -1)) __PYX_ERR(0, 6, __pyx_L1_error)\n",
       "  }\n",
       "  __pyx_pybuffernd_history.diminfo[0].strides = __pyx_pybuffernd_history.rcbuffer-&gt;pybuffer.strides[0]; __pyx_pybuffernd_history.diminfo[0].shape = __pyx_pybuffernd_history.rcbuffer-&gt;pybuffer.shape[0]; __pyx_pybuffernd_history.diminfo[1].strides = __pyx_pybuffernd_history.rcbuffer-&gt;pybuffer.strides[1]; __pyx_pybuffernd_history.diminfo[1].shape = __pyx_pybuffernd_history.rcbuffer-&gt;pybuffer.shape[1];\n",
       "/* … */\n",
       "  /* function exit code */\n",
       "  __pyx_r = Py_None; <span class='pyx_macro_api'>__Pyx_INCREF</span>(Py_None);\n",
       "  goto __pyx_L0;\n",
       "  __pyx_L1_error:;\n",
       "  { PyObject *__pyx_type, *__pyx_value, *__pyx_tb;\n",
       "    __Pyx_PyThreadState_declare\n",
       "    __Pyx_PyThreadState_assign\n",
       "    <span class='pyx_c_api'>__Pyx_ErrFetch</span>(&amp;__pyx_type, &amp;__pyx_value, &amp;__pyx_tb);\n",
       "    <span class='pyx_c_api'>__Pyx_SafeReleaseBuffer</span>(&amp;__pyx_pybuffernd_coeff.rcbuffer-&gt;pybuffer);\n",
       "    <span class='pyx_c_api'>__Pyx_SafeReleaseBuffer</span>(&amp;__pyx_pybuffernd_history.rcbuffer-&gt;pybuffer);\n",
       "    <span class='pyx_c_api'>__Pyx_SafeReleaseBuffer</span>(&amp;__pyx_pybuffernd_result.rcbuffer-&gt;pybuffer);\n",
       "    <span class='pyx_c_api'>__Pyx_SafeReleaseBuffer</span>(&amp;__pyx_pybuffernd_x.rcbuffer-&gt;pybuffer);\n",
       "  <span class='pyx_c_api'>__Pyx_ErrRestore</span>(__pyx_type, __pyx_value, __pyx_tb);}\n",
       "  <span class='pyx_c_api'>__Pyx_AddTraceback</span>(\"_cython_magic_1244b7f71a88bf2503cd245b8a20ee30.cython4_parallel_filter\", __pyx_clineno, __pyx_lineno, __pyx_filename);\n",
       "  __pyx_r = NULL;\n",
       "  goto __pyx_L2;\n",
       "  __pyx_L0:;\n",
       "  <span class='pyx_c_api'>__Pyx_SafeReleaseBuffer</span>(&amp;__pyx_pybuffernd_coeff.rcbuffer-&gt;pybuffer);\n",
       "  <span class='pyx_c_api'>__Pyx_SafeReleaseBuffer</span>(&amp;__pyx_pybuffernd_history.rcbuffer-&gt;pybuffer);\n",
       "  <span class='pyx_c_api'>__Pyx_SafeReleaseBuffer</span>(&amp;__pyx_pybuffernd_result.rcbuffer-&gt;pybuffer);\n",
       "  <span class='pyx_c_api'>__Pyx_SafeReleaseBuffer</span>(&amp;__pyx_pybuffernd_x.rcbuffer-&gt;pybuffer);\n",
       "  __pyx_L2:;\n",
       "  <span class='refnanny'>__Pyx_XGIVEREF</span>(__pyx_r);\n",
       "  <span class='refnanny'>__Pyx_RefNannyFinishContext</span>();\n",
       "  return __pyx_r;\n",
       "}\n",
       "/* … */\n",
       "  __pyx_tuple__7 = <span class='py_c_api'>PyTuple_Pack</span>(13, __pyx_n_s_x, __pyx_n_s_result, __pyx_n_s_coeff, __pyx_n_s_history, __pyx_n_s_nsamp, __pyx_n_s_nstreams, __pyx_n_s_ntaps, __pyx_n_s_icoeff, __pyx_n_s_iresult, __pyx_n_s_istream, __pyx_n_s_itap, __pyx_n_s_ihistory, __pyx_n_s_isamp); if (unlikely(!__pyx_tuple__7)) __PYX_ERR(0, 6, __pyx_L1_error)\n",
       "  <span class='refnanny'>__Pyx_GOTREF</span>(__pyx_tuple__7);\n",
       "  <span class='refnanny'>__Pyx_GIVEREF</span>(__pyx_tuple__7);\n",
       "/* … */\n",
       "  __pyx_t_1 = PyCFunction_NewEx(&amp;__pyx_mdef_46_cython_magic_1244b7f71a88bf2503cd245b8a20ee30_1cython4_parallel_filter, NULL, __pyx_n_s_cython_magic_1244b7f71a88bf2503); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 6, __pyx_L1_error)\n",
       "  <span class='refnanny'>__Pyx_GOTREF</span>(__pyx_t_1);\n",
       "  if (<span class='py_c_api'>PyDict_SetItem</span>(__pyx_d, __pyx_n_s_cython4_parallel_filter, __pyx_t_1) &lt; 0) __PYX_ERR(0, 6, __pyx_L1_error)\n",
       "  <span class='pyx_macro_api'>__Pyx_DECREF</span>(__pyx_t_1); __pyx_t_1 = 0;\n",
       "</pre><pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">07</span>:     <span class=\"k\">cdef</span> <span class=\"kt\">int</span> <span class=\"nf\">nsamp</span> <span class=\"o\">=</span> <span class=\"n\">x</span><span class=\"o\">.</span><span class=\"n\">shape</span><span class=\"p\">[</span><span class=\"mf\">1</span><span class=\"p\">]</span></pre>\n",
       "<pre class='cython code score-0 '>  __pyx_v_nsamp = (__pyx_v_x-&gt;dimensions[1]);\n",
       "</pre><pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">08</span>:     <span class=\"k\">cdef</span> <span class=\"kt\">int</span> <span class=\"nf\">nstreams</span> <span class=\"o\">=</span> <span class=\"n\">x</span><span class=\"o\">.</span><span class=\"n\">shape</span><span class=\"p\">[</span><span class=\"mf\">0</span><span class=\"p\">]</span></pre>\n",
       "<pre class='cython code score-0 '>  __pyx_v_nstreams = (__pyx_v_x-&gt;dimensions[0]);\n",
       "</pre><pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">09</span>:     <span class=\"k\">cdef</span> <span class=\"kt\">int</span> <span class=\"nf\">ntaps</span> <span class=\"o\">=</span> <span class=\"n\">coeff</span><span class=\"o\">.</span><span class=\"n\">shape</span><span class=\"p\">[</span><span class=\"mf\">0</span><span class=\"p\">]</span></pre>\n",
       "<pre class='cython code score-0 '>  __pyx_v_ntaps = (__pyx_v_coeff-&gt;dimensions[0]);\n",
       "</pre><pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">10</span>:     <span class=\"k\">cdef</span> <span class=\"kt\">int</span> <span class=\"nf\">icoeff</span> <span class=\"o\">=</span> <span class=\"mf\">0</span></pre>\n",
       "<pre class='cython code score-0 '>  __pyx_v_icoeff = 0;\n",
       "</pre><pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">11</span>:     <span class=\"k\">cdef</span> <span class=\"kt\">int</span> <span class=\"nf\">iresult</span> <span class=\"o\">=</span><span class=\"mf\">0</span></pre>\n",
       "<pre class='cython code score-0 '>  __pyx_v_iresult = 0;\n",
       "</pre><pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">12</span>:     <span class=\"k\">cdef</span> <span class=\"kt\">int</span> <span class=\"nf\">istream</span> <span class=\"o\">=</span><span class=\"mf\">0</span></pre>\n",
       "<pre class='cython code score-0 '>  __pyx_v_istream = 0;\n",
       "</pre><pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">13</span>:     <span class=\"k\">cdef</span> <span class=\"kt\">int</span> <span class=\"nf\">itap</span><span class=\"o\">=</span><span class=\"mf\">0</span></pre>\n",
       "<pre class='cython code score-0 '>  __pyx_v_itap = 0;\n",
       "</pre><pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">14</span>:     <span class=\"k\">cdef</span> <span class=\"kt\">int</span> <span class=\"nf\">ihistory</span><span class=\"o\">=</span><span class=\"mf\">0</span></pre>\n",
       "<pre class='cython code score-0 '>  __pyx_v_ihistory = 0;\n",
       "</pre><pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">15</span>:     <span class=\"k\">cdef</span> <span class=\"kt\">int</span> <span class=\"nf\">isamp</span> <span class=\"o\">=</span><span class=\"mf\">0</span></pre>\n",
       "<pre class='cython code score-0 '>  __pyx_v_isamp = 0;\n",
