# NumPy

[NumPy](http://www.numpy.org) is the fundamental package for scientific computing with Python.

## Basics <a name="basics"></a>

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 basic statistics, linear algebra, histograms, etc.</br>
The most important difference for data science is the ability to do **element-wise calculations** with *NumPy arrays*.

`axis 0` always refers to row </br>
`axis 1` always refers to column

| Operator | Description | Documentation |
| :------------- | :------------- | :--------|
|`np.array([1,2,3])`|1d array|[link](https://docs.scipy.org/doc/numpy/reference/generated/numpy.array.html#numpy.array)|
|`np.array([(1,2,3),(4,5,6)])`|2d array|see above|
|`np.arange(start,stop,step)`|range array|[link](https://docs.scipy.org/doc/numpy/reference/generated/numpy.arange.html)|

| Operators | Description |Documentation|
| :------------- | :------------- |:---------- |
|`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)|
|`np.zeros((1,2))`|Create and array filled with zeros|[link](https://docs.scipy.org/doc/numpy/reference/generated/numpy.zeros.html)|
|`np.ones((1,2))`|Creates an array filled with ones|[link](https://docs.scipy.org/doc/numpy/reference/generated/numpy.ones.html#numpy.ones)|
|`np.random.randint(0, 5, (5,5))`|Creates random array|[link](https://numpy.org/doc/stable/reference/random/generated/numpy.random.randint.html)|
|`np.empty((2,2))`|Creates an empty array|[link](https://docs.scipy.org/doc/numpy/reference/generated/numpy.empty.html)|

### Examples <a name="ex"></a>

import numpy as np

# 1 dimensional
x = np.array([1,2,3])
# 2 dimensional
y = np.array([(1,2,3),(4,5,6)])

x = np.arange(3)
>>> array([0, 1, 2])

y = np.arange(3.0)
>>> array([ 0.,  1.,  2.])

x = np.arange(3,7)
>>> array([3, 4, 5, 6])

y = np.arange(3,7,2)
>>> array([3, 5])

</br>

## Array <a name="arrays"></a>
### Array Properties <a name="props"></a>
|Syntax|Description|Documentation|
|:-------------|:-------------|:-----------|
|`array.shape`|Dimensions (Rows,Columns)|[link](https://docs.scipy.org/doc/numpy/reference/generated/numpy.ndarray.shape.html)|
|`len(array)`|Length of Array|[link](https://docs.python.org/3.5/library/functions.html#len)|
|`array.ndim`|Number of Array Dimensions|[link](https://docs.scipy.org/doc/numpy/reference/generated/numpy.ndarray.ndim.html)|
|`array.size`|Number of Array Elements|[link](https://docs.scipy.org/doc/numpy/reference/generated/numpy.ndarray.size.html)|
|`array.dtype`|Data Type|[link](https://docs.scipy.org/doc/numpy/reference/arrays.dtypes.html)|
|`array.astype(type)`|Converts to Data Type|[link](https://docs.scipy.org/doc/numpy/reference/generated/numpy.ndarray.astype.html)|
|`type(array)`|Type of Array|[link](https://docs.scipy.org/doc/numpy/user/basics.types.html)|

### Copying <a name="gops"></a>
| Operators | Descriptions | Documentation |
| :------------- | :------------- | :----------- |
|`np.copy(array)`|Creates copy of array|[link](https://docs.scipy.org/doc/numpy/reference/generated/numpy.copy.html)|
|`other = array.copy()`|Creates deep copy of array|see above|

## Array Manipulation Routines <a name="man"></a>

### 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 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>

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>

### Combining Arrays <a name="comb"></a>
|Operator|Description|Documentation|
|:---------|:-------|:---------|
|`np.concatenate((a,b),axis=0)`|Concatenates 2 arrays, adds to end|[link](https://docs.scipy.org/doc/numpy/reference/generated/numpy.concatenate.html)|
|`np.vstack((a,b))`|Stack array row-wise|[link](https://docs.scipy.org/doc/numpy/reference/generated/numpy.vstack.html)|
|`np.hstack((a,b))`|Stack array column wise|[link](https://docs.scipy.org/doc/numpy/reference/generated/numpy.hstack.html#numpy.hstack)|

