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some care for all() in matrix2
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@fchapoton
fchapoton committed May 31, 2019
1 parent 9b91a09 commit d00fa13
Showing 1 changed file with 32 additions and 24 deletions.
56 changes: 32 additions & 24 deletions src/sage/matrix/matrix2.pyx
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Expand Up @@ -25,14 +25,14 @@ AUTHORS:

"""

#*****************************************************************************
# ****************************************************************************
# Copyright (C) 2005, 2006 William Stein <wstein@gmail.com>
#
# Distributed under the terms of the GNU General Public License (GPL)
# as published by the Free Software Foundation; either version 2 of
# the License, or (at your option) any later version.
# https://www.gnu.org/licenses/
#*****************************************************************************
# ****************************************************************************
from __future__ import print_function, absolute_import, division

from cpython cimport *
Expand Down Expand Up @@ -67,6 +67,7 @@ from sage.matrix.matrix_misc import permanental_minor_polynomial
# used to deprecate only adjoint method
from sage.misc.superseded import deprecated_function_alias


cdef class Matrix(Matrix1):
"""
Base class for matrices, part 2
Expand Down Expand Up @@ -8539,7 +8540,7 @@ cdef class Matrix(Matrix1):
row_sums == col_sums and\
row_sums == len(row_sums) * [col_sums[0]] and\
((not normalized) or col_sums[0] == self.base_ring()(1)) and\
all(entry>=0 for row in self for entry in row)
all(entry >= 0 for row in self for entry in row)

def is_normal(self):
r"""
Expand Down Expand Up @@ -10330,7 +10331,7 @@ cdef class Matrix(Matrix1):
for eval,size in blocks:
# Find a block with the right size
for index,chain in enumerate(jordan_chains[eval]):
if len(chain)==size:
if len(chain) == size:
jordan_basis += jordan_chains[eval].pop(index)
break

Expand Down Expand Up @@ -11992,7 +11993,7 @@ cdef class Matrix(Matrix1):
sage: M.is_immutable()
True
sage: P, L, U = A.LU(format='plu')
sage: all([A.is_mutable() for A in [P, L, U]])
sage: all(A.is_mutable() for A in [P, L, U])
True

Partial pivoting is based on the absolute values of entries
Expand Down Expand Up @@ -14983,8 +14984,8 @@ cdef class Matrix(Matrix1):
sage: set_random_seed()
sage: K1 = random_cone(max_ambient_dim=5)
sage: K2 = random_cone(max_ambient_dim=5)
sage: all([ L.change_ring(SR).is_positive_operator_on(K1,K2)
....: for L in K1.positive_operators_gens(K2) ]) # long time
sage: all(L.change_ring(SR).is_positive_operator_on(K1, K2)
....: for L in K1.positive_operators_gens(K2)) # long time
True

Technically we could test this, but for now only closed convex cones
Expand Down Expand Up @@ -15025,14 +15026,14 @@ cdef class Matrix(Matrix1):
# ``self*x`` is symbolic, polynomial, or otherwise
# contains something unexpected. For example, ``e in
# Cone([(1,)])`` is true, but returns ``False``.
return all([ self*x in K2 for x in K1 ])
return all(self * x in K2 for x in K1)
else:
# Fall back to inequality-checking when the entries of
# this matrix might be symbolic, polynomial, or something
# else weird.
return all([ s*(self*x) >= 0 for x in K1 for s in K2.dual() ])
return all(s * (self * x) >= 0 for x in K1 for s in K2.dual())

def is_cross_positive_on(self,K):
def is_cross_positive_on(self, K):
r"""
Determine if this matrix is cross-positive on a cone.

Expand Down Expand Up @@ -15126,8 +15127,8 @@ cdef class Matrix(Matrix1):

sage: set_random_seed()
sage: K = random_cone(max_ambient_dim=5)
sage: all([L.change_ring(SR).is_cross_positive_on(K)
....: for L in K.cross_positive_operators_gens()]) # long time
sage: all(L.change_ring(SR).is_cross_positive_on(K)
....: for L in K.cross_positive_operators_gens()) # long time
True

Technically we could test this, but for now only closed convex cones
Expand Down Expand Up @@ -15160,10 +15161,10 @@ cdef class Matrix(Matrix1):
msg = 'The base ring of the matrix is neither symbolic nor exact.'
raise ValueError(msg)

return all([ s*(self*x) >= 0
for (x,s) in K.discrete_complementarity_set() ])
return all(s * (self * x) >= 0
for (x, s) in K.discrete_complementarity_set())

def is_Z_operator_on(self,K):
def is_Z_operator_on(self, K):
r"""
Determine if this matrix is a Z-operator on a cone.

