Numpy.ipynb

{
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Index\n",
    "* [The Basics](#thebasics)\n",
    "* [Shape Manipulation](#shapemanipulation)\n",
    "* [Copies and Views](#copiesnviews)\n",
    "* [Broadcasting Rules](#broadcastingrules)\n",
    "* [Advanced Indexing and Tricks](#advancedindexing)\n",
    "* [Linear Algebra](#linearalgebra)\n",
    "* [Tricks and Tips](#tricksntips)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'1.18.4'"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "np.__version__"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id=\"thebasics\"></a>\n",
    "## The Basics\n",
    "\n",
    "Numpy's array class is called ```ndarray```, also known by the alias ```array```. Note that ```np.array``` is not the same as Standard Python Library class ```array.array```.\n",
    "\n",
    "### Important Attributes\n",
    "- ```ndarray.ndim```\n",
    "- ```ndarray.shape```\n",
    "- ```ndarray.size```\n",
    "- ```ndarray.dtype```\n",
    "- ```ndarray.data```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a:\n",
      "[[[10]\n",
      "  [12]\n",
      "  [14]\n",
      "  [16]\n",
      "  [18]]\n",
      "\n",
      " [[20]\n",
      "  [22]\n",
      "  [24]\n",
      "  [26]\n",
      "  [28]]]\n",
      "\n",
      "type of a:\n",
      "<class 'numpy.ndarray'>\n",
      "\n",
      "ndim of a:\n",
      "3\n",
      "\n",
      "shape of a:\n",
      "(2, 5, 1)\n",
      "\n",
      "size of a:\n",
      "10\n",
      "\n",
      "dtype of a:\n",
      "int64\n",
      "\n",
      "b:\n",
      "[1.3 2.6 3.7]\n",
      "\n",
      "dtype of b:\n",
      "float64\n",
      "\n",
      "c:\n",
      "[[0.76495447 0.70306371]\n",
      " [0.62643073 0.94684424]\n",
      " [0.84711915 0.67685197]]\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# ARRAY CREATION\n",
    "a = np.arange(10,30,2).reshape(2,5,1)\n",
    "\n",
    "print(f\"a:\\n{a}\\n\")\n",
    "print(f\"type of a:\\n{type(a)}\\n\")\n",
    "print(f\"ndim of a:\\n{a.ndim}\\n\")\n",
    "print(f\"shape of a:\\n{a.shape}\\n\")\n",
    "print(f\"size of a:\\n{a.size}\\n\")\n",
    "print(f\"dtype of a:\\n{a.dtype}\\n\")\n",
    "\n",
    "b = np.array([1.3, 2.6, 3.7])\n",
    "print(f\"b:\\n{b}\\n\")\n",
    "print(f\"dtype of b:\\n{b.dtype}\\n\")\n",
    "\n",
    "c = np.random.rand(3,2)\n",
    "print(f\"c:\\n{c}\\n\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "b:\n",
      "[[1 2]\n",
      " [3 4]]\n",
      "\n",
      "dim of b:\n",
      "2\n",
      "\n",
      "shape of b:\n",
      "(2, 2)\n",
      "\n",
      "c:\n",
      "[[[ 7.]\n",
      "  [ 8.]]\n",
      "\n",
      " [[ 9.]\n",
      "  [10.]]\n",
      "\n",
      " [[11.]\n",
      "  [12.]]]\n",
      "\n",
      "dim of c:\n",
      "3\n",
      "\n",
      "shape of c:\n",
      "(3, 2, 1)\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# array transforms sequences of sequences into 2D arrays\n",
    "# sequences of sequences of sequences into 3D arrays\n",
    "b = np.array([(1, 2), (3, 4)]) \n",
    "print(f\"b:\\n{b}\\n\")\n",
    "print(f\"dim of b:\\n{b.ndim}\\n\")\n",
    "print(f\"shape of b:\\n{b.shape}\\n\")\n",
    "\n",
    "c = np.array([([7], [8]), ([9], [10]), ([11], [12])], dtype=float) \n",
    "print(f\"c:\\n{c}\\n\")\n",
