numpy_tutorial.ipynb

{
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  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## numpy チュートリアル\n",
    "\n",
    "Tomonori Kodaira"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# numpy\n",
    "## 行列とか扱いやすくするやつ"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##  ndarray"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0 1 2 3]\n",
      " [9 8 7 6]]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "numpy.ndarray"
      ]
     },
     "execution_count": 136,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = numpy.array([[0,1,2,3], [9,8,7,6]]); print(x)\n",
    "x.__class__"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "shape, size:  (2, 4) 8\n",
      "any, all:  True False\n",
      "sum:  36\n",
      "flatten:  [0 1 2 3 9 8 7 6]\n",
      "Transpose: \n",
      "[[0 9]\n",
      " [1 8]\n",
      " [2 7]\n",
      " [3 6]]\n",
      "fill: \n",
      "[[10 10 10 10]\n",
      " [10 10 10 10]]\n"
     ]
    }
   ],
   "source": [
    "print(\"shape, size: \", x.shape, x.size)\n",
    "print(\"any, all: \", x.any(), x.all())\n",
    "print(\"sum: \", x.sum())\n",
    "print(\"flatten: \", x.flatten())\n",
    "print(\"Transpose: \", x.T, sep='\\n')\n",
    "x.fill(10)\n",
    "print(\"fill: \", x, sep='\\n')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# よく使うコマンド"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# zeros, arange, ones, random.*, concatenate, stack etc.."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## zeros, ones"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 232,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.]])"
      ]
     },
     "execution_count": 232,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "numpy.zeros((1, 10))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.])"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "numpy.ones(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 233,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[ 0.,  0.,  0.],\n",
       "        [ 0.,  0.,  0.],\n",
       "        [ 0.,  0.,  0.],\n",
       "        [ 0.,  0.,  0.]],\n",
       "\n",
       "       [[ 0.,  0.,  0.],\n",
       "        [ 0.,  0.,  0.],\n",
       "        [ 0.,  0.,  0.],\n",
       "        [ 0.,  0.,  0.]]])"
      ]
     },
     "execution_count": 233,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "numpy.zeros((2, 4, 3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## random, arange"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 239,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.21240213,  0.51893698,  0.37301441,  0.52153013,  0.4189147 ,\n",
       "         0.50376525,  0.58299756,  0.37359483,  0.88470023,  0.57319329],\n",
       "       [ 0.22352932,  0.6454468 ,  0.04963214,  0.57786814,  0.20154706,\n",
       "         0.8007831 ,  0.49362569,  0.33227308,  0.32134634,  0.43553474]])"
      ]
     },
     "execution_count": 239,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "numpy.random.random((2, 10))\n",
    "# numpy.random.randint(0, 10, (2, 4))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 177,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
      ]
     },
     "execution_count": 177,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "numpy.arange(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "# concat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 245,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0  1  2  3  4  5  6  7  8  9]\n",
      " [10 11 12 13 14 15 16 17 18 19]]\n"
     ]
    }
   ],
   "source": [
    "x = numpy.arange(20).reshape(2, 10); print(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 222,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0  1  2  3  4  5  6  7  8  9]\n",
      " [10 11 12 13 14 15 16 17 18 19]\n",
      " [ 0  1  2  3  4  5  6  7  8  9]\n",
      " [10 11 12 13 14 15 16 17 18 19]] (4, 10)\n",
      "\n",
      "[[ 0  1  2  3  4  5  6  7  8  9  0  1  2  3  4  5  6  7  8  9]\n",
      " [10 11 12 13 14 15 16 17 18 19 10 11 12 13 14 15 16 17 18 19]] (2, 20)\n"
     ]
    }
   ],
   "source": [
    "cx = numpy.concatenate((x, x)); print(cx, cx.shape, end=\"\\n\\n\")\n",
    "cx = numpy.concatenate((x, x), axis=1); print(cx, cx.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "# stack"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 252,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[[  0   2   2   3 100   5   6   7   8   9]\n",
      "  [ 10  11  12  13  14  15  16  17  18  19]]\n",
      "\n",
      " [[  0   2   2   3 100   5   6   7   8   9]\n",
      "  [ 10  11  12  13  14  15  16  17  18  19]]] (2, 2, 10)\n"
     ]
    }
   ],
   "source": [
    "sx = numpy.stack((x, x))\n",
    "print(sx, sx.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 225,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[[ 0  1  2  3  4  5  6  7  8  9]\n",
