From 8492b6f01186a5c5df9f7ccb007604958ffdf1f1 Mon Sep 17 00:00:00 2001 From: Michael Orlitzky Date: Wed, 24 Feb 2021 20:31:48 -0500 Subject: [PATCH] eja: make gram_schmidt work in Cartesian product algebras. --- mjo/eja/eja_utils.py | 23 ++++++++++++++++++----- 1 file changed, 18 insertions(+), 5 deletions(-) diff --git a/mjo/eja/eja_utils.py b/mjo/eja/eja_utils.py index 29edf5b..e8ed4db 100644 --- a/mjo/eja/eja_utils.py +++ b/mjo/eja/eja_utils.py @@ -110,9 +110,6 @@ def gram_schmidt(v, inner_product=None): inner_product = lambda x,y: x.inner_product(y) norm = lambda x: inner_product(x,x).sqrt() - def proj(x,y): - return (inner_product(x,y)/inner_product(x,x))*x - v = list(v) # make a copy, don't clobber the input # Drop all zero vectors before we start. @@ -124,10 +121,26 @@ def gram_schmidt(v, inner_product=None): R = v[0].base_ring() + # Define a scaling operation that can be used on tuples. + # Oh and our "zero" needs to belong to the right space. + scale = lambda x,alpha: x*alpha + zero = v[0].parent().zero() + if hasattr(v[0], 'cartesian_factors'): + P = v[0].parent() + scale = lambda x,alpha: P(tuple( x_i*alpha + for x_i in x.cartesian_factors() )) + + + def proj(x,y): + return scale(x, (inner_product(x,y)/inner_product(x,x))) + # First orthogonalize... for i in range(1,len(v)): # Earlier vectors can be made into zero so we have to ignore them. - v[i] -= sum( proj(v[j],v[i]) for j in range(i) if not v[j].is_zero() ) + v[i] -= sum( (proj(v[j],v[i]) + for j in range(i) + if not v[j].is_zero() ), + zero ) # And now drop all zero vectors again if they were "orthogonalized out." v = [ v_i for v_i in v if not v_i.is_zero() ] @@ -136,6 +149,6 @@ def gram_schmidt(v, inner_product=None): # them here because then our subalgebra would have a bigger field # than the superalgebra. for i in range(len(v)): - v[i] = v[i] / norm(v[i]) + v[i] = scale(v[i], ~norm(v[i])) return v -- 2.43.2