notebooks/Lecture 03 - Introduction to NumPy.ipynb

{
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   "source": [
    "# **SIN 393 – Introduction to Computer Vision (2023)**\n",
    "\n",
    "# Lecture 03 - Introduction to NumPy\n",
    "\n",
    "Prof. João Fernando Mari ([*joaofmari.github.io*](https://joaofmari.github.io/))\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e9bc27c3-4af7-40dc-b98f-a4d95cb07b95",
   "metadata": {},
   "source": [
    "* Material based on **Scipy Lecture Notes**.\n",
    "     * Available at: http://www.scipy-lectures.org/"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "422088fd-31cc-4dd7-9499-6238e4ee428e",
   "metadata": {},
   "source": [
    "## Importing NumPy\n",
    "---\n",
    "* Import conventions.\n",
    "* NumPy documentation:\n",
    "    * http://docs.scipy.org/"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "2d206104-7582-4094-97d5-bcb5b12b8e4f",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4a494044-6793-46af-ac66-32a12f37f745",
   "metadata": {},
   "source": [
    "## NumPy arrays\n",
    "---\n",
    "* NumPy arrays are containers that provide fast numerical operations and efficient memory usage."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "2c187495-5edf-4eb3-a154-e64ead9eca38",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3])"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.array([0, 1, 2, 3])\n",
    "a"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cfb698cf-0dd0-4670-8e1e-adbd7aded273",
   "metadata": {},
   "source": [
    "* Computing the square of a sequence of 1000 integers using Python lists."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "e40f0f8c-4df0-4356-a5dd-289f9b063208",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "472 µs ± 55 µs per loop (mean ± std. dev. of 7 runs, 1,000 loops each)\n"
     ]
    }
   ],
   "source": [
    "# A Python list with 1000 integer numbers\n",
    "L = range(1000)\n",
    "\n",
    "%timeit [i**2 for i in L]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bbc0f669-01e4-40b4-a62b-286964ef9cb7",
   "metadata": {},
   "source": [
    "* Computing the square of a sequence of 1000 integers using NumPy arrays."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "d49b0432-5028-4327-859c-3cd9c0b7153e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.41 µs ± 644 ns per loop (mean ± std. dev. of 7 runs, 100,000 loops each)\n"
     ]
    }
   ],
   "source": [
    "# NumPy array with 1000 numbers\n",
    "a = np.arange(1000)\n",
    "%timeit a**2"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b406881e-acb0-4e04-903a-591860d7b0ae",
   "metadata": {},
   "source": [
    "## Creating NumPy arrays\n",
    "---\n",
    "\n",
    "### Creating arrays manually"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7270fa7f-9ce0-43ec-b164-e61006ed1239",
   "metadata": {},
   "source": [
    "#### 1D arrays"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "4a0d7016-c8d7-4746-aa24-bcdb28783f42",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.array([0, 1, 2, 3])\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "dd1cbe9c-55f0-4956-82d3-d5fcc88674af",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 1 2 3]\n",
      "<class 'numpy.ndarray'>\n",
      "4\n",
      "1\n",
      "(4,)\n"
     ]
    }
   ],
   "source": [
    "print(a)\n",
    "print(type(a))\n",
    "print(len(a))      \n",
    "print(a.ndim)\n",
    "print(a.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d09abdce-a041-4122-8cbf-f5f2f31a0ab5",
   "metadata": {},
   "source": [
    "#### 2D arrays"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "ddf9386f-fdfa-4577-b876-5085dae13f7f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 1, 2],\n",
       "       [3, 4, 5]])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b = np.array([[0, 1, 2], \n",
    "              [3, 4, 5]])\n",
    "b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "526a4b2a-111d-483a-8e59-a48ab3656dc5",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0 1 2]\n",
      " [3 4 5]]\n",
      "<class 'numpy.ndarray'>\n",
      "2\n",
      "2\n",
      "(2, 3)\n"
     ]
    }
   ],
   "source": [
    "print(b)\n",
    "print(type(b))\n",
    "print(len(b))      \n",
    "print(b.ndim)\n",
    "print(b.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2244880b-498c-43ed-83d8-dc7aaa29dd6f",
   "metadata": {},
   "source": [
    "#### 3D arrays"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "b536afff-9318-4ff0-aab5-2831f99d79f6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[ 1,  2,  3,  1],\n",
       "        [ 4,  5,  6,  5],\n",
       "        [ 7,  8,  9,  9]],\n",
       "\n",
       "       [[10, 11, 12, 10],\n",
       "        [13, 14, 15, 14],\n",
       "        [16, 17, 18, 18]]])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c = np.array([[[1,  2,  3,  1],\n",
    "               [4,  5,  6,  5],\n",
    "               [7,  8,  9,  9]],\n",
    "              [[10, 11, 12, 10],\n",
    "               [13, 14, 15, 14],\n",
    "               [16, 17, 18, 18]]])\n",
    "c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "06e82f32-10f3-431f-b183-b8a40c188b2a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[[ 1  2  3  1]\n",
      "  [ 4  5  6  5]\n",
      "  [ 7  8  9  9]]\n",
      "\n",
      " [[10 11 12 10]\n",
      "  [13 14 15 14]\n",
      "  [16 17 18 18]]]\n",
      "<class 'numpy.ndarray'>\n",
      "2\n",
      "3\n",
      "(2, 3, 4)\n"
     ]
    }
   ],
   "source": [
    "print(c)\n",
    "print(type(c))\n",
    "print(len(c))      \n",
    "print(c.ndim)\n",
    "print(c.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3ed40b0b-cf5c-4465-9a4f-ae3ca3249d09",
   "metadata": {},
   "source": [
    "### Functions for creating arrays\n",
    "\n",
    "* In practice, arrays are rarely created manually."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "81aad77f-093f-42f6-8ed4-506d65f2b74c",
   "metadata": {},
   "source": [
    "#### Equaly spaced arrays"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "af85e6c4-4bc7-4c5a-bb07-baa0327054a1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.arange(10) # 0 .. n-1\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "89595562-0796-4ca7-b742-8a55394ed9a3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 3, 5, 7])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b = np.arange(1, 9, 2)\n",
    "b"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aed8135c-5b00-4bbc-892c-147757566ebd",
   "metadata": {},
   "source": [
    "* By number of points.\n",
    "     * Syntax: ```np.linspace(ini_val, end_val, num_points)```\n",
    "         - ```ini_val```: initial value;\n",
    "         - ```end_val```: final value;\n",
    "         - ```num_points```: number of points."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "4e0bf11d-4849-4af8-8246-9026e6818d4e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0. , 0.2, 0.4, 0.6, 0.8, 1. ])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c = np.linspace(0, 1, 6)\n",
    "c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "85db5056-4b63-4bec-92f5-d3e3eb12aeb1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0. , 0.2, 0.4, 0.6, 0.8])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d = np.linspace(0, 1, 5, endpoint=False)\n",
    "d"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c9ba85c1-b132-483e-a4b7-55805cfeda29",
   "metadata": {},
   "source": [
    "### Common arrays"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "78f14d9a-0489-4be5-8278-72596aedf4c5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1., 1., 1.],\n",
       "       [1., 1., 1.],\n",
       "       [1., 1., 1.]])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.ones((3,3)) # (3, 3) é uma tupla\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "9b41a63b-a3c5-4293-9d3c-34d88faaa902",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0., 0.],\n",
       "       [0., 0.]])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b = np.zeros((2,2))\n",
    "b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "c4feec7f-6407-402c-b7d3-f519dbd4f1d3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1., 0., 0.],\n",