       "</pre><pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">16</span>:     <span class=\"k\">for</span> <span class=\"n\">istream</span> <span class=\"ow\">in</span> <span class=\"nb\">range</span><span class=\"p\">(</span><span class=\"n\">nstreams</span><span class=\"p\">):</span></pre>\n",
       "<pre class='cython code score-0 '>  __pyx_t_1 = __pyx_v_nstreams;\n",
       "  for (__pyx_t_2 = 0; __pyx_t_2 &lt; __pyx_t_1; __pyx_t_2+=1) {\n",
       "    __pyx_v_istream = __pyx_t_2;\n",
       "</pre><pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">17</span>:         <span class=\"k\">for</span> <span class=\"n\">itap</span> <span class=\"ow\">in</span> <span class=\"nb\">range</span><span class=\"p\">(</span><span class=\"n\">ntaps</span><span class=\"p\">):</span></pre>\n",
       "<pre class='cython code score-0 '>    __pyx_t_3 = __pyx_v_ntaps;\n",
       "    for (__pyx_t_4 = 0; __pyx_t_4 &lt; __pyx_t_3; __pyx_t_4+=1) {\n",
       "      __pyx_v_itap = __pyx_t_4;\n",
       "</pre><pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">18</span>:             <span class=\"n\">icoeff</span> <span class=\"o\">=</span> <span class=\"mf\">0</span></pre>\n",
       "<pre class='cython code score-0 '>      __pyx_v_icoeff = 0;\n",
       "</pre><pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">19</span>:             <span class=\"k\">for</span> <span class=\"n\">ihistory</span> <span class=\"ow\">in</span> <span class=\"nb\">range</span><span class=\"p\">(</span><span class=\"n\">itap</span><span class=\"p\">,</span><span class=\"n\">ntaps</span><span class=\"p\">):</span></pre>\n",
       "<pre class='cython code score-0 '>      __pyx_t_5 = __pyx_v_ntaps;\n",
       "      for (__pyx_t_6 = __pyx_v_itap; __pyx_t_6 &lt; __pyx_t_5; __pyx_t_6+=1) {\n",
       "        __pyx_v_ihistory = __pyx_t_6;\n",
       "</pre><pre class=\"cython line score-4\" onclick='toggleDiv(this)'>+<span class=\"\">20</span>:                 <span class=\"n\">result</span><span class=\"p\">[</span><span class=\"n\">istream</span><span class=\"p\">,</span><span class=\"n\">itap</span><span class=\"p\">]</span> <span class=\"o\">+=</span> <span class=\"n\">coeff</span><span class=\"p\">[</span><span class=\"n\">icoeff</span><span class=\"p\">]</span><span class=\"o\">*</span><span class=\"n\">history</span><span class=\"p\">[</span><span class=\"n\">istream</span><span class=\"p\">,</span><span class=\"n\">ihistory</span><span class=\"p\">]</span></pre>\n",
       "<pre class='cython code score-4 '>        __pyx_t_7 = __pyx_v_icoeff;\n",
       "        __pyx_t_8 = __pyx_v_istream;\n",
       "        __pyx_t_9 = __pyx_v_ihistory;\n",
       "        __pyx_t_10 = (*__Pyx_BufPtrStrided2d(__pyx_t_float_complex *, __pyx_pybuffernd_history.rcbuffer-&gt;pybuffer.buf, __pyx_t_8, __pyx_pybuffernd_history.diminfo[0].strides, __pyx_t_9, __pyx_pybuffernd_history.diminfo[1].strides));\n",
       "        __pyx_t_11 = __Pyx_c_prod_npy_float32(__pyx_t_npy_float32_complex_from_parts((*__Pyx_BufPtrStrided1d(__pyx_t_5numpy_float32_t *, __pyx_pybuffernd_coeff.rcbuffer-&gt;pybuffer.buf, __pyx_t_7, __pyx_pybuffernd_coeff.diminfo[0].strides)), 0), __pyx_t_npy_float32_complex_from_parts(<span class='pyx_macro_api'>__Pyx_CREAL</span>(__pyx_t_10), <span class='pyx_macro_api'>__Pyx_CIMAG</span>(__pyx_t_10)));\n",
       "        __pyx_t_12 = __pyx_v_istream;\n",
       "        __pyx_t_13 = __pyx_v_itap;\n",
       "        *__Pyx_BufPtrStrided2d(__pyx_t_float_complex *, __pyx_pybuffernd_result.rcbuffer-&gt;pybuffer.buf, __pyx_t_12, __pyx_pybuffernd_result.diminfo[0].strides, __pyx_t_13, __pyx_pybuffernd_result.diminfo[1].strides) += __pyx_t_float_complex_from_parts(<span class='pyx_macro_api'>__Pyx_CREAL</span>(__pyx_t_11), <span class='pyx_macro_api'>__Pyx_CIMAG</span>(__pyx_t_11));\n",
       "</pre><pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">21</span>:                 <span class=\"n\">icoeff</span> <span class=\"o\">+=</span> <span class=\"mf\">1</span></pre>\n",
       "<pre class='cython code score-0 '>        __pyx_v_icoeff = (__pyx_v_icoeff + 1);\n",
       "      }\n",
       "</pre><pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">22</span>:             <span class=\"k\">for</span> <span class=\"n\">isamp</span> <span class=\"ow\">in</span> <span class=\"nb\">range</span><span class=\"p\">(</span><span class=\"mf\">0</span><span class=\"p\">,</span><span class=\"n\">itap</span><span class=\"p\">):</span></pre>\n",
       "<pre class='cython code score-0 '>      __pyx_t_5 = __pyx_v_itap;\n",
       "      for (__pyx_t_6 = 0; __pyx_t_6 &lt; __pyx_t_5; __pyx_t_6+=1) {\n",
       "        __pyx_v_isamp = __pyx_t_6;\n",
       "</pre><pre class=\"cython line score-4\" onclick='toggleDiv(this)'>+<span class=\"\">23</span>:                 <span class=\"n\">result</span><span class=\"p\">[</span><span class=\"n\">istream</span><span class=\"p\">,</span><span class=\"n\">itap</span><span class=\"p\">]</span> <span class=\"o\">+=</span> <span class=\"n\">coeff</span><span class=\"p\">[</span><span class=\"n\">icoeff</span><span class=\"p\">]</span><span class=\"o\">*</span><span class=\"n\">x</span><span class=\"p\">[</span><span class=\"n\">istream</span><span class=\"p\">,</span><span class=\"n\">isamp</span><span class=\"p\">]</span></pre>\n",
       "<pre class='cython code score-4 '>        __pyx_t_14 = __pyx_v_icoeff;\n",
       "        __pyx_t_15 = __pyx_v_istream;\n",
       "        __pyx_t_16 = __pyx_v_isamp;\n",
       "        __pyx_t_10 = (*__Pyx_BufPtrStrided2d(__pyx_t_float_complex *, __pyx_pybuffernd_x.rcbuffer-&gt;pybuffer.buf, __pyx_t_15, __pyx_pybuffernd_x.diminfo[0].strides, __pyx_t_16, __pyx_pybuffernd_x.diminfo[1].strides));\n",
       "        __pyx_t_11 = __Pyx_c_prod_npy_float32(__pyx_t_npy_float32_complex_from_parts((*__Pyx_BufPtrStrided1d(__pyx_t_5numpy_float32_t *, __pyx_pybuffernd_coeff.rcbuffer-&gt;pybuffer.buf, __pyx_t_14, __pyx_pybuffernd_coeff.diminfo[0].strides)), 0), __pyx_t_npy_float32_complex_from_parts(<span class='pyx_macro_api'>__Pyx_CREAL</span>(__pyx_t_10), <span class='pyx_macro_api'>__Pyx_CIMAG</span>(__pyx_t_10)));\n",
       "        __pyx_t_17 = __pyx_v_istream;\n",
       "        __pyx_t_18 = __pyx_v_itap;\n",
       "        *__Pyx_BufPtrStrided2d(__pyx_t_float_complex *, __pyx_pybuffernd_result.rcbuffer-&gt;pybuffer.buf, __pyx_t_17, __pyx_pybuffernd_result.diminfo[0].strides, __pyx_t_18, __pyx_pybuffernd_result.diminfo[1].strides) += __pyx_t_float_complex_from_parts(<span class='pyx_macro_api'>__Pyx_CREAL</span>(__pyx_t_11), <span class='pyx_macro_api'>__Pyx_CIMAG</span>(__pyx_t_11));\n",
       "</pre><pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">24</span>:                 <span class=\"n\">icoeff</span> <span class=\"o\">+=</span> <span class=\"mf\">1</span></pre>\n",
