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# NumPy Cheat Sheet
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[NumPy](http://www.numpy.org) is the fundamental package for scientific computing with Python.
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### Installation
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If you don't already have it **installed**, you can do so using Pip or Anaconda:
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```
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$ pip install numpy
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```
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or
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```
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$ conda install numpy
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```
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This cheat sheet acts as a intro to Python for data science.
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## Index
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1. [Basics](#basics)
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- [Placeholders](#place)
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- [Examples](#ex)
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2. [Arrays](#arrays)
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- [Properties](#props)
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- [Copying/Sorting](#gops)
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* [Examples](#array-example)
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- [Array Manipulation](#man)
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* [Adding/Removing Elements](#addrem)
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+ [Examples](#array-elements-examples)
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* [Combining Arrays](#comb)
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+ [Examples](#array-combine-examples)
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* [Splitting Arrays](#split)
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+ [Examples](#array-split-examples)
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* [Shaping](#shape)
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* [Misc](#misc)
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3. [Mathematics](#maths)
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- [Arithmetic Operations](#ops)
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* [Examples](#operations-examples)
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- [Comparison](#comparison)
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* [Examples](#comparison-example)
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- [Basic Statistics](#stats)
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* [Examples](#stats-examples)
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- [More](#more)
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4. [Slicing and Subsetting](#ss)
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- [Examples](#exp)
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5. [Tricks](#tricks)
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6. [Credits](#creds)
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</br>
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## Basics <a name="basics"></a>
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One of the most commonly used functions of NumPy are *NumPy arrays*: The essential difference between *lists* and *NumPy arrays* is functionality and speed. *lists* give you basic operation, but *NumPy* adds FFTs, convolutions, fast searching, basic statistics, linear algebra, histograms, etc.</br>
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The most important difference for data science is the ability to do **element-wise calculations** with *NumPy arrays*.
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`axis 0` always refers to row </br>
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`axis 1` always refers to column
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| Operator | Description | Documentation |
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| :------------- | :------------- | :--------|
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|`np.array([1,2,3])`|1d array|[link](https://docs.scipy.org/doc/numpy/reference/generated/numpy.array.html#numpy.array)|
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|`np.array([(1,2,3),(4,5,6)])`|2d array|see above|
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|`np.arange(start,stop,step)`|range array|[link](https://docs.scipy.org/doc/numpy/reference/generated/numpy.arange.html)|
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### Placeholders <a name="place"></a>
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| Operators | Description |Documentation|
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| :------------- | :------------- |:---------- |
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|`np.linspace(0,2,9)`|Add evenly spaced values btw interval to array of length |[link](https://docs.scipy.org/doc/numpy/reference/generated/numpy.linspace.html)|
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|`np.zeros((1,2))`|Create and array filled with zeros|[link](https://docs.scipy.org/doc/numpy/reference/generated/numpy.zeros.html)|
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|`np.ones((1,2))`|Creates an array filled with ones|[link](https://docs.scipy.org/doc/numpy/reference/generated/numpy.ones.html#numpy.ones)|
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|`np.random.random((5,5))`|Creates random array|[link](https://docs.scipy.org/doc/numpy/reference/generated/numpy.random.random.html)|
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|`np.empty((2,2))`|Creates an empty array|[link](https://docs.scipy.org/doc/numpy/reference/generated/numpy.empty.html)|
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### Examples <a name="ex"></a>
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```python
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import numpy as np
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# 1 dimensional
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x = np.array([1,2,3])
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# 2 dimensional
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y = np.array([(1,2,3),(4,5,6)])
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x = np.arange(3)
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>>> array([0, 1, 2])
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y = np.arange(3.0)
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>>> array([ 0., 1., 2.])