    "print(f\"dim of c:\\n{c.ndim}\\n\")\n",
    "print(f\"shape of c:\\n{c.shape}\\n\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.+0.j 0.+0.j 0.+0.j 0.+0.j]\n",
      " [0.+0.j 0.+0.j 0.+0.j 0.+0.j]\n",
      " [0.+0.j 0.+0.j 0.+0.j 0.+0.j]]\n",
      "[[[1 1 1]\n",
      "  [1 1 1]]\n",
      "\n",
      " [[1 1 1]\n",
      "  [1 1 1]]\n",
      "\n",
      " [[1 1 1]\n",
      "  [1 1 1]]\n",
      "\n",
      " [[1 1 1]\n",
      "  [1 1 1]]\n",
      "\n",
      " [[1 1 1]\n",
      "  [1 1 1]]]\n",
      "[[[ 7.]\n",
      "  [ 8.]\n",
      "  [ 9.]]\n",
      "\n",
      " [[10.]\n",
      "  [11.]\n",
      "  [12.]]]\n"
     ]
    }
   ],
   "source": [
    "print(np.zeros((3,4), dtype=complex))\n",
    "print(np.ones((5,2,3), dtype=int))\n",
    "print(np.empty((2,3,1))) # default is float64"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.        , 0.44879895, 0.8975979 , 1.34639685, 1.7951958 ],\n",
       "       [2.24399475, 2.6927937 , 3.14159265, 3.5903916 , 4.03919055],\n",
       "       [4.48798951, 4.93678846, 5.38558741, 5.83438636, 6.28318531]])"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from numpy import pi\n",
    "\n",
    "# Linspace takes the min value, max value and no. of elements we want\n",
    "# divide the space equally for us\n",
    "np.linspace(0, 2*pi, 15).reshape(3, 5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Basic Operations\n",
    "\n",
    "Arithmetic operators on arrays apply **elementwise**. A new array is created and filled with the result. \n",
    "\n",
    "For example: product operator ```*``` operates elementwise in NumPy arrays. Matrix product can be performed using ```@``` operator or the ```dot``` function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a:\n",
      "[[0 1]\n",
      " [2 3]]\n",
      "b:\n",
      "[[1. 1.]\n",
      " [1. 1.]]\n",
      "a - b:\n",
      "[[-1.  0.]\n",
      " [ 1.  2.]]\n",
      "\n",
      "a * b:\n",
      "[[0. 1.]\n",
      " [2. 3.]]\n",
      "\n",
      "a <= 5:\n",
      "[[ True  True]\n",
      " [ True  True]]\n",
      "\n",
      "Matrix product using @:\n",
      "[[1. 1.]\n",
      " [5. 5.]]\n",
      "\n",
      "using dot:\n",
      "[[1. 1.]\n",
      " [5. 5.]]\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([[1., 2.],\n",
       "       [3., 4.]])"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.arange(4).reshape(2,2)\n",
    "b = np.ones((2,2))\n",
    "\n",
    "print(f\"a:\\n{a}\\nb:\\n{b}\\na - b:\\n{a-b}\\n\")\n",
    "print(f\"a * b:\\n{a*b}\\n\")\n",
    "print(f\"a <= 5:\\n{a<=5}\\n\")\n",
    "\n",
    "print(f\"Matrix product using @:\\n{a@b}\\n\")\n",
    "print(f\"using dot:\\n{a.dot(b)}\\n\")\n",
    "\n",
    "b += a\n",
    "b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 219,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0 1 2]\n",
      " [3 4 5]]\n",
      "\n",
      "column sum: axis=0\n",
      "[3 5 7]\n",
      "\n",
      "row sum: axis=1\n",
      "[ 3 12]\n",
      "\n",
      "min of each row:\n",
      "[0 3]\n",
      "\n",
      "cumulative sum along each row:\n",
      "[[ 0  1  3]\n",
      " [ 3  7 12]]\n",
      "\n",
      "mean of each col:\n",
      "[1.5 2.5 3.5]\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Sum\n",