       "<pre class='cython code score-0 '>        __pyx_v_icoeff = (__pyx_v_icoeff + 1);\n",
       "      }\n",
       "    }\n",
       "</pre><pre class=\"cython line score-0\">&#xA0;<span class=\"\">25</span>: </pre>\n",
       "<pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">26</span>:         <span class=\"k\">for</span> <span class=\"n\">iresult</span> <span class=\"ow\">in</span> <span class=\"nb\">range</span><span class=\"p\">(</span><span class=\"n\">ntaps</span><span class=\"p\">,</span><span class=\"n\">nsamp</span><span class=\"p\">):</span></pre>\n",
       "<pre class='cython code score-0 '>    __pyx_t_3 = __pyx_v_nsamp;\n",
       "    for (__pyx_t_4 = __pyx_v_ntaps; __pyx_t_4 &lt; __pyx_t_3; __pyx_t_4+=1) {\n",
       "      __pyx_v_iresult = __pyx_t_4;\n",
       "</pre><pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">27</span>:             <span class=\"k\">for</span> <span class=\"n\">icoeff</span> <span class=\"ow\">in</span> <span class=\"nb\">range</span><span class=\"p\">(</span><span class=\"n\">ntaps</span><span class=\"p\">):</span></pre>\n",
       "<pre class='cython code score-0 '>      __pyx_t_5 = __pyx_v_ntaps;\n",
       "      for (__pyx_t_6 = 0; __pyx_t_6 &lt; __pyx_t_5; __pyx_t_6+=1) {\n",
       "        __pyx_v_icoeff = __pyx_t_6;\n",
       "</pre><pre class=\"cython line score-4\" onclick='toggleDiv(this)'>+<span class=\"\">28</span>:                 <span class=\"n\">result</span><span class=\"p\">[</span><span class=\"n\">istream</span><span class=\"p\">,</span><span class=\"n\">iresult</span><span class=\"p\">]</span> <span class=\"o\">+=</span> <span class=\"n\">coeff</span><span class=\"p\">[</span><span class=\"n\">icoeff</span><span class=\"p\">]</span><span class=\"o\">*</span><span class=\"n\">x</span><span class=\"p\">[</span><span class=\"n\">istream</span><span class=\"p\">,</span><span class=\"n\">iresult</span><span class=\"o\">-</span><span class=\"n\">ntaps</span><span class=\"o\">+</span><span class=\"n\">icoeff</span><span class=\"p\">]</span></pre>\n",
       "<pre class='cython code score-4 '>        __pyx_t_19 = __pyx_v_icoeff;\n",
       "        __pyx_t_20 = __pyx_v_istream;\n",
       "        __pyx_t_21 = ((__pyx_v_iresult - __pyx_v_ntaps) + __pyx_v_icoeff);\n",
       "        __pyx_t_10 = (*__Pyx_BufPtrStrided2d(__pyx_t_float_complex *, __pyx_pybuffernd_x.rcbuffer-&gt;pybuffer.buf, __pyx_t_20, __pyx_pybuffernd_x.diminfo[0].strides, __pyx_t_21, __pyx_pybuffernd_x.diminfo[1].strides));\n",
       "        __pyx_t_11 = __Pyx_c_prod_npy_float32(__pyx_t_npy_float32_complex_from_parts((*__Pyx_BufPtrStrided1d(__pyx_t_5numpy_float32_t *, __pyx_pybuffernd_coeff.rcbuffer-&gt;pybuffer.buf, __pyx_t_19, __pyx_pybuffernd_coeff.diminfo[0].strides)), 0), __pyx_t_npy_float32_complex_from_parts(<span class='pyx_macro_api'>__Pyx_CREAL</span>(__pyx_t_10), <span class='pyx_macro_api'>__Pyx_CIMAG</span>(__pyx_t_10)));\n",
       "        __pyx_t_22 = __pyx_v_istream;\n",
       "        __pyx_t_23 = __pyx_v_iresult;\n",
       "        *__Pyx_BufPtrStrided2d(__pyx_t_float_complex *, __pyx_pybuffernd_result.rcbuffer-&gt;pybuffer.buf, __pyx_t_22, __pyx_pybuffernd_result.diminfo[0].strides, __pyx_t_23, __pyx_pybuffernd_result.diminfo[1].strides) += __pyx_t_float_complex_from_parts(<span class='pyx_macro_api'>__Pyx_CREAL</span>(__pyx_t_11), <span class='pyx_macro_api'>__Pyx_CIMAG</span>(__pyx_t_11));\n",
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     },
     "execution_count": 4,
     "metadata": {},
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    }
   ],
   "source": [
    "%%cython --cplus --annotate\n",
    "\n",
    "cimport numpy as np\n",
    "cimport cython\n",
    "@cython.boundscheck(False)\n",
    "@cython.wraparound(False)\n",
    "def cython4_parallel_filter(np.ndarray[np.complex64_t, ndim=2] x, np.ndarray[np.complex64_t, ndim=2] result,np.ndarray[np.float32_t, ndim=1] coeff,np.ndarray[np.complex64_t, ndim=2] history):\n",
    "    cdef int nsamp = x.shape[1]\n",
    "    cdef int nstreams = x.shape[0]\n",
    "    cdef int ntaps = coeff.shape[0]\n",
    "    cdef int icoeff = 0\n",
    "    cdef int iresult =0\n",
    "    cdef int istream =0\n",
    "    cdef int itap=0\n",
    "    cdef int ihistory=0\n",
    "    cdef int isamp =0\n",
    "    for istream in range(nstreams):\n",
    "        for itap in range(ntaps):\n",
    "            icoeff = 0\n",
    "            for ihistory in range(itap,ntaps):\n",
    "                result[istream,itap] += coeff[icoeff]*history[istream,ihistory]\n",
    "                icoeff += 1\n",
    "            for isamp in range(0,itap):\n",
    "                result[istream,itap] += coeff[icoeff]*x[istream,isamp]\n",
    "                icoeff += 1\n",
    "                \n",
    "        for iresult in range(ntaps,nsamp):\n",
    "            for icoeff in range(ntaps):\n",
    "                result[istream,iresult] += coeff[icoeff]*x[istream,iresult-ntaps+icoeff]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "100 loops, best of 3: 11.1 ms per loop\n"
     ]
    }
   ],
   "source": [
    "%timeit cython4_parallel_filter(x,result,coeff,history)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "ntaps = 128\n",
    "x = np.zeros((512,2**12),dtype=np.complex64)\n",
    "coeff = np.ones((ntaps,),dtype=np.float32)\n",
    "history = x[:,:ntaps].copy()\n",
    "result = np.zeros_like(x)\n",
    "H = np.fft.fft(coeff,n=x.shape[1]).astype('complex64')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 172,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "100 loops, best of 3: 14.2 ms per loop\n"
     ]
    }
   ],
   "source": [
    "%timeit np.moveaxis(x.view(np.float32).reshape((512,2**12,2)),2,1).copy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 177,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "100 loops, best of 3: 13.9 ms per loop\n"
     ]
    }
   ],
   "source": [
    "%timeit np.transpose(x.view(np.float32).reshape((512,2**12,2)),(0,2,1)).copy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 173,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "100 loops, best of 3: 6.64 ms per loop\n"
     ]
    }
   ],
   "source": [
    "%timeit x.copy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 176,
   "metadata": {
    "collapsed": false
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   "outputs": [
    {
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     },
     "execution_count": 176,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(2**9*2**12)/16e6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 175,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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       "146.653986013986"
      ]
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     "execution_count": 175,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "((2**9*2**12)/14.3e-3)/1e6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 174,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "  C_CONTIGUOUS : True\n",
