X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Fcone%2Fcompletely_positive.py;h=8bb4b6236b74d31921cb7eb2bf09c598e014ca1c;hb=a339e89c225bb46379332ecb8b0c50b918d34ac6;hp=ac5f14435713b4b524c53a2e1c73607ee004b323;hpb=46c389b0eafe43e54afc9f81f855bfb5f889d25d;p=sage.d.git diff --git a/mjo/cone/completely_positive.py b/mjo/cone/completely_positive.py index ac5f144..8bb4b62 100644 --- a/mjo/cone/completely_positive.py +++ b/mjo/cone/completely_positive.py @@ -1,18 +1,14 @@ -""" +r""" The completely positive cone `$\mathcal{K}$` over `\mathbb{R}^{n}$` is the set of all matrices `$A$`of the form `$\sum uu^{T}$` for `$u \in \mathbb{R}^{n}_{+}$`. Equivalently, `$A = XX{T}$` where all entries of `$X$` are nonnegative. """ -# Sage doesn't load ~/.sage/init.sage during testing (sage -t), so we -# have to explicitly mangle our sitedir here so that "mjo.cone" -# resolves. -from os.path import abspath -from site import addsitedir -addsitedir(abspath('../../')) +from sage.all import * from mjo.cone.symmetric_psd import factor_psd, is_symmetric_psd -from mjo.cone.doubly_nonnegative import is_doubly_nonnegative, is_extreme_doubly_nonnegative +from mjo.cone.doubly_nonnegative import (is_doubly_nonnegative, + is_extreme_doubly_nonnegative) def is_completely_positive(A): """ @@ -30,6 +26,10 @@ def is_completely_positive(A): Either ``True`` if ``A`` is completely positive, or ``False`` otherwise. + SETUP:: + + sage: from mjo.cone.completely_positive import is_completely_positive + EXAMPLES: Generate an extreme completely positive matrix and check that we @@ -124,6 +124,10 @@ def is_extreme_completely_positive(A): 1. Berman, Abraham and Shaked-Monderer, Naomi. Completely Positive Matrices. World Scientific, 2003. + SETUP:: + + sage: from mjo.cone.completely_positive import is_extreme_completely_positive + EXAMPLES: Generate an extreme completely positive matrix and check that we