Correlation of two one dimensional arrays.
JAX implementation of numpy.correlate().
Correlation of one dimensional arrays is defined as:
\[c_k = \sum_j a_{k + j} \overline{v_j}\]
where \(\overline{v_j}\) is the complex conjugate of \(v_j\).
a (ArrayLike) – left-hand input to the correlation. Must have a.ndim == 1.
v (ArrayLike) – right-hand input to the correlation. Must have v.ndim == 1.
mode (str) –
controls the size of the output. Available operations are:
"full": output the full correlation of the inputs.
"same": return a centered portion of the "full" output which is the same size as a.
"valid": (default) return the portion of the "full" output which do not depend on padding at the array edges.
precision (PrecisionLike) – Specify the precision of the computation. Refer to jax.lax.Precision for a description of available values.
preferred_element_type (DTypeLike | None) – A datatype, indicating to accumulate results to and return a result with that datatype. Default is None, which means the default accumulation type for the input types.
Array containing the cross-correlation result.
Examples
>>> x = jnp.array([1, 2, 3, 2, 1]) >>> y = jnp.array([4, 5, 6])
Since default mode = 'valid', jax.numpy.correlate returns only the portion of correlation where the two arrays fully overlap:
>>> jnp.correlate(x, y) Array([32., 35., 28.], dtype=float32)
Specifying mode = 'full' returns full correlation using implicit zero-padding at the edges.
>>> jnp.correlate(x, y, mode='full') Array([ 6., 17., 32., 35., 28., 13., 4.], dtype=float32)
Specifying mode = 'same' returns a centered correlation the same size as the first input:
>>> jnp.correlate(x, y, mode='same') Array([17., 32., 35., 28., 13.], dtype=float32)
If both the inputs arrays are real-valued and symmetric then the result will also be symmetric and will be equal to the result of jax.numpy.convolve.
>>> x1 = jnp.array([1, 2, 3, 2, 1]) >>> y1 = jnp.array([4, 5, 4]) >>> jnp.correlate(x1, y1, mode='full') Array([ 4., 13., 26., 31., 26., 13., 4.], dtype=float32) >>> jnp.convolve(x1, y1, mode='full') Array([ 4., 13., 26., 31., 26., 13., 4.], dtype=float32)
For complex-valued inputs:
>>> x2 = jnp.array([3+1j, 2, 2-3j]) >>> y2 = jnp.array([4, 2-5j, 1]) >>> jnp.correlate(x2, y2, mode='full') Array([ 3. +1.j, 3.+17.j, 18.+11.j, 27. +4.j, 8.-12.j], dtype=complex64)
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