    "a = np.arange(6).reshape(2,3)\n",
    "print(a)\n",
    "\n",
    "col_sum = a.sum(axis=0) # sum of each column\n",
    "row_sum = a.sum(axis=1) # sum of each row\n",
    "print(f\"\\ncolumn sum: axis=0\\n{col_sum}\\n\")\n",
    "print(f\"row sum: axis=1\\n{row_sum}\\n\")\n",
    "\n",
    "min_of_row = a.min(axis=1) # min of each row\n",
    "print(f\"min of each row:\\n{min_of_row}\\n\")\n",
    "\n",
    "cum_sum = a.cumsum(axis=1) # cumulative sum along each row\n",
    "print(f\"cumulative sum along each row:\\n{cum_sum}\\n\")\n",
    "\n",
    "avg_col = a.mean(axis=0) # mean of each col\n",
    "print(f\"mean of each col:\\n{avg_col}\\n\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Indexing, slicing and iterating"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a:\n",
      "[[7 4 1 4]\n",
      " [4 5 5 1]\n",
      " [2 0 0 5]\n",
      " [2 4 3 6]\n",
      " [2 2 3 3]\n",
      " [8 2 5 5]]\n",
      "\n",
      "first row: a[0]\n",
      "[7 4 1 4]\n",
      "\n",
      "second till third row: a[1:3]\n",
      "[[4 5 5 1]\n",
      " [2 0 0 5]]\n",
      "\n",
      "third col: a[:,2]\n",
      "[1 5 0 3 3 5]\n",
      "\n",
      "first col till third col: a[:,:3]\n",
      "[[7 4 1]\n",
      " [4 5 5]\n",
      " [2 0 0]\n",
      " [2 4 3]\n",
      " [2 2 3]\n",
      " [8 2 5]]\n",
      "\n",
      "even num row: a[1:6:2]\n",
      "[[4 5 5 1]\n",
      " [2 4 3 6]\n",
      " [8 2 5 5]]\n",
      "\n",
      "a:\n",
      "[[7 4 1 4]\n",
      " [4 5 5 1]\n",
      " [2 0 0 5]\n",
      " [2 4 3 6]\n",
      " [2 2 3 3]\n",
      " [8 2 5 5]]\n",
      "\n",
      "odd num col: a[:,0:4:2]\n",
      "[[7 1]\n",
      " [4 5]\n",
      " [2 0]\n",
      " [2 3]\n",
      " [2 3]\n",
      " [8 5]]\n",
      "\n",
      "even num idx elements: a[1:6:2,1:4:2]\n",
      "[[5 1]\n",
      " [4 6]\n",
      " [2 5]]\n",
      "\n",
      "reverse a: a[::-1]\n",
      "[[8 2 5 5]\n",
      " [2 2 3 3]\n",
      " [2 4 3 6]\n",
      " [2 0 0 5]\n",
      " [4 5 5 1]\n",
      " [7 4 1 4]]\n",
      "\n",
      "last third to fifth row: a[-5:-2]\n",
      "[[4 5 5 1]\n",
      " [2 0 0 5]\n",
      " [2 4 3 6]]\n",
      "\n"
     ]
    }
   ],
   "source": [
    "a = np.random.randint(9, size=(6,4))\n",
    "\n",
    "print(f\"a:\\n{a}\\n\")\n",
    "print(f\"first row: a[0]\\n{a[0]}\\n\")\n",
    "print(f\"second till third row: a[1:3]\\n{a[1:3]}\\n\")\n",
    "print(f\"third col: a[:,2]\\n{a[:,2]}\\n\")\n",
    "print(f\"first col till third col: a[:,:3]\\n{a[:,:3]}\\n\")\n",
    "print(f\"even num row: a[1:6:2]\\n{a[1:6:2]}\\n\")\n",
    "\n",
    "print(f\"a:\\n{a}\\n\")\n",
    "print(f\"odd num col: a[:,0:4:2]\\n{a[:,0:4:2]}\\n\")\n",
    "print(f\"even num idx elements: a[1:6:2,1:4:2]\\n{a[1:6:2,1:4:2]}\\n\")\n",
    "print(f\"reverse a: a[::-1]\\n{a[::-1]}\\n\")\n",
    "print(f\"last third to fifth row: a[-5:-2]\\n{a[-5:-2]}\\n\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id=\"shapemanipulation\"></a>\n",
    "## Shape Manipulation\n",
    "\n",
    "### Changing the shape of array\n",
    "* ```reshape```\n",
    "* ```ravel```\n",
    "* ```transpose```\n",
    "* ```resize```\n",
    "* ```vstack```\n",
    "* ```hstack```\n",
    "* ```concatenate```\n",
    "* ```hsplit```\n",
    "* ```vsplit```\n",
    "\n",