       "       [0., 1., 0.],\n",
       "       [0., 0., 1.]])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c = np.eye(3)\n",
    "c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "1b09692c-f7ac-4894-92a7-a1551ec0de07",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 0, 0, 0],\n",
       "       [0, 2, 0, 0],\n",
       "       [0, 0, 3, 0],\n",
       "       [0, 0, 0, 4]])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d = np.diag(np.array([1, 2, 3, 4]))\n",
    "d"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d6a4f12c-cf4f-4014-9206-0e8627ca67ed",
   "metadata": {},
   "source": [
    "#### Random numbers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "a5160650-c084-4872-b8b1-31ce81e199c5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.65611111, 0.33186913, 0.70212741, 0.51597449])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.random.rand(4) # distribuição uniforme\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "48878f04-a6dd-4455-9f00-31fbfbd576a8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.99489439,  1.68063416, -0.66264699, -0.95745025])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b = np.random.randn(4) # distribuição gaussiana\n",
    "b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "b039b70b-616a-4748-9c78-a4a6170d392b",
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(1234) # define a semente para geração dos números aleatórios"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eff80343-dbd2-4709-ab6b-fbfa2cab993f",
   "metadata": {},
   "source": [
    "## Array data types\n",
    "---\n",
    "\n",
    "* The default data type of NumPy is float64"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "9879ca92-c51f-411c-9cf4-acb9bb653def",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dtype('float64')"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c = np.ones((3, 3))\n",
    "c.dtype"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cadca218-8a33-4887-8d11-5d3288156306",
   "metadata": {},
   "source": [
    "* When the array is created directly, the type is inferred from the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "ffccd412-b6bb-4b07-8a9d-0e30264ab3a0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dtype('int32')"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c = np.array([1, 2, 3]) # inteiros (32 bits)\n",
    "c.dtype"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "f6f174c1-f0e3-4600-872c-63638e7e243a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dtype('float64')"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c = np.array([1., 2, 3]) # float (64 bits)\n",
    "c.dtype"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6b834ad3-f7dc-471e-a7a2-e6386c09e1c4",
   "metadata": {},
   "source": [
    "* Other data types allowed:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "b4f30fb5-37ec-4800-9f2d-5b29483a42be",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dtype('complex128')"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d = np.array([1+2j, 3+4j, 5+6j])\n",
    "d.dtype"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "2ab8b38e-f6dc-4efd-adc4-40f3bd1bc8aa",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dtype('<U5')"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f = np.array(['One', 'Two', 'Forty'])\n",
    "f.dtype"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "24966b96-992f-48f5-bbad-dcd04fa25b55",
   "metadata": {},
   "source": [
    "* Other data types allowed:\n",
    "    * int16\n",
    "    * int32\n",
    "    * int64\n",
    "    * uint32\n",
    "    * float32\n",
    "    * ..."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4616f2de-0bfc-4621-971c-5993474c3760",
   "metadata": {},
   "source": [
    "## Basic visualization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "69a4b75e-145a-4009-b804-7d59871bbc20",
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "86df2129-655c-4ddf-aa8f-d849a1415657",
   "metadata": {},
   "source": [
    "### Ploting 1D arrays "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "9015ee66-b027-46e5-b6ad-b75e59920878",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.        , 0.15789474, 0.31578947, 0.47368421, 0.63157895,\n",
       "       0.78947368, 0.94736842, 1.10526316, 1.26315789, 1.42105263,\n",
       "       1.57894737, 1.73684211, 1.89473684, 2.05263158, 2.21052632,\n",
       "       2.36842105, 2.52631579, 2.68421053, 2.84210526, 3.        ])"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.linspace(0, 3, 20)\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "cc3cf761-6a97-44d1-a3e9-91008d2b6085",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.        , 0.02493075, 0.09972299, 0.22437673, 0.39889197,\n",
       "       0.6232687 , 0.89750693, 1.22160665, 1.59556787, 2.01939058,\n",
       "       2.49307479, 3.0166205 , 3.5900277 , 4.2132964 , 4.88642659,\n",
       "       5.60941828, 6.38227147, 7.20498615, 8.07756233, 9.        ])"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y = x ** 2\n",
    "y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "d7fc1d68-5e85-4711-9710-c9114e5362f6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x2dfbf47e790>]"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, y) # Plota uma linha"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "733bdf0b-3f65-4df9-a009-78cb3ea48a0a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x2dfbf4d6820>]"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, y, 'o')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "7367e0cb-ff47-4055-942f-ca85a55c4caa",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x2dfbf54dbb0>]"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, y)\n",
    "plt.plot(x, y, 'o')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d8447aba-9d27-48d9-9445-016d23b75917",
   "metadata": {},
   "source": [
    "### Ploting 2D arrays"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "cf1e6ec0-dca0-461b-8b25-d7c1831df64b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x2dfbf5eb940>"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "imagem = np.random.rand(30, 30)\n",
    "plt.imshow(imagem)\n",
    "plt.colorbar()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "689c573c-669c-45b9-aaa8-dcc38372a948",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x2dfc16c8bb0>"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(imagem, cmap='gray')\n",
    "plt.colorbar()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4d7188f8-8d98-43af-bfd1-e24f689a8a9f",
   "metadata": {},
   "source": [
    "## Indexing and slicing\n",
    "\n",
    "* Elements of an array can be accessed and assigned by indexing and slicing in a similar way to Python collections (lists, tuples, ...)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "bc1c0f63-46f9-4570-b4c6-d3eed90f55b4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0, 10, 20, 30, 40, 50, 60, 70, 80, 90])"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.arange(10) # 0 .. 9 \n",
    "a = a * 10\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "8214b747-b4ad-43c3-b69b-1b7b18d36b50",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0, 20, 90, 80)"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[0], a[2], a[-1], a[-2]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "85655c8e-50a2-4f02-801a-74de5c396319",
   "metadata": {},
   "source": [
    "* Obtendo um arranjo na ordem reversa"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "d298fc6c-645b-4957-96ff-8b8e036655b6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([90, 80, 70, 60, 50, 40, 30, 20, 10,  0])"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[::-1]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cf013b4a-ccfe-411e-8045-74d02a0c81c6",
   "metadata": {},
   "source": [
    "### Indexing multidimensional arrays\n",
    "\n",
    "* Indices in multidimensional arrays are integer tuples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 171,
   "id": "91c26186-5dc6-441d-87c5-0d79b4491738",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 0, 0],\n",
