Skip to main content
`Ctrl`+`K`
scipy.fft.

# ifht

scipy.fft.ifht(A, dln, mu, offset=0.0, bias=0.0)

  Compute the inverse fast Hankel transform.

  Computes the discrete inverse Hankel transform of a logarithmically spaced periodic sequence. This is the inverse operation to `fht`.

  Parameters:
    A array_like (…, n)

      Real periodic input array, uniformly logarithmically spaced. For multidimensional input, the transform is performed over the last axis.

    dln float

      Uniform logarithmic spacing of the input array.

    mu float

      Order of the Hankel transform, any positive or negative real number.

    offset float, optional

      Offset of the uniform logarithmic spacing of the output array.

    bias float, optional

      Exponent of power law bias, any positive or negative real number.

  Returns:
    a array_like (…, n)

      The transformed output array, which is real, periodic, uniformly logarithmically spaced, and of the same shape as the input array.

  See also

  `fht`

    Definition of the fast Hankel transform.

  `fhtoffset`

    Return an optimal offset for `ifht`.

  Notes

  This function computes a discrete version of the Hankel transform

  \[a(r) = \int_{0}^{\infty} \! A(k) \, J_\mu(kr) \, r \, dk \;,\]

  where \(J_\mu\) is the Bessel function of order \(\mu\). The index \(\mu\) may be any real number, positive or negative. Note that the numerical inverse Hankel transform uses an integrand of \(r \, dk\), while the mathematical inverse Hankel transform is commonly defined using \(k \, dk\).

  See `fht` for further details.

  Array API Standard Support

  `ifht` has experimental support for Python Array API Standard compatible backends in addition to NumPy. Please consider testing these features by setting an environment variable `SCIPY_ARRAY_API=1` and providing CuPy, PyTorch, JAX, or Dask arrays as array arguments. The following combinations of backend and device (or other capability) are supported.

  Library | CPU | GPU
  --- | --- | ---
  NumPy | ✅ | n/a
  CuPy | n/a | ✅
  PyTorch | ✅ | ✅
  JAX | ✅ | ✅
  Dask | ⚠️ computes graph | n/a

  > See Support for the array API standard for more information.