    "The ```reshape``` function returns its argument with a modified shape, whereas the ```resize``` method modified the array itself."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 201,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1. 1. 1.]\n",
      " [1. 1. 1.]\n",
      " [1. 1. 1.]\n",
      " [1. 1. 1.]\n",
      " [0. 0. 0.]\n",
      " [0. 0. 0.]]\n",
      "[[0.3062563  0.59499114]\n",
      " [0.01513637 0.11232361]]\n",
      "\n",
      "add extra dimension:\n",
      "[[[0.3062563  0.59499114]\n",
      "  [0.01513637 0.11232361]]](1, 2, 2)\n"
     ]
    }
   ],
   "source": [
    "b = np.ones((3,4))\n",
    "b.resize(6,3)\n",
    "print(b)\n",
    "\n",
    "a = np.random.rand(2,2)\n",
    "print(a)\n",
    "extra_dim = a[None,:]\n",
    "print(f\"\\nadd extra dimension:\\n{extra_dim}{extra_dim.shape}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 186,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a:\n",
      "[[4.64410575e-01 3.07544601e-01 5.18033352e-01 5.98523524e-01]\n",
      " [7.65630672e-01 7.95722557e-01 8.18135722e-01 2.60016175e-01]\n",
      " [5.11082587e-01 1.72819773e-01 1.47962561e-01 2.58445712e-04]]\n",
      "\n",
      "reshape to (6,2):\n",
      "[[4.64410575e-01 3.07544601e-01]\n",
      " [5.18033352e-01 5.98523524e-01]\n",
      " [7.65630672e-01 7.95722557e-01]\n",
      " [8.18135722e-01 2.60016175e-01]\n",
      " [5.11082587e-01 1.72819773e-01]\n",
      " [1.47962561e-01 2.58445712e-04]]\n",
      "\n",
      "using (4,-1):\n",
      "[[4.64410575e-01 3.07544601e-01 5.18033352e-01]\n",
      " [5.98523524e-01 7.65630672e-01 7.95722557e-01]\n",
      " [8.18135722e-01 2.60016175e-01 5.11082587e-01]\n",
      " [1.72819773e-01 1.47962561e-01 2.58445712e-04]]\n",
      "\n",
      "flatten:\n",
      "[4.64410575e-01 3.07544601e-01 5.18033352e-01 5.98523524e-01\n",
      " 7.65630672e-01 7.95722557e-01 8.18135722e-01 2.60016175e-01\n",
      " 5.11082587e-01 1.72819773e-01 1.47962561e-01 2.58445712e-04]\n",
      "\n",
      "transpose:\n",
      "[[4.64410575e-01 7.65630672e-01 5.11082587e-01]\n",
      " [3.07544601e-01 7.95722557e-01 1.72819773e-01]\n",
      " [5.18033352e-01 8.18135722e-01 1.47962561e-01]\n",
      " [5.98523524e-01 2.60016175e-01 2.58445712e-04]]\n",
      "\n",
      "resize a to (2,2):\n",
      "[[0.46441057 0.3075446 ]\n",
      " [0.51803335 0.59852352]]\n",
      "\n"
     ]
    }
   ],
   "source": [
    "a = np.random.rand(3,4)\n",
    "a_resize = np.resize(a, (2,2))\n",
    "\n",
    "print(f\"a:\\n{a}\\n\")\n",
    "print(f\"reshape to (6,2):\\n{a.reshape(6,2)}\\n\")\n",
    "print(f\"using (4,-1):\\n{a.reshape(4,-1)}\\n\")\n",
    "print(f\"flatten:\\n{a.ravel()}\\n\")\n",
    "print(f\"transpose:\\n{a.T}\\n\")\n",
    "print(f\"resize a to (2,2):\\n{a_resize}\\n\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 220,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a:\n",
      "[[1. 1.]\n",
      " [1. 1.]]\n",
      "\n",
      "b:\n",
      "[[0. 0.]\n",
      " [0. 0.]]\n",
      "\n",
      "vstack a,b:\n",
      "[[1. 1.]\n",
      " [1. 1.]\n",
      " [0. 0.]\n",
      " [0. 0.]]\n",
      "\n",
      "hstack b,a:\n",
      "[[0. 0. 1. 1.]\n",
      " [0. 0. 1. 1.]]\n",
      "\n",
      "c:\n",
      "[[-10 -11]]\n",
      "\n",
      "d:\n",
