NumPy is a popular Python library used for numerical computations. It provides various mathematical functions and tools for manipulating arrays, which are multi-dimensional data structures that can hold homogeneous data. To add ‘n’ to each element indexed by a second vector using NumPy, we can use the following methods:

#### 1. Using “np.add.at()”:

Here, you first import the NumPy library and then create two random arrays `Z`

and `I`

. Here, `'n'`

is the number that you want to increment in the first vector’s element, whose index is present in the second vector. Then, you can use the `np.add.at()`

function to add the count of each index in `I`

to the corresponding element in `Z`

. This function allows you to specify the indices and values to add and handles duplicates correctly.

#### 2. Using a “for loop”:

Here, you first import the NumPy library and then create two random arrays `Z`

and `I`

. Here, `'n'`

is the number that you want to increment in the first vector’s element, whose index is present in the second vector. You can loop over the indices in `I`

and add `1`

to the corresponding element in `Z`

. This method is less efficient than using `np.add.at()`

, but is more explicit and easier to understand.