X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Fcone%2Fsymmetric_psd.py;h=fd6f9508196942cd59a578fc208324e87b7f326d;hb=a339e89c225bb46379332ecb8b0c50b918d34ac6;hp=40fd90c0e3b1d20cf8e522e8504ef8f55804b959;hpb=b4b48ce895557cc5708b090568cfa33e7d09817f;p=sage.d.git diff --git a/mjo/cone/symmetric_psd.py b/mjo/cone/symmetric_psd.py index 40fd90c..fd6f950 100644 --- a/mjo/cone/symmetric_psd.py +++ b/mjo/cone/symmetric_psd.py @@ -1,4 +1,4 @@ -""" +r""" The positive semidefinite cone `$S^{n}_{+}$` is the cone consisting of all symmetric positive-semidefinite matrices (as a subset of `$\mathbb{R}^{n \times n}$` @@ -29,6 +29,7 @@ def is_symmetric_psd(A): Every completely positive matrix is symmetric positive-semidefinite:: + sage: set_random_seed() sage: v = vector(map(abs, random_vector(ZZ, 10))) sage: A = v.column() * v.row() sage: is_symmetric_psd(A) @@ -260,6 +261,7 @@ def random_symmetric_psd(V, accept_zero=True, rank=None): Well, it doesn't crash at least:: + sage: set_random_seed() sage: V = VectorSpace(QQ, 2) sage: A = random_symmetric_psd(V) sage: A.matrix_space() @@ -269,6 +271,7 @@ def random_symmetric_psd(V, accept_zero=True, rank=None): A matrix with the desired rank is returned:: + sage: set_random_seed() sage: V = VectorSpace(QQ, 5) sage: A = random_symmetric_psd(V,False,1) sage: A.rank() @@ -288,6 +291,7 @@ def random_symmetric_psd(V, accept_zero=True, rank=None): If the user asks for a rank that's too high, we fail:: + sage: set_random_seed() sage: V = VectorSpace(QQ, 2) sage: A = random_symmetric_psd(V,False,3) Traceback (most recent call last):