*Last updated: 2023-03-16.*
# tf_quant_finance.math.interpolation.linear.interpolate
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Performs linear interpolation for supplied points.
```python
tf_quant_finance.math.interpolation.linear.interpolate(
x, x_data, y_data, left_slope=None, right_slope=None, validate_args=False,
optimize_for_tpu=False, dtype=None, name=None
)
```
Given a set of knots whose x- and y- coordinates are in `x_data` and `y_data`,
this function returns y-values for x-coordinates in `x` via piecewise
linear interpolation.
`x_data` must be non decreasing, but `y_data` don't need to be because we do
not require the function approximated by these knots to be monotonic.
#### Examples
```python
import tf_quant_finance as tff
x = [-10, -1, 1, 3, 6, 7, 8, 15, 18, 25, 30, 35]
x_data = [-1, 2, 6, 8, 18, 30.0]
y_data = [10, -1, -5, 7, 9, 20]
tff.math.interpolation.linear.interpolate(x, x_data, y_data,
dtype=tf.float64)
# Expected: [ 10, 10, 2.66666667, -2, -5, 1, 7, 8.4, 9, 15.41666667, 20, 20]
```
#### Args:
* `x`: x-coordinates for which we need to get interpolation. A N-D
`Tensor` of real dtype. First N-1 dimensions represent batching
dimensions.
* `x_data`: x coordinates. A N-D `Tensor` of real dtype. Should be sorted
in non decreasing order. First N-1 dimensions represent batching
dimensions.
* `y_data`: y coordinates. A N-D `Tensor` of real dtype. Should have the
compatible shape as `x_data`. First N-1 dimensions represent batching
dimensions.
* `left_slope`: The slope to use for extrapolation with x-coordinate smaller
than the min `x_data`. It's a 0-D or N-D `Tensor`.
Default value: `None`, which maps to `0.0` meaning constant extrapolation,
i.e. extrapolated value will be the leftmost `y_data`.
* `right_slope`: The slope to use for extrapolation with x-coordinate greater
than the max `x_data`. It's a 0-D or N-D `Tensor`.
Default value: `None` which maps to `0.0` meaning constant extrapolation,
i.e. extrapolated value will be the rightmost `y_data`.
* `validate_args`: Python `bool` that indicates whether the function performs
the check if the shapes of `x_data` and `y_data` are equal and that the
elements in `x_data` are non decreasing. If this value is set to `False`
and the elements in `x_data` are not increasing, the result of linear
interpolation may be wrong.
Default value: `False`.
* `optimize_for_tpu`: A Python bool. If `True`, the algorithm uses one-hot
encoding to lookup indices of `x` in `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 tf.dtype for `x`, x_data`, `y_data`, `left_slope` and
`right_slope`.
Default value: `None` which means that the `dtype` inferred from
`x`.
* `name`: Python str. The name prefixed to the ops created by this function.
Default value: `None` which maps to 'linear_interpolation'.
#### Returns:
A N-D `Tensor` of real dtype corresponding to the x-values in `x`.