# tfp.experimental.substrates.jax.math.interp_regular_1d_grid

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

Given reference values, this function computes a piecewise linear interpolant and evaluates it on a new set of 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.

If rank(y_ref) > 1, then dimension axis indexes C reference values of a shape y_ref.shape[:axis] + y_ref.shape[axis + 1:] Tensor.

If rank(x) > 1, then the output is obtained by effectively flattening x, interpolating along axis, then expanding the result to shape y_ref.shape[:axis] + x.shape + y_ref.shape[axis + 1:].

These shape semantics are equivalent to scipy.interpolate.interp1d.

x Numeric Tensor The x-coordinates of the interpolated output values.
x_ref_min Scalar Tensor of same dtype as x. The minimum value of the (implicitly defined) reference x_ref.
x_ref_max Scalar Tensor of same dtype as x. The maximum value of the (implicitly defined) reference x_ref.
y_ref N-D Tensor (N > 0) of same dtype as x. The reference output values.
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: 'interp_regular_1d_grid'.

y_interp Interpolation between members of y_ref, at points x. Tensor of same dtype as x, and shape y.shape[:axis] + x.shape + y.shape[axis + 1:]

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

#### Examples

Interpolate a function of one variable:

y_ref = tf.exp(tf.linspace(start=0., stop=10., num=200))

interp_regular_1d_grid(
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 matrix-valued function of one variable:

mat_0 = [[1., 0.], [0., 1.]]
mat_1 = [[0., -1], [1, 0]]
y_ref = [mat_0, mat_1]

# Get three output matrices at once.
tfp.math.interp_regular_1d_grid(
x=[0., 0.5, 1.], x_ref_min=0., x_ref_max=1., y_ref=y_ref, axis=0)
==> [mat_0, 0.5 * mat_0 + 0.5 * mat_1, mat_1]

Interpolate a scalar valued function, and get a matrix of results:

y_ref = tf.exp(tf.linspace(start=0., stop=10., num=200))
x = [[1.1, 1.2], [2.1, 2.2]]
tfp.math.interp_regular_1d_grid(x, x_ref_min=0., x_ref_max=10., y_ref=y_ref)
==> tf.exp(x)

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)

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)]