|---|
| [ View source on GitHub](https://github.com/tensorflow/probability/blob/v0.25.0/tensorflow_probability/python/math/interpolation.py#L689-L907) |
Multi-linear interpolation on a rectilinear grid.
tfp.math.batch_interp_rectilinear_nd_grid(
x,
x_grid_points,
y_ref,
axis,
fill_value='constant_extension',
name=None
)
Given \[a batch of\] reference values, this function computes a multi-linear
interpolant and evaluates it on \[a batch of\] new `x` values. This is a
multi-dimensional generalization of [Bilinear Interpolation](https://en.wikipedia.org/wiki/Bilinear_interpolation).
The interpolant is built from reference values indexed by `nd` dimensions
of `y_ref`, starting at `axis`.
The x grid is defined by `1-D` points along each dimension. These points must
be sorted, but may have unequal spacing.
For example, take the case of a `2-D` scalar valued function and no leading
batch dimensions. In this case, `y_ref.shape = [C1, C2]` and `y_ref[i, j]`
is the reference value corresponding to grid point
`[x_grid_points[0][i], x_grid_points[1][j]]`
In the general case, dimensions to the left of `axis` in `y_ref` are broadcast
with leading dimensions in `x`, and `x_grid_points[k]`, `k = 0, ..., nd - 1`.
| ## Args ||
|---|---|
| `x` | Numeric `Tensor` The x-coordinates of the interpolated output values for each batch. Shape `[..., D, nd]`, designating \[a batch of\] `D` coordinates in `nd` space. `D` must be `>= 1` and is not a batch dim. |
| `x_grid_points` | Tuple of dimension points. `x_grid_points[k]` are a shape `[..., Ck]` `Tensor` of the same dtype as `x` that must be sorted along the innermost (-1) axis. These represent \[a batch of\] points defining the `kth` dimension values. |
| `y_ref` | `Tensor` of same `dtype` as `x`. The reference output values. Shape `[..., C1, ..., Cnd, B1,...,BM]`, designating \[a batch of\] reference values indexed by `nd` dimensions, of a shape `[B1,...,BM]` valued function (for `M >= 0`). |
| `axis` | Scalar integer `Tensor`. Dimensions `[axis, axis + nd)` of `y_ref` index the interpolation table. E.g. `3-D` interpolation of a scalar valued function requires `axis=-3` and a `3-D` matrix valued function requires `axis=-5`. |
| `fill_value` | Determines what values output should take for `x` values that are below/above the min/max values in `x_grid_points`. 'constant_extension' ==\> Extend as constant function. Default value: `'constant_extension'` |
| `name` | A name to prepend to created ops. Default value: `'batch_interp_rectilinear_nd_grid'`. |
| ## Returns ||
|---|---|
| `y_interp` | Interpolation between members of `y_ref`, at points `x`. `Tensor` of same `dtype` as `x`, and shape `[..., D, B1, ..., BM].` |
Exceptions will be raised if shapes are statically determined to be wrong.
| ## Raises ||
|---|---|
| `ValueError` | If `rank(x) < 2` |
| `ValueError` | If `axis` is not a scalar. |
| `ValueError` | If `axis + nd > rank(y_ref)`. |
| `ValueError` | If `x_grid_points[k].shape[-1] != y_ref.shape[axis + k]`. |
#### Examples
Interpolate a function of one variable.
x_grid = tf.linspace(0., 1., 20)**2 # Nonlinearly spaced
y_ref = tf.exp(x_grid)
tfp.math.batch_interp_rectilinear_nd_grid(
# x.shape = [3, 1], with the trailing `1` for `1-D`.
x=[[6.0], [0.5], [3.3]], x_grid_points=(x_grid,), y_ref=y_ref, axis=0)
==> approx [exp(6.0), exp(0.5), exp(3.3)]
Interpolate a scalar function of two variables.
x0_grid = tf.linspace(0., 2 * np.pi, num=100),
x1_grid = tf.linspace(0., 2 * np.pi, num=100),
# Build y_ref.
x0s, x1s = tf.meshgrid(x0_grid, x1_grid, indexing='ij')
def func(x0, x1):
return tf.sin(x0) * tf.cos(x1)
y_ref = func(x0s, x1s)
x = np.pi * tf.random.uniform(shape=(10, 2))
tfp.math.batch_interp_regular_nd_grid(x, x_grid_points=(x0_grid, x1_grid),
y_ref, axis=-2)
==> tf.sin(x[:, 0]) * tf.cos(x[:, 1])