notebook-3.ipynb

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   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b239aa8b",
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   "source": [
    "# Part 3 - A mix of things"
   ]
  },
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   "source": [
    "## 3.1 Loading and saving arrays\n",
    "\n",
    "Simple, with ```np.load``` and ```np.save```. File contains only *one* array. "
   ]
  },
  {
   "cell_type": "code",
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   "source": [
    "a = np.random.randint(1, 10, (100, 100))\n",
    "\n",
    "np.save('data/random', a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "13468213",
   "metadata": {
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   },
   "outputs": [],
   "source": [
    "np.save('data/random_notpickled', a, allow_pickle=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "26f57c22",
   "metadata": {
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   },
   "source": [
    "loading with ```np.load```\n"
   ]
  },
  {
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   "execution_count": 5,
   "id": "091a7c9d",
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4, 4, 7, ..., 2, 8, 4],\n",
       "       [5, 9, 5, ..., 3, 6, 5],\n",
       "       [1, 6, 4, ..., 3, 4, 3],\n",
       "       ...,\n",
       "       [2, 5, 9, ..., 6, 3, 5],\n",
       "       [4, 4, 9, ..., 8, 7, 4],\n",
       "       [2, 2, 4, ..., 1, 4, 9]])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.load('data/random.npy')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e91298f4",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "For several arrays: ```np.savez``` saves in ```.npz``` format."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
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   "source": [
    "b = np.random.randint(1, 10, (100, 100))\n",
    "\n",
    "np.savez('data/arrays.npz', x=a, y=b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "1765b8dd",
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "['x', 'y']"
      ]
     },
     "execution_count": 7,
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   ],
   "source": [
    "data = np.load('data/arrays.npz')\n",
    "data.files"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "d839d450",
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    {
     "data": {
      "text/plain": [
       "array([[4, 4, 7, ..., 2, 8, 4],\n",
       "       [5, 9, 5, ..., 3, 6, 5],\n",
       "       [1, 6, 4, ..., 3, 4, 3],\n",
       "       ...,\n",
       "       [2, 5, 9, ..., 6, 3, 5],\n",
       "       [4, 4, 9, ..., 8, 7, 4],\n",
       "       [2, 2, 4, ..., 1, 4, 9]])"
      ]
     },
     "execution_count": 8,
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   "source": [
    "data['x']"
   ]
  },
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   "id": "6ea6f5b4",
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   },
   "source": [
    "## 3.2 Masked arrays\n",
    "\n",
    "Sometimes you have an array with *invalid* values, or values you for want to omit, for one reason or another.\n",
    "\n",
    "One option is to create a boolean mask as we have previously seen.\n"
   ]
  },
  {
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   "id": "366e1850",
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   "outputs": [],
   "source": [
    "a = np.array([5, 2, 1, -1, 2.0]) # -1 is an invalid entry, an error in measurement for example."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "d437070c",
   "metadata": {
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   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ True,  True,  True, False,  True])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "i = a>=0\n",
    "i"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "68f309df",
   "metadata": {
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.5"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[i].mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "24b8224e",
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   },
   "source": [
    "But another, more neat option, is to create an *masked array*."