       "  F_CONTIGUOUS : False\n",
       "  OWNDATA : True\n",
       "  WRITEABLE : True\n",
       "  ALIGNED : True\n",
       "  UPDATEIFCOPY : False"
      ]
     },
     "execution_count": 174,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.moveaxis(x.view(np.float32).reshape((512,2**12,2)),2,1).copy().flags"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def fftconv(x,H,fftlib,**kwargs):\n",
    "    return fftlib.ifft(H*fftlib.fft(x,axis=1,**kwargs),axis=1,**kwargs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10 loops, best of 3: 115 ms per loop\n"
     ]
    }
   ],
   "source": [
    "%timeit np.fft.fft(x,axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import scipy.fftpack as sfft"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10 loops, best of 3: 32.8 ms per loop\n"
     ]
    }
   ],
   "source": [
    "%timeit sfft.fft(x,axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import pyfftw"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "pyfftw.interfaces.cache.enable()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "pyfftw.interfaces.cache.set_keepalive_time(86400)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "100 loops, best of 3: 18.3 ms per loop\n"
     ]
    }
   ],
   "source": [
    "%timeit pyfftw.interfaces.scipy_fftpack.fft(x,axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10 loops, best of 3: 50.6 ms per loop\n"
     ]
    }
   ],
   "source": [
    "%timeit fftconv(x,H,fftlib=pyfftw.interfaces.scipy_fftpack)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10 loops, best of 3: 38.4 ms per loop\n"
     ]
    }
   ],
   "source": [
    "%timeit fftconv(x,H,fftlib=pyfftw.interfaces.scipy_fftpack,threads=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 loop, best of 3: 292 ms per loop\n"
     ]
    }
   ],
   "source": [
    "%timeit fftconv(x,H,fftlib=np.fft)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10 loops, best of 3: 81.2 ms per loop\n"
     ]
    }
   ],
   "source": [
    "%timeit fftconv(x,H,fftlib=sfft)"
   ]
  },
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    "collapsed": false
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   "cell_type": "code",
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   "metadata": {
    "collapsed": false
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    {
     "name": "stdout",
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     "text": [
      "1 loop, best of 3: 359 ms per loop\n"
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    }
   ],
   "source": [
    "%timeit cython4_parallel_filter(x,result,coeff,history)"
   ]
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       "<pre class=\"cython line score-98\" onclick='toggleDiv(this)'>+<span class=\"\">06</span>: <span class=\"k\">def</span> <span class=\"nf\">real_parallel_filter</span><span class=\"p\">(</span><span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">ndarray</span><span class=\"p\">[</span><span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">float32_t</span><span class=\"p\">,</span> <span class=\"n\">ndim</span><span class=\"o\">=</span><span class=\"mf\">2</span><span class=\"p\">]</span> <span class=\"n\">x</span><span class=\"p\">,</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">ndarray</span><span class=\"p\">[</span><span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">float32_t</span><span class=\"p\">,</span> <span class=\"n\">ndim</span><span class=\"o\">=</span><span class=\"mf\">2</span><span class=\"p\">]</span> <span class=\"n\">result</span><span class=\"p\">,</span><span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">ndarray</span><span class=\"p\">[</span><span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">float32_t</span><span class=\"p\">,</span> <span class=\"n\">ndim</span><span class=\"o\">=</span><span class=\"mf\">1</span><span class=\"p\">]</span> <span class=\"n\">coeff</span><span class=\"p\">,</span><span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">ndarray</span><span class=\"p\">[</span><span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">float32_t</span><span class=\"p\">,</span> <span class=\"n\">ndim</span><span class=\"o\">=</span><span class=\"mf\">2</span><span class=\"p\">]</span> <span class=\"n\">history</span><span class=\"p\">):</span></pre>\n",
       "<pre class='cython code score-98 '>/* Python wrapper */\n",
       "static PyObject *__pyx_pw_46_cython_magic_43716c8a966dc355e0df2f4f292e2a93_1real_parallel_filter(PyObject *__pyx_self, PyObject *__pyx_args, PyObject *__pyx_kwds); /*proto*/\n",
       "static PyMethodDef __pyx_mdef_46_cython_magic_43716c8a966dc355e0df2f4f292e2a93_1real_parallel_filter = {\"real_parallel_filter\", (PyCFunction)__pyx_pw_46_cython_magic_43716c8a966dc355e0df2f4f292e2a93_1real_parallel_filter, METH_VARARGS|METH_KEYWORDS, 0};\n",
       "static PyObject *__pyx_pw_46_cython_magic_43716c8a966dc355e0df2f4f292e2a93_1real_parallel_filter(PyObject *__pyx_self, PyObject *__pyx_args, PyObject *__pyx_kwds) {\n",
       "  PyArrayObject *__pyx_v_x = 0;\n",
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       "  <span class='refnanny'>__Pyx_RefNannySetupContext</span>(\"real_parallel_filter (wrapper)\", 0);\n",
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       "    PyObject* values[4] = {0,0,0,0};\n",
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       "        case  1: values[0] = <span class='py_macro_api'>PyTuple_GET_ITEM</span>(__pyx_args, 0);\n",
       "        case  0: break;\n",
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       "        if (likely((values[1] = <span class='py_c_api'>PyDict_GetItem</span>(__pyx_kwds, __pyx_n_s_result)) != 0)) kw_args--;\n",
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       "        if (likely((values[2] = <span class='py_c_api'>PyDict_GetItem</span>(__pyx_kwds, __pyx_n_s_coeff)) != 0)) kw_args--;\n",
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       "        if (likely((values[3] = <span class='py_c_api'>PyDict_GetItem</span>(__pyx_kwds, __pyx_n_s_history)) != 0)) kw_args--;\n",
       "        else {\n",
       "          <span class='pyx_c_api'>__Pyx_RaiseArgtupleInvalid</span>(\"real_parallel_filter\", 1, 4, 4, 3); __PYX_ERR(0, 6, __pyx_L3_error)\n",
       "        }\n",
       "      }\n",
       "      if (unlikely(kw_args &gt; 0)) {\n",
       "        if (unlikely(<span class='pyx_c_api'>__Pyx_ParseOptionalKeywords</span>(__pyx_kwds, __pyx_pyargnames, 0, values, pos_args, \"real_parallel_filter\") &lt; 0)) __PYX_ERR(0, 6, __pyx_L3_error)\n",
       "      }\n",
       "    } else if (<span class='py_macro_api'>PyTuple_GET_SIZE</span>(__pyx_args) != 4) {\n",
       "      goto __pyx_L5_argtuple_error;\n",
       "    } else {\n",
