Add quadratic entropy

[cmccoy]

guppy pentropy should be renamed guppy entropy, with two entropy measures:

• phylogenetic entropy (see #189)
• quadratic entropy, described in a phylogenetic context in this paper.

The original formula is for quadratic entropy is:

Q = \sum_{i<j} p_i p_j \delta_{ij}

Where p_i, p_j are the proportion of mass on taxon i and j respectively, and \delta_{ij} is the phylogenetic distance between them.

To make things a little faster, this can be rearranged so that:

Q = \sum_{s in S} l(s) (\sum_{i in R_s} p_i}) (\sum_{j in N_s} p_j)

Where S contains all snippets on the tree between placements, R_s contains all placements on the proximal side of snippet s, and N_s contains all placements on the distal side of s, and p_i contains the proportion of the total mass on on placement i.

[matsen]

Great. Let's have the two columns be named "phylogenetic" and "quadratic".

The docs should include these descriptions in the docs. They can be specified in RST like in guppy_kr.rst:

.. math::
    Z(P,Q) =
    \int_T \left| P(\tau(y)) - Q(\tau(y)) \right| \, \lambda(dy).

On Fri, Dec 23, 2011 at 10:04 AM, Connor McCoy reply@reply.github.com wrote:

guppy pentropy should be renamed guppy entropy, which two entropy measures:

• phylogenetic entropy (see #189)
• quadratic entropy, described in a phylogenetic context in this paper.

The original formula is for quadratic entropy is:

   Q = \sum_{i<j} p_i pj \delta{ij}

Where p_i, pj are the proportion of mass on taxon i and j respectively, and `\delta{ij}` is the phylogenetic distance between them.

To make things a little faster, this can be rearranged so that:

   Q = \sum{s in S} l(s) (\sum{i in R_s} pi}) (\sum{j in N_s} p_j)

Where S contains all snippets on the tree between placements, R_s contains all placements on the proximal side of snippet s, and N_s contains all placements on the distal side of s.

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Reply to this email directly or view it on GitHub: https://github.com/matsen/pplacer/issues/199

Frederick "Erick" Matsen, Assistant Member Fred Hutchinson Cancer Research Center http://matsen.fhcrc.org/