       "       [0, 1, 0],\n",
       "       [0, 0, 2]])"
      ]
     },
     "execution_count": 171,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.diag(np.arange(3)) # 3 x 3 identity matrix\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "47884b4f-d795-468c-b571-b12b9f5afa4f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[1, 1] # row 1, column 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "30354885-1a86-41e5-8cc1-4ff15c9001ef",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a [2, 1] # row 2 (third row), column 1 (second column)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "49ad6da2-6617-4d4a-8137-212c2e86fea8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 0])"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[1,:] # entire line 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "0a04c2a0-b988-412b-bd47-af7f63926da0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 0, 2])"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[:,2] # entire column 2"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3f5d5beb-7871-4e3e-984a-efe535309b1c",
   "metadata": {},
   "source": [
    "### Atribuição por indexação"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "5ecdcf99-d67a-4263-b746-243ea4dc1b46",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  0,  0],\n",
       "       [ 0,  1,  0],\n",
       "       [ 0, 10,  2]])"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[2, 1] = 10\n",
    "a"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "66584e81-2a46-4f7f-b585-fe51c889a920",
   "metadata": {},
   "source": [
    "### Slicing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "6c066859-4d59-44fa-b312-ce2a2fdf7de8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.arange(10)\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "dd7a3d79-3b09-4d4d-8ce6-836018897423",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2, 5, 8])"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[2:9:3] # inicio : fim (exclusivo) : passo"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e3bd1e50-42f2-4ada-b9d3-fece96de803f",
   "metadata": {},
   "source": [
    "* As with Python lists, the end is not included"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "7e9c9af8-256f-4cfb-80ac-758b4a5c9c79",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3])"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[:4]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "596107ef-bf00-4644-ac72-59bea35c0d4f",
   "metadata": {},
   "source": [
    "* None of the three slicing components (start, end, step) is mandatory.\n",
    "* If omitted:\n",
    "     * start = 0;\n",
    "     * end = last element;\n",
    "     * step = 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "17590296-5059-4a19-ad8a-836631607180",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "a4310a01-f9bb-46d0-8fc9-57910f1d3d79",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 2])"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[1:3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "ca93972c-bf9f-4020-9b98-913c60de48b6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 2, 4, 6, 8])"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[::2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "d278d4b0-d0e4-41ed-95cf-24d709ffb949",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([3, 4, 5, 6, 7, 8, 9])"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[3:]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ca357ead-b3d0-4823-8f31-e37147d7fd28",
   "metadata": {},
   "source": [
    "* Attribution with slicing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "cf80188b-7f89-4925-b352-5bc40aa40bb5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0, 99, 99,  3,  4,  5,  6,  7,  8,  9])"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[1:3] = 99\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "df276ff5-a5c1-4d0a-9808-a3c8b024dd84",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0, 99, 99,  3,  4, 88, 99,  7,  8,  9])"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[5:7] = np.array([88, 99])\n",
    "a"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7a5ec07e-4625-4af1-8855-8866a47acdea",
   "metadata": {},
   "source": [
    "### Combining indexing and slicing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "dd0a1862-ae27-4c28-b7cf-e7b65789c412",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.arange(10)\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "ff234f7f-29e8-4d4e-b6f9-b0569f472822",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0,  1,  2,  3,  4, 10, 10, 10, 10, 10])"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[5:] = 10\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "acc42565-f9a1-427a-a735-32a732923662",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3, 4])"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b = np.arange(5)\n",
    "b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "45e1b346-6fc3-4c3c-b090-33fbaf85c3bf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3, 4, 4, 3, 2, 1, 0])"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[5:] = b[::-1]\n",
    "a"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f7f5713e-fde6-4504-80ff-8cf8b42a43d5",
   "metadata": {},
   "source": [
    "### Illustration of indexing and slicing in NumPy arrays"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7328fffd-6ef8-499b-b415-179bd62a8a58",
   "metadata": {},
   "source": [
    "<img src='figures/slicing_numpy_example.png' style=\"height:300px\">\n",
    "<center>Fonte: [2].</center>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "91c37e1f-db65-4fa2-b42b-179f4bb519ab",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  1,  2,  3,  4,  5],\n",
       "       [10, 11, 12, 13, 14, 15],\n",
       "       [20, 21, 22, 23, 24, 25],\n",
       "       [30, 31, 32, 33, 34, 35],\n",
       "       [40, 41, 42, 43, 44, 45],\n",
       "       [50, 51, 52, 53, 54, 55]])"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.arange(6) + np.arange(0, 51, 10)[:, np.newaxis]\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "b6c63ad6-686c-4795-a98d-da8cf490d84e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([3, 4])"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Orange\n",
    "a[0, 3:5] "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "4b70898d-b385-4d72-b6ac-088f2aa820eb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[44, 45],\n",
       "       [54, 55]])"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Dark green\n",
    "a[4:, 4:] "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "4f8ef5b0-940c-4de3-ae59-38e0dc941090",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 2, 12, 22, 32, 42, 52])"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Red\n",
    "a[:, 2] "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "id": "7177f7ae-9af5-4669-b07c-70886e0f356b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[20, 22, 24],\n",
       "       [40, 42, 44]])"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Verde claro\n",
    "a[2::2, ::2] "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "42685d41-aec4-457e-a7f5-c11084416d61",
   "metadata": {},
   "source": [
    "## Copies and views\n",
    "\n",
    "* When the view is modified, the original arrangement is also modified."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "890f39f6-a0ad-499e-bb11-67a3a4a4d585",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.arange(10)\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "bb3a4180-e9ee-486d-b255-f97e79d5ed70",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 2, 4, 6, 8])"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b = a[::2]\n",
    "b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "id": "3ac78183-dec7-4f2b-a54b-bc66cc0e7676",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.may_share_memory(a, b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "id": "aeb0f10d-9a82-4fc5-b443-593532373b0f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([12,  2,  4,  6,  8])"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b[0] = 12\n",