       "      values[0] = <span class='py_macro_api'>PyTuple_GET_ITEM</span>(__pyx_args, 0);\n",
       "      values[1] = <span class='py_macro_api'>PyTuple_GET_ITEM</span>(__pyx_args, 1);\n",
       "      values[2] = <span class='py_macro_api'>PyTuple_GET_ITEM</span>(__pyx_args, 2);\n",
       "      values[3] = <span class='py_macro_api'>PyTuple_GET_ITEM</span>(__pyx_args, 3);\n",
       "    }\n",
       "    __pyx_v_x = ((PyArrayObject *)values[0]);\n",
       "    __pyx_v_result = ((PyArrayObject *)values[1]);\n",
       "    __pyx_v_coeff = ((PyArrayObject *)values[2]);\n",
       "    __pyx_v_history = ((PyArrayObject *)values[3]);\n",
       "  }\n",
       "  goto __pyx_L4_argument_unpacking_done;\n",
       "  __pyx_L5_argtuple_error:;\n",
       "  <span class='pyx_c_api'>__Pyx_RaiseArgtupleInvalid</span>(\"real_parallel_filter\", 1, 4, 4, <span class='py_macro_api'>PyTuple_GET_SIZE</span>(__pyx_args)); __PYX_ERR(0, 6, __pyx_L3_error)\n",
       "  __pyx_L3_error:;\n",
       "  <span class='pyx_c_api'>__Pyx_AddTraceback</span>(\"_cython_magic_43716c8a966dc355e0df2f4f292e2a93.real_parallel_filter\", __pyx_clineno, __pyx_lineno, __pyx_filename);\n",
       "  <span class='refnanny'>__Pyx_RefNannyFinishContext</span>();\n",
       "  return NULL;\n",
       "  __pyx_L4_argument_unpacking_done:;\n",
       "  if (unlikely(!<span class='pyx_c_api'>__Pyx_ArgTypeTest</span>(((PyObject *)__pyx_v_x), __pyx_ptype_5numpy_ndarray, 1, \"x\", 0))) __PYX_ERR(0, 6, __pyx_L1_error)\n",
       "  if (unlikely(!<span class='pyx_c_api'>__Pyx_ArgTypeTest</span>(((PyObject *)__pyx_v_result), __pyx_ptype_5numpy_ndarray, 1, \"result\", 0))) __PYX_ERR(0, 6, __pyx_L1_error)\n",
       "  if (unlikely(!<span class='pyx_c_api'>__Pyx_ArgTypeTest</span>(((PyObject *)__pyx_v_coeff), __pyx_ptype_5numpy_ndarray, 1, \"coeff\", 0))) __PYX_ERR(0, 6, __pyx_L1_error)\n",
       "  if (unlikely(!<span class='pyx_c_api'>__Pyx_ArgTypeTest</span>(((PyObject *)__pyx_v_history), __pyx_ptype_5numpy_ndarray, 1, \"history\", 0))) __PYX_ERR(0, 6, __pyx_L1_error)\n",
       "  __pyx_r = __pyx_pf_46_cython_magic_43716c8a966dc355e0df2f4f292e2a93_real_parallel_filter(__pyx_self, __pyx_v_x, __pyx_v_result, __pyx_v_coeff, __pyx_v_history);\n",
       "\n",
       "  /* function exit code */\n",
       "  goto __pyx_L0;\n",
       "  __pyx_L1_error:;\n",
       "  __pyx_r = NULL;\n",
       "  __pyx_L0:;\n",
       "  <span class='refnanny'>__Pyx_RefNannyFinishContext</span>();\n",
       "  return __pyx_r;\n",
       "}\n",
       "\n",
       "static PyObject *__pyx_pf_46_cython_magic_43716c8a966dc355e0df2f4f292e2a93_real_parallel_filter(CYTHON_UNUSED PyObject *__pyx_self, PyArrayObject *__pyx_v_x, PyArrayObject *__pyx_v_result, PyArrayObject *__pyx_v_coeff, PyArrayObject *__pyx_v_history) {\n",
       "  int __pyx_v_nsamp;\n",
       "  int __pyx_v_nstreams;\n",
       "  int __pyx_v_ntaps;\n",
       "  int __pyx_v_icoeff;\n",
       "  int __pyx_v_iresult;\n",
       "  int __pyx_v_istream;\n",
       "  int __pyx_v_itap;\n",
       "  int __pyx_v_ihistory;\n",
       "  int __pyx_v_isamp;\n",
       "  int __pyx_v_idx;\n",
       "  __Pyx_LocalBuf_ND __pyx_pybuffernd_coeff;\n",
       "  __Pyx_Buffer __pyx_pybuffer_coeff;\n",
       "  __Pyx_LocalBuf_ND __pyx_pybuffernd_history;\n",
       "  __Pyx_Buffer __pyx_pybuffer_history;\n",
       "  __Pyx_LocalBuf_ND __pyx_pybuffernd_result;\n",
       "  __Pyx_Buffer __pyx_pybuffer_result;\n",
       "  __Pyx_LocalBuf_ND __pyx_pybuffernd_x;\n",
       "  __Pyx_Buffer __pyx_pybuffer_x;\n",
       "  PyObject *__pyx_r = NULL;\n",
       "  <span class='refnanny'>__Pyx_RefNannyDeclarations</span>\n",
       "  <span class='refnanny'>__Pyx_RefNannySetupContext</span>(\"real_parallel_filter\", 0);\n",
       "  __pyx_pybuffer_x.pybuffer.buf = NULL;\n",
       "  __pyx_pybuffer_x.refcount = 0;\n",
       "  __pyx_pybuffernd_x.data = NULL;\n",
       "  __pyx_pybuffernd_x.rcbuffer = &amp;__pyx_pybuffer_x;\n",
       "  __pyx_pybuffer_result.pybuffer.buf = NULL;\n",
       "  __pyx_pybuffer_result.refcount = 0;\n",
       "  __pyx_pybuffernd_result.data = NULL;\n",
       "  __pyx_pybuffernd_result.rcbuffer = &amp;__pyx_pybuffer_result;\n",
       "  __pyx_pybuffer_coeff.pybuffer.buf = NULL;\n",
       "  __pyx_pybuffer_coeff.refcount = 0;\n",
       "  __pyx_pybuffernd_coeff.data = NULL;\n",
       "  __pyx_pybuffernd_coeff.rcbuffer = &amp;__pyx_pybuffer_coeff;\n",
       "  __pyx_pybuffer_history.pybuffer.buf = NULL;\n",
       "  __pyx_pybuffer_history.refcount = 0;\n",
       "  __pyx_pybuffernd_history.data = NULL;\n",
       "  __pyx_pybuffernd_history.rcbuffer = &amp;__pyx_pybuffer_history;\n",
       "  {\n",
       "    __Pyx_BufFmt_StackElem __pyx_stack[1];\n",
       "    if (unlikely(<span class='pyx_c_api'>__Pyx_GetBufferAndValidate</span>(&amp;__pyx_pybuffernd_x.rcbuffer-&gt;pybuffer, (PyObject*)__pyx_v_x, &amp;__Pyx_TypeInfo_nn___pyx_t_5numpy_float32_t, PyBUF_FORMAT| PyBUF_STRIDES, 2, 0, __pyx_stack) == -1)) __PYX_ERR(0, 6, __pyx_L1_error)\n",
       "  }\n",
       "  __pyx_pybuffernd_x.diminfo[0].strides = __pyx_pybuffernd_x.rcbuffer-&gt;pybuffer.strides[0]; __pyx_pybuffernd_x.diminfo[0].shape = __pyx_pybuffernd_x.rcbuffer-&gt;pybuffer.shape[0]; __pyx_pybuffernd_x.diminfo[1].strides = __pyx_pybuffernd_x.rcbuffer-&gt;pybuffer.strides[1]; __pyx_pybuffernd_x.diminfo[1].shape = __pyx_pybuffernd_x.rcbuffer-&gt;pybuffer.shape[1];\n",
       "  {\n",
       "    __Pyx_BufFmt_StackElem __pyx_stack[1];\n",
       "    if (unlikely(<span class='pyx_c_api'>__Pyx_GetBufferAndValidate</span>(&amp;__pyx_pybuffernd_result.rcbuffer-&gt;pybuffer, (PyObject*)__pyx_v_result, &amp;__Pyx_TypeInfo_nn___pyx_t_5numpy_float32_t, PyBUF_FORMAT| PyBUF_STRIDES| PyBUF_WRITABLE, 2, 0, __pyx_stack) == -1)) __PYX_ERR(0, 6, __pyx_L1_error)\n",
       "  }\n",
       "  __pyx_pybuffernd_result.diminfo[0].strides = __pyx_pybuffernd_result.rcbuffer-&gt;pybuffer.strides[0]; __pyx_pybuffernd_result.diminfo[0].shape = __pyx_pybuffernd_result.rcbuffer-&gt;pybuffer.shape[0]; __pyx_pybuffernd_result.diminfo[1].strides = __pyx_pybuffernd_result.rcbuffer-&gt;pybuffer.strides[1]; __pyx_pybuffernd_result.diminfo[1].shape = __pyx_pybuffernd_result.rcbuffer-&gt;pybuffer.shape[1];\n",
       "  {\n",
       "    __Pyx_BufFmt_StackElem __pyx_stack[1];\n",
       "    if (unlikely(<span class='pyx_c_api'>__Pyx_GetBufferAndValidate</span>(&amp;__pyx_pybuffernd_coeff.rcbuffer-&gt;pybuffer, (PyObject*)__pyx_v_coeff, &amp;__Pyx_TypeInfo_nn___pyx_t_5numpy_float32_t, PyBUF_FORMAT| PyBUF_STRIDES, 1, 0, __pyx_stack) == -1)) __PYX_ERR(0, 6, __pyx_L1_error)\n",
       "  }\n",
       "  __pyx_pybuffernd_coeff.diminfo[0].strides = __pyx_pybuffernd_coeff.rcbuffer-&gt;pybuffer.strides[0]; __pyx_pybuffernd_coeff.diminfo[0].shape = __pyx_pybuffernd_coeff.rcbuffer-&gt;pybuffer.shape[0];\n",
       "  {\n",
       "    __Pyx_BufFmt_StackElem __pyx_stack[1];\n",