   ]
  },
  {
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "masked_array(data=[5.0, 2.0, 1.0, --, 2.0],\n",
       "             mask=[False, False, False,  True, False],\n",
       "       fill_value=1e+20)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b = np.ma.masked_array(a, a<0) # second argument is the mask, True for values that you *dont*  want\n",
    "b"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "41c2ee04",
   "metadata": {
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   },
   "source": [
    "Now the array has the information of which values to omit *inside* the array, it is not another variable.\n",
    "\n",
    "Every operation you do with the array will consider the mask and omit those values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "271f7fb3",
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.5"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b.mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "30db8538",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
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   "source": [
    "Another way of creating masked arrays is using some specific functions from the module  \n",
    "- ```np.ma.greater```, ```np.ma.greater_equal``` \n",
    "- ```np.ma.less```, ```np.ma.less_equal```\n",
    "- ```np.ma.masked_outside```\n",
    "- ```np.ma.masked_inside```\n",
    "- ```np.ma.masked_invalid``` marks NaNs as masked.\n",
    "... etc\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "38dc45b6",
   "metadata": {
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 5.,  2.,  1., -1.,  2.])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "d3ca2a8a",
   "metadata": {
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "masked_array(data=[5.0, 2.0, 1.0, --, 2.0],\n",
       "             mask=[False, False, False,  True, False],\n",
       "       fill_value=1e+20)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.ma.masked_less(a, 0)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6aed954f",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Accessing the full data is easy with the attribute ```data```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "6bccdc7b",
   "metadata": {
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 5.,  2.,  1., -1.,  2.])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b.data"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4a13805c",
   "metadata": {
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   "source": [
    "and the mask with attribute ```mask```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "0c004d92",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
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   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([False, False, False,  True, False])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b.mask"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4dc547a2",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Modifying the mask: setting a new value to be masked by assigning ```np.ma.masked```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "5fcc6657",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "b[0] = np.ma.masked"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "ad92c5b2",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "masked_array(data=[--, 2.0, 1.0, --, 2.0],\n",