    "b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "id": "2b15443e-a3c8-4788-9f95-768bf1540130",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([12,  1,  2,  3,  4,  5,  6,  7,  8,  9])"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4a8d6960-45a1-4054-9463-d5c122dd6dc8",
   "metadata": {},
   "source": [
    "* Forcing copying of an arrangement."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "id": "5a27bc22-6aa7-470b-9659-c706b785d5c7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.arange(10)\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "id": "f0e97434-29ea-471b-8c8a-8b7b1c08909b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 2, 4, 6, 8])"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c = a[::2].copy()  # Força a cópia\n",
    "c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "id": "5ad00ef4-8fcb-4f37-8eaa-75a76090efca",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.may_share_memory(a, c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "id": "bf65019d-4d21-4446-a294-7690b162ad91",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([12,  2,  4,  6,  8])"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c[0] = 12\n",
    "c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "id": "90171e57-c5ff-4733-9870-0aaa0730f37c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0813b8b5-fdc4-45a6-9cc7-a72c11aa2dbd",
   "metadata": {},
   "source": [
    "* The use of views allows for memory savings and faster operations."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "73dbaeb4-a50d-44d5-b2c2-e192d70af6e9",
   "metadata": {},
   "source": [
    "## Fancy indexing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "id": "7b928d58-0117-40fe-8455-6e63a499748a",
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "id": "5d9ea02c-1cf9-41e4-a4e1-8add7e713e16",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([10,  3,  8,  0, 19, 10, 11,  9, 10,  6,  0, 20, 12,  7, 14])"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.random.randint(0, 21, 15)\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "id": "5d9d9e29-35aa-49af-820f-7e0c400ad853",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([False,  True, False,  True, False, False, False,  True, False,\n",
       "        True,  True, False,  True, False, False])"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(a % 3) == 0 # True: multiples of 3;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "id": "bb30425b-1c7a-4871-80a4-ff49eaf7401a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 3,  0,  9,  6,  0, 12])"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mascara = (a % 3 == 0)\n",
    "extract_from_a = a[mascara]  # Or:  a[a%3==0]\n",
    "extract_from_a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "id": "162ab391-0d0c-47fa-8e65-d3490c528700",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([False, False, False, False,  True, False,  True, False, False,\n",
       "       False, False,  True,  True, False,  True])"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mascara = a > 10\n",
    "mascara"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "id": "5ad33122-5876-42a6-9c43-520e1bf720b6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([19, 11, 20, 12, 14])"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a_10 = a[mascara]\n",
    "a_10"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "18975795-02af-4666-9a92-2632159255a2",
   "metadata": {},
   "source": [
    "### Mask indexing for assigning values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "id": "fc7fdde2-cbe4-4e22-b24f-e6581ae5f8c7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([10,  3,  8,  0, 19, 10, 11,  9, 10,  6,  0, 20, 12,  7, 14])"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "id": "0a22824d-617c-4d55-9251-7dd57856d350",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([10, -1,  8, -1, 19, 10, 11, -1, 10, -1, -1, 20, -1,  7, 14])"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[a % 3 == 0] = -1\n",
    "a"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3975659f-f4a3-4c95-96b3-e41e5f1d5291",
   "metadata": {},
   "source": [
    "### Indexing with integer arrays"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 172,
   "id": "68c6235c-19b9-496a-9c93-d94c33239021",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0, 10, 20, 30, 40, 50, 60, 70, 80, 90])"
      ]
     },
     "execution_count": 172,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.arange(0, 100, 10)  # De 0 até 100 (exclusivo), de 10 em 10.\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "id": "121e7361-8d52-48de-aede-542863eb9da4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([20, 60, 30, 90])"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lista_indices = [2, 6, 3, 9]\n",
    "a[lista_indices]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "22a0b3d0-de9a-4dab-a95f-967217f43e87",
   "metadata": {},
   "source": [
    "* Or directly:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "id": "f77f4b95-03d4-4c1b-9eb8-03cb7ea3c060",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([20, 60, 30, 90])"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[[2, 6, 3, 9]]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "618eb17c-e3bf-4407-8492-bbf33e65088b",
   "metadata": {},
   "source": [
    "* It is possible to repeat some index."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "id": "c433f2f7-0859-44ae-a2cd-8e39ba9744ac",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([20, 60, 30, 20, 90, 30])"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[[2, 6, 3, 2, 9, 3]]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "67e33681-6ce8-415e-b979-b156ef7dac6e",
   "metadata": {},
   "source": [
    "* It is also possible to assign values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "id": "fced275f-190d-4218-b39f-8de17bfc8edc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([   0,   10,   20,   30,   40,   50,   60, -100,   80, -100])"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[[9, 7]] = -100\n",
    "a"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a5dc4470-4c5b-40fd-8239-76e4a36f150e",
   "metadata": {},
   "source": [
    "* The result of indexing by integer arrays has the format of the index array."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "id": "27924985-4e83-4f3d-95b5-d1b9b9cc87e1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0, 10, 20, 30, 40, 50, 60, 70, 80, 90])"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.arange(10) * 10\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "id": "868cb4c5-95e8-4bcd-b51a-b8c629842b4d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(10,)"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "id": "a867aa57-f593-43f5-a386-28c6eb8140d8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[3, 4],\n",
       "       [9, 7]])"
      ]
     },
     "execution_count": 87,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "indices = np.array([[3, 4], [9, 7]])\n",
    "indices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "id": "8a996e8d-5a98-43da-a04c-e4b6b200483e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2, 2)"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "indices.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "id": "44c52712-2e62-4978-8691-07a69858868b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[30, 40],\n",
       "       [90, 70]])"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[indices]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "54c0af0b-7c06-4f7a-8e8a-9db1cb05b8dd",
   "metadata": {},
   "source": [
    "### Illustration of several fancy indexing examples"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "afd305fb-7cb5-46a0-91b1-5db0c026d5ca",
   "metadata": {},
   "source": [
    "<img src='figures/fancy_example.png' style=\"height:300px\">\n",
    "<center>Fonte: [2].</center>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "id": "26381386-39ce-48e9-b366-1493c74869e9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  1,  2,  3,  4,  5],\n",
       "       [10, 11, 12, 13, 14, 15],\n",
       "       [20, 21, 22, 23, 24, 25],\n",