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x = np.arange(3,7)
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>>> array([3, 4, 5, 6])
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y = np.arange(3,7,2)
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>>> array([3, 5])
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```
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</br>
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## Array <a name="arrays"></a>
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### Array Properties <a name="props"></a>
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|Syntax|Description|Documentation|
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|:-------------|:-------------|:-----------|
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|`array.shape`|Dimensions (Rows,Columns)|[link](https://docs.scipy.org/doc/numpy/reference/generated/numpy.ndarray.shape.html)|
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|`len(array)`|Length of Array|[link](https://docs.python.org/3.5/library/functions.html#len)|
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|`array.ndim`|Number of Array Dimensions|[link](https://docs.scipy.org/doc/numpy/reference/generated/numpy.ndarray.ndim.html)|
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|`array.size`|Number of Array Elements|[link](https://docs.scipy.org/doc/numpy/reference/generated/numpy.ndarray.size.html)|
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|`array.dtype`|Data Type|[link](https://docs.scipy.org/doc/numpy/reference/arrays.dtypes.html)|
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|`array.astype(type)`|Converts to Data Type|[link](https://docs.scipy.org/doc/numpy/reference/generated/numpy.ndarray.astype.html)|
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|`type(array)`|Type of Array|[link](https://docs.scipy.org/doc/numpy/user/basics.types.html)|
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### Copying/Sorting <a name="gops"></a>
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| Operators | Descriptions | Documentation |
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| :------------- | :------------- | :----------- |
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|`np.copy(array)`|Creates copy of array|[link](https://docs.scipy.org/doc/numpy/reference/generated/numpy.copy.html)|
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|`other = array.copy()`|Creates deep copy of array|see above|
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|`array.sort()`|Sorts an array|[link](https://docs.scipy.org/doc/numpy/reference/generated/numpy.sort.html)|
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|`array.sort(axis=0)`|Sorts axis of array|see above|
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#### Examples <a name="array-example"></a>
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```python
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import numpy as np
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# Sort sorts in ascending order
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y = np.array([10, 9, 8, 7, 6, 5, 4, 3, 2, 1])
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y.sort()
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print(y)
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>>> [ 1 2 3 4 5 6 7 8 9 10]
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```
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## Array Manipulation Routines <a name="man"></a>
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### Adding or Removing Elements <a name="addrem"></a>
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|Operator|Description|Documentation|
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|:-----------|:--------|:---------|
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|`np.append(a,b)`|Append items to array|[link](https://docs.scipy.org/doc/numpy/reference/generated/numpy.append.html)|
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|`np.insert(array, 1, 2, axis)`|Insert items into array at axis 0 or 1|[link](https://docs.scipy.org/doc/numpy/reference/generated/numpy.insert.html)|
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|`np.resize((2,4))`|Resize array to shape(2,4)|[link](https://docs.scipy.org/doc/numpy/reference/generated/numpy.resize.html)|
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|`np.delete(array,1,axis)`|Deletes items from array|[link](https://docs.scipy.org/doc/numpy/reference/generated/numpy.delete.html)|
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#### Example <a name="array-elements-examples"></a>
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```python
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import numpy as np
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# Append items to array
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a = np.array([(1, 2, 3),(4, 5, 6)])
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b = np.append(a, [(7, 8, 9)])
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print(b)
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>>> [1 2 3 4 5 6 7 8 9]
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# Remove index 2 from previous array
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print(np.delete(b, 2))
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>>> [1 2 4 5 6 7 8 9]
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```
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### Combining Arrays <a name="comb"></a>
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|Operator|Description|Documentation|
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|:---------|:-------|:---------|
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|`np.concatenate((a,b),axis=0)`|Concatenates 2 arrays, adds to end|[link](https://docs.scipy.org/doc/numpy/reference/generated/numpy.concatenate.html)|
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|`np.vstack((a,b))`|Stack array row-wise|[link](https://docs.scipy.org/doc/numpy/reference/generated/numpy.vstack.html)|
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|`np.hstack((a,b))`|Stack array column wise|[link](https://docs.scipy.org/doc/numpy/reference/generated/numpy.hstack.html#numpy.hstack)|
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#### Example <a name="array-combine-examples"></a>
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```python
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import numpy as np
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a = np.array([1, 3, 5])
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b = np.array([2, 4, 6])
