tfp.math.batch_interp_regular_nd_grid

Multi-linear interpolation on a regular (constant spacing) grid.

tfp.math.batch_interp_regular_nd_grid(
    x, x_ref_min, x_ref_max, 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] of new x values.

The interpolant is built from reference values indexed by nd dimensions of y_ref, starting at axis.

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_ref_min[0] + i * (x_ref_max[0] - x_ref_min[0]) / (C1 - 1),
 x_ref_min[1] + j * (x_ref_max[1] - x_ref_min[1]) / (C2 - 1)]

In the general case, dimensions to the left of axis in y_ref are broadcast with leading dimensions in x, x_ref_min, x_ref_max.

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_ref_min`	`Tensor` of same `dtype` as `x`. The minimum values of the (implicitly defined) reference `x_ref`. Shape `[..., nd]`.
`x_ref_max`	`Tensor` of same `dtype` as `x`. The maximum values of the (implicitly defined) reference `x_ref`. Shape `[..., nd]`.
`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 `x_ref_min` or above `x_ref_max`. Scalar `Tensor` or 'constant_extension' ==> Extend as constant function. Default value: `'constant_extension'`
`name`	A name to prepend to created ops. Default value: `'batch_interp_regular_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].`

Raises
`ValueError`	If `rank(x) < 2` is determined statically.
`ValueError`	If `axis` is not a scalar is determined statically.
`ValueError`	If `axis + nd > rank(y_ref)` is determined statically.

Examples

Interpolate a function of one variable.

y_ref = tf.exp(tf.linspace(start=0., stop=10., num=20))

tfp.math.batch_interp_regular_nd_grid(
    # x.shape = [3, 1], x_ref_min/max.shape = [1].  Trailing `1` for `1-D`.
    x=[[6.0], [0.5], [3.3]], x_ref_min=[0.], x_ref_max=[10.], y_ref=y_ref,
    axis=0)
==> approx [exp(6.0), exp(0.5), exp(3.3)]

Interpolate a scalar function of two variables.

x_ref_min = [0., 0.]
x_ref_max = [2 * np.pi, 2 * np.pi]

# Build y_ref.
x0s, x1s = tf.meshgrid(
    tf.linspace(x_ref_min[0], x_ref_max[0], num=100),
    tf.linspace(x_ref_min[1], x_ref_max[1], num=100),
    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_ref_min, x_ref_max, y_ref, axis=-2)
==> tf.sin(x[:, 0]) * tf.cos(x[:, 1])

tfp.math.batch_interp_regular_nd_grid

Args

Returns

Raises

Examples