jax.numpy.correlate

jax.numpy.correlate(a, v, mode='valid', *, precision=None)[source]

Cross-correlation of two 1-dimensional sequences.

LAX-backend implementation of correlate(). In addition to the original NumPy arguments listed below, also supports precision for extra control over matrix-multiplication precision on supported devices. precision may be set to None, which means default precision for the backend, or any jax.lax.Precision enum value (Precision.DEFAULT, Precision.HIGH or Precision.HIGHEST).

Original docstring below.

This function computes the correlation as generally defined in signal processing texts:

c_{av}[k] = sum_n a[n+k] * conj(v[n])

with a and v sequences being zero-padded where necessary and conj being the conjugate.

Parameters
  • v (a,) – Input sequences.

  • mode ({'valid', 'same', 'full'}, optional) – Refer to the convolve docstring. Note that the default is ‘valid’, unlike convolve, which uses ‘full’.

Returns

out – Discrete cross-correlation of a and v.

Return type

ndarray

See also

convolve()

Discrete, linear convolution of two one-dimensional sequences.

multiarray.correlate()

Old, no conjugate, version of correlate.

Notes

The definition of correlation above is not unique and sometimes correlation may be defined differently. Another common definition is:

c'_{av}[k] = sum_n a[n] conj(v[n+k])

which is related to c_{av}[k] by c'_{av}[k] = c_{av}[-k].

Examples

>>> np.correlate([1, 2, 3], [0, 1, 0.5])
array([3.5])
>>> np.correlate([1, 2, 3], [0, 1, 0.5], "same")
array([2. ,  3.5,  3. ])
>>> np.correlate([1, 2, 3], [0, 1, 0.5], "full")
array([0.5,  2. ,  3.5,  3. ,  0. ])

Using complex sequences:

>>> np.correlate([1+1j, 2, 3-1j], [0, 1, 0.5j], 'full')
array([ 0.5-0.5j,  1.0+0.j ,  1.5-1.5j,  3.0-1.j ,  0.0+0.j ])

Note that you get the time reversed, complex conjugated result when the two input sequences change places, i.e., c_{va}[k] = c^{*}_{av}[-k]:

>>> np.correlate([0, 1, 0.5j], [1+1j, 2, 3-1j], 'full')
array([ 0.0+0.j ,  3.0+1.j ,  1.5+1.5j,  1.0+0.j ,  0.5+0.5j])