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Linear 1-D interpolation on a regular (constant spacing) grid.

Given [batch of] reference values, this function computes a piecewise linear interpolant and evaluates it on a [batch of] of new x values.

The interpolant is built from C reference values indexed by one dimension of y_ref (specified by the axis kwarg).

If y_ref is a vector, then each value y_ref[i] is considered to be equal to f(x_ref[i]), for C (implicitly defined) reference values between x_ref_min and x_ref_max:

x_ref[i] = x_ref_min + i * (x_ref_max - x_ref_min) / (C - 1),
i = 0, ..., C - 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.

x Numeric Tensor The x-coordinates of the interpolated output values for each batch. Shape broadcasts with [A1, ..., AN, D], N >= 0.
x_ref_min Tensor of same dtype as x. The minimum value of the each batch of the (implicitly defined) reference x_ref. Shape broadcasts with [A1, ..., AN], N >= 0.
x_ref_max Tensor of same dtype as x. The maximum value of the each batch of the (implicitly defined) reference x_ref. Shape broadcasts with [A1, ..., AN], N >= 0.
y_ref Tensor of same dtype as x. The reference output values. y_ref.shape[:axis] broadcasts with the batch shape [A1, ..., AN], and y_ref.shape[axis:] is [C, B1, ..., BM], so the trailing dimensions index C reference values of a rank M Tensor (M >= 0).
axis Scalar Tensor designating the dimension of y_ref that indexes values of the interpolation table. Default value: -1, the rightmost axis.
fill_value Determines what values output should take for x values that are below x_ref_min or above x_ref_max. Tensor or one of the strings 'constant_extension' ==> Extend as constant function. 'extrapolate' ==> Extrapolate in a linear fashion. Default value: 'constant_extension'
fill_value_below Optional override of fill_value for x < x_ref_min.
fill_value_above Optional override of fill_value for x > x_ref_max.
grid_regularizing_transform Optional transformation g which regularizes the implied spacing of the x reference points. In other words, if provided, we assume g(x_ref_i) is a regular grid between g(x_ref_min) and g(x_ref_max).
name A name to prepend to created ops. Default value: 'batch_interp_regular_1d_grid'.

y_interp Interpolation between members of y_ref, at points x. Tensor of same dtype as x, and shape [A1, ..., AN, D, B1, ..., BM]

ValueError If fill_value is not an allowed string.
ValueError If axis is not a scalar.


Interpolate a function of one variable:

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

    x=[6.0, 0.5, 3.3], x_ref_min=0., x_ref_max=10., y_ref=y_ref)
==> approx [exp(6.0), exp(0.5), exp(3.3)]

Interpolate a batch of functions of one variable.

# First batch member is an exponential function, second is a log.
implied_x_ref = [tf.linspace(-3., 3.2, 200), tf.linspace(0.5, 3., 200)]
y_ref = tf.stack(  # Shape [2, 200], 2 batches, 200 reference values per batch
    [tf.exp(implied_x_ref[0]), tf.log(implied_x_ref[1])], axis=0)

x = [[-1., 1., 0.],  # Shape [2, 3], 2 batches, 3 values per batch.
     [1., 2., 3.]]

y = tfp.math.batch_interp_regular_1d_grid(  # Shape [2, 3]
    x_ref_min=[-3., 0.5],
    x_ref_max=[3.2, 3.],

# y[0] approx tf.exp(x[0])
# y[1] approx tf.log(x[1])

Interpolate a function of one variable on a log-spaced grid:

x_ref = tf.exp(tf.linspace(tf.log(1.), tf.log(100000.), num_pts))
y_ref = tf.log(x_ref + x_ref**2)

batch_interp_regular_1d_grid(x=[1.1, 2.2], x_ref_min=1., x_ref_max=100000.,
    y_ref, grid_regularizing_transform=tf.log)
==> [tf.log(1.1 + 1.1**2), tf.log(2.2 + 2.2**2)]