       "             mask=[ True, False, False,  True, False],\n",
       "       fill_value=1e+20)"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bf21fbcb",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Unmasking by assigning the original value "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "60d4767a",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "b[0]=b.data[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "9b4bb7d5",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "masked_array(data=[5.0, 2.0, 1.0, --, 2.0],\n",
       "             mask=[False, False, False,  True, False],\n",
       "       fill_value=1e+20)"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9a709044",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Slicing and indexing works as you would expect, omiting masked values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "08b62982",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.5"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b[2:].mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "82a8dd2f",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "All *ufuncs* work as expected, ignoring the masked values (despite warning...)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "c54a366c",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_39858/1512873993.py:1: RuntimeWarning: invalid value encountered in log\n",
      "  l = np.log(b)\n"
     ]
    }
   ],
   "source": [
    "l = np.log(b)\n",
    "#np.ma.masked_invalid(np.log(a))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "8117db44",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.995732273553991"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum(l)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "3740130e",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.995732273553991"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum(np.log(b[i]))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1dc56312",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Numerical operations can be easily performed without worrying about missing values, dividing by zero, square roots of negative numbers, etc."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "a4539e69",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1.0 -- -- 1.4142135623730951 -- --]\n"
     ]
    }
   ],
   "source": [
    "x = np.ma.array([1., -1., 3., 4., 5., 6.], mask=[0,0,0,0,1,0])\n",
    "y = np.ma.array([1., 2., 0., 2., 5., 6.], mask=[0,0,0,0,0,1])\n",
    "\n",
    "print(np.ma.sqrt(x/y))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a5c8a510",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Exercises\n",
    "\n",
    "### Exercise 1\n",