      "[[0.97427294 0.83711985]\n",
      " [0.84042664 0.04809956]]\n",
      "\n",
      "concatenate c,d axis=0:\n",
      "[[-10.         -11.        ]\n",
      " [  0.97427294   0.83711985]\n",
      " [  0.84042664   0.04809956]]\n",
      "\n",
      "concatenate d,c axis=0:\n",
      "[[  0.97427294   0.83711985]\n",
      " [  0.84042664   0.04809956]\n",
      " [-10.         -11.        ]]\n",
      "\n",
      "concatenate d,cT axis=1:\n",
      "[[  0.97427294   0.83711985 -10.        ]\n",
      " [  0.84042664   0.04809956 -11.        ]]\n",
      "\n",
      "concatenate axis=None:\n",
      "[-10.         -11.           0.97427294   0.83711985   0.84042664\n",
      "   0.04809956]\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Stacking together different arrays\n",
    "a = np.ones((2,2))\n",
    "b = np.zeros((2,2))\n",
    "\n",
    "print(f\"a:\\n{a}\\n\")\n",
    "print(f\"b:\\n{b}\\n\")\n",
    "print(f\"vstack a,b:\\n{np.vstack((a,b))}\\n\")\n",
    "print(f\"hstack b,a:\\n{np.hstack((b,a))}\\n\")\n",
    "\n",
    "c = np.array([[-10, -11]])\n",
    "d = np.random.rand(2,2)\n",
    "print(f\"c:\\n{c}\\n\")\n",
    "print(f\"d:\\n{d}\\n\")\n",
    "print(f\"concatenate c,d axis=0:\\n{np.concatenate((c,d), axis=0)}\\n\")\n",
    "print(f\"concatenate d,c axis=0:\\n{np.concatenate((d,c), axis=0)}\\n\")\n",
    "print(f\"concatenate d,cT axis=1:\\n{np.concatenate((d,c.T), axis=1)}\\n\")\n",
    "print(f\"concatenate axis=None:\\n{np.concatenate((c,d), axis=None)}\\n\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 227,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a:\n",
      "[[0.         0.14285714]\n",
      " [0.28571429 0.42857143]\n",
      " [0.57142857 0.71428571]\n",
      " [0.85714286 1.        ]]\n",
      "\n",
      "hsplit into 2:\n",
      "[array([[0.        ],\n",
      "       [0.28571429],\n",
      "       [0.57142857],\n",
      "       [0.85714286]]), array([[0.14285714],\n",
      "       [0.42857143],\n",
      "       [0.71428571],\n",
      "       [1.        ]])]\n",
      "\n",
      "vsplit into 4:\n",
      "[array([[0.        , 0.14285714]]), array([[0.28571429, 0.42857143]]), array([[0.57142857, 0.71428571]]), array([[0.85714286, 1.        ]])]\n",
      "\n"
     ]
    }
   ],
   "source": [
    "a = np.linspace(0,1,8).reshape(4,2)\n",
    "hsplit_a = np.hsplit(a,2)\n",
    "vsplit_a = np.vsplit(a,4)\n",
    "\n",
    "print(f\"a:\\n{a}\\n\")\n",
    "print(f\"hsplit into 2:\\n{hsplit_a}\\n\")\n",
    "print(f\"vsplit into 4:\\n{vsplit_a}\\n\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id=\"copiesnviews\"></a>\n",
    "## Copies and Views\n",
    "When operating and manipulating arrays, the data is sometimes copied into a new array and **sometimes not**. There are 3 cases:\n",
    "* No Copy at All\n",
    "* View or Shallow Copy\n",
    "* Deep Copy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 233,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n",
      "a:\n",
      "[[0.    0.125 0.25 ]\n",
      " [0.375 0.5   0.625]\n",
      " [0.75  0.875 1.   ]]\n",
      "\n",
      "after modified:\n",
      "[[-1.     0.125  0.25 ]\n",
      " [ 0.375  0.5    0.625]\n",
      " [ 0.75   0.875  1.   ]]\n",
      "\n",
      "b after modified: exact the same as a\n",
