> For the complete documentation index, see [llms.txt](https://docs.seldon.ai/alibi-explain/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://docs.seldon.ai/alibi-explain/api-reference/utils/approximation_methods.md).

# alibi.utils.approximation\_methods

## Constants

### `SUPPORTED_RIEMANN_METHODS`

```python
SUPPORTED_RIEMANN_METHODS: list = ['riemann_left', 'riemann_right', 'riemann_middle', 'riemann_trapezoid']
```

Built-in mutable sequence.

If no argument is given, the constructor creates a new empty list. The argument must be an iterable if specified.

### `SUPPORTED_METHODS`

```python
SUPPORTED_METHODS: list = ['riemann_left', 'riemann_right', 'riemann_middle', 'riemann_trapezoid', 'gau...
```

Built-in mutable sequence.

If no argument is given, the constructor creates a new empty list. The argument must be an iterable if specified.

## `Riemann`

*Inherits from:* `Enum`

An enumeration.

## Functions

### `approximation_parameters`

```python
approximation_parameters(method: str) -> Tuple[Callable[[.[<class 'int'>]], List[float]], Callable[[.[<class 'int'>]], List[float]]]
```

Retrieves parameters for the input approximation `method`.

| Name     | Type  | Default | Description                                                                                                                                                                                                              |
| -------- | ----- | ------- | ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ |
| `method` | `str` |         | The name of the approximation method. Currently supported only: `'riemann_*'` and `'gausslegendre`'. Check :py:data:`alibi.utils.approximation_methods.SUPPORTED_RIEMANN_METHODS` for all `'riemann_*'` possible values. |

**Returns**

* Type: `Tuple[Callable[[.[<class 'int'>]], List[float]], Callable[[.[<class 'int'>]], List[float]]]`

### `gauss_legendre_builders`

```python
gauss_legendre_builders() -> Tuple[Callable[[.[<class 'int'>]], List[float]], Callable[[.[<class 'int'>]], List[float]]]
```

`np.polynomial.legendre` function helps to compute step sizes and alpha coefficients using gauss-legendre quadrature rule. Since `numpy` returns the integration parameters in different scales we need to rescale them to adjust to the desired scale.

Gauss Legendre quadrature rule for approximating the integrals was originally proposed by \[Xue Feng and her intern Hauroun Habeeb] (<https://research.fb.com/people/feng-xue/>).

| Name | Type | Default | Description                      |
| ---- | ---- | ------- | -------------------------------- |
| `n`  |      |         | The number of integration steps. |

**Returns**

* Type: `Tuple[Callable[[.[<class 'int'>]], List[float]], Callable[[.[<class 'int'>]], List[float]]]`

### `riemann_builders`

```python
riemann_builders(method: alibi.utils.approximation_methods.Riemann = <Riemann.trapezoid: 4>) -> Tuple[Callable[[.[<class 'int'>]], List[float]], Callable[[.[<class 'int'>]], List[float]]]
```

Step sizes are identical and alphas are scaled in \[0, 1].

| Name     | Type                                        | Default                  | Description                      |
| -------- | ------------------------------------------- | ------------------------ | -------------------------------- |
| `method` | `alibi.utils.approximation_methods.Riemann` | `<Riemann.trapezoid: 4>` | Riemann method: `Riemann.left`   |
| `n`      |                                             |                          | The number of integration steps. |

**Returns**

* Type: `Tuple[Callable[[.[<class 'int'>]], List[float]], Callable[[.[<class 'int'>]], List[float]]]`


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