YouTipNumpy Broadcast
# NumPy Broadcast
Broadcasting is NumPy's way of performing numerical operations on arrays with different shapes. Arithmetic operations on arrays are typically performed element-wise.
If two arrays `a` and `b` have the same shape, i.e., `a.shape == b.shape`, then `a * b` results in the element-wise product of `a` and `b`. This requires the number of dimensions to be the same, and the length of each dimension to be the same.
## Example
```python
import numpy as np
a = np.array([1,2,3,4])
b = np.array([10,20,30,40])
c = a * b
print(c)
Output:
When the two arrays in an operation have different shapes, NumPy automatically triggers the broadcasting mechanism. For example:
## Example
```python
import numpy as np
a = np.array([[0, 0, 0],
[10,10,10],
[20,20,20],
[30,30,30]])
b = np.array([0,1,2])
print(a + b)
Output:
[
]
The image below illustrates how array `b` is broadcast to be compatible with array `a`.
!(#)
Adding a 4x3 two-dimensional array to a one-dimensional array of length 3 is equivalent to repeating array `b` 4 times in the second dimension before performing the operation:
## Example
```python
import numpy as np
a = np.array([[0, 0, 0],
[10,10,10],
[20,20,20],
[30,30,30]])
b = np.array([1,2,3])
bb = np.tile(b, (4, 1)) # Repeat b along each dimension
print(a + bb)
Output:
[
]
**Rules of Broadcasting:**
* All input arrays are aligned with the array having the longest shape. Missing dimensions are padded by adding 1 at the beginning.
* The shape of the output array is the maximum value across each dimension of the input array shapes.
* An input array can be used for computation if its length in a particular dimension is the same as the output array's corresponding dimension or is 1. Otherwise, an error occurs.
* When the length of an input array in a particular dimension is 1, the first value along that dimension is used for all computations along that dimension.
**Simple Understanding:** For two arrays, compare each of their dimensions (ignoring a dimension if one array doesn't have it). The following conditions must be met:
* The arrays have the same shape.
* The values in the current dimension are equal.
* One of the values in the current dimension is 1.
If the conditions are not met, a **"ValueError: frames are not aligned"** exception is raised.