      "[[-1.     0.125  0.25 ]\n",
      " [ 0.375  0.5    0.625]\n",
      " [ 0.75   0.875  1.   ]]\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# NO COPY AT ALL\n",
    "a = np.linspace(0, 1, 9).reshape(3,3)\n",
    "b = a # no new object is created\n",
    "print(b is a) # a and b are 2 names for the same ndarray object\n",
    "\n",
    "print(f\"a:\\n{a}\\n\")\n",
    "a[0,0] = -1\n",
    "print(f\"after modified:\\n{a}\\n\")\n",
    "print(f\"b after modified: exact the same as a\\n{b}\\n\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 250,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1. 1.]\n",
      " [1. 1.]]\n",
      "False\n",
      "\n",
      "after modified:\n",
      "[[0. 1.]\n",
      " [1. 1.]]\n",
      "\n",
      "c after modified: exact the same as a\n",
      "[[0. 1.]\n",
      " [1. 1.]]\n",
      "\n",
      "a after c's reshape to 4,1: No change\n",
      "[[0. 1.]\n",
      " [1. 1.]]\n",
      "\n",
      "a after c's value change:\n",
      "[[-1.  1.]\n",
      " [ 1.  1.]]\n",
      "\n",
      "a after value of d changed:\n",
      "[[100.   1.]\n",
      " [100.   1.]]\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# VIEW OR SHALLOW COPY\n",
    "a = np.ones((2,2))\n",
    "c = a.view()\n",
    "\n",
    "print(c)\n",
    "print(c is a) # c is a view of the data owned by a\n",
    "\n",
    "a[0][0] = 0\n",
    "print(f\"\\nafter modified:\\n{a}\\n\")\n",
    "print(f\"c after modified: exact the same as a\\n{c}\\n\")\n",
    "\n",
    "c = c.reshape((4,1))\n",
    "print(f\"a after c's reshape to 4,1: No change\\n{a}\\n\")\n",
    "\n",
    "c[0,0] = -1\n",
    "print(f\"a after c's value change:\\n{a}\\n\")\n",
    "\n",
    "d = a[:, 0]\n",
    "d[:] = 100 # d[:] is a view of d.\n",
    "print(f\"a after value of d changed:\\n{a}\\n\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 256,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "False\n",
      "False\n",
      "\n",
      "k:\n",
      "[[  0.   0.   0.   0.   0.]\n",
      " [  0.   0.   0.   0.   0.]\n",
      " [  0.   0.   0.   0.   0.]\n",
      " [100. 100. 100. 100. 100.]\n",
      " [  0.   0.   0.   0.   0.]]\n",
      "\n",
      "a after k[3] = 100:\n",
      "[[0. 0. 0. 0. 0.]\n",
      " [0. 0. 0. 0. 0.]\n",
      " [0. 0. 0. 0. 0.]\n",
      " [0. 0. 0. 0. 0.]\n",
      " [0. 0. 0. 0. 0.]]\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# DEEP COPY\n",
    "a = np.zeros((5,5))\n",
    "k = a.copy()\n",
    "\n",
    "print(k is a) # a new array object k with new data is created\n",
    "print(k.base is a) # k doesn't share anything with a\n",
    "\n",
    "k[3] = 100\n",
    "print(f\"\\nk:\\n{k}\\n\")\n",
    "print(f\"a after k[3] = 100:\\n{a}\\n\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id=\"broadcastingrules\"></a>\n",
    "## Broadcasting Rules\n",
    "\n",
    "Broadcasting allows universal functions to deal in a meaningful way with inputs that do not have exactly the same shape.\n",
    "\n",
    "### First Rule\n",
    "> If all input arrays do not have the same number of dimensions, a \"1\" will be repeatedly prepended to the shapes of the smaller arrays until all the arrays have the same number of dimensions\n",
    "\n",
    "### Second Rule\n",