    "\n",
    "- Create a vector of 1000 random samples that are normally distributed with mean 0 and standard deviation of 1. Use ```np.random.normal``` for it (consult the documentation of the function if needed, by typing ```np.random.normal?```).\n",
    "\n",
    "- Cut all the samples above and below mean +- 1 standard deviations of the sample.\n",
    "- Visualize the distribution of samples before and after so that you can compare them.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "35da075d",
   "metadata": {},
   "outputs": [],
   "source": [
    "a = np.random.normal(loc=0, scale=1, size=1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "b2a02613",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5040008827134241"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b = np.ma.masked_outside(a, a.mean() - 1*a.std(), a.mean() + 1*a.std())\n",
    "b.std()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "e1bd2852",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-3.0, 3.0)"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(2,1)\n",
    "ax[0].hist(a)\n",
    "ax[1].hist(b)\n",
    "ax[0].set_xlim((-3, 3))\n",
    "ax[1].set_xlim((-3, 3))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "69d68117",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Exercise 2\n",
    "\n",
    "We will create a circular mask and apply it to the following image. Then we will compute the mean gray value in the masked image. The image is already loaded in numpy array ```img```."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "3e3cbf05",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7f080eda4370>"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from PIL import Image\n",
    "\n",
    "img = np.asarray(Image.open('imgs/einstein.png').convert('L'))\n",
    "plt.imshow(img, cmap='gray')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "649a1d13",
   "metadata": {},
   "source": [
    "\n",
    "Step 1. Create a circular mask as shown below. Size of the array should be the same as the image. You can choose the radius, here shown is a radius of 100 pixels.\n",
    "\n",
    "![imgs/mask.png](imgs/mask.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "e3ad7952",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7f080eda0760>"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAQEAAAD8CAYAAAB3lxGOAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/YYfK9AAAACXBIWXMAAAsTAAALEwEAmpwYAAAajklEQVR4nO3deXiU9b338fc3QwhIDIQlEAKagMFqTstiFMUepbaCoFeRU6u4orXmVJaKwuPWWu15qrYoVo8CR6gU20NFLrHq42NRj2ipEgyLCIQ1EiyBsCMEkZDMfM8fGXCEbGSW38zc39d15ZqZ32wfbsiHe79FVTHGeFeK6wDGGLesBIzxOCsBYzzOSsAYj7MSMMbjrASM8biolYCIXCEiG0SkTETuj9b3GGPCI9HYT0BEfMBG4HKgAlgKXK+qayP+ZcaYsERrTuACoExVN6vqUWAuMCJK32WMCUOrKH1uDrA15HEFMLChF3fu6NPcnqlRimKMAVi+qnqPqnY5cTxaJSD1jH1juUNEioAigDNyWlHyds8oRTHGAPiyyz6vbzxaiwMVQOhvdQ9ge+gLVHWGqhaqamGXTr4oxTDGNCVaJbAUyBeRPBFpDYwC3ojSdxljwhCVxQFVrRWRccDbgA+Ypaql0fguY0x4orVOAFV9C3grWp9vjIkM22PQGI+zEjDG46wEjPE4KwFjPM5KwBiPsxIwxuOsBIzxOCsBYzzOSsAYj7MSMMbjrASM8TgrAWM8zkrAGI+zEjDG