From 9f5ea6c361ba75f19ebfdbcb74bdc8a0fb1f3c1a Mon Sep 17 00:00:00 2001 From: Michael Orlitzky Date: Mon, 13 Feb 2017 10:33:02 -0500 Subject: [PATCH] Clean up some of the is_foo_on doctests. --- mjo/cone/cone.py | 87 ++++++++++++++++++++++++------------------------ 1 file changed, 44 insertions(+), 43 deletions(-) diff --git a/mjo/cone/cone.py b/mjo/cone/cone.py index 01ef5f9..b564661 100644 --- a/mjo/cone/cone.py +++ b/mjo/cone/cone.py @@ -17,7 +17,10 @@ def is_positive_on(L,K): OUTPUT: ``True`` if it can be proven that ``L`` is positive on ``K``, - and ``False`` otherwise. + and ``False`` otherwise. If ``L`` is over an exact ring (the + rationals, for example), then you can trust the answer. Only + for symbolic ``L`` might there be difficulty in proving + positivity. .. WARNING:: @@ -30,8 +33,8 @@ def is_positive_on(L,K): EXAMPLES: - Positive operators on the nonnegative orthant are nonnegative - matrices:: + Nonnegative matrices are positive operators on the nonnegative + orthant:: sage: K = Cone([(1,0,0),(0,1,0),(0,0,1)]) sage: L = random_matrix(QQ,3).apply_map(abs) @@ -40,17 +43,17 @@ def is_positive_on(L,K): TESTS: - The identity is always positive in a nontrivial space:: + The identity operator is always positive:: sage: set_random_seed() - sage: K = random_cone(min_ambient_dim=1, max_ambient_dim=8) + sage: K = random_cone(max_ambient_dim=8) sage: L = identity_matrix(K.lattice_dim()) sage: is_positive_on(L,K) True - As is the "zero" transformation:: + The "zero" operator is always positive:: - sage: K = random_cone(min_ambient_dim=1, max_ambient_dim=8) + sage: K = random_cone(max_ambient_dim=8) sage: R = K.lattice().vector_space().base_ring() sage: L = zero_matrix(R, K.lattice_dim()) sage: is_positive_on(L,K) @@ -59,12 +62,12 @@ def is_positive_on(L,K): Everything in ``K.positive_operators_gens()`` should be positive on ``K``:: - sage: K = random_cone(min_ambient_dim=1, max_ambient_dim=6) - sage: all([ is_positive_on(L,K) - ....: for L in K.positive_operators_gens() ]) + sage: K = random_cone(max_ambient_dim=5) + sage: all([ is_positive_on(L,K) # long time + ....: for L in K.positive_operators_gens() ]) # long time True - sage: all([ is_positive_on(L.change_ring(SR),K) - ....: for L in K.positive_operators_gens() ]) + sage: all([ is_positive_on(L.change_ring(SR),K) # long time + ....: for L in K.positive_operators_gens() ]) # long time True """ @@ -114,17 +117,17 @@ def is_cross_positive_on(L,K): EXAMPLES: - The identity is always cross-positive in a nontrivial space:: + The identity operator is always cross-positive:: sage: set_random_seed() - sage: K = random_cone(min_ambient_dim=1, max_ambient_dim=8) + sage: K = random_cone(max_ambient_dim=8) sage: L = identity_matrix(K.lattice_dim()) sage: is_cross_positive_on(L,K) True - As is the "zero" transformation:: + The "zero" operator is always cross-positive:: - sage: K = random_cone(min_ambient_dim=1, max_ambient_dim=8) + sage: K = random_cone(max_ambient_dim=8) sage: R = K.lattice().vector_space().base_ring() sage: L = zero_matrix(R, K.lattice_dim()) sage: is_cross_positive_on(L,K) @@ -135,12 +138,12 @@ def is_cross_positive_on(L,K): Everything in ``K.cross_positive_operators_gens()`` should be cross-positive on ``K``:: - sage: K = random_cone(min_ambient_dim=1, max_ambient_dim=6) - sage: all([ is_cross_positive_on(L,K) - ....: for L in K.cross_positive_operators_gens() ]) + sage: K = random_cone(max_ambient_dim=5) + sage: all([ is_cross_positive_on(L,K) # long time + ....: for L in K.cross_positive_operators_gens() ]) # long time True - sage: all([ is_cross_positive_on(L.change_ring(SR),K) - ....: for L in K.cross_positive_operators_gens() ]) + sage: all([ is_cross_positive_on(L.change_ring(SR),K) # long time + ....: for L in K.cross_positive_operators_gens() ]) # long time True """ @@ -189,17 +192,17 @@ def is_Z_on(L,K): EXAMPLES: - The identity is always a Z-operator in a nontrivial space:: + The identity operator is always a Z-operator:: sage: set_random_seed() - sage: K = random_cone(min_ambient_dim=1, max_ambient_dim=8) + sage: K = random_cone(max_ambient_dim=8) sage: L = identity_matrix(K.lattice_dim()) sage: is_Z_on(L,K) True - As is the "zero" transformation:: + The "zero" operator is always a Z-operator:: - sage: K = random_cone(min_ambient_dim=1, max_ambient_dim=8) + sage: K = random_cone(max_ambient_dim=8) sage: R = K.lattice().vector_space().base_ring() sage: L = zero_matrix(R, K.lattice_dim()) sage: is_Z_on(L,K) @@ -210,12 +213,12 @@ def is_Z_on(L,K): Everything in ``K.Z_operators_gens()`` should be a Z-operator on ``K``:: - sage: K = random_cone(min_ambient_dim=1, max_ambient_dim=6) - sage: all([ is_Z_on(L,K) - ....: for L in K.Z_operators_gens() ]) + sage: K = random_cone(max_ambient_dim=5) + sage: all([ is_Z_on(L,K) # long time + ....: for L in K.Z_operators_gens() ]) # long time True - sage: all([ is_Z_on(L.change_ring(SR),K) - ....: for L in K.Z_operators_gens() ]) + sage: all([ is_Z_on(L.change_ring(SR),K) # long time + ....: for L in K.Z_operators_gens() ]) # long time True """ @@ -254,8 +257,8 @@ def is_lyapunov_like_on(L,K): EXAMPLES: - Lyapunov-like operators on the nonnegative orthant are diagonal - matrices:: + Diagonal matrices are Lyapunov-like operators on the nonnegative + orthant:: sage: K = Cone([(1,0,0),(0,1,0),(0,0,1)]) sage: L = diagonal_matrix(random_vector(QQ,3)) @@ -264,17 +267,17 @@ def is_lyapunov_like_on(L,K): TESTS: - The identity is always Lyapunov-like in a nontrivial space:: + The identity operator is always Lyapunov-like:: sage: set_random_seed() - sage: K = random_cone(min_ambient_dim=1, max_ambient_dim=8) + sage: K = random_cone(max_ambient_dim=8) sage: L = identity_matrix(K.lattice_dim()) sage: is_lyapunov_like_on(L,K) True - As is the "zero" transformation:: + The "zero" operator is always Lyapunov-like:: - sage: K = random_cone(min_ambient_dim=1, max_ambient_dim=8) + sage: K = random_cone(max_ambient_dim=8) sage: R = K.lattice().vector_space().base_ring() sage: L = zero_matrix(R, K.lattice_dim()) sage: is_lyapunov_like_on(L,K) @@ -283,18 +286,16 @@ def is_lyapunov_like_on(L,K): Everything in ``K.lyapunov_like_basis()`` should be Lyapunov-like on ``K``:: - sage: K = random_cone(min_ambient_dim=1, max_ambient_dim=6) - sage: all([ is_lyapunov_like_on(L,K) - ....: for L in K.lyapunov_like_basis() ]) + sage: K = random_cone(max_ambient_dim=5) + sage: all([ is_lyapunov_like_on(L,K) # long time + ....: for L in K.lyapunov_like_basis() ]) # long time True - sage: all([ is_lyapunov_like_on(L.change_ring(SR),K) - ....: for L in K.lyapunov_like_basis() ]) + sage: all([ is_lyapunov_like_on(L.change_ring(SR),K) # long time + ....: for L in K.lyapunov_like_basis() ]) # long time True """ if L.base_ring().is_exact() or L.base_ring() is SR: - # The "fast method" of creating a vector space based on a - # ``lyapunov_like_basis`` is actually slower than this. return all([ s*(L*x) == 0 for (x,s) in K.discrete_complementarity_set() ]) else: -- 2.44.2