    "> Arrays with size of 1 along a particular dimension act as if they had the size of the array with the largest shape along that dimension. The value of the array element is assumed to be the same along that dimension for the \"boradcast\" array.\n",
    "\n",
    "After applying these two rules of broadcasting, the sizes of all arrays must match."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 266,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a:\n",
      "[[[ 0  1]\n",
      "  [ 2  3]\n",
      "  [ 4  5]]\n",
      "\n",
      " [[ 6  7]\n",
      "  [ 8  9]\n",
      "  [10 11]]]\n",
      "\n",
      "b:\n",
      "[[0 1]\n",
      " [2 3]\n",
      " [4 5]]\n",
      "\n",
      "a+b:\n",
      "[[[ 0  2]\n",
      "  [ 4  6]\n",
      "  [ 8 10]]\n",
      "\n",
      " [[ 6  8]\n",
      "  [10 12]\n",
      "  [14 16]]]\n",
      "\n"
     ]
    }
   ],
   "source": [
    "a = np.arange(12).reshape((2,3,2))\n",
    "b = np.arange(6).reshape((3,2))\n",
    "\n",
    "print(f\"a:\\n{a}\\n\")\n",
    "print(f\"b:\\n{b}\\n\")\n",
    "print(f\"a+b:\\n{a+b}\\n\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id=\"advancedindexing\"></a>\n",
    "## Advanced Indexing and Tricks\n",
    "Arrays can be indexed by arrays of integers and arrays of booleans."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 270,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a:\n",
      "[ 0  1  4  9 16 25]\n",
      "\n",
      "a with i idx: [1,3,5]\n",
      "[ 1  9 25]\n",
      "\n",
      "a bidimensional:[[1,2], [3,5]]:\n",
      "[[ 1  4]\n",
      " [ 9 25]]\n",
      "\n"
     ]
    }
   ],
   "source": [
    "a = np.arange(6)**2\n",
    "i = np.array([1, 3, 5])\n",
    "j = np.array([[1,2], [3,5]])\n",
    "\n",
    "print(f\"a:\\n{a}\\n\")\n",
    "print(f\"a with i idx: [1,3,5]\\n{a[i]}\\n\")\n",
    "print(f\"a bidimensional:[[1,2], [3,5]]:\\n{a[j]}\\n\")b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 274,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a:\n",
      "[[0.    0.125 0.25 ]\n",
      " [0.375 0.5   0.625]\n",
      " [0.75  0.875 1.   ]]\n",
      "\n",
      "b:\n",
      "[[ True  True  True]\n",
      " [ True  True False]\n",
      " [False False False]]\n",
      "\n",
      "a[b]:\n",
      "[0.    0.125 0.25  0.375 0.5  ]\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Indexing with Boolean Arrays\n",
    "a = np.linspace(0,1,9).reshape((3,3))\n",
    "b = a <= 0.5\n",
    "\n",
    "print(f\"a:\\n{a}\\n\")\n",
    "print(f\"b:\\n{b}\\n\")\n",
    "print(f\"a[b]:\\n{a[b]}\\n\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 283,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7ff2d38cfa60>"
      ]
     },
     "execution_count": 283,
     "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": [
    "# Using boolean indexing to generate image of Mandelbrot set\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "def mandelbrot(h, w, maxit=20):\n",
    "    \"\"\"Display image of mandelbrot\"\"\"\n",
    "    y, x = np.ogrid[-1.4:1.4:h*1j, -2:0.8:w*1j]\n",
    "    c = x + y * 1j\n",
    "    z = c\n",
    "    divtime = maxit + np.zeros(z.shape, dtype=int)\n",
    "    \n",
    "    for i in range(maxit):\n",
    "        z = z**2 + c\n",
    "        diverge = z*np.conj(z) > 2**2          # who is diverging\n",