       "    if (unlikely(<span class='pyx_c_api'>__Pyx_GetBufferAndValidate</span>(&amp;__pyx_pybuffernd_history.rcbuffer-&gt;pybuffer, (PyObject*)__pyx_v_history, &amp;__Pyx_TypeInfo_nn___pyx_t_5numpy_float32_t, PyBUF_FORMAT| PyBUF_STRIDES, 2, 0, __pyx_stack) == -1)) __PYX_ERR(0, 6, __pyx_L1_error)\n",
       "  }\n",
       "  __pyx_pybuffernd_history.diminfo[0].strides = __pyx_pybuffernd_history.rcbuffer-&gt;pybuffer.strides[0]; __pyx_pybuffernd_history.diminfo[0].shape = __pyx_pybuffernd_history.rcbuffer-&gt;pybuffer.shape[0]; __pyx_pybuffernd_history.diminfo[1].strides = __pyx_pybuffernd_history.rcbuffer-&gt;pybuffer.strides[1]; __pyx_pybuffernd_history.diminfo[1].shape = __pyx_pybuffernd_history.rcbuffer-&gt;pybuffer.shape[1];\n",
       "/* … */\n",
       "  /* function exit code */\n",
       "  __pyx_r = Py_None; <span class='pyx_macro_api'>__Pyx_INCREF</span>(Py_None);\n",
       "  goto __pyx_L0;\n",
       "  __pyx_L1_error:;\n",
       "  { PyObject *__pyx_type, *__pyx_value, *__pyx_tb;\n",
       "    __Pyx_PyThreadState_declare\n",
       "    __Pyx_PyThreadState_assign\n",
       "    <span class='pyx_c_api'>__Pyx_ErrFetch</span>(&amp;__pyx_type, &amp;__pyx_value, &amp;__pyx_tb);\n",
       "    <span class='pyx_c_api'>__Pyx_SafeReleaseBuffer</span>(&amp;__pyx_pybuffernd_coeff.rcbuffer-&gt;pybuffer);\n",
       "    <span class='pyx_c_api'>__Pyx_SafeReleaseBuffer</span>(&amp;__pyx_pybuffernd_history.rcbuffer-&gt;pybuffer);\n",
       "    <span class='pyx_c_api'>__Pyx_SafeReleaseBuffer</span>(&amp;__pyx_pybuffernd_result.rcbuffer-&gt;pybuffer);\n",
       "    <span class='pyx_c_api'>__Pyx_SafeReleaseBuffer</span>(&amp;__pyx_pybuffernd_x.rcbuffer-&gt;pybuffer);\n",
       "  <span class='pyx_c_api'>__Pyx_ErrRestore</span>(__pyx_type, __pyx_value, __pyx_tb);}\n",
       "  <span class='pyx_c_api'>__Pyx_AddTraceback</span>(\"_cython_magic_43716c8a966dc355e0df2f4f292e2a93.real_parallel_filter\", __pyx_clineno, __pyx_lineno, __pyx_filename);\n",
       "  __pyx_r = NULL;\n",
       "  goto __pyx_L2;\n",
       "  __pyx_L0:;\n",
       "  <span class='pyx_c_api'>__Pyx_SafeReleaseBuffer</span>(&amp;__pyx_pybuffernd_coeff.rcbuffer-&gt;pybuffer);\n",
       "  <span class='pyx_c_api'>__Pyx_SafeReleaseBuffer</span>(&amp;__pyx_pybuffernd_history.rcbuffer-&gt;pybuffer);\n",
       "  <span class='pyx_c_api'>__Pyx_SafeReleaseBuffer</span>(&amp;__pyx_pybuffernd_result.rcbuffer-&gt;pybuffer);\n",
       "  <span class='pyx_c_api'>__Pyx_SafeReleaseBuffer</span>(&amp;__pyx_pybuffernd_x.rcbuffer-&gt;pybuffer);\n",
       "  __pyx_L2:;\n",
       "  <span class='refnanny'>__Pyx_XGIVEREF</span>(__pyx_r);\n",
       "  <span class='refnanny'>__Pyx_RefNannyFinishContext</span>();\n",
       "  return __pyx_r;\n",
       "}\n",
       "/* … */\n",
       "  __pyx_tuple__7 = <span class='py_c_api'>PyTuple_Pack</span>(14, __pyx_n_s_x, __pyx_n_s_result, __pyx_n_s_coeff, __pyx_n_s_history, __pyx_n_s_nsamp, __pyx_n_s_nstreams, __pyx_n_s_ntaps, __pyx_n_s_icoeff, __pyx_n_s_iresult, __pyx_n_s_istream, __pyx_n_s_itap, __pyx_n_s_ihistory, __pyx_n_s_isamp, __pyx_n_s_idx); if (unlikely(!__pyx_tuple__7)) __PYX_ERR(0, 6, __pyx_L1_error)\n",
       "  <span class='refnanny'>__Pyx_GOTREF</span>(__pyx_tuple__7);\n",
       "  <span class='refnanny'>__Pyx_GIVEREF</span>(__pyx_tuple__7);\n",
       "/* … */\n",
       "  __pyx_t_1 = PyCFunction_NewEx(&amp;__pyx_mdef_46_cython_magic_43716c8a966dc355e0df2f4f292e2a93_1real_parallel_filter, NULL, __pyx_n_s_cython_magic_43716c8a966dc355e0); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 6, __pyx_L1_error)\n",
       "  <span class='refnanny'>__Pyx_GOTREF</span>(__pyx_t_1);\n",
       "  if (<span class='py_c_api'>PyDict_SetItem</span>(__pyx_d, __pyx_n_s_real_parallel_filter, __pyx_t_1) &lt; 0) __PYX_ERR(0, 6, __pyx_L1_error)\n",
       "  <span class='pyx_macro_api'>__Pyx_DECREF</span>(__pyx_t_1); __pyx_t_1 = 0;\n",
       "</pre><pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">07</span>:     <span class=\"k\">cdef</span> <span class=\"kt\">int</span> <span class=\"nf\">nsamp</span> <span class=\"o\">=</span> <span class=\"n\">x</span><span class=\"o\">.</span><span class=\"n\">shape</span><span class=\"p\">[</span><span class=\"mf\">1</span><span class=\"p\">]</span></pre>\n",
       "<pre class='cython code score-0 '>  __pyx_v_nsamp = (__pyx_v_x-&gt;dimensions[1]);\n",
       "</pre><pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">08</span>:     <span class=\"k\">cdef</span> <span class=\"kt\">int</span> <span class=\"nf\">nstreams</span> <span class=\"o\">=</span> <span class=\"n\">x</span><span class=\"o\">.</span><span class=\"n\">shape</span><span class=\"p\">[</span><span class=\"mf\">0</span><span class=\"p\">]</span></pre>\n",
       "<pre class='cython code score-0 '>  __pyx_v_nstreams = (__pyx_v_x-&gt;dimensions[0]);\n",
       "</pre><pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">09</span>:     <span class=\"k\">cdef</span> <span class=\"kt\">int</span> <span class=\"nf\">ntaps</span> <span class=\"o\">=</span> <span class=\"n\">coeff</span><span class=\"o\">.</span><span class=\"n\">shape</span><span class=\"p\">[</span><span class=\"mf\">0</span><span class=\"p\">]</span></pre>\n",
       "<pre class='cython code score-0 '>  __pyx_v_ntaps = (__pyx_v_coeff-&gt;dimensions[0]);\n",
       "</pre><pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">10</span>:     <span class=\"k\">cdef</span> <span class=\"kt\">int</span> <span class=\"nf\">icoeff</span> <span class=\"o\">=</span> <span class=\"mf\">0</span></pre>\n",
       "<pre class='cython code score-0 '>  __pyx_v_icoeff = 0;\n",
       "</pre><pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">11</span>:     <span class=\"k\">cdef</span> <span class=\"kt\">int</span> <span class=\"nf\">iresult</span> <span class=\"o\">=</span><span class=\"mf\">0</span></pre>\n",
       "<pre class='cython code score-0 '>  __pyx_v_iresult = 0;\n",
       "</pre><pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">12</span>:     <span class=\"k\">cdef</span> <span class=\"kt\">int</span> <span class=\"nf\">istream</span> <span class=\"o\">=</span><span class=\"mf\">0</span></pre>\n",
       "<pre class='cython code score-0 '>  __pyx_v_istream = 0;\n",
       "</pre><pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">13</span>:     <span class=\"k\">cdef</span> <span class=\"kt\">int</span> <span class=\"nf\">itap</span><span class=\"o\">=</span><span class=\"mf\">0</span></pre>\n",
       "<pre class='cython code score-0 '>  __pyx_v_itap = 0;\n",
       "</pre><pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">14</span>:     <span class=\"k\">cdef</span> <span class=\"kt\">int</span> <span class=\"nf\">ihistory</span><span class=\"o\">=</span><span class=\"mf\">0</span></pre>\n",
       "<pre class='cython code score-0 '>  __pyx_v_ihistory = 0;\n",