       "       [30, 31, 32, 33, 34, 35],\n",
       "       [40, 41, 42, 43, 44, 45],\n",
       "       [50, 51, 52, 53, 54, 55]])"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.arange(6) + np.arange(0, 51, 10)[:, np.newaxis]\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "id": "5f189f3b-a16e-4017-94e2-06322b788bb4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1, 12, 23, 34, 45])"
      ]
     },
     "execution_count": 91,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[(0, 1, 2, 3, 4), (1, 2, 3, 4, 5)] # orange"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "id": "ba564529-a604-4d18-b3a2-9f2511cf5f04",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[30, 32, 35],\n",
       "       [40, 42, 45],\n",
       "       [50, 52, 55]])"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[3:, [0, 2, 5]] # blue "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "id": "ccc478a2-be7a-4ca8-a99c-747f4b70619a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 2, 22, 52])"
      ]
     },
     "execution_count": 93,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mascara = np.array([1, 0, 1, 0, 0, 1], dtype=bool)\n",
    "a[mascara, 2] # red"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8a5d162d-7b89-4b8c-8e10-d3a5ca232e76",
   "metadata": {},
   "source": [
    "## Numerical operations with arrays\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5ff1296e-6c29-446c-a93b-b017863a75f3",
   "metadata": {},
   "source": [
    "### Basic operations"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2fd88a89-d0af-4397-b3b0-bb91960ed43f",
   "metadata": {},
   "source": [
    "* With scalars."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "id": "c3aa36f7-f70b-4f5f-b57e-604e1e754150",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2, 3, 4, 5])"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.array([1, 2, 3, 4])\n",
    "a + 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "id": "2a995862-44ef-47cc-b9c1-8b8a6722a6e3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 2, 3, 4])"
      ]
     },
     "execution_count": 95,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "id": "252d1481-2d78-48b4-8cde-b67f4ba4f76e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 2,  4,  8, 16], dtype=int32)"
      ]
     },
     "execution_count": 96,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b = 2 ** a\n",
    "b"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0ead9321-d5f8-4652-a0b9-50b059950c15",
   "metadata": {},
   "source": [
    "* With arrays."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "id": "58f72ae3-2ab8-4b74-a1c9-46d3a0b3ed73",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2., 2., 2., 2.])"
      ]
     },
     "execution_count": 97,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b = np.ones(4) + 1\n",
    "b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "id": "cf6bd274-928f-455b-b4ed-269eab60271e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 2, 3, 4])"
      ]
     },
     "execution_count": 98,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "id": "8c396266-3107-4d82-8af5-8bd99cb6e0ea",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-1.,  0.,  1.,  2.])"
      ]
     },
     "execution_count": 99,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a - b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "id": "f677cbe0-8eca-4fc5-ac5f-e5678cc6f352",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2., 4., 6., 8.])"
      ]
     },
     "execution_count": 100,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a * b # Note: it is not a scalar product."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c253e41c-0fa4-4c95-b751-6fe7295d82e8",
   "metadata": {},
   "source": [
    "* These operations are much faster than when implemented in pure Python."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "id": "889e79c6-ba45-4185-bed1-b9f4a787a554",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "32.8 µs ± 8.65 µs per loop (mean ± std. dev. of 7 runs, 10,000 loops each)\n"
     ]
    }
   ],
   "source": [
    "a = np.arange(10000)\n",
    "%timeit a + 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "id": "19605afd-57a3-4c68-89d9-1eafd595990e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.62 ms ± 895 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n"
     ]
    }
   ],
   "source": [
    "l = range(10000)\n",
    "%timeit [i+1 for i in l]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bf962194-021c-43ab-9751-2bf4ab820988",
   "metadata": {},
   "source": [
    "* Note: Array multiplication is not matrices multiplication"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "id": "4804ae01-e7da-41d3-87a6-ec1a72689b97",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1., 1., 1.],\n",
       "       [1., 1., 1.],\n",
       "       [1., 1., 1.]])"
      ]
     },
     "execution_count": 103,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c = np.ones((3, 3))\n",
    "c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "id": "4017efce-4948-4b60-a170-db3a6a03564b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1., 1., 1.],\n",
       "       [1., 1., 1.],\n",
       "       [1., 1., 1.]])"
      ]
     },
     "execution_count": 104,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c * c"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d8851474-b57f-418f-9a6c-68f62751a790",
   "metadata": {},
   "source": [
    "* For matrix multiplication:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "id": "cd5a4be0-6992-4a66-8729-5f9544b90a5f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[3., 3., 3.],\n",
       "       [3., 3., 3.],\n",
       "       [3., 3., 3.]])"
      ]
     },
     "execution_count": 105,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c.dot(c)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1aecd2a5-cb99-4c46-ac27-9414fe2f97e8",
   "metadata": {},
   "source": [
    "### Comparing arrays"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "id": "27b53077-6989-4cf1-a83f-806f1b9591ba",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([False,  True, False,  True])"
      ]
     },
     "execution_count": 106,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.array([1, 2, 3, 4])\n",
    "b = np.array([4, 2, 2, 4])\n",
    "a == b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "id": "bfd0ca43-3678-4e93-9d53-1303f3460a5a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([False, False,  True, False])"
      ]
     },
     "execution_count": 107,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a > b"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ebee6fa1-0243-449c-8c60-c7cac1af17aa",
   "metadata": {},
   "source": [
    "* Comparing the entire array."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "id": "4d70d366-61f5-4c79-8e32-cad299c6306a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 108,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c = np.array([1, 2, 3, 4])\n",
    "np.array_equal(a, c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "id": "e707e76d-4901-4737-9af3-3668602b8903",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 109,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.array_equal(a, b)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "77b8e56d-7574-4496-a1d6-2652ccc61708",
   "metadata": {},
   "source": [
    "### Logical operations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "id": "ece3a5f0-8155-45e9-822e-56fdd33688ee",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ True,  True,  True, False])"
      ]
     },
     "execution_count": 110,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.array([1, 1, 0, 0], dtype=bool)\n",
    "b = np.array([1, 0, 1, 0], dtype=bool)\n",
    "np.logical_or(a, b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "id": "765cdd0a-d48a-44a2-842e-00fbd2089f39",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ True, False, False, False])"
      ]
     },
     "execution_count": 111,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.logical_and(a, b)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "da919e8c-491d-46e5-99df-d27c5f465d09",