    "        div_now = diverge & (divtime == maxit) # who is diverging now\n",
    "        divtime[div_now] = i                   # when diverge\n",
    "        z[diverge] = 3                         # avoid diverging too much\n",
    "    \n",
    "    return divtime\n",
    "\n",
    "plt.imshow(mandelbrot(500,500))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id=\"linearalgebra\"></a>\n",
    "## Linear Algebra"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 293,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a:\n",
      "[[0 1]\n",
      " [2 3]]\n",
      "\n",
      "a.T:\n",
      "[[0 2]\n",
      " [1 3]]\n",
      "\n",
      "a transpose:\n",
      "[[0 2]\n",
      " [1 3]]\n",
      "\n",
      "inverse of a: inv\n",
      "[[-1.5  0.5]\n",
      " [ 1.   0. ]]\n",
      "\n",
      "pseudo inverse: pinv\n",
      "[[-1.50000000e+00  5.00000000e-01]\n",
      " [ 1.00000000e+00  4.21097322e-17]]\n",
      "\n",
      "I:\n",
      "[[1. 0. 0.]\n",
      " [0. 1. 0.]\n",
      " [0. 0. 1.]]\n",
      "\n",
      "diagonal sum: np.trace\n",
      "3.0\n",
      "\n",
      "flip I:\n",
      "[[0. 0. 1.]\n",
      " [0. 1. 0.]\n",
      " [1. 0. 0.]]\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Simple Array Operations\n",
    "a = np.arange(4).reshape((2,2))\n",
    "\n",
    "print(f\"a:\\n{a}\\n\")\n",
    "print(f\"a.T:\\n{a.T}\\n\")\n",
    "print(f\"a transpose:\\n{a.transpose()}\\n\")\n",
    "print(f\"inverse of a: inv\\n{np.linalg.inv(a)}\\n\")\n",
    "print(f\"pseudo inverse: pinv\\n{np.linalg.pinv(a)}\\n\")\n",
    "\n",
    "I = np.eye(3) # identity matrix\n",
    "print(f\"I:\\n{I}\\n\")\n",
    "print(f\"diagonal sum: np.trace\\n{np.trace(I)}\\n\")\n",
    "I_flip = np.fliplr(I)\n",
    "print(f\"flip I:\\n{I_flip}\\n\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id=\"tricksntips\"></a>\n",
    "## Tricks and Tips"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 295,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(5, 2, 5)\n",
      "[[[ 0  1  2  3  4]\n",
      "  [ 5  6  7  8  9]]\n",
      "\n",
      " [[10 11 12 13 14]\n",
      "  [15 16 17 18 19]]\n",
      "\n",
      " [[20 21 22 23 24]\n",
      "  [25 26 27 28 29]]\n",
      "\n",
      " [[30 31 32 33 34]\n",
      "  [35 36 37 38 39]]\n",
      "\n",
      " [[40 41 42 43 44]\n",
      "  [45 46 47 48 49]]]\n"
     ]
    }
   ],
   "source": [
    "# \"Automatic\" Reshaping\n",
    "a = np.arange(50)\n",
    "b = a.reshape((5,2,-1))\n",
    "print(b.shape)\n",
    "print(b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 299,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7ff2bc148ee0>]"
      ]
     },
     "execution_count": 299,
     "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": [
    "# Histograms\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Build a vector of 10000 normal deviates with variance 0.5^2 and mu 5\n",
    "rg = np.random.default_rng(1)\n",
    "mu, sigma = 2, 0.5\n",
    "v = rg.normal(mu, sigma, 10000)\n",
    "\n",
    "plt.hist(v, bins=50, density=1)\n",
    "(n, bins) = np.histogram(v, bins=50, density=True)\n",
    "plt.plot(.5*(bins[1:]+bins[:-1]), n)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.8.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}