46wEjPE4KwFjPM5KwBiPsxIwxuOsBIzxOCsBYzzOSsAYj7MSMMbjrASM8TgrAWM8zkrAGI+L2hWITOIpPfoV/novKB2e06WWvNT0iH+uiQwrAQ+7Y+vFbDvc/uuBa2vw794d8e85esX5tL1v2/HHw7JKGZ9Z71WyjQNWAh5SUHwjNZsyjj/On7oV/9aKqH9v6wVL8S/4+vFrl/2AZ4e0Pv740u+tYmbPj6Kew9TPSiBJVWsNAPv81Vw3/h5SapXc5f+kdsfXF4eudZSt1cLl5C38+vG2grMZnHsH+89KpeTeZ46Pp0mqg3TeYyWQRJZXH+Ufh/uweH9vqoYdPT7etqoEcPdL3xR/6QbSSqGbCFfPugwA6dqZIa9/AsANGaVk+dq5jJjUwioBEdkCVAF+oFZVC0WkI/AykAtsAa5V1f3hxTSNORw4St9FRWS+05bM2cXAXteRWkaVQFVV3f2qKv5W0AGAaY9NolP/XRT3ne8uWxITVW35m+tKoFBV94SMTQb2qepvReR+IFNV72vscwr7ttGSt3u2OIdXjdl2IcWzB5BSq3SesQTC+LuMd76uWVRecxYAf5z0e/qlpTlOlHh82WXLVbXwxPFolMAGYLCqVopINvCBqp7d2OdYCTTfHv+XbPf7mHjTz2i9ZTe1FduaflOS8fXpzfahXZkzcQp5rXycltK66TeZqJVAObAfUOB5VZ0hIl+oaoeQ1+xX1czGPsdKoGnVWsN1ZVdR/mpvuj2z2HWcuLFx5vkM67eaaTlLXEeJew2VQLgrBi9W1e0ikgW8KyLrm/tGESkCigDOyLH1k425ZPVIdi7tRu5DS+imO13HiSt97ljK5z1yyB93J7cNX8iDnTe4jpRwwpoT+MYHiTwCHALuwBYHwlajft75qh2TJ9xC+pod1G75p+tIcU8K/4UDfdL54IlnaYUPn9he8aEamhNo8VQSkXYicvqx+8AQYA3wBjA6+LLRwOst/Q6vWl59lMvGj+G5/ufT5s0SK4Bm0mVryPjLEkae833OnT2WXf4vXUdKCOHMh3cF/ioixz7nL6q6QESWAvNE5Hbgn8CPw4/pDYcCRxjwYREdFrQj89ViAq4DJSj/wYPk/qKYf2USHQfYpsWmRGxxIBy2OFDnnBljOOMRW+kXSb4uXdg8tRvrv/tn11Gci9aKQROmGvUzoORmejwU4MxNy3FfycnFv3s3ve70Myx7FMNfLrYDl+phJeDYeUtvovvItTbrH0X+vftg7z7+9t1eVC5sz2NdV7mOFFds9akjN20ZTP5/30nODfY/U6z49+/nk5vP5aw5dzL/UEbTb/AIKwEHfrnr2+z7aRa97i0mcPiw6zieEliznt7/p5jpRddQWXvIdZy4YCUQY0/s682KSzLxr93oOoqn+T5YwejrxrLoiOsk7lkJxMjsg1n0WXQLH1x5Lv6DB13HMYAUf8pDPy+iz6JbKK/x7lyBlUAMLDoCs+8ZQd6oVdR+vtV1HBOizZsl5I1axb9Nvtd1FGesBKKsvOYQj117E2lvLXUdxTQia/rH9P/NGPb7vbeOxkogiuZWZVJ0y3h02RrXUUxTAn6ypi1m8JRJlB79ynWamLISiJK5VZlMu/fHpPz9E9dRzCno9vRibnh6IgcC3ikCK4EoKK85xAtFV9P29RLXUUwLdHt6MYMfn4hfvbELl5VAhC06Anf+6Gc2B5DgsqYVU/jYOD7zwFYDK4EImn0wi1+Nu8PWASQDVbKmLmbkf96b9JsPrQQi6LGVV9hWgCSTPWUx//gq13WMqLISiJAn9vUm/z47s3oymnPrcCqSeBdjK4EI+OWub/P+oBzbEShZLVnFraN/zrxD7Zt+bQKyEgjTTVsGs+KGc2xX4CTne38Fz943KimLwEogTB9/eI4dDOQRp/31Y17ZddKJeRKelUAL1aifviXXc9Yjn7qOYmLo0FW1PLv/TNcxIspKoIUGlNxMt6vX2fkAPMb/xQEWDP8OY7Zd6DpKxFgJtFCPh7yxN5k5We3nW/lozgDXMSLGSuAUHQoc4ZwZY9BN5a6jGIdy/nsDfUuuT4pdi60ETtGAD4s445HFaHW16yjGIf+evXQbuZ7ZB7u7jhI2K4FTsLz6KB0WtHMdw8QLVSa/OjLh5wasBJrJrwEmTBxP5uxi11FMHMl7eCkFL4x1HSMsVgLN9O5XbUl/d63rGCbOaG0t3T+sSegTkVgJNNPjd48mUFXlOoaJQ6nvLGPEK3e7jtFiVgLNcMnqkaSv2ek6holjef+vmqlfJOb1NK0EmlCtNexc2o3acrtSkGlYyt8/4bXKfq5jtIiVQBOuK7uK3IeWuI5hEkDK5dvZWPOl6xinrMkSEJFZIrJLRNaEjHUUkXdFZFPwNjPkuQdEpExENojI0GgFj4U9/i8pf7U3xMHl200CCPgZ+vYE1ylOWXPmBGYDV5wwdj/wnqrmA+8FHyMi5wKjgILge6aJiC9iaWNsu99Ht2cWu45hEsi3nku8lcdNloCqLgL2nTA8AngxeP9F4OqQ8bmqWq2q5UAZcEFkosbepBt/5jqCSTCBNZsoeHaM6xinpKXrBLqqaiVA8DYrOJ4DhJ5epyI4dhIRKRKRZSKybPdefwtjRM+YbReS+vlu1zFMogn46by6lj8d7Ow6SbNFesWg1DNW7wK1qs5Q1UJVLezSKf6WGIpnD6C2YpvrGCYBtXmzhN98cqXrGM3W0hLYKSLZAMHbXcHxCiB0Y2kPYHvL47lxOHCUlFpbGWharrbGlzDHFLS0BN4ARgfvjwZeDxkfJSJpIpIH5AMJdxmevouK6DzDNgualssf/QkzDyTGzkPN2UT4ElAMnC0iFSJyO/Bb4HIR2QRcHnyMqpYC84C1wAJgrKrG3wJ/I5ZXHyXznba2WdCER5WnXvthQswNiMbBP/bCvm205O34aM2n9+fyt4IOrmOYJODr0J7XSxeSGidbyX3ZZctV9aQzpdoegydYvL+36wgmWQSUj46kuk7RJCuBENVaQ9Wwo65jmCThP3iQX93zU9cxmmQlYIzHWQmE2Oe38waayBJ/3clp