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# NumPy | triu Method

NumPy
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schedule Jul 1, 2022
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Numpy's `triu(~)` method returns the upper triangle of a matrix as a new Numpy array.

# Parameters

1. `a` | `array_like`

The array from which to extract the upper triangle.

2. `k`link | `number` | `optional`

The number of diagonals to exclude or include.

A positive value for `k` represents exclusion. `k=1` means that the main diagonal is excluded. `k=2` means that the main diagonal and the diagonal on top are excluded.

A negative value for `k` represents inclusion. `k=-1` means that we include an additional diagonal below the main diagonal.

By default, `k=0`, which means that a perfect upper triangle is returned.

# Return value

A new Numpy array containing the upper triangle of the provided input array.

Like almost all arrays returned Numpy's methods, the returned array of `triu(~)` is copied, that is, modifying this returned array will not have an impact on the original input array - the original input array is left intact.

# Examples

## Basic usage

To get the upper triangle as a new Numpy array:

``` x = np.array([[1, 2, 3], [4 ,5, 6], [7, 8, 9]])np.triu(x) array([[1, 2, 3], [0, 5, 6], [0, 0, 9]]) ```

## Specifying a positive k

To exclude the main diagonal by setting `k=1`:

``` x = np.array([[1, 2, 3], [4 ,5, 6], [7, 8, 9]])np.triu(x, k=1) array([[0, 2, 3], [0, 0, 6], [0, 0, 0]]) ```

To exclude the next diagonal as well, set `k=2`:

``` x = np.array([[1, 2, 3], [4 ,5, 6], [7, 8, 9]])np.triu(x, k=2) array([[0, 0, 3], [0, 0, 0], [0, 0, 0]]) ```

## Specifying a negative k

To include an additional diagonal, set `k=-1`:

``` x = np.array([[1, 2, 3], [4 ,5, 6], [7, 8, 9]])np.triu(x, k=-1) array([[1, 2, 3], [4, 5, 6], [0, 8, 9]]) ```