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{
"cell_type": "markdown",
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"source": [
"# `ndarray` – an N-dimensional array object\n",
"\n",
"`ndarray` allows mathematical operations on whole blocks of data, using a similar syntax to similar operations between [scalar](https://en.wikipedia.org/wiki/Scalar_(mathematics)) elements. In NumPy, there are many different types for describing scalars, mostly based on types from the C language and those compatible with Python.\n",
"\n",
"\n",
"\n",
"**See also:**\n",
"\n",
"* [Array Scalars](https://numpy.org/devdocs/reference/arrays.scalars.html)\n",
"
\n",
"\n",
"\n",
"**Note:**\n",
"\n",
"Whenever this tutorial talks about _array_ or `ndarray`, in most cases it refers to the `ndarray` object.\n",
"
"
]
},
{
"cell_type": "code",
"execution_count": 1,
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"source": [
"import numpy as np"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "f0dbdbe9",
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"source": [
"py_list = [2020, 2021, 20222]\n",
"array_1d = np.array(py_list)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "dab65ddf",
"metadata": {
"execution": {
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"outputs": [
{
"data": {
"text/plain": [
"array([ 2020, 2021, 20222])"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"array_1d"
]
},
{
"cell_type": "markdown",
"id": "b3b0a43c",
"metadata": {},
"source": [
"Nested sequences, such as a list of lists of equal length, can be converted into a multidimensional array:"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "c4ca7f18",
"metadata": {
"execution": {
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"outputs": [],
"source": [
"list_of_lists = [[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12]]\n",
"array_2d = np.array(list_of_lists)"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "5908e6ef",
"metadata": {
"execution": {
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"outputs": [
{
"data": {
"text/plain": [
"array([[ 1, 2, 3, 4],\n",
" [ 5, 6, 7, 8],\n",
" [ 9, 10, 11, 12]])"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"array_2d"
]
},
{
"cell_type": "markdown",
"id": "2ca45895",
"metadata": {},
"source": [
"Since `list_of_lists` was a list with three lists, the NumPy array `array_2d` has two dimensions whose shape is derived from the data. With the attributes [ndim](https://numpy.org/devdocs/reference/generated/numpy.ndarray.ndim.html) and [shape](https://numpy.org/devdocs/reference/generated/numpy.ndarray.shape.html) we can output the number of dimensions and the outline of `array_2d`:"
]
},
{
"cell_type": "code",
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"execution": {
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{
"data": {
"text/plain": [
"2"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"array_2d.ndim"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "3bef667e",
"metadata": {
"execution": {
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"outputs": [
{
"data": {
"text/plain": [
"(3, 4)"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"array_2d.shape"
]
},
{
"cell_type": "markdown",
"id": "1a9267d8",
"metadata": {},
"source": [
"To give you an idea of the syntax, I first create an array of random numbers with five columns and seven `slices`:"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "8a008d03",
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"outputs": [
{
"data": {
"text/plain": [
"array([[0.92924119, 0.56249986, 0.89913907],\n",
" [0.74688464, 0.71027425, 0.11651989],\n",
" [0.45495343, 0.19435449, 0.20933617],\n",
" [0.31051074, 0.99903966, 0.79290766],\n",
" [0.77962503, 0.58949486, 0.85441874],\n",
" [0.36481064, 0.53221103, 0.18984443],\n",
" [0.46607016, 0.54310155, 0.33321979]])"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"rng = np.random.default_rng()\n",
"data = rng.random((7, 3))\n",
"data"
]
},
{
"cell_type": "markdown",
"id": "f3b875e5",
"metadata": {},
"source": [
"`ndarray` is a generic multidimensional container. Each array has a shape, a tuple, which indicates the size of the individual dimensions. With `shape`, I can output the number of rows and columns in an array:"
]
},
{
"cell_type": "markdown",
"id": "c6284a5e",
"metadata": {},
"source": [
"In addition to `np.array`, there are a number of other functions for creating new arrays. [zeros](https://numpy.org/doc/stable/reference/generated/numpy.zeros.html) and [ones](https://numpy.org/doc/stable/reference/generated/numpy.ones.html), for example, create arrays of zeros and ones, respectively, with a specific length or shape. [empty](https://numpy.org/doc/stable/reference/generated/numpy.empty.html) creates an array without initialising its values to a specific value. To create a higher dimensional array using these methods, pass a tuple for the shape:"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "535012fb",
"metadata": {
"execution": {
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"outputs": [
{
"data": {
"text/plain": [
"array([0., 0., 0., 0.])"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.zeros(4)"
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "06c5c70f",
"metadata": {
"execution": {
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"outputs": [
{
"data": {
"text/plain": [
"array([[1., 1., 1., 1.],\n",
" [1., 1., 1., 1.],\n",
" [1., 1., 1., 1.]])"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.ones((3, 4))"
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "b452ec6c",
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"execution": {
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{
"data": {
"text/plain": [
"array([[[0., 0., 0., 0.],\n",
" [0., 0., 0., 0.],\n",
" [0., 0., 0., 0.]],\n",
"\n",
" [[0., 0., 0., 0.],\n",
" [0., 0., 0., 0.],\n",
" [0., 0., 0., 0.]]])"
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
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"source": [
"np.empty((2, 3, 4))"
]
},
{
"cell_type": "markdown",
"id": "7faf6f63",
"metadata": {},
"source": [
"\n",
"\n",
"**Note:**\n",
"\n",
"You may not safely assume that the `np.empty` function returns an array of zeros, as it returns uninitialised memory and may therefore contain garbage values.\n",
"
"
]
},
{
"cell_type": "markdown",
"id": "c11209a9",
"metadata": {},
"source": [
"[arange](https://numpy.org/doc/stable/reference/generated/numpy.arange.html) is an array-valued version of the Built-in Python [range](https://docs.python.org/3/library/functions.html#func-range) function:"
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "91c43273",
"metadata": {
"execution": {
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"outputs": [
{
"data": {
"text/plain": [
"array([0, 1, 2, 3])"
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
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],
"source": [
"np.arange(4)"
]
},
{
"cell_type": "markdown",
"id": "025541bc",
"metadata": {},
"source": [
"Other NumPy standard functions for creating arrays are:\n",
"\n",
"Function | Description\n",
":------- | :----------\n",
"`array` | converts input data (list, tuple, array or other sequence types) into an `ndarray` by either deriving a `dtype` or explicitly specifying a `dtype`; by default, copies the input data into the array\n",
"`asarray` | converts the input to an `ndarray`, but does not copy if the input is already an `ndarray`\n",
"`arange` | like Python built-in `range`, but returns an `ndarray` instead of a list\n",
"`ones`, `ones_like` | `ones` creates an array of 1s in the given form and `dtype`; `ones_like` takes another array and creates an `ones` array in the same form and dtype\n",
"`zeros`, `zeros_like` | like `ones` and `ones_like`, but creates arrays with 0s instead\n",
"`empty`, `empty_like` | creates new arrays by allocating new memory, but does not fill them with values like `ones` and `zeros`\n",
"`full`, `full_like` | creates an array of the given `shape` and `dtype`, setting all values to the given fill value; `full_like` takes another array and creates a filled array with the same `shape` and `dtype`\n",
"`eye`, `identity` | creates a square N × N identity matrix (1s on the diagonal and 0s elsewhere)"
]
}
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