#### Example <a name="array-combine-examples"></a>

import numpy as np
a = np.array([1, 3, 5])
b = np.array([2, 4, 6])

# Stack two arrays row-wise
print(np.vstack((a,b)))
>>> [[1 3 5]
     [2 4 6]]

# Stack two arrays column-wise
print(np.hstack((a,b)))
>>> [1 3 5 2 4 6]

### Shaping Arrays <a name="shape"></a>
|Operator|Description|Documentation|
|:---------|:-------|:------|
|`other = ndarray.flatten()`|Flattens a 2d array to 1d|[link](https://docs.scipy.org/doc/numpy/reference/generated/numpy.ndarray.flatten.html)|
|`ravel`|Return a contiguous flattened array|[link](https://numpy.org/doc/stable/reference/generated/numpy.ravel.html)|
|`reshape`|reshape an array|[link](https://numpy.org/doc/stable/reference/generated/numpy.reshape.html)|
|`resize`|Return a new array with the specified shape|[link](https://numpy.org/doc/stable/reference/generated/numpy.resize.html)|
|`array = np.transpose(other)`</br> `array.T` |Transpose array|[link](https://docs.scipy.org/doc/numpy/reference/generated/numpy.transpose.html)|

</br>

## Mathematics <a name="maths"></a>

### Operations <a name="ops"></a>
| Operator | Description |Documentation|
| :------------- | :------------- |:---------|
|`np.add(x,y)`<br/>`x + y`|Addition|[link](https://docs.scipy.org/doc/numpy/reference/generated/numpy.add.html)|
|`np.substract(x,y)`<br/>`x - y`|Subtraction|[link](https://docs.scipy.org/doc/numpy/reference/generated/numpy.subtract.html#numpy.subtract)|
|`np.divide(x,y)`<br/>`x / y`|Division|[link](https://docs.scipy.org/doc/numpy/reference/generated/numpy.divide.html#numpy.divide)|
|`np.multiply(x,y)`<br/>`x * y`|Multiplication|[link](https://docs.scipy.org/doc/numpy/reference/generated/numpy.multiply.html#numpy.multiply)|
|`np.sqrt(x)`|Square Root|[link](https://docs.scipy.org/doc/numpy/reference/generated/numpy.sqrt.html#numpy.sqrt)|
|`np.sin(x)`|Element-wise sine|[link](https://docs.scipy.org/doc/numpy/reference/generated/numpy.sin.html#numpy.sin)|
|`np.cos(x)`|Element-wise cosine|[link](https://docs.scipy.org/doc/numpy/reference/generated/numpy.cos.html#numpy.cos)|
|`np.log(x)`|Element-wise natural log|[link](https://docs.scipy.org/doc/numpy/reference/generated/numpy.log.html#numpy.log)|
|`np.dot(x,y)`|Dot product, `x @ y`|[link](https://docs.scipy.org/doc/numpy/reference/generated/numpy.dot.html)|

Remember: NumPy array operations work element-wise.

#### Example <a name="operations-examples"></a>

# If a 1d array is added to a 2d array (or the other way), NumPy
# chooses the array with smaller dimension and adds it to the one
# with bigger dimension
a = np.array([1, 2, 3])
b = np.array([(1, 2, 3), (4, 5, 6)])
print(np.add(a, b))
>>> [[2 4 6]
     [5 7 9]]

### Comparison
| Operator | Description | Documentation |
| :------------- | :------------- |:---------|
|`np.array_equal(x,y)`|Array-wise comparison|[link](https://docs.scipy.org/doc/numpy/reference/generated/numpy.array_equal.html)|

#### Example <a name="comparison-example"></a>

# Using comparison operators will create boolean NumPy arrays
z = np.array([1, 2, 3, 4, 5, 6, 7, 8, 9, 10])
c = z < 6
print(c)
>>> [ True  True  True  True  True False False False False False]

### More (Reduction) <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||

</br>