   "metadata": {},
   "source": [
    "### Transcendental functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "id": "497e6caa-5f17-4a15-a592-9fe75be544cb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16,\n",
       "       17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33,\n",
       "       34, 35, 36, 37, 38, 39])"
      ]
     },
     "execution_count": 112,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.arange(40)\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "id": "8f641b89-0ff6-457c-bdbd-42ff265dae71",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.        ,  0.84147098,  0.90929743,  0.14112001, -0.7568025 ,\n",
       "       -0.95892427, -0.2794155 ,  0.6569866 ,  0.98935825,  0.41211849,\n",
       "       -0.54402111, -0.99999021, -0.53657292,  0.42016704,  0.99060736,\n",
       "        0.65028784, -0.28790332, -0.96139749, -0.75098725,  0.14987721,\n",
       "        0.91294525,  0.83665564, -0.00885131, -0.8462204 , -0.90557836,\n",
       "       -0.13235175,  0.76255845,  0.95637593,  0.27090579, -0.66363388,\n",
       "       -0.98803162, -0.40403765,  0.55142668,  0.99991186,  0.52908269,\n",
       "       -0.42818267, -0.99177885, -0.64353813,  0.29636858,  0.96379539])"
      ]
     },
     "execution_count": 113,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sin_a = np.sin(a)\n",
    "sin_a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "id": "5e9477c0-cee6-4061-ad43-1566d7e219b5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.        ,  0.54030231, -0.41614684, -0.9899925 , -0.65364362,\n",
       "        0.28366219,  0.96017029,  0.75390225, -0.14550003, -0.91113026,\n",
       "       -0.83907153,  0.0044257 ,  0.84385396,  0.90744678,  0.13673722,\n",
       "       -0.75968791, -0.95765948, -0.27516334,  0.66031671,  0.98870462,\n",
       "        0.40808206, -0.54772926, -0.99996083, -0.53283302,  0.42417901,\n",
       "        0.99120281,  0.64691932, -0.29213881, -0.96260587, -0.74805753,\n",
       "        0.15425145,  0.91474236,  0.83422336, -0.01327675, -0.84857027,\n",
       "       -0.90369221, -0.12796369,  0.76541405,  0.95507364,  0.26664293])"
      ]
     },
     "execution_count": 114,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cos_a = np.cos(a)\n",
    "cos_a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "id": "6ac2bcc0-b199-4ff1-9aeb-d1cde434aa76",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\joaof\\AppData\\Local\\Temp\\ipykernel_11604\\3627395186.py:1: RuntimeWarning: divide by zero encountered in log\n",
      "  log_a = np.log(a)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([      -inf, 0.        , 0.69314718, 1.09861229, 1.38629436,\n",
       "       1.60943791, 1.79175947, 1.94591015, 2.07944154, 2.19722458,\n",
       "       2.30258509, 2.39789527, 2.48490665, 2.56494936, 2.63905733,\n",
       "       2.7080502 , 2.77258872, 2.83321334, 2.89037176, 2.94443898,\n",
       "       2.99573227, 3.04452244, 3.09104245, 3.13549422, 3.17805383,\n",
       "       3.21887582, 3.25809654, 3.29583687, 3.33220451, 3.36729583,\n",
       "       3.40119738, 3.4339872 , 3.4657359 , 3.49650756, 3.52636052,\n",
       "       3.55534806, 3.58351894, 3.61091791, 3.63758616, 3.66356165])"
      ]
     },
     "execution_count": 115,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "log_a = np.log(a)\n",
    "log_a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "id": "52184e9f-bf55-4609-877b-b2fb4e7499e2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x2dfc17f0190>]"
      ]
     },
     "execution_count": 116,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(a, sin_a)\n",
    "plt.plot(a, cos_a)\n",
    "plt.plot(a, log_a)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c91756f7-ed71-47ca-b2ac-f712b21d747c",
   "metadata": {},
   "source": [
    "* Matrix transposition"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "id": "075b7991-a7f3-444e-8270-2ed72d81a6fa",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0., 1., 1.],\n",
       "       [0., 0., 1.],\n",
       "       [0., 0., 0.]])"
      ]
     },
     "execution_count": 117,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Creates an array. \"triu\" only keeps the upper diagonal of the matrix.\n",
    "a = np.triu(np.ones((3,3)), 1) \n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "id": "d9dc3ed0-62f3-4843-91b7-b4cb70490059",
   "metadata": {},
   "outputs": [],
   "source": [
    "b = a.T # Transposition of a."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "20a67c37-ca23-4645-9f2a-763753cc0bb7",
   "metadata": {},
   "source": [
    "* Note: The result of the transposition is a vision."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "id": "f320af41-54e8-4638-9d5f-ddacba2a2f42",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 119,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.may_share_memory(a, b)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c2cc5be4-96da-4f61-aa74-004c486a577a",
   "metadata": {},
   "source": [
    "## Reductions\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9b8faf7d-92f9-49b5-9d63-ee5bba199417",
   "metadata": {},
   "source": [
    "<img src='figures/axis.png' style=\"height:300px\">\n",
    "<center>Fonte: [2].</center>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0244a26d-0258-44fd-b73a-002f9223a814",
   "metadata": {},
   "source": [
    "### Sum"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "id": "965269b8-63e6-4ddf-af20-47732c1045a4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 2, 3, 4])"
      ]
     },
     "execution_count": 120,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.array([1, 2, 3, 4])\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "id": "1bf65e9a-eb64-46b1-81ca-a61e493ad9ec",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10"
      ]
     },
     "execution_count": 121,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a.sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "id": "bdaf2a8d-0509-4eab-a44d-2ef92d0a37e7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10"
      ]
     },
     "execution_count": 122,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum(a)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3cfa12e1-4bf9-4471-8cc0-7f770dbefaa1",
   "metadata": {},
   "source": [
    "* Sum of rows and columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "id": "31afa84d-7a6c-4356-95dd-81c15d2a6378",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 1],\n",
       "       [2, 2]])"
      ]
     },
     "execution_count": 123,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.array([[1, 1],\n",
    "              [2, 2]])\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "id": "db0a4a13-dfe1-4e6d-9bd3-68c14a7e9e83",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6"
      ]
     },
     "execution_count": 124,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "id": "66a7bc66-bc62-4f01-bd7e-3a8f1639d4e6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([3, 3])"
      ]
     },
     "execution_count": 125,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.sum(axis=0) # lines (first dimension)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "id": "7ca1ba03-d529-4ee9-ad82-2c8f9fd7551e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2, 4])"
      ]
     },
     "execution_count": 126,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.sum(axis=1) # columns (second dimension)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e981c710-70b0-46ad-9546-06c83f560a18",
   "metadata": {},
   "source": [
    "* Other reductions work the same way."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ecdc8987-5088-44f2-990a-3db73dcc6e08",
   "metadata": {},
   "source": [
    "### Extremes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "id": "8953ecb1-e6b6-4231-bcd8-9d8cb933b38e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 127,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.array([2, 5, 1, 3])\n",
    "x.min()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "id": "46e5feb7-5fec-4253-ab90-268ef707dd00",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5"