      "  [ 0  1  2  3  4  5  6  7  8  9]]\n",
      "\n",
      " [[10 11 12 13 14 15 16 17 18 19]\n",
      "  [10 11 12 13 14 15 16 17 18 19]]] (2, 2, 10)\n"
     ]
    }
   ],
   "source": [
    "sx = numpy.stack((x, x), axis=1); print(sx, sx.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "# index\n",
    "- カンマ区切りで要素にアクセスできる\n",
    "- リストが入れられる．"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 258,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "cannot reshape array of size 40 into shape (2,2,5)",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-258-afe23daab318>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mnumpy\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m \u001b[0mx\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnumpy\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0marange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m40\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mreshape\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m2\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m5\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      3\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m3\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m5\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      4\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mValueError\u001b[0m: cannot reshape array of size 40 into shape (2,2,5)"
     ]
    }
   ],
   "source": [
    "import numpy \n",
    "x = numpy.arange(40).reshape(2, 2, 5)\n",
    "print(x[:, 1, [1, 3, 5]])\n",
    "x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "# where"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 266,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x =\n",
      " [[[ 0  1  2  3  4  5  6  7  8  9]\n",
      "  [10 11 12 13 14 15 16 17 18 19]]\n",
      "\n",
      " [[20 21 22 23 24 25 26 27 28 29]\n",
      "  [30 31 32 33 34 35 36 37 38 39]]]\n",
      "[[[2 2 2 2 2 2 2 2 2 2]\n",
      "  [2 2 2 2 2 2 2 2 2 2]]\n",
      "\n",
      " [[1 1 1 1 1 1 1 1 1 1]\n",
      "  [1 1 1 1 1 1 1 1 1 1]]] (2, 2, 10)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([[[2, 0, 2, 0, 2, 0, 2, 0, 2, 0],\n",
       "        [2, 0, 2, 0, 2, 0, 2, 0, 2, 0]],\n",
       "\n",
       "       [[1, 0, 1, 0, 1, 0, 1, 0, 1, 0],\n",
       "        [1, 0, 1, 0, 1, 0, 1, 0, 1, 0]]])"
      ]
     },
     "execution_count": 266,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print(\"x =\\n\", x)\n",
    "# print(\"\\nx % 2 == 0,if True 1 else 0\\n\", numpy.where(x % 2 == 0, 1, 0))\n",
    "two = numpy.where(x % 2 == 0)\n",
    "# print(\"\\nwhere\", *two, sep='\\n')\n",
    "ones = numpy.ones_like(x);ones[0] += 1; zeros = numpy.zeros_like(x)\n",
    "print(ones, zeros.shape)\n",
    "numpy.where(x % 2 == 0, ones, zeros)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "# 線形代数的な"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 269,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1 2 3 4 5]\n",
      "[0 1 0 0 1]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "7"
      ]
     },
     "execution_count": 269,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xx = numpy.arange(5).reshape(5) + 1; print(xx)\n",
    "w = numpy.random.randint(0, 3, (5, )); print(w.flatten())\n",
    "w.dot(xx)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# 加減乗除\n",
    "###### 基本的にどこかの次元と形が合っていれば勝手にやってくれる"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[ 0,  1,  2,  3],\n",
       "        [ 4,  5,  6,  7],\n",
       "        [ 8,  9, 10, 11]],\n",
       "\n",
       "       [[12, 13, 14, 15],\n",
       "        [16, 17, 18, 19],\n",
       "        [20, 21, 22, 23]]])"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sample = numpy.arange(24).reshape(2, 3, 4) # shape(2, 3, 4)\n",
    "sample"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[ 0,  3,  6,  9],\n",
       "        [12, 15, 18, 21],\n",
       "        [24, 27, 30, 33]],\n",
       "\n",
       "       [[36, 39, 42, 45],\n",
       "        [48, 51, 54, 57],\n",
       "        [60, 63, 66, 69]]])"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sample * 3 # shape(, )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 173,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[[  0   4  12  24]\n",
      "  [  8  20  36  56]\n",
      "  [ 16  36  60  88]]\n",
      "\n",
      " [[ 24  52  84 120]\n",
      "  [ 32  68 108 152]\n",
      "  [ 40  84 132 184]]]\n",
      "\n",
      "[[[ 0  3  6  9]\n",
      "  [ 8 10 12 14]\n",
      "  [ 8  9 10 11]]\n",
      "\n",
      " [[36 39 42 45]\n",
      "  [32 34 36 38]\n",
      "  [20 21 22 23]]]\n"
     ]
    }
   ],
   "source": [
    "print(sample * [2, 4, 6, 8], end='\\n\\n') # shape (4, )\n",
    "print(sample * [[3], [2], [1]]) # shape(3, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[  0,   3,  12,  27],\n",
       "        [  4,  20,  42,  70],\n",
