Hi,
I tried the following, added to the Matrix class definition in matrix/
matrix0.pyx:
def is_symmetric(self):
"""
Returns True if this is a symmetric matrix.
"""
if self._ncols != self._nrows: return False
cdef int i,j
for i from 1 <= i < self._nrows:
for j from 0 <= j < self._ncols:
if self[i,j] != self[j,i]: return False
return True
While testing and timing this, I tried the following, out of a
perverse sort of curiosity:
def is_sym3(self):
"""
Returns True if this is a symmetric matrix.
"""
if self._ncols != self._nrows: return False
for i in xrange(1,self._nrows):
for j in xrange(0,i):
if self[i,j] != self[j,i]: return False
return True
Turns out that this, both as a method in the Matrix class and as a
raw hunk of python code, performs better than the above:
sage: time Doit1(M2,1000)
CPU times: user 37.21 s, sys: 0.24 s, total: 37.45 s
Wall time: 38.10
sage: time Doit2(M2,1000)
CPU times: user 23.50 s, sys: 0.18 s, total: 23.68 s
Wall time: 24.55
sage: time Doit1(M3,1000)
CPU times: user 55.87 s, sys: 0.41 s, total: 56.29 s
Wall time: 58.48
sage: time Doit2(M3,1000)
CPU times: user 31.52 s, sys: 0.23 s, total: 31.76 s
Wall time: 32.83
sage: time Doit1(M4,1000)
CPU times: user 58.94 s, sys: 0.71 s, total: 59.65 s
Wall time: 63.05
sage: time Doit2(M4,1000)
CPU times: user 32.64 s, sys: 0.43 s, total: 33.08 s
Wall time: 35.05
Doit1 is a loop that calls ".is_symmetric()", for the given count.
Doit2 is a loop that calls "issym()", for the given count.
M2 is a 200x200 integer symmetric matrix, with entries in the range
1..300000.
M3 is a 200x200 integer symmetric matrix, with entries in the range
1..200000000000000000.
M4 is a 200x200 integer symmetric matrix, with entries in the range
1..2000000000000000000000000000000000000000000000000000000.
Expected? Unexpected?
Justin
--
Justin C. Walker, Curmudgeon-at-Large
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