tfp.math.batch_interp_rectilinear_nd_grid

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.

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])

tfp.math.batch_interp_rectilinear_nd_grid

Args

Returns

Raises

Examples