       "        [ 16,  45,  80, 121]],\n",
       "\n",
       "       [[  0,  39,  84, 135],\n",
       "        [ 16,  68, 126, 190],\n",
       "        [ 40, 105, 176, 253]]])"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sample * [[0, 3, 6, 9], [1, 4, 7, 10], [2, 5, 8, 11]] # shape (3, 4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "operands could not be broadcast together with shapes (2,3,4) (2,3) ",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-92-0539d9cc838c>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0;31m# sample.shape = 2, 3, 4\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m \u001b[0msample\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mnumpy\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0marray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m3\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m6\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m4\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m7\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mreshape\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m3\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;31m# shape (2, 3)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m: operands could not be broadcast together with shapes (2,3,4) (2,3) "
     ]
    }
   ],
   "source": [
    "# sample.shape = 2, 3, 4\n",
    "sample * numpy.array([[0, 3, 6], [1, 4, 7]]).reshape((2,3)) # shape (2, 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# broadcast_to\n",
    "### 次元の拡張を行う．"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 273,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[ 0,  3,  6,  9],\n",
       "        [ 1,  4,  7, 10],\n",
       "        [ 2,  5,  8, 11]],\n",
       "\n",
       "       [[ 0,  3,  6,  9],\n",
       "        [ 1,  4,  7, 10],\n",
       "        [ 2,  5,  8, 11]]])"
      ]
     },
     "execution_count": 273,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "temp = numpy.array([[0, 3, 6, 9], [1, 4, 7, 10], [2, 5, 8, 11]]) # shape (3, 4)\n",
    "numpy.broadcast_to(temp, (2, 3, 4)) \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## broadcast_to関数が扱えるようなshapeに直せばいい"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 275,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[[0]\n",
      "  [3]\n",
      "  [6]]\n",
      "\n",
      " [[1]\n",
      "  [4]\n",
      "  [7]]]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([[[  0,   0,   0,   0],\n",
       "        [ 12,  15,  18,  21],\n",
       "        [ 48,  54,  60,  66]],\n",
       "\n",
       "       [[ 12,  13,  14,  15],\n",
       "        [ 64,  68,  72,  76],\n",
       "        [140, 147, 154, 161]]])"
      ]
     },
     "execution_count": 275,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "temp = numpy.array([[0, 3, 6], [1, 4, 7]]).reshape((2,3)) # shape (2, 3)\n",
    "temp = temp.reshape(2, 3, 1); print(temp)\n",
    "temp * sample\n",
    "# numpy.broadcast_to(temp, (2, 3, 4))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# 各要素に関数を当てる"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[[ 0  1  2  3]\n",
      "  [ 4  5  6  7]\n",
      "  [ 8  9 10 11]]\n",
      "\n",
      " [[12 13 14 15]\n",
      "  [16 17 18 19]\n",
      "  [20 21 22 23]]]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([[ 6, 22, 38],\n",
       "       [54, 70, 86]])"
      ]
     },
     "execution_count": 140,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print(sample)\n",
    "numpy.apply_along_axis(numpy.sum, axis=2, arr=sample)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 6, 22, 38],\n",
       "       [54, 70, 86]])"
      ]
     },
     "execution_count": 142,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "numpy.sum(sample, axis=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# axis\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 284,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[[ 0  1  2  3]\n",
      "  [ 4  5  6  7]\n",
      "  [ 8  9 10 11]]\n",
      "\n",
      " [[12 13 14 15]\n",
      "  [16 17 18 19]\n",
      "  [20 21 22 23]]] (2, 3, 4)\n",
      "-----------------------\n",
      "Default 276 ()\n",
      "axis=1:\n",
      " [[12 15 18 21]\n",
      " [48 51 54 57]] (2, 4)\n",
      "axis=2:\n",
      " [[ 6 22 38]\n",
      " [54 70 86]] (2, 3)\n"
     ]
    }
   ],
   "source": [
    "print(sample, sample.shape)\n",
    "print(\"-----------------------\")\n",
    "sums = sample.sum(axis=None); print(\"Default\", sums, sums.shape)\n",
    "# sums = sample.sum(axis=0); print(\"axis=0:\\n\", sums, sums.shape)\n",
    "sums = sample.sum(axis=1); print(\"axis=1:\\n\", sums, sums.shape)\n",
    "sums = sample.sum(axis=2); print(\"axis=2:\\n\", sums, sums.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true,
    "scrolled": true,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": []
  }
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