*Last updated: 2023-03-16.*
# tf_quant_finance.math.interpolation.cubic.interpolate
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Interpolates spline values for the given `x` and the `spline_data`.
```python
tf_quant_finance.math.interpolation.cubic.interpolate(
x, spline_data, optimize_for_tpu=False, dtype=None, name=None
)
```
Constant extrapolation is performed for the values outside the domain
`spline_data.x_data`. This means that for `x > max(spline_data.x_data)`,
`interpolate(x, spline_data) = spline_data.y_data[-1]`
and for `x < min(spline_data.x_data)`,
`interpolate(x, spline_data) = spline_data.y_data[0]`.
For the interpolation formula refer to p.548 of [1].
#### References:
[1]: R. Sedgewick, Algorithms in C, 1990, p. 545-550.
Link: http://index-of.co.uk/Algorithms/Algorithms%20in%20C.pdf
#### Args:
* `x`: A real `Tensor` of shape `batch_shape + [num_points]`.
* `spline_data`: An instance of `SplineParameters`. `spline_data.x_data` should
have the same batch shape as `x`.
* `optimize_for_tpu`: A Python bool. If `True`, the algorithm uses one-hot
encoding to lookup indices of `x` in `spline_data.x_data`. This
significantly improves performance of the algorithm on a TPU device but
may slow down performance on the CPU.
Default value: `False`.
* `dtype`: Optional dtype for `x`.
Default value: `None` which maps to the default dtype inferred by
TensorFlow.
* `name`: Python `str` name prefixed to ops created by this function.
Default value: `None` which is mapped to the default name
`cubic_spline_interpolate`.
#### Returns:
A `Tensor` of the same shape and `dtype` as `x`. Represents
the interpolated values.
#### Raises:
* `ValueError`: If `x` batch shape is different from `spline_data.x_data` batch
shape.