Expand Down Expand Up @@ -15258,8 +15259,8 @@ cdef class Matrix(Matrix1):

sage: set_random_seed()
sage: K = random_cone(max_ambient_dim=5)
sage: all([ L.change_ring(SR).is_Z_operator_on(K)
....: for L in K.Z_operators_gens() ]) # long time
sage: all(L.change_ring(SR).is_Z_operator_on(K)
....: for L in K.Z_operators_gens()) # long time
True

Technically we could test this, but for now only closed convex cones
Expand Down Expand Up @@ -15380,8 +15381,8 @@ cdef class Matrix(Matrix1):

sage: set_random_seed()
sage: K = random_cone(max_ambient_dim=5)
sage: all([ L.change_ring(SR).is_lyapunov_like_on(K)
....: for L in K.lyapunov_like_basis() ]) # long time
sage: all(L.change_ring(SR).is_lyapunov_like_on(K)
....: for L in K.lyapunov_like_basis()) # long time
True

Technically we could test this, but for now only closed convex cones
Expand Down Expand Up @@ -15432,8 +15433,8 @@ cdef class Matrix(Matrix1):
# :meth:`is_cross_positive_on` twice: doing so checks twice as
# many inequalities as the number of equalities that we're
# about to check.
return all([ s*(self*x) == 0
for (x,s) in K.discrete_complementarity_set() ])
return all(s * (self * x) == 0
for (x, s) in K.discrete_complementarity_set())

# A limited number of access-only properties are provided for matrices
@property
Expand Down Expand Up @@ -15538,7 +15539,8 @@ def _smith_diag(d, transformation=True):
for j in xrange(i+1,n):
if dp[j,j] not in I:
t = R.ideal([dp[i,i], dp[j,j]]).gens_reduced()
if len(t) > 1: raise ArithmeticError
if len(t) > 1:
raise ArithmeticError
t = t[0]
# find lambda, mu such that lambda*d[i,i] + mu*d[j,j] = t
lamb = R(dp[i,i]/t).inverse_mod( R.ideal(dp[j,j]/t))
Expand Down Expand Up @@ -15676,6 +15678,7 @@ def _generic_clear_column(m):

return left_mat, a


def _smith_onestep(m):
r"""
Carry out one step of Smith normal form for matrix m. Returns three matrices a,b,c over
Expand Down Expand Up @@ -15732,6 +15735,7 @@ def _smith_onestep(m):

return left_mat, a, right_mat


def decomp_seq(v):
"""
This function is used internally be the decomposition matrix
Expand All @@ -15751,6 +15755,7 @@ def decomp_seq(v):
list.sort(v, key=lambda x: x[0].dimension())
return Sequence(v, universe=tuple, check=False, cr=True)


def _choose(Py_ssize_t n, Py_ssize_t t):
"""
Returns all possible sublists of length t from range(n)
Expand Down Expand Up @@ -15814,6 +15819,7 @@ def _choose(Py_ssize_t n, Py_ssize_t t):

return x


def _binomial(Py_ssize_t n, Py_ssize_t k):
"""
Fast and unchecked implementation of binomial(n,k) This is only for
Expand Down Expand Up @@ -15846,6 +15852,7 @@ def _binomial(Py_ssize_t n, Py_ssize_t k):
i, n, k = i + 1, n - 1, k - 1
return result


def _jordan_form_vector_in_difference(V, W):
r"""
Given two lists of vectors ``V`` and ``W`` over the same base field,
Expand All @@ -15865,16 +15872,17 @@ def _jordan_form_vector_in_difference(V, W):
sage: sage.matrix.matrix2._jordan_form_vector_in_difference([v,w], [u])
(1, 0, 0, 0)
"""
if len(V) == 0:
if not V:
return None
if len(W) == 0:
if not W:
return V[0]
W_space = sage.all.span(W)
for v in V:
if v not in W_space:
return v
return None


def _matrix_power_symbolic(A, n):
r"""
Return the symbolic `n`-th power `A^n` of the matrix `A`
Expand Down

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