[Numpy-svn] [numpy/numpy] 332d62: ENH: Improve accuracy of numpy.gradient at edges

[GitHub]

  Branch: refs/heads/master
  Home:   https://github.com/numpy/numpy
  Commit: 332d628744a0670234585053dbe32a3e82e0c4db
      https://github.com/numpy/numpy/commit/332d628744a0670234585053dbe32a3e82e0c4db
  Author: danieljfarrell <danieljfarrel at me.com>
  Date:   2013-09-07 (Sat, 07 Sep 2013)

  Changed paths:
    M numpy/lib/function_base.py
    M numpy/lib/tests/test_function_base.py

  Log Message:
  -----------
  ENH: Improve accuracy of numpy.gradient at edges

* numpy.gradient has been enhanced to use a second order accurate
  one-sided finite difference stencil at boundary elements of the
  array. Second order accurate central difference are still used for
  the interior elements. The result is a fully second order accurate
  approximation of the gradient over the full domain.

* The one-sided stencil uses 3 elements each with a different weight. A
  forward difference is used for the first element,
     dy/dx ~ -(3.0*y[0] - 4.0*y[1] + y[2]) / (2.0*dx)
  and backwards difference is used for the last element,
     dy/dx ~ (3.0*y[-1] - 4.0*y[-2] + y[-3]) / (2.0*dx)

* Because the datetime64 datatype cannot be multiplied a view is taken
  of datetime64 arrays and cast to int64. The gradient algorithm is
  then applied to the view rather than the input array.

* Previously no dimension checks were performed on the input array. Now
  if the array size along the differentiation axis is less than 2, a
  ValueError is raised which explains that more elements are needed. If
  the size is exactly two the function falls back to using a 2 point
  stencil (the old behaviour). If the size is 3 and above then the
  higher accuracy methods are used.

* A new test has been added which validates the higher accuracy. Old
  tests have been updated to pass. Note, this should be expected
  because the boundary elements now return different (more accurate)
  values.


  Commit: 089cc017cdc0b8105d40d74eae15539b1e309e01
      https://github.com/numpy/numpy/commit/089cc017cdc0b8105d40d74eae15539b1e309e01
  Author: Charles Harris <charlesr.harris at gmail.com>
  Date:   2013-09-07 (Sat, 07 Sep 2013)

  Changed paths:
    M numpy/lib/function_base.py
    M numpy/lib/tests/test_function_base.py

  Log Message:
  -----------
  Merge branch 'gradient'

* gradient:
  ENH: Improve accuracy of numpy.gradient at edges


Compare: https://github.com/numpy/numpy/compare/7679c14ab9b2...089cc017cdc0