45mVQIjrxt9jJw4xEdXmzRL6vTzBdYxGWQmEsB2ETFQE6tuRNn5YCQQVFN9Iu+X/dB3DJKH8OQd4eHeB6xgNshIIqtmUQe0OO4WYibzAyrV8+kUP1zEaZCVgjMdZCRjjcVYCwB1bLyZ/6tamX2hMC1WPzeSzmkOuY9SrlesA8WDb4fb4t1a4jmGSWGDNeo5ofBxDcCKbEzDG46wEjPE4z5dA6dGv4Me2u7CJvgmj4/MEpJ4vAT+Cf89e1zGMB6TuOew6Qr08XwLGeJ2VgDEeZyVgjMdZCRjjcVYCxniclYAxHmclYIzHWQkY43FWAsZ4nJWAMR5nJWCMx1kJGONxVgLGeJyVgDEe12QJiMgsEdklImtCxh4RkW0isjL4MzzkuQdEpExENojI0GgFN8ZERnPmBGYDV9Qz/ntV7Rf8eQtARM4FRgEFwfdME4mTi7MbY+rVZAmo6iJgXzM/bwQwV1WrVbUcKAMuCCOfMSbKwlknME5EVgUXFzKDYzlA6Lm7K4JjJxGRIhFZJiLLdu/1hxHDGBOOlpbAdKA30A+oBKYEx+u78mK9V/lU1RmqWqiqhV062RKDMa60qARUdaeq+lU1AMzk61n+CqBnyEt7ANvDi2iMiaYWlYCIZIc8HAkc23LwBjBKRNJEJA/IB0rCixhdp0stR68433UM4wHbhnRyHaFeTV6BSEReAgYDnUWkAngYGCwi/aib1d8C/DuAqpaKyDxgLVALjFXVuF7gz0tNp+192/AvcJ3EJLu/3DUFaOs6xkmaLAFVvb6e4Rcaef2jwKPhhDLGxI7tMWiMx1kJAMOySqm97DzXMUwS23/rRXTxBVzHqJeVADA+83O2DmntOoZJYt1v20yWr53rGPWyEjDG46wEjPE4K4GgS7+3Cl/B2a5jmCT05TUDuTm72HWMBlkJBM3s+RGHczNcxzBJaMfAFH6UftB1jAZZCYTYf1YqSH2HPxjTMr4O7Ql0rXYdo1FWAiFK7n2GlPR01zFMEjl06dls/sEs1zEaZSVgjMdZCZxAunZ2HcEkker28X+YvJVAiDRJZcjrn7iOYZKEr0N7Pnz8OdcxmmQlYIzHWQmc4IaMUsofu8h1DJME9szJIjUBzrNrJXCCLF87OvXfha9rlusoJoH58nsxKf8d1zGaxUqgHsV951N5zVmuY5gEVvYfp3Nt+gHXMZrFSsAYj7MSaMAfJ/0eX5/ermOYBLT39otYePFU1zGazUqgAf3S0tg+tKvrGCbB+DIy2Duwlh6tEmfPUyuBRsyZOKXpFxkTQnO7U37VTNcxTomVQCPyWvnYONNOR26ar/uMCtcRTpmVQCNOS2nNsH6radWj3iupGfMNvoKzebh74p273kqgCdNylrBx3BmuY5gEkP78Hs5IoHUBx1gJNMNtwxcihf/iOoaJY/t+chHjur/nOkaLWAk0w4OdN/DF2YnX8CY2JLU1e88LcEkb10laxkqgmf4++Vl8GXb6MXOyw1f2Y/PI513HaDErgWZqhY/P7itwHcPEmZQ2bfji1irXMcJiJdBMPknhH7c8aUcYmm/YO78nqy54yXWMsFgJnILjRxh26eI6iokDrXrlcl/+265jhM1K4BQV953P5qnd8HXq6DqKcUj6F3Dmyzvi+lTizdVkCYhITxF5X0TWiUipiNwVHO8oIu+KyKbgbWbIex4QkTIR2SAiQ6P5B3Bh/Xf/jGbb+Qa8rPLS9kzLWeI6RkQ0Z06gFpioqucAFwJjReRc4H7gPVXNB94LPib43CigALgCmCaSAKdXOUXDXy7Gl5nZ9AtN0tFBfZl119OuY0RMkyWgqpWquiJ4vwpYB+QAI4AXgy97Ebg6eH8EMFdVq1W1HCgDLohwbufGZ37OgPf3kPKdb7mOYmKo5gfnMWvuVM5LS56rWJ/SOgERyQX6Ax8DXVW1EuqKAjg2f5wDbA15W0Vw7MTPKhKRZSKybPdefwuiu/ebrNVsutnmBrwk69flCXWYcHM0uwREJB2YD0xQ1cbWhtR3HS89aUB1hqoWqmphl06Ju7TwuxFz8A8e4DqGiYEddw/i4Zw3XceIuGaVgIikUlcAc1T11eDwThHJDj6fDewKjlcAPUPe3gPYHpm48edH6Qf585/+E72or+soJlpSfOwcP4hFE6dwTuvTXKeJuOZsHRDgBWCdqj4V8tQbwOjg/dHA6yHjo0QkTUTygHygJHKR4092q3R+OedFjlyVdKs+DLBj/EBWPjCN9iltXUeJiubMCVwM3AxcJiIrgz/Dgd8Cl4vIJuDy4GNUtRSYB6wFFgBjVTUxF/pPwSVtoPKmI65jmCiYeOc81xGiSlRPWlyPucK+bbTk7Z5NvzDOldcc4t+euJesaR9DIOl7L+lJWhobpn2b1UOfIz0lQQ8RDOHLLluuqoUnjtsegxGUl5rOJw9OY9fPBrqOYsLky8hgwzN9KR/2h6QogMZYCUTBwgeeZMeEQa5jmDCse6oP5T+c4TpGTFgJREGm7zT+MmGKFUGC2jirkPXDpruOETNWAlFS0LotiyZNYdfYQSD17Tph4o0vI4ONfyhk/dDppEmq6zgxYyUQRe1T2rLswefYNcbOQRDvJC2NdZO/RfnwP3iqAMBKIOp8ksIr906mcqItGsSzDdO+7Zl1ACeyEoiB3qnpvP7zydy4vgIu/I7rOOaYFB877hrEjesrWD30OddpnLESiJG81HRuydjDC/Om4f+eHWsQD3aOHcin903jlow9Sb8ZsDFWAjHWo1U6Rc/P5/BI25fApR13D+Lv99m1JsFKwIlr0w8w/ndzaf9hJ3wd2ruO4ym13z+PzI86MveuJ5P2WIBTZSXgyLXpB5jX6z2GfbSFVmcm/i7TiUAH9eXFPz7D3LyFSXk0YEtZCTg2PvNzznxlNzsmDMLXuZPrOElJ+hewY8IgHp8zM+lOCBIJrVwHMHUXPeXeJfQdfD3dRu6DODioK1m06pXLmTM+Y0HOEiB5TgkWSTYnEEdWnD+Ha9dWsuXRi5BW1s/hSGnThn1v9uEnCxYmzVmBo8X+pcURn6Rwe/sd3HrrVAr8Y+n+