Is it assymptotically 10% or is it 10% for the case in which you are
testing it? In the first case I would be surprised in the second case it is
not that weird.
See the late_import function in src/sage/rings/complex_field.py for how you
can speed up the import statement for the cyclic import case.
On Friday, 15 September 2017 20:31:51 UTC+2, Martin R wrote:
>
> I am now trying to speed up Permutation.to_matrix, which is meanwhile one
> of the worst offenders in my application. After some profiling I found the
> following, which is quite a mystery to me. Apparently it is possible that
> importing a module in a method costs a significant amount of time!
>
> QUESTION: is this an oversight or is there a good reason to import modules
> in a relatively fundamental method like MatrixSpace.matrix?
>
> (I checked, moving out the first import makes the whole thing
> (Permutation.to_matrix()) 10% faster. I'm not saying that this is huge,
> but it seems like a significant improvement to me. Unfortunately, the
> second module cannot be easily moved out, because of an import loop)
>
> This is #23870
>
> Martin
>
> sage: l = [pi for pi in Permutations(8)]
> sage: %lprun -f Permutation.to_matrix -f MatrixSpace.matrix
> [pi.to_matrix() for pi in l]
> Timer unit: 1e-06 s
>
> Total time: 41.8048 s
> File:
> /home/martin/sage-develop/local/lib/python2.7/site-packages/sage/matrix/matrix_space.py
> Function: matrix at line 1354
>
> Line # Hits Time Per Hit % Time Line Contents
> ==============================================================
> 1354 def matrix(self, x=0,
> coerce=True, copy=True):
> ...
> 1493 362880 2800013 7.7 6.7 if x is None or
> isinstance(x, (int, integer.Integer)) and x == 0:
> 1494 if
> self._copy_zero: # faster to copy than to create a new one.
> 1495 return
> self.zero_matrix().__copy__()
> 1496 else:
> 1497 return
> self.__matrix_class(self, None, False, False)
> 1498 362880 2344112 6.5 5.6 if isinstance(x,
> (int, integer.Integer)) and x == 1:
> 1499 return
> self.identity_matrix().__copy__()
> 1500 362880 1577558 4.3 3.8 m, n, sparse =
> self.__nrows, self.__ncols, self.__is_sparse
> 1501 362880 1462412 4.0 3.5 if
> matrix.is_Matrix(x):
> 1502 if x.parent()
> is self:
> 1503 if
> x.is_immutable():
> 1504
> return x
> 1505 else:
> 1506
> return x.__copy__()
> 1507 else:
> 1508 if
> x.nrows() == m and x.ncols() == n:
> 1509 if
> (x.base_ring() == self.base_ring()
> 1510
> and x.is_sparse() and not sparse):
> 1511 #
> If x is sparse and large, calling x.dense_matrix()
> 1512 #
> is much faster than calling x.list(). See #20470.
> 1513
> return x.dense_matrix()
> 1514 x =
> x.list()
> 1515 else:
> 1516 raise
> ValueError("a matrix from %s cannot be converted to "
> 1517
> "a matrix in %s!" % (x.parent(), self))
> 1518 362880 5492940 15.1 13.1 from
> sage.groups.matrix_gps.group_element import \
> 1519
> is_MatrixGroupElement
> 1520 362880 4978054 13.7 11.9 from
> sage.modular.arithgroup.arithgroup_element import \
> 1521
> ArithmeticSubgroupElement
> 1522 362880 2613184 7.2 6.3 if
> is_MatrixGroupElement(x) or isinstance(x, ArithmeticSubgroupElement):
> 1523 return
> self(x.matrix(), copy=False)
> 1524 362880 2036306 5.6 4.9 if isinstance(x,
> (types.GeneratorType,)):
> 1525 x = list(x)
> 1526 362880 1226969 3.4 2.9 if not sparse and
> isinstance(x, dict):
> 1527 x =
> dict_to_list(x, m, n)
> 1528 coerce = True
> 1529 copy = False
> 1530 362880 1354039 3.7 3.2 MC =
> self.__matrix_class
> 1531 362880 2139861 5.9 5.1 if isinstance(x,
> (list, tuple)) and x:
> 1532 if len(x) ==
> m: # Try unpacking elements
> 1533 unpacked
> = True
> 1534 new_x = []
> 1535 for v in
> x:
> 1536 l =
> len(new_x)
> 1537 try:
> 1538
> from sage.structure.element import is_Vector
> 1539
> if isinstance(v, (list, tuple)) or is_Vector(v):
> 1540
> # The isinstance check should prevent the "flattening"
> 1541
> # of v if v is an iterable but not meant to be
> 1542
> # iterated (e.g., an element of a combinatorial free
> 1543
> # module).
> 1544
> new_x.extend(v)
> 1545
> else:
> 1546
> raise TypeError
> 1547
> if len(new_x) - l != n:
> 1548
> raise TypeError
> 1549
> except TypeError:
> 1550
> unpacked = False
> 1551 if
> unpacked:
> 1552 try:
> 1553
> if sparse:
> 1554
> return MC(self, list_to_dict(new_x, m, n),
> 1555
> copy=False, coerce=coerce)
> 1556
> else:
> 1557
> return MC(self, new_x, copy=False, coerce=coerce)
> 1558
> except (TypeError, ValueError):
> 1559
> pass
> 1560 if len(x) !=
> m * n:
> 1561 raise
> TypeError("cannot construct an element of {} from {}!"
> 1562
> .format(self, x))
> 1563 if sparse:
> 1564 x =
> list_to_dict(x, m, n)
> 1565 copy =
> False
> 1566 362880 13779340 38.0 33.0 return MC(self,
> x, copy=copy, coerce=coerce)
>
>
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