Numpy broadcasting

Numpy_broadcasting.ipynb

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   "source": [
    "import numpy as np\n",
    "from IPython.display import display as disp"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Leg med broadcasting"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Definer to arrays, `a` og `b`, begge 1d, deres 2d-kopier, `aa` og `bb` og 3d kopien af `a`, kaldet `aaa`."
   ]
  },
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   "cell_type": "code",
   "execution_count": 2,
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 2, 3])"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
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     "data": {
      "text/plain": [
       "(3,)"
      ]
     },
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   ],
   "source": [
    "a = np.array([1, 2, 3])\n",
    "disp(a, a.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2, 4, 6])"
      ]
     },
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     "output_type": "display_data"
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       "(3,)"
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   ],
   "source": [
    "b = np.array([2, 4, 6])\n",
    "disp(b, b.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3]])"
      ]
     },
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     "output_type": "display_data"
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    {
     "data": {
      "text/plain": [
       "(1, 3)"
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     },
     "metadata": {},
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   ],
   "source": [
    "aa = a[np.newaxis, :]\n",
    "disp(aa, aa.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[2],\n",
       "       [4],\n",
       "       [6]])"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "(3, 1)"
      ]
     },
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   ],
   "source": [
    "bb = b.reshape(-1, 1)\n",
    "disp(bb, bb.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[1]],\n",
       "\n",
       "       [[2]],\n",
       "\n",
       "       [[3]]])"
      ]
     },
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    {
     "data": {
      "text/plain": [
       "(3, 1, 1)"
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   ],
   "source": [
    "aaa = a.reshape(-1, 1, 1) \n",
    "disp(aaa, aaa.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Se hvordan deres form påvirker vektoriserede operationer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 2,  8, 18])"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
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    {
     "data": {
      "text/plain": [
       "(3,)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
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   ],
   "source": [
    "ab = a*b\n",
    "disp(ab, ab.shape)"
   ]
  },
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   "cell_type": "code",
   "execution_count": 8,
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 2,  8, 18]])"
      ]
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    {
     "data": {
      "text/plain": [
       "(1, 3)"
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   ],
   "source": [
    "aab = aa*b\n",
    "disp(aab, aab.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 2,  4,  6],\n",
       "       [ 4,  8, 12],\n",
       "       [ 6, 12, 18]])"
      ]
     },
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     "output_type": "display_data"
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    {
     "data": {
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       "(3, 3)"
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     },
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   ],
   "source": [
    "abb = a*bb\n",
    "disp(abb, abb.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[ 2,  4,  6]],\n",
       "\n",
       "       [[ 4,  8, 12]],\n",
       "\n",
       "       [[ 6, 12, 18]]])"
      ]
     },
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    {
     "data": {
      "text/plain": [
       "(3, 1, 3)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "aaab = aaa*b\n",
    "disp(aaab, aaab.shape)"
   ]
  },
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   "cell_type": "code",
   "execution_count": 11,
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     "data": {
      "text/plain": [
       "array([[[ 2],\n",
       "        [ 4],\n",
       "        [ 6]],\n",
       "\n",
       "       [[ 4],\n",
       "        [ 8],\n",
       "        [12]],\n",
       "\n",
       "       [[ 6],\n",
       "        [12],\n",
       "        [18]]])"
      ]
     },
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    },
    {
     "data": {
      "text/plain": [
       "(3, 3, 1)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "aaabb = aaa*bb\n",
    "disp(aaabb, aaabb.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
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    {
     "data": {
      "text/plain": [
       "array([[[ 2,  4,  6],\n",
       "        [ 4,  8, 12],\n",
       "        [ 6, 12, 18]]])"
      ]
     },
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    {
     "data": {
      "text/plain": [
       "(1, 3, 3)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "aaaTbb = aaa.T*bb\n",
    "disp(aaaTbb, aaaTbb.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Der er forresten flere måder at ændre et arrays antal dimmensioner på…"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3]])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.expand_dims(a, axis=0) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3]])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a.reshape(1, -1)  # -1 betyder \"resten\", se evt. eksempel i bunden"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1],\n",
       "       [2],\n",
       "       [3]])"
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     "execution_count": 15,
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   "source": [
    "a.reshape(-1, 1) "
   ]
  },
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   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11])"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "(12,)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "foo = np.arange(12)\n",
    "disp(foo, foo.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Reshape til 3 rækker, og brug resten af elementerne (-1) til at danne det nødvendige antal søjler."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
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    "collapsed": false
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  1,  2,  3],\n",
       "       [ 4,  5,  6,  7],\n",
       "       [ 8,  9, 10, 11]])"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
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    {
     "data": {
      "text/plain": [
       "(3, 4)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fooRshp = foo.reshape(3, -1)\n",
    "disp(fooRshp, fooRshp.shape)"
   ]
  }
 ],
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