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# Stack two arrays row-wise
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print(np.vstack((a,b)))
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>>> [[1 3 5]
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[2 4 6]]
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# Stack two arrays column-wise
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print(np.hstack((a,b)))
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>>> [1 3 5 2 4 6]
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```
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### Splitting Arrays <a name="split"></a>
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|Operator|Description|Documentation|
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|:---------|:-------|:------|
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|`numpy.split()`||[link](https://docs.scipy.org/doc/numpy/reference/generated/numpy.split.html)|
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|`np.array_split(array, 3)`|Split an array in sub-arrays of (nearly) identical size|[link](https://docs.scipy.org/doc/numpy/reference/generated/numpy.array_split.html#numpy.array_split)|
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|`numpy.hsplit(array, 3)`|Split the array horizontally at 3rd index|[link](https://docs.scipy.org/doc/numpy/reference/generated/numpy.hsplit.html#numpy.hsplit)|
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#### Example <a name="array-split-examples"></a>
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```python
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# Split array into groups of ~3
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a = np.array([1, 2, 3, 4, 5, 6, 7, 8])
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print(np.array_split(a, 3))
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>>> [array([1, 2, 3]), array([4, 5, 6]), array([7, 8])]
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```
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### Shaping Arrays <a name="shape"></a>
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##### TODO
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|Operator|Description|Documentation|
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|:---------|:-------|:------|
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|`other = ndarray.flatten()`|Flattens a 2d array to 1d|[link](https://docs.scipy.org/doc/numpy/reference/generated/numpy.ndarray.flatten.html)|
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|numpy.flip()|Flips order of elements in 1D array||
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|np.ndarray[::-1]|Same as above||
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|reshape|||
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|squeeze|||
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|expand_dims|||
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### Misc <a name="misc"></a>
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|Operator|Description|Documentation|
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|:--------|:--------|:--------|
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|`other = ndarray.flatten()`|Flattens a 2d array to 1d|[link](https://docs.scipy.org/doc/numpy/reference/generated/numpy.ndarray.flatten.html)|
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|`array = np.transpose(other)`</br> `array.T` |Transpose array|[link](https://docs.scipy.org/doc/numpy/reference/generated/numpy.transpose.html)|
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|`inverse = np.linalg.inv(matrix)`|Inverse of a given matrix|[link](https://docs.scipy.org/doc/numpy/reference/generated/numpy.linalg.inv.html) |
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</br>
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#### Example <a name="inverse of a matrix"></a>
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```python
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# Find inverse of a given matrix
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>>> np.linalg.inv([[3,1],[2,4]])
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array([[ 0.4, -0.1],
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[-0.2, 0.3]])
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```
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## Mathematics <a name="maths"></a>
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### Operations <a name="ops"></a>
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| Operator | Description |Documentation|
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| :------------- | :------------- |:---------|
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|`np.add(x,y)`<br/>`x + y`|Addition|[link](https://docs.scipy.org/doc/numpy/reference/generated/numpy.add.html)|
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|`np.substract(x,y)`<br/>`x - y`|Subtraction|[link](https://docs.scipy.org/doc/numpy/reference/generated/numpy.subtract.html#numpy.subtract)|
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|`np.divide(x,y)`<br/>`x / y`|Division|[link](https://docs.scipy.org/doc/numpy/reference/generated/numpy.divide.html#numpy.divide)|
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|`np.multiply(x,y)`<br/>`x @ y`|Multiplication|[link](https://docs.scipy.org/doc/numpy/reference/generated/numpy.multiply.html#numpy.multiply)|
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|`np.sqrt(x)`|Square Root|[link](https://docs.scipy.org/doc/numpy/reference/generated/numpy.sqrt.html#numpy.sqrt)|
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|`np.sin(x)`|Element-wise sine|[link](https://docs.scipy.org/doc/numpy/reference/generated/numpy.sin.html#numpy.sin)|
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|`np.cos(x)`|Element-wise cosine|[link](https://docs.scipy.org/doc/numpy/reference/generated/numpy.cos.html#numpy.cos)|
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|`np.log(x)`|Element-wise natural log|[link](https://docs.scipy.org/doc/numpy/reference/generated/numpy.log.html#numpy.log)|
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|`np.dot(x,y)`|Dot product|[link](https://docs.scipy.org/doc/numpy/reference/generated/numpy.dot.html)|
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|
|`np.roots([1,0,-4])`|Roots of a given polynomial coefficients|[link](https://docs.scipy.org/doc/numpy/reference/generated/numpy.roots.html)|
|
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|
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|
Remember: NumPy array operations work element-wise.