       "</pre><pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">15</span>:     <span class=\"k\">cdef</span> <span class=\"kt\">int</span> <span class=\"nf\">isamp</span> <span class=\"o\">=</span><span class=\"mf\">0</span></pre>\n",
       "<pre class='cython code score-0 '>  __pyx_v_isamp = 0;\n",
       "</pre><pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">16</span>:     <span class=\"k\">cdef</span> <span class=\"kt\">int</span> <span class=\"nf\">idx</span><span class=\"o\">=</span><span class=\"mf\">0</span></pre>\n",
       "<pre class='cython code score-0 '>  __pyx_v_idx = 0;\n",
       "</pre><pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">17</span>:     <span class=\"k\">for</span> <span class=\"n\">istream</span> <span class=\"ow\">in</span> <span class=\"nb\">range</span><span class=\"p\">(</span><span class=\"n\">nstreams</span><span class=\"p\">):</span></pre>\n",
       "<pre class='cython code score-0 '>  __pyx_t_1 = __pyx_v_nstreams;\n",
       "  for (__pyx_t_2 = 0; __pyx_t_2 &lt; __pyx_t_1; __pyx_t_2+=1) {\n",
       "    __pyx_v_istream = __pyx_t_2;\n",
       "</pre><pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">18</span>:         <span class=\"k\">for</span> <span class=\"n\">itap</span> <span class=\"ow\">in</span> <span class=\"nb\">range</span><span class=\"p\">(</span><span class=\"n\">ntaps</span><span class=\"p\">):</span></pre>\n",
       "<pre class='cython code score-0 '>    __pyx_t_3 = __pyx_v_ntaps;\n",
       "    for (__pyx_t_4 = 0; __pyx_t_4 &lt; __pyx_t_3; __pyx_t_4+=1) {\n",
       "      __pyx_v_itap = __pyx_t_4;\n",
       "</pre><pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">19</span>:             <span class=\"n\">icoeff</span> <span class=\"o\">=</span> <span class=\"mf\">0</span></pre>\n",
       "<pre class='cython code score-0 '>      __pyx_v_icoeff = 0;\n",
       "</pre><pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">20</span>:             <span class=\"k\">for</span> <span class=\"n\">ihistory</span> <span class=\"ow\">in</span> <span class=\"nb\">range</span><span class=\"p\">(</span><span class=\"n\">itap</span><span class=\"p\">,</span><span class=\"n\">ntaps</span><span class=\"p\">):</span></pre>\n",
       "<pre class='cython code score-0 '>      __pyx_t_5 = __pyx_v_ntaps;\n",
       "      for (__pyx_t_6 = __pyx_v_itap; __pyx_t_6 &lt; __pyx_t_5; __pyx_t_6+=1) {\n",
       "        __pyx_v_ihistory = __pyx_t_6;\n",
       "</pre><pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">21</span>:                 <span class=\"n\">result</span><span class=\"p\">[</span><span class=\"n\">istream</span><span class=\"p\">,</span><span class=\"n\">itap</span><span class=\"p\">]</span> <span class=\"o\">+=</span> <span class=\"n\">coeff</span><span class=\"p\">[</span><span class=\"n\">icoeff</span><span class=\"p\">]</span><span class=\"o\">*</span><span class=\"n\">history</span><span class=\"p\">[</span><span class=\"n\">istream</span><span class=\"p\">,</span><span class=\"n\">ihistory</span><span class=\"p\">]</span></pre>\n",
       "<pre class='cython code score-0 '>        __pyx_t_7 = __pyx_v_icoeff;\n",
       "        __pyx_t_8 = __pyx_v_istream;\n",
       "        __pyx_t_9 = __pyx_v_ihistory;\n",
       "        __pyx_t_10 = __pyx_v_istream;\n",
       "        __pyx_t_11 = __pyx_v_itap;\n",
       "        *__Pyx_BufPtrStrided2d(__pyx_t_5numpy_float32_t *, __pyx_pybuffernd_result.rcbuffer-&gt;pybuffer.buf, __pyx_t_10, __pyx_pybuffernd_result.diminfo[0].strides, __pyx_t_11, __pyx_pybuffernd_result.diminfo[1].strides) += ((*__Pyx_BufPtrStrided1d(__pyx_t_5numpy_float32_t *, __pyx_pybuffernd_coeff.rcbuffer-&gt;pybuffer.buf, __pyx_t_7, __pyx_pybuffernd_coeff.diminfo[0].strides)) * (*__Pyx_BufPtrStrided2d(__pyx_t_5numpy_float32_t *, __pyx_pybuffernd_history.rcbuffer-&gt;pybuffer.buf, __pyx_t_8, __pyx_pybuffernd_history.diminfo[0].strides, __pyx_t_9, __pyx_pybuffernd_history.diminfo[1].strides)));\n",
       "</pre><pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">22</span>:                 <span class=\"n\">icoeff</span> <span class=\"o\">+=</span> <span class=\"mf\">1</span></pre>\n",
       "<pre class='cython code score-0 '>        __pyx_v_icoeff = (__pyx_v_icoeff + 1);\n",
       "      }\n",
       "</pre><pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">23</span>:             <span class=\"k\">for</span> <span class=\"n\">isamp</span> <span class=\"ow\">in</span> <span class=\"nb\">range</span><span class=\"p\">(</span><span class=\"mf\">0</span><span class=\"p\">,</span><span class=\"n\">itap</span><span class=\"p\">):</span></pre>\n",
       "<pre class='cython code score-0 '>      __pyx_t_5 = __pyx_v_itap;\n",
       "      for (__pyx_t_6 = 0; __pyx_t_6 &lt; __pyx_t_5; __pyx_t_6+=1) {\n",
       "        __pyx_v_isamp = __pyx_t_6;\n",
       "</pre><pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">24</span>:                 <span class=\"n\">result</span><span class=\"p\">[</span><span class=\"n\">istream</span><span class=\"p\">,</span><span class=\"n\">itap</span><span class=\"p\">]</span> <span class=\"o\">+=</span> <span class=\"n\">coeff</span><span class=\"p\">[</span><span class=\"n\">icoeff</span><span class=\"p\">]</span><span class=\"o\">*</span><span class=\"n\">x</span><span class=\"p\">[</span><span class=\"n\">istream</span><span class=\"p\">,</span><span class=\"n\">isamp</span><span class=\"p\">]</span></pre>\n",
       "<pre class='cython code score-0 '>        __pyx_t_12 = __pyx_v_icoeff;\n",
       "        __pyx_t_13 = __pyx_v_istream;\n",
       "        __pyx_t_14 = __pyx_v_isamp;\n",
       "        __pyx_t_15 = __pyx_v_istream;\n",
       "        __pyx_t_16 = __pyx_v_itap;\n",
       "        *__Pyx_BufPtrStrided2d(__pyx_t_5numpy_float32_t *, __pyx_pybuffernd_result.rcbuffer-&gt;pybuffer.buf, __pyx_t_15, __pyx_pybuffernd_result.diminfo[0].strides, __pyx_t_16, __pyx_pybuffernd_result.diminfo[1].strides) += ((*__Pyx_BufPtrStrided1d(__pyx_t_5numpy_float32_t *, __pyx_pybuffernd_coeff.rcbuffer-&gt;pybuffer.buf, __pyx_t_12, __pyx_pybuffernd_coeff.diminfo[0].strides)) * (*__Pyx_BufPtrStrided2d(__pyx_t_5numpy_float32_t *, __pyx_pybuffernd_x.rcbuffer-&gt;pybuffer.buf, __pyx_t_13, __pyx_pybuffernd_x.diminfo[0].strides, __pyx_t_14, __pyx_pybuffernd_x.diminfo[1].strides)));\n",
       "</pre><pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">25</span>:                 <span class=\"n\">icoeff</span> <span class=\"o\">+=</span> <span class=\"mf\">1</span></pre>\n",
       "<pre class='cython code score-0 '>        __pyx_v_icoeff = (__pyx_v_icoeff + 1);\n",
       "      }\n",
       "    }\n",
       "</pre><pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">26</span>:         <span class=\"k\">for</span> <span class=\"n\">iresult</span> <span class=\"ow\">in</span> <span class=\"nb\">range</span><span class=\"p\">(</span><span class=\"n\">ntaps</span><span class=\"p\">,</span><span class=\"n\">nsamp</span><span class=\"p\">):</span></pre>\n",
