gradient

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gradient#

class saiunit.math.gradient(f, *varargs, axis=None, edge_order=None)#

Computes the gradient of a scalar field.

Return the gradient of an N-dimensional array.

The gradient is computed using second order accurate central differences in the interior points and either first or second order accurate one-sides (forward or backwards) differences at the boundaries. The returned gradient hence has the same shape as the input array.

Parameters:

  • f (Array | ndarray | bool | number | bool | int | float | complex | saiunit.Quantity) – An N-dimensional array containing samples of a scalar function.

  • varargs (Array | ndarray | bool | number | bool | int | float | complex | saiunit.Quantity) –

    Spacing between f values. Default unitary spacing for all dimensions. Spacing can be specified using:

    1. single scalar to specify a sample distance for all dimensions.

    2. N scalars to specify a constant sample distance for each dimension. i.e. dx, dy, dz, …

    3. N arrays to specify the coordinates of the values along each dimension of F. The length of the array must match the size of the corresponding dimension

    4. Any combination of N scalars/arrays with the meaning of 2. and 3.

    If axis is given, the number of varargs must equal the number of axes. Default: 1.

  • edge_order (int | None) – Gradient is calculated using N-th order accurate differences at the boundaries. Default: 1.

  • axis (int | Sequence[int] | None) – Gradient is calculated only along the given axis or axes The default (axis = None) is to calculate the gradient for all the axes of the input array. axis may be negative, in which case it counts from the last to the first axis.

Returns:

gradient – A list of ndarrays (or a single ndarray if there is only one dimension) corresponding to the derivatives of f with respect to each dimension. Each derivative has the same shape as f.

Return type:

Array | list[Array] | saiunit.Quantity | list[saiunit.Quantity]

Examples

>>> import jax.numpy as jnp
>>> import saiunit.math as sumath
>>> f = jnp.array([1., 2., 4., 7., 11.])
>>> sumath.gradient(f)
Array([1. , 1.5, 2.5, 3.5, 4. ], dtype=float32)
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