      ]
     },
     "execution_count": 128,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.max()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "id": "d4c17994-bef3-4929-a924-bf4a83c832a0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 129,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.argmin()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "id": "91a74342-111a-4123-8a6c-8cf8331f1fdc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 130,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.argmax()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9a347dca-70e5-4b14-b855-9d20a295c72f",
   "metadata": {},
   "source": [
    "### Logical reductions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "id": "9b57dddc-0251-4a65-ab20-878fcba0214c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 131,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.all([True, True, False])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "id": "8fd51629-204b-401b-9603-88572532738b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 132,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.all([True, True, True])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "id": "4859e9d8-a275-470b-b51a-a62158641364",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 133,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.any([True, True, False])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "id": "d01a58c5-4a0a-477d-9c91-342ac409e27b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 134,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.any([False, False, False])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0ff7bb4e-3027-4689-ae7c-71eda7a5e804",
   "metadata": {},
   "source": [
    "### Statistics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "id": "c196f6cb-fcfa-47cf-a6b8-4899824cfb68",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.75"
      ]
     },
     "execution_count": 135,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.array([2, 5, 1, 3])\n",
    "x.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "id": "5fb4bb6b-208f-431c-9d71-8637f21531b4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.479019945774904"
      ]
     },
     "execution_count": 136,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.std()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "id": "84af2187-dc7f-47e9-8430-3552919c3d40",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.5"
      ]
     },
     "execution_count": 137,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.median(x) "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b0dffeea-5157-4d49-8809-180ffec8d6e9",
   "metadata": {},
   "source": [
    "## *Broadcasting*"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fd1785e3-485e-4e0e-939e-0eef11a0a886",
   "metadata": {},
   "source": [
    "* Basic operations in Python are performed point-by-point.\n",
    "* To do this, the arrays must be the same size.\n",
    "* However, it is possible to operate arrays with different sizes\n",
    "     * If Python can transform these arrays so that they have the same size."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f30c16e7-7873-4977-83d0-333c4f5fb69b",
   "metadata": {},
   "source": [
    "<img src='figures/broadcasting.png' style=\"height:400px\">\n",
    "<center>Fonte: [2].</center>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 138,
   "id": "d4df7c0f-9853-4de0-b22a-6aef4815d7b8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  0,  0],\n",
       "       [10, 10, 10],\n",
       "       [20, 20, 20],\n",
       "       [30, 30, 30]])"
      ]
     },
     "execution_count": 138,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.tile(np.arange(0, 40, 10), (3, 1)).T\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 139,
   "id": "d43b74a7-8098-4869-b7b4-5ee4ce6a9fce",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 1, 1])"
      ]
     },
     "execution_count": 139,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b = np.array([1, 1, 1])\n",
    "b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "id": "4d56d032-5df7-4203-b409-0bd9f27d160b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1,  1,  1],\n",
       "       [11, 11, 11],\n",
       "       [21, 21, 21],\n",
       "       [31, 31, 31]])"
      ]
     },
     "execution_count": 140,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a + b"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2c90d376-7537-41c8-b416-6243a86c072a",
   "metadata": {},
   "source": [
    "* Obs.: Broadcasting has already been used without us knowing."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 141,
   "id": "e5a6e39e-1de6-481d-9e1a-7281234ddf54",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1., 1., 1., 1., 1.],\n",
       "       [1., 1., 1., 1., 1.],\n",
       "       [1., 1., 1., 1., 1.],\n",
       "       [1., 1., 1., 1., 1.]])"
      ]
     },
     "execution_count": 141,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.ones((4, 5))\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "id": "e25c69d5-e189-4458-b8e4-579ca54bac0f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[2., 2., 2., 2., 2.],\n",
       "       [1., 1., 1., 1., 1.],\n",
       "       [1., 1., 1., 1., 1.],\n",
       "       [1., 1., 1., 1., 1.]])"
      ]
     },
     "execution_count": 142,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[0] = 2\n",
    "a"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ed7d0d27-788d-4c96-b50a-2b5c2bb70f5c",
   "metadata": {},
   "source": [
    "* Adding new dimensions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "id": "f5a9ad14-c681-4f35-81c6-0f519d78e072",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0, 10, 20, 30])"
      ]
     },
     "execution_count": 143,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.arange(0, 40, 10)\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 144,
   "id": "2df9d297-d75d-45da-b02b-ccf5e18389b9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 (4,)\n"
     ]
    }
   ],
   "source": [
    "print(a.ndim, a.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "id": "69f86a88-483b-42de-8a47-de3a9c6e2a2d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0],\n",
       "       [10],\n",
       "       [20],\n",
       "       [30]])"
      ]
     },
     "execution_count": 145,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = a[:, np.newaxis] # adds a new axis: 1D -> 2D \n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "id": "15079d3d-2d47-4e0b-9692-05135706dfd7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2 (4, 1)\n"
     ]
    }
   ],
   "source": [
    "print(a.ndim, a.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "id": "bf28c17a-9334-420e-8a1b-2fca890e0d80",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 1, 1])"
      ]
     },
     "execution_count": 147,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "id": "8b00f792-62d6-4424-9ca0-acceffabfd6f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1,  1,  1],\n",
       "       [11, 11, 11],\n",
       "       [21, 21, 21],\n",
       "       [31, 31, 31]])"
      ]
     },
     "execution_count": 148,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a + b"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d54d6385-5d39-4474-ab3c-74d2e275f58f",
   "metadata": {},
   "source": [
    "## Manipulating the shape of arrangements"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "12406d80-cf27-4576-9e2c-642c0fdc29c4",
   "metadata": {},
   "source": [
    "### Flattening"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "id": "950f7534-d104-4f3a-a974-c8ac75d387ab",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3],\n",
       "       [4, 5, 6]])"
      ]
     },
     "execution_count": 149,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.array([[1, 2, 3], [4, 5, 6]])\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 150,
   "id": "f190030f-e4ec-45f2-822e-fecb262f0f0b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 2, 3, 4, 5, 6])"
      ]
     },
