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# NumPy | tri method

Programming
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Python
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NumPy
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Documentation
schedule Mar 10, 2022
Last updated
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Numpy's `tri(~)` method creates a 2D Numpy array that represents a lower triangular matrix. The values at and below the main diagonal are filled with 1s, while everywhere else with 0s.

# Parameters

1. `N` | `int`

The number of rows of the resulting array.

2. `M` | `int` | `optional`

The number of columns of the resulting array. By default, `M=N`.

3. `k`link | `int` | `optional`

The number of diagonals to exclude or include.

A positive value for `k` represents inclusion. `k=1` means that we include an additional diagonal on top of main diagonal.

A negative value for `k` represents exclusion. `k=-1` means that the main diagonal is excluded. `k=-2` means that the main diagonal and the diagonal underneath are excluded.

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

4. `dtype` | `string` or `type` | `optional`

The data type of the resulting array. By default, `dtype=float`.

# Return value

A Numpy array representing a lower triangular matrix.

# Examples

## Basic usage

To create a 3 by 3 lower triangular matrix:

``` np.tri(3) array([[ 1., 0., 0.], [ 1., 1., 0.], [ 1., 1., 1.]]) ```

To create a 3 by 4 lower triangular matrix of type `int`:

``` np.tri(3, 4, dtype=int) array([[1, 0, 0, 0], [1, 1, 0, 0], [1, 1, 1, 0]]) ```

## Specifying a positive k

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

``` np.tri(3, k=1, dtype=int) array([[1, 1, 0], [1, 1, 1], [1, 1, 1]]) ```

## Specifying a negative k

To exclude the main diagonal, set `k=-1`:

``` np.tri(3, k=-1) array([[ 0., 0., 0.], [ 1., 0., 0.], [ 1., 1., 0.]]) ```