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|
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#### Example <a name="operations-examples"></a>
|
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|
```python
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# If a 1d array is added to a 2d array (or the other way), NumPy
|
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|
# chooses the array with smaller dimension and adds it to the one
|
||||||
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# with bigger dimension
|
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a = np.array([1, 2, 3])
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|
b = np.array([(1, 2, 3), (4, 5, 6)])
|
||||||
|
print(np.add(a, b))
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>>> [[2 4 6]
|
||||||
|
[5 7 9]]
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||||||
|
|
||||||
|
# Example of np.roots
|
||||||
|
# Consider a polynomial function (x-1)^2 = x^2 - 2*x + 1
|
||||||
|
# Whose roots are 1,1
|
||||||
|
>>> np.roots([1,-2,1])
|
||||||
|
array([1., 1.])
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# Similarly x^2 - 4 = 0 has roots as x=±2
|
||||||
|
>>> np.roots([1,0,-4])
|
||||||
|
array([-2., 2.])
|
||||||
|
```
|
||||||
|
|
||||||
|
### Comparison
|
||||||
|
| Operator | Description | Documentation |
|
||||||
|
| :------------- | :------------- |:---------|
|
||||||
|
|`==`|Equal|[link](https://docs.python.org/2/library/stdtypes.html)|
|
||||||
|
|`!=`|Not equal|[link](https://docs.python.org/2/library/stdtypes.html)|
|
||||||
|
|`<`|Smaller than|[link](https://docs.python.org/2/library/stdtypes.html)|
|
||||||
|
|`>`|Greater than|[link](https://docs.python.org/2/library/stdtypes.html)|
|
||||||
|
|`<=`|Smaller than or equal|[link](https://docs.python.org/2/library/stdtypes.html)|
|
||||||
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|`>=`|Greater than or equal|[link](https://docs.python.org/2/library/stdtypes.html)|
|
||||||
|
|`np.array_equal(x,y)`|Array-wise comparison|[link](https://docs.scipy.org/doc/numpy/reference/generated/numpy.array_equal.html)|
|
||||||
|
|
||||||
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#### Example <a name="comparison-example"></a>
|
||||||
|
```python
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# Using comparison operators will create boolean NumPy arrays
|
||||||
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z = np.array([1, 2, 3, 4, 5, 6, 7, 8, 9, 10])
|
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|
c = z < 6
|
||||||
|
print(c)
|
||||||
|
>>> [ True True True True True False False False False False]
|
||||||
|
```
|
||||||
|
### Basic Statistics <a name="stats"></a>
|
||||||
|
| Operator | Description | Documentation |
|
||||||
|
| :------------- | :------------- |:--------- |
|
||||||
|
|`np.mean(array)`|Mean|[link](https://docs.scipy.org/doc/numpy/reference/generated/numpy.mean.html#numpy.mean)|
|
||||||
|
|`np.median(array)`|Median|[link](https://docs.scipy.org/doc/numpy/reference/generated/numpy.median.html#numpy.median)|
|
||||||
|
|`array.corrcoef()`|Correlation Coefficient|[link](https://docs.scipy.org/doc/numpy/reference/generated/numpy.corrcoef.html#numpy.corrcoef)|
|
||||||
|
|`np.std(array)`|Standard Deviation|[link](https://docs.scipy.org/doc/numpy/reference/generated/numpy.std.html#numpy.std)|
|
||||||
|
|
||||||
|
#### Example <a name="stats-examples"></a>
|
||||||
|
```python
|
||||||
|
# Statistics of an array
|
||||||