       "<pre class='cython code score-0 '>    __pyx_t_3 = __pyx_v_nsamp;\n",
       "    for (__pyx_t_4 = __pyx_v_ntaps; __pyx_t_4 &lt; __pyx_t_3; __pyx_t_4+=1) {\n",
       "      __pyx_v_iresult = __pyx_t_4;\n",
       "</pre><pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">27</span>:             <span class=\"n\">idx</span> <span class=\"o\">=</span> <span class=\"n\">iresult</span><span class=\"o\">-</span><span class=\"n\">ntaps</span></pre>\n",
       "<pre class='cython code score-0 '>      __pyx_v_idx = (__pyx_v_iresult - __pyx_v_ntaps);\n",
       "</pre><pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">28</span>:             <span class=\"k\">for</span> <span class=\"n\">icoeff</span> <span class=\"ow\">in</span> <span class=\"nb\">range</span><span class=\"p\">(</span><span class=\"n\">ntaps</span><span class=\"p\">):</span></pre>\n",
       "<pre class='cython code score-0 '>      __pyx_t_5 = __pyx_v_ntaps;\n",
       "      for (__pyx_t_6 = 0; __pyx_t_6 &lt; __pyx_t_5; __pyx_t_6+=1) {\n",
       "        __pyx_v_icoeff = __pyx_t_6;\n",
       "</pre><pre class=\"cython line score-0\">&#xA0;<span class=\"\">29</span>: </pre>\n",
       "<pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">30</span>:                 <span class=\"n\">result</span><span class=\"p\">[</span><span class=\"n\">istream</span><span class=\"p\">,</span><span class=\"n\">iresult</span><span class=\"p\">]</span> <span class=\"o\">+=</span> <span class=\"n\">coeff</span><span class=\"p\">[</span><span class=\"n\">icoeff</span><span class=\"p\">]</span><span class=\"o\">*</span><span class=\"n\">x</span><span class=\"p\">[</span><span class=\"n\">istream</span><span class=\"p\">,</span><span class=\"n\">idx</span><span class=\"p\">]</span></pre>\n",
       "<pre class='cython code score-0 '>        __pyx_t_17 = __pyx_v_icoeff;\n",
       "        __pyx_t_18 = __pyx_v_istream;\n",
       "        __pyx_t_19 = __pyx_v_idx;\n",
       "        __pyx_t_20 = __pyx_v_istream;\n",
       "        __pyx_t_21 = __pyx_v_iresult;\n",
       "        *__Pyx_BufPtrStrided2d(__pyx_t_5numpy_float32_t *, __pyx_pybuffernd_result.rcbuffer-&gt;pybuffer.buf, __pyx_t_20, __pyx_pybuffernd_result.diminfo[0].strides, __pyx_t_21, __pyx_pybuffernd_result.diminfo[1].strides) += ((*__Pyx_BufPtrStrided1d(__pyx_t_5numpy_float32_t *, __pyx_pybuffernd_coeff.rcbuffer-&gt;pybuffer.buf, __pyx_t_17, __pyx_pybuffernd_coeff.diminfo[0].strides)) * (*__Pyx_BufPtrStrided2d(__pyx_t_5numpy_float32_t *, __pyx_pybuffernd_x.rcbuffer-&gt;pybuffer.buf, __pyx_t_18, __pyx_pybuffernd_x.diminfo[0].strides, __pyx_t_19, __pyx_pybuffernd_x.diminfo[1].strides)));\n",
       "</pre><pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">31</span>:                 <span class=\"n\">idx</span> <span class=\"o\">+=</span> <span class=\"mf\">1</span></pre>\n",
       "<pre class='cython code score-0 '>        __pyx_v_idx = (__pyx_v_idx + 1);\n",
       "      }\n",
       "    }\n",
       "  }\n",
       "</pre></div></body></html>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%%cython --cplus --annotate\n",
    "\n",
    "cimport numpy as np\n",
    "cimport cython\n",
    "@cython.boundscheck(False)\n",
    "@cython.wraparound(False)\n",
    "def real_parallel_filter(np.ndarray[np.float32_t, ndim=2] x, np.ndarray[np.float32_t, ndim=2] result,np.ndarray[np.float32_t, ndim=1] coeff,np.ndarray[np.float32_t, ndim=2] history):\n",
    "    cdef int nsamp = x.shape[1]\n",
    "    cdef int nstreams = x.shape[0]\n",
    "    cdef int ntaps = coeff.shape[0]\n",
    "    cdef int icoeff = 0\n",
    "    cdef int iresult =0\n",
    "    cdef int istream =0\n",
    "    cdef int itap=0\n",
    "    cdef int ihistory=0\n",
    "    cdef int isamp =0\n",
    "    cdef int idx=0\n",
    "    for istream in range(nstreams):\n",
    "        for itap in range(ntaps):\n",
    "            icoeff = 0\n",
    "            for ihistory in range(itap,ntaps):\n",
    "                result[istream,itap] += coeff[icoeff]*history[istream,ihistory]\n",
    "                icoeff += 1\n",
    "            for isamp in range(0,itap):\n",
    "                result[istream,itap] += coeff[icoeff]*x[istream,isamp]\n",
    "                icoeff += 1\n",
    "        for iresult in range(ntaps,nsamp):\n",
    "            idx = iresult-ntaps\n",
    "            for icoeff in range(ntaps):\n",
    "                \n",
    "                result[istream,iresult] += coeff[icoeff]*x[istream,idx]\n",
    "                idx += 1\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "ntaps = 32\n",
    "x = np.zeros((1024,2**10),dtype=np.float32)\n",
    "coeff = np.ones((ntaps,),dtype=np.float32)\n",
    "history = x[:,:ntaps].copy()\n",
    "result = np.zeros_like(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10 loops, best of 3: 154 ms per loop\n"
     ]
    }
   ],
   "source": [
    "%timeit real_parallel_filter(x,result,coeff,history)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6.944211920529801"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(2**20./151e-3)/1e6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "220.75284210526317"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(2**25./.152)/1e6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import scipy.signal as signal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "signal.freqz?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "signal.butter?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "signal.firwin()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 153,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "w = np.linspace(0,10/128.,1024)\n",
    "w,h = signal.freqz(np.ones(128,)/2**7.,1,worN=w)\n",
    "w,h_kaiser = signal.freqz(signal.kaiser(128*8,64),1,worN=w)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 157,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-80, 5)"
      ]
     },
     "execution_count": 157,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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YU9UYc9jr55HGmOrGmDrGmPmB2o9SOU2URPHxbR9z4vwJBs8a/PuInkWKwJEj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\n5TD/DxIRoZrUeeAfAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb41e489350>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(128*w/(2*np.pi),20*np.log10(np.abs(h)))\n",
    "plot(128*w/(2*np.pi),20*np.log10(np.abs(h_kaiser)/np.abs(h_kaiser).max()))\n",
    "#axvline(1/128.)\n",
    "axhline(-13)\n",
    "ylim(-80,5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.04908738521234052"
      ]
     },
     "execution_count": 135,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "2*np.pi/128."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.11"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}