YQ2p7yxzHSuhSGprDl/Zjy9urWLVgMS+MlCsWAnEIZ+ksP6n0ym95StGvHI3uW8exffBCtex4t6+n1zE3vMCCX1xUBesBOJYQeu2lN3wX0wd3pPXKvuRcvl2O1lJPXwFZ5P+/B5+0X16wl4e3CUrgQQwtsNWxnbYysbyLxn69gS+9VwVgTWbPF0IvowMNLc73WdU8HD3FzjD1vq3mJVAAumT2o7yq2bCVVDw7Bg6r66lzZtJfQ7Xeu29/SL2DqytmxYAWAGEw0ogQZWOn8acqk78+qYr8df4OOuWlUm9adGX34uy/1v3y75w0BO2vT+CrAQS2I2n7+XGS/6EXwPMLO3JU6/9kLMmr4WA4j+Y+FfLPbZL9Z45WUzKf4dr0w8En7ECiCQ723AS8WuAAMpHR1L51T0/BUD8JMwig69Dew5dejYA1e19fPh43eG9qcl3PVsnGjrbsM0JJBGfpOADBrcNsGh63QkyDgWO0O/lCRAQ8uccILByrdOM9fnymoHsGJhCoGs1m38QemIP++WPBSuBJJee0oay6/8LgIeHFPDpFz2OP1c9NpPAmvUxz7T/1ovoftvm44+Lsl/iR+mJv/iSqKwEPOTXXUqhS+nxx+X//xBH9Os9x8ffNo7U3Ycj/r3bhnTk5Z8/efxxJ99HZPnaRfx7TMtYCXhYXuo3V7D9z5xZUfw2O3Q3XtkBRMZ4nJWAMR5nJWCMxzVZAiLSU0TeF5F1IlIqIncFxx8RkW0nXK782HseEJEyEdkgIkOj+QcwxoSnOSsGa4GJqrpCRE4HlovIu8Hnfq+qT4a+WETOBUYBBUB34H9EpI+qevdoF2PiWJNzAqpaqaorgvergHVATiNvGQHMVdVqVS0HyoALIhHWGBN5p7ROQERygf7Ax8GhcSKySkRmiUhmcCwH2BrytgoaLw1jjEPNLgERSQfmAxNU9SAwHegN9AMqgWNXcqjvErwnHaAgIkUiskxElu3ea0sKxrjSrBIQkVTqCmCOqr4KoKo7VdWvqgFgJl/P8lcAoUcD9QC2n/iZqjpDVQtVtbBLJ9tH3BhXmrN1QIAXgHWq+lTIeHbIy0YCa4L33wBGiUiaiOQB+UBiHMZmjAc1Z+vAxcDNwGoRWRkcexC4XkT6UTervwX4dwBVLRWRecBa6rYsjLUtA8bEryZLQFU/pP7l/Lcaec+jwKNh5DLGxIjtMWiMx1kJGONxVgLGeJyVgDEeZyVgjMdZCRjjcVYCxniclYAxHmclYIzHWQkY43FWAsZ4nJWAMR5nJWCMx1kJGONxVgLGeJyVgDEeZyVgjMdZCRjjcaJ60tnAYx9CZDfwJbDHdZYGdCY+s8VrLrBsLRXNbGeqapcTB+OiBABEZJmqFrrOUZ94zRavucCytZSLbLY4YIzHWQkY43HxVAIzXAdoRLxmi9dcYNlaKubZ4madgDHGjXiaEzDGOOC8BETkChHZICJlInJ/HOTZIiKrRWSliCwLjnUUkXdFZFPwNrOpz4lQllkisktE1oSMNZhFRB4ITscNIjLUQbZHRGRbcNqtFJHhsc4mIj1F5H0RWScipSJyV3Dc+XRrJJvb6aaqzn4AH/AZ0AtoDXwKnOs40xag8wljk4H7g/fvB34XoyyXAAOANU1lAc4NTr80IC84XX0xzvYIMKme18YsG5ANDAjePx3YGPx+59OtkWxOp5vrOYELgDJV3ayqR4G5wAjHmeozAngxeP9F4OpYfKmqLgL2NTPLCGCuqlarajlQxteXi49VtobELJuqVqrqiuD9KmAdkEMcTLdGsjUkJtlcl0AOsDXkcQWNT5RYUOAdEVkuIkXBsa6qWgl1f5FAlrN0DWeJl2k5TkRWBRcXjs1yO8kmIrlAf+Bj4my6nZANHE431yVQ39WOXW+uuFhVBwDDgLEiconjPM0VD9NyOtAb6AdUAlOC4zHPJiLpwHxggqoebOyl9YzFOpvT6ea6BCqAniGPewDbHWUBQFW3B293AX+lbvZrp4hkAwRvd7lL2GAW59NSVXeqql9VA8BMvp51jWk2EUml7pdsjqq+GhyOi+lWXzbX0811CSwF8kUkT0RaA6OAN1yFEZF2InL6sfvAEGBNMNPo4MtGA6+7SQiNZHkDGCUiaSKSB+QDJbEMduyXLGgkddMuptlERIAXgHWq+lTIU86nW0PZnE+3aKwFPcU1psOpW0v6GfALx1l6Ubc29lOg9FgeoBPwHrApeNsxRnleom72sIa6/xVubywL8IvgdNwADHOQ7c/AamBV8B9wdqyzAd+lbpZ5FbAy+DM8HqZbI9mcTjfbY9AYj3O9OGCMccxKwBiPsxIwxuOsBIzxOCsBYzzOSsAYj7MSMMbjrASM8bj/BSCc8UWtGbOYAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# solution cell\n",
    "center = img.shape\n",
    "radius = 100\n",
    "\n",
    "y, x = np.mgrid[0:img.shape[0], 0:img.shape[1]]\n",
    "x = x - img.shape[0]/2\n",
    "y = y - img.shape[1]/2.0\n",
    "\n",
    "circle = (x**2)+(y**2)\n",
    "i = circle>=radius**2\n",
    "\n",
    "#fig = plt.figure(figsize=(4, 4))\n",
    "plt.imshow(i)\n",
    "#fig.savefig('mask.png')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9904ce32",
   "metadata": {},
   "source": [
    "Step 2: create a masked array, using the circular mask and applying it to the image."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "3cad37ef",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "masked_array(\n",