|
a = np.array([1, 1, 2, 5, 8, 10, 11, 12])
|
||||||
|
|
||||||
|
# Standard deviation
|
||||||
|
print(np.std(a))
|
||||||
|
>>> 4.2938910093294167
|
||||||
|
|
||||||
|
# Median
|
||||||
|
print(np.median(a))
|
||||||
|
>>> 6.5
|
||||||
|
```
|
||||||
|
|
||||||
|
|
||||||
|
### More <a name="more"></a>
|
||||||
|
| Operator | Description | Documentation |
|
||||||
|
| :------------- | :------------- |:--------- |
|
||||||
|
|`array.sum()`|Array-wise sum|[link](https://docs.scipy.org/doc/numpy/reference/generated/numpy.sum.html)|
|
||||||
|
|`array.min()`|Array-wise minimum value|[link](https://docs.scipy.org/doc/numpy/reference/generated/numpy.ndarray.min.html)|
|
||||||
|
|`array.max(axis=0)`|Maximum value of specified axis||
|
||||||
|
|`array.cumsum(axis=0)`|Cumulative sum of specified axis|[link](https://docs.scipy.org/doc/numpy/reference/generated/numpy.cumsum.html)|
|
||||||
|
|
||||||
|
</br>
|
||||||
|
|
||||||
|
## Slicing and Subsetting <a name="ss"></a>
|
||||||
|
|Operator|Description|Documentation|
|
||||||
|
| :------------- | :------------- | :------------- |
|
||||||
|
|`array[i]`|1d array at index i|[link](https://docs.scipy.org/doc/numpy/reference/arrays.indexing.html)|
|
||||||
|
|`array[i,j]`|2d array at index[i][j]|see above|
|
||||||
|
|`array[i<4]`|Boolean Indexing, see [Tricks](#tricks)|see above|
|
||||||
|
|`array[0:3]`|Select items of index 0, 1 and 2|see above|
|
||||||
|
|`array[0:2,1]`|Select items of rows 0 and 1 at column 1|see above|
|
||||||
|
|`array[:1]`|Select items of row 0 (equals array[0:1, :])|see above|
|
||||||
|
|`array[1:2, :]`|Select items of row 1|see above|
|
||||||
|
[comment]: <> (|`array[1,...]`|equals array[1,:,:]|see above|)
|
||||||
|
|`array[ : :-1]`|Reverses `array`|see above|
|
||||||
|
|
||||||
|
|
||||||
|
#### Examples <a name="exp"></a>
|
||||||
|
```python
|
||||||
|
b = np.array([(1, 2, 3), (4, 5, 6)])
|
||||||
|
|
||||||
|
# The index *before* the comma refers to *rows*,
|
||||||
|
# the index *after* the comma refers to *columns*
|
||||||
|
print(b[0:1, 2])
|
||||||
|
>>> [3]
|
||||||
|
|
||||||
|
print(b[:len(b), 2])
|
||||||
|
>>> [3 6]
|
||||||
|
|
||||||
|
print(b[0, :])
|
||||||
|
>>> [1 2 3]
|
||||||
|
|
||||||
|
print(b[0, 2:])
|
||||||
|
>>> [3]
|
||||||
|
|
||||||
|
print(b[:, 0])
|
||||||
|
>>> [1 4]
|
||||||
|
|
||||||
|
c = np.array([(1, 2, 3), (4, 5, 6)])
|
||||||
|
d = c[1:2, 0:2]
|
||||||
|
print(d)
|
||||||
|
>>> [[4 5]]
|
||||||
|
|
||||||
|
```
|
||||||
|
|
||||||
|
</br>
|
||||||
|
|
||||||
|
## Tricks <a name="tricks"></a>
|
||||||
|
This is a growing list of examples. Know a good trick? Let me know in a issue or fork it and create a pull request.
|
||||||
|
|
||||||
|
*boolean indexing*
|
||||||
|
```python
|
||||||
|
# Index trick when working with two np-arrays
|
||||||
|
a = np.array([1,2,3,6,1,4,1])
|
||||||
|
b = np.array([5,6,7,8,3,1,2])
|
||||||
|
|
||||||
|
# Only saves a at index where b == 1
|
||||||
|
other_a = a[b == 1]
|
||||||
|
#Saves every spot in a except at index where b != 1
|
||||||
|
other_other_a = a[b != 1]
|
||||||
|
```
|
||||||
|
|
||||||
|
```python
|
||||||
|
import numpy as np
|
||||||
|
x = np.array([4,6,8,1,2,6,9])
|
||||||
|
y = x > 5
|
||||||
|
print(x[y])
|
||||||
|
>>> [6 8 6 9]
|
||||||
|
|
||||||
|
# Even shorter
|
||||||
|
x = np.array([1, 2, 3, 4, 4, 35, 212, 5, 5, 6])
|
||||||
|
print(x[x < 5])
|
||||||
|
>>> [1 2 3 4 4]
|
||||||
|
|
||||||
|
```
|
||||||
|
|
||||||
|
</br>
|
||||||
Reference in New Issue
Block a user