[Numpy-svn] [numpy/numpy] 0650d0: MAINT: Improve computation of scaled companion mat...

[GitHub]

  Branch: refs/heads/master
  Home:   https://github.com/numpy/numpy
  Commit: 0650d04078666997c3dac3beec6fe872dca797dd
      https://github.com/numpy/numpy/commit/0650d04078666997c3dac3beec6fe872dca797dd
  Author: Charles Harris <charlesr.harris at gmail.com>
  Date:   2014-10-04 (Sat, 04 Oct 2014)

  Changed paths:
    M numpy/polynomial/hermite.py
    M numpy/polynomial/hermite_e.py

  Log Message:
  -----------
  MAINT: Improve computation of scaled companion matrices.

The previous method used for hermite and hermite_e polynomials suffered
from double overflow for polynomials of large degree. Those numbers were
later scaled down by equally large numbers, but the result was NaN. The
wanted values are now computed in such a way that overflow in some
entries is replaced by underflow in others. The resulting zeros are a
negligible perturbation of the companion matrix.


  Commit: dc002061a0a7bf3cb1c6b7c9e3c68553b5d22f82
      https://github.com/numpy/numpy/commit/dc002061a0a7bf3cb1c6b7c9e3c68553b5d22f82
  Author: Charles Harris <charlesr.harris at gmail.com>
  Date:   2014-10-04 (Sat, 04 Oct 2014)

  Changed paths:
    M numpy/polynomial/hermite.py
    M numpy/polynomial/hermite_e.py

  Log Message:
  -----------
  MAINT: Improve computation of gauss weights for hermite and hermite_e.

The new computations use normalized polynomials. Those polynomials are
less subject to overflow and allow the determination of the weights and
roots up to about degree 350, at which point the weights underflow.

Two private functions are added for computing the values of the
normalized polynomials:

1. _normed_hermite_n
2. _normed_hermite_e_n


  Commit: d6d67957d3af1f4a4845ba3bc2d8b1fdd9e49e96
      https://github.com/numpy/numpy/commit/d6d67957d3af1f4a4845ba3bc2d8b1fdd9e49e96
  Author: Charles Harris <charlesr.harris at gmail.com>
  Date:   2014-10-10 (Fri, 10 Oct 2014)

  Changed paths:
    M numpy/polynomial/hermite.py
    M numpy/polynomial/hermite_e.py

  Log Message:
  -----------
  Merge pull request #5154 from charris/improve-gauss-hermite

Improve gauss hermite


Compare: https://github.com/numpy/numpy/compare/7eff5b881b7d...d6d67957d3af