       "  data=[[--, --, --, ..., --, --, --],\n",
       "        [--, --, --, ..., --, --, --],\n",
       "        [--, --, --, ..., --, --, --],\n",
       "        ...,\n",
       "        [--, --, --, ..., --, --, --],\n",
       "        [--, --, --, ..., --, --, --],\n",
       "        [--, --, --, ..., --, --, --]],\n",
       "  mask=[[ True,  True,  True, ...,  True,  True,  True],\n",
       "        [ True,  True,  True, ...,  True,  True,  True],\n",
       "        [ True,  True,  True, ...,  True,  True,  True],\n",
       "        ...,\n",
       "        [ True,  True,  True, ...,  True,  True,  True],\n",
       "        [ True,  True,  True, ...,  True,  True,  True],\n",
       "        [ True,  True,  True, ...,  True,  True,  True]],\n",
       "  fill_value=999999,\n",
       "  dtype=uint8)"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "img2 = np.ma.masked_array(img, i)\n",
    "img2"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3c73d55f",
   "metadata": {},
   "source": [
    "Step 3: visualize the masked image with ```plt.imshow```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "c86edf0d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7f080d507190>"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(img2, cmap='gray')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5c6ac121",
   "metadata": {},
   "source": [
    "Final step: compute the mean value across both axis, that is, the means taken horizontally and taken vertically. Visualize the distribution as a histogram"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "3223e16c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([10., 12., 19., 23., 42., 41., 18., 13.,  2., 19.]),\n",
       " array([ 91.34482759,  96.52600748, 101.70718737, 106.88836726,\n",
       "        112.06954715, 117.25072705, 122.43190694, 127.61308683,\n",
       "        132.79426672, 137.97544661, 143.15662651]),\n",
       " <BarContainer object of 10 artists>)"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(img2.mean(axis=0))\n",
    "plt.hist(img2.mean(axis=1))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7799bb5f",
   "metadata": {},
   "source": [
    "You will see that the distributions are different, as the image is not spatially homogeneous.\n",
    "\n",
    "If you try to do this with boolean indexing, you'll see that it is much more complicated, because regular indexing with a boolean mask returns you a 1-D vector. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "4358c008",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([92, 67, 57, ..., 61, 57, 56], dtype=uint8)"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "img[i]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "4222b37e",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "celltoolbar": "Slideshow",
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.13"
  },
  "rise": {
   "scroll": true
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}