     "execution_count": 150,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a.ravel()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e1976128-8b43-464c-84b1-2cf13acc0f7f",
   "metadata": {},
   "source": [
    "### Reshaping"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 151,
   "id": "f1c6fb23-447c-46e4-a404-9de71f8c67a3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3],\n",
       "       [4, 5, 6]])"
      ]
     },
     "execution_count": 151,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 152,
   "id": "cfdfdce2-ee6f-49d8-bace-39633271e8ba",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2, 3)"
      ]
     },
     "execution_count": 152,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 153,
   "id": "0ac1a509-2144-444e-bbe4-246e70b2335e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 2, 3, 4, 5, 6])"
      ]
     },
     "execution_count": 153,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b = a.ravel()\n",
    "b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 154,
   "id": "52ebbc5f-2f7b-4191-b3c0-b308da705498",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(6,)"
      ]
     },
     "execution_count": 154,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 155,
   "id": "084e3789-9bd3-4d56-891a-2ced3b7efc05",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3],\n",
       "       [4, 5, 6]])"
      ]
     },
     "execution_count": 155,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c = b.reshape(2, -1)\n",
    "c"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e305efdc-e690-49da-9d5e-08bc9e5f8b1a",
   "metadata": {},
   "source": [
    "* **Careful!** np.reshape can return a view or a copy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 156,
   "id": "ec64ae5b-437b-4f40-97f2-16d0d34c7633",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[99,  2,  3],\n",
       "       [ 4,  5,  6]])"
      ]
     },
     "execution_count": 156,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c[0, 0] = 99 # visão\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 157,
   "id": "c93ce7b9-c27e-4b02-a63d-171c6fa8003f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[99,  4,  2],\n",
       "       [ 5,  3,  6]])"
      ]
     },
     "execution_count": 157,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d = c.T.reshape(2,3)\n",
    "d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 158,
   "id": "bd30169f-2eb1-4047-b060-c1b6a0470f99",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[99,  2,  3],\n",
       "       [ 4,  5,  6]])"
      ]
     },
     "execution_count": 158,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d[1, 1] = 99 # cópia\n",
    "c"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c3cf3044-20a6-42e5-912b-c0f035df00f3",
   "metadata": {},
   "source": [
    "## Sorting"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "db6b922b-1985-4822-a905-d2979edb6fe4",
   "metadata": {},
   "source": [
    "### *In-place*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 159,
   "id": "0f8ac4ba-c366-4f1f-b405-27826d1fc51d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4, 3, 5],\n",
       "       [1, 2, 1]])"
      ]
     },
     "execution_count": 159,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.array([[4, 3, 5],\n",
    "              [1, 2, 1]])\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 160,
   "id": "ac57b4de-ad3b-46ed-be0c-5c652138a1c3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[3, 4, 5],\n",
       "       [1, 1, 2]])"
      ]
     },
     "execution_count": 160,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a.sort() # Sort each line individually. Same as a.sort(axis=1)\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 161,
   "id": "f61e0e0b-9aac-4dc9-a565-16819d4bd71b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 1, 2],\n",
       "       [3, 4, 5]])"
      ]
     },
     "execution_count": 161,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a.sort(axis=0) # Sort each column individually\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 162,
   "id": "c6006c2b-99ba-4870-aad3-53e4e43bae45",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4, 3, 5],\n",
       "       [1, 2, 1]])"
      ]
     },
     "execution_count": 162,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.array([[4, 3, 5],\n",
    "              [1, 2, 1]])\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 163,
   "id": "dde404d1-7af4-415d-a221-83098c34e07c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[3, 4, 5],\n",
       "       [1, 1, 2]])"
      ]
     },
     "execution_count": 163,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b = np.sort(a)\n",
    "b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 164,
   "id": "6b04fe16-874d-4dc9-8ba1-ea3736ba3fc7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 1, 2],\n",
       "       [3, 4, 5]])"
      ]
     },
     "execution_count": 164,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c = np.sort(b, axis=0) # Ordena as colunas\n",
    "c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 165,
   "id": "3fb55552-07ea-4431-b1af-0255a0ef54ec",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([4, 3, 1, 2])"
      ]
     },
     "execution_count": 165,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.array([4, 3, 1, 2])\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 166,
   "id": "3075f13c-dd33-4163-89a4-1cdad2d96f40",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2, 3, 1, 0], dtype=int64)"
      ]
     },
     "execution_count": 166,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "j = np.argsort(a)\n",
    "j"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 167,
   "id": "8b9b54ee-74f8-4752-8a19-d66d29db56fa",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 2, 3, 4])"
      ]
     },
     "execution_count": 167,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[j]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "536fa9f3-337a-4f4f-8f0c-ac30736e724d",
   "metadata": {},
   "source": [
    "## Reading and writing text files"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 168,
   "id": "f94df961-2654-4d21-bbe3-b51901e3e739",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1900., 30000.,  4000., 48300.],\n",
       "       [ 1901., 47200.,  6100., 48200.],\n",
       "       [ 1902., 70200.,  9800., 41500.],\n",
       "       [ 1902., 77400., 35200., 38200.]])"
      ]
     },
     "execution_count": 168,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = np.array([[1900.,   30e3,    4e3, 48300],\n",
    "                 [1901., 47.2e3,  6.1e3, 48200],\n",
    "                 [1902., 70.2e3,  9.8e3, 41500],\n",
    "                 [1902., 77.4e3, 35.2e3, 38200]])\n",
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 169,
   "id": "6a8f49fa-c0d2-465b-979f-880d091218e8",
   "metadata": {},
   "outputs": [],
   "source": [
    "np.savetxt('data.txt', data)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "40b056ef-9761-4dc7-a949-4122b53385ec",
   "metadata": {},
   "source": [
    "### Reading a 2D array from a text file."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 170,
   "id": "802597c6-3cc4-4626-ac01-75fee2d3736b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1900., 30000.,  4000., 48300.],\n",
       "       [ 1901., 47200.,  6100., 48200.],\n",
       "       [ 1902., 70200.,  9800., 41500.],\n",
       "       [ 1902., 77400., 35200., 38200.]])"
      ]
     },
     "execution_count": 170,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_2 = np.loadtxt('data.txt')\n",
    "data_2"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9d8edef6-48a6-4556-9a45-df39459c2bb3",
   "metadata": {},
   "source": [
    "## Bibliography\n",
    "---\n",
    "\n",
    "* **Scipy Lecture Notes**.\n",
    "    * Available in: http://www.scipy-lectures.org/ \n",
    "* NumPy documentation.\n",
    "    * http://docs.scipy.org/\n",
    "* Introduction to NumPy (SciPy 2015).\n",
    "    * https://github.com/enthought/Numpy-Tutorial-SciPyConf-2015 \n",
    "    * Note: Includes Matplotlib."
   ]
  }
 ],
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