From 839b90b46009aeb42d2615884972949664d154ad Mon Sep 17 00:00:00 2001 From: Michael Orlitzky Date: Thu, 25 Feb 2021 07:48:49 -0500 Subject: [PATCH] eja: add some tests for new utility functions. --- mjo/eja/eja_utils.py | 43 ++++++++++++++++++++++++++++++++++++++++++- 1 file changed, 42 insertions(+), 1 deletion(-) diff --git a/mjo/eja/eja_utils.py b/mjo/eja/eja_utils.py index 803ec63..38e7576 100644 --- a/mjo/eja/eja_utils.py +++ b/mjo/eja/eja_utils.py @@ -6,6 +6,26 @@ def _all2list(x): r""" Flatten a vector, matrix, or cartesian product of those things into a long list. + + EXAMPLES:: + + sage: from mjo.eja.eja_utils import _all2list + sage: V1 = VectorSpace(QQ,2) + sage: V2 = MatrixSpace(QQ,2) + sage: x1 = V1([1,1]) + sage: x2 = V1([1,-1]) + sage: y1 = V2.one() + sage: y2 = V2([0,1,1,0]) + sage: _all2list((x1,y1)) + [1, 1, 1, 0, 0, 1] + sage: _all2list((x2,y2)) + [1, -1, 0, 1, 1, 0] + sage: M = cartesian_product([V1,V2]) + sage: _all2list(M((x1,y1))) + [1, 1, 1, 0, 0, 1] + sage: _all2list(M((x2,y2))) + [1, -1, 0, 1, 1, 0] + """ if hasattr(x, 'list'): # Easy case... @@ -92,6 +112,28 @@ def gram_schmidt(v, inner_product=None): [0 0], [1/2*sqrt(2) 0], [0 1] ] + It even works on Cartesian product spaces whose factors are vector + or matrix spaces:: + + sage: V1 = VectorSpace(AA,2) + sage: V2 = MatrixSpace(AA,2) + sage: M = cartesian_product([V1,V2]) + sage: x1 = V1([1,1]) + sage: x2 = V1([1,-1]) + sage: y1 = V2.one() + sage: y2 = V2([0,1,1,0]) + sage: z1 = M((x1,y1)) + sage: z2 = M((x2,y2)) + sage: def ip(a,b): + ....: return a[0].inner_product(b[0]) + (a[1]*b[1]).trace() + sage: U = gram_schmidt([z1,z2], inner_product=ip) + sage: ip(U[0],U[1]) + 0 + sage: ip(U[0],U[0]) + 1 + sage: ip(U[1],U[1]) + 1 + TESTS: Ensure that zero vectors don't get in the way:: @@ -102,7 +144,6 @@ def gram_schmidt(v, inner_product=None): sage: v = [v1,v2,v3] sage: len(gram_schmidt(v)) == 2 True - """ if inner_product is None: inner_product = lambda x,y: x.inner_product(y) -- 2.43.2