*Last updated: 2023-03-16.*
# tf_quant_finance.rates.constant_fwd.interpolate
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Performs the constant forward interpolation for supplied points.
```python
tf_quant_finance.rates.constant_fwd.interpolate(
interpolation_times, reference_times, reference_yields, dtype=None, name=None
)
```
Given an interest rate yield curve whose maturities and the corresponding
(continuously compounded) yields are in `reference_times` and
`reference_yields`, this function returns interpolated yields at
`interpolation_times` using the constant forward interpolation.
Let `t_i, i=1,...,n` and `y_i, i=1,...,n` denote the reference_times and
reference_yields respectively. If `t` is a maturity for which the
interpolation is desired such that t_{i-1} <= t <= t_i, then constant forward
interpolation produces the corresponding yield, `y_t`, such that the forward
rate in the interval `[t_{i-1},t]` is the same as the forward rate in the
interval `[t_{i-1},t_i]`. Mathematically, this is the same as linearly
interpolating `t*y_t` using the curve `t_i, t_i*y_i`.
`reference_times` must be strictly increasing but `reference_yields` don't
need to be because we don't require the rate curve to be monotonic.
#### Examples
```python
interpolation_times = [1, 3, 6, 7, 8, 15, 18, 25, 30]
# `reference_times` must be increasing, but `reference_yields` don't need to
# be.
reference_times = [0.0, 2.0, 6.0, 8.0, 18.0, 30.0]
reference_yields = [0.01, 0.02, 0.015, 0.014, 0.02, 0.025]
result = interpolate(interpolation_times, reference_times, reference_yields)
```
#### Args:
* `interpolation_times`: The times at which interpolation is desired. A N-D
`Tensor` of real dtype where the first N-1 dimensions represent the
batching dimensions.
* `reference_times`: Maturities in the input yield curve. A N-D `Tensor` of
real dtype where the first N-1 dimensions represent the batching
dimensions. Should be sorted in increasing order.
* `reference_yields`: Continuously compounded yields corresponding to
`reference_times`. A N-D `Tensor` of real dtype. Should have the
compatible shape as `x_data`.
* `dtype`: Optional tf.dtype for `interpolation_times`, reference_times`,
and `reference_yields`. If not specified, the dtype of the inputs will be
used.
* `name`: Python str. The name prefixed to the ops created by this function. If
not supplied, the default name 'constant_fwd_interpolation' is used.
#### Returns:
A N-D `Tensor` of real dtype with the same shape as `interpolations_times`
containing the interpolated yields.