Opened 8 months ago
Closed 7 months ago
#30061 closed defect (fixed)
Speed up constructing highdimensional Euclidean spaces
Reported by:  mkoeppe  Owned by:  

Priority:  major  Milestone:  sage9.2 
Component:  geometry  Keywords:  
Cc:  egourgoulhon, tscrim, nbruin, ghmwageringel, ghmjungmath  Merged in:  
Authors:  Eric Gourgoulhon  Reviewers:  Matthias Koeppe 
Report Upstream:  N/A  Work issues:  
Branch:  3ce0c15 (Commits, GitHub, GitLab)  Commit:  3ce0c15fc9b3d71842946ad6a0b0449771b1ada7 
Dependencies:  #30065, #30074  Stopgaps: 
Description (last modified by )
The ndimensional Euclidean space is available in Sage in many variants.
This ticket brings the speed of the most basic operation (constructing the space) of EuclideanSpace
(from sagemanifolds) closer to that of the other variants.
Spaces without scalar product:
sage: VectorSpace(QQ, 5).category() Category of finite dimensional vector spaces with basis over (number fields and quotient fields and metric spaces) sage: %time VectorSpace(QQ, 5) CPU times: user 28 µs, sys: 9 µs, total: 37 µs Wall time: 40.1 µs Vector space of dimension 5 over Rational Field sage: %time VectorSpace(QQ, 80) CPU times: user 218 µs, sys: 1 µs, total: 219 µs Wall time: 223 µs Vector space of dimension 80 over Rational Field sage: %time VectorSpace(QQ, 1000) CPU times: user 208 µs, sys: 1 µs, total: 209 µs Wall time: 213 µs Vector space of dimension 1000 over Rational Field sage: for n in 5, 80, 1000, 4000, 10000, 100000: print("n = {}".format(n)); print("Construction: ", timeit("V = VectorSpace(QQ, {})".format(n),number=1,repeat=1)); u = [ x for x i ....: n range(n) ]; v = [ x + 1 for x in range(n) ]; V = VectorSpace(QQ, n); print("Distance: ", timeit("norm(V(u)  V(v))")) n = 5 Construction: 1 loop, best of 1: 56.1 ms per loop Distance: 625 loops, best of 3: 81.7 μs per loop n = 80 Construction: 1 loop, best of 1: 159 μs per loop Distance: 625 loops, best of 3: 299 μs per loop n = 1000 Construction: 1 loop, best of 1: 236 μs per loop Distance: 125 loops, best of 3: 3.18 ms per loop n = 4000 Construction: 1 loop, best of 1: 147 μs per loop Distance: 25 loops, best of 3: 11.3 ms per loop n = 10000 Construction: 1 loop, best of 1: 149 μs per loop Distance: 25 loops, best of 3: 28.7 ms per loop n = 100000 Construction: 1 loop, best of 1: 162 μs per loop Distance: 5 loops, best of 3: 296 ms per loop
sage: CombinatorialFreeModule(QQ, range(5)).category() Category of finite dimensional vector spaces with basis over Rational Field sage: %time CombinatorialFreeModule(QQ, range(5)) CPU times: user 80 µs, sys: 0 ns, total: 80 µs Wall time: 86.1 µs Free module generated by {0, 1, 2, 3, 4} over Rational Field sage: %time CombinatorialFreeModule(QQ, range(80)) CPU times: user 244 µs, sys: 10 µs, total: 254 µs Wall time: 259 µs Free module generated by {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79} over Rational Field sage: %time CombinatorialFreeModule(QQ, range(1000)) CPU times: user 322 µs, sys: 26 µs, total: 348 µs Wall time: 354 µs
sage: AffineSpace(RR, 5).category() Category of schemes over Real Field with 53 bits of precision sage: %time AffineSpace(RR, 5) CPU times: user 47 µs, sys: 1 µs, total: 48 µs Wall time: 51 µs Affine Space of dimension 5 over Real Field with 53 bits of precision sage: %time AffineSpace(RR, 80) CPU times: user 2 ms, sys: 39 µs, total: 2.04 ms Wall time: 2.04 ms Affine Space of dimension 80 over Real Field with 53 bits of precision sage: %time AffineSpace(RR, 1000) CPU times: user 62.8 ms, sys: 1.45 ms, total: 64.3 ms Wall time: 63.5 ms Affine Space of dimension 1000 over Real Field with 53 bits of precision
Spaces with scalar product:
sage: VectorSpace(QQ, 5, inner_product_matrix=matrix.identity(5)).category() Category of finite dimensional vector spaces with basis over (number fields and quotient fields and metric spaces) sage: %time VectorSpace(QQ, 5, inner_product_matrix=matrix.identity(5)) CPU times: user 6.55 ms, sys: 666 µs, total: 7.22 ms Wall time: 6.88 ms Ambient quadratic space of dimension 5 over Rational Field Inner product matrix: [1 0 0 0 0] [0 1 0 0 0] [0 0 1 0 0] [0 0 0 1 0] [0 0 0 0 1] sage: %time VectorSpace(QQ, 80, inner_product_matrix=matrix.identity(80)) CPU times: user 14.1 ms, sys: 439 µs, total: 14.6 ms Wall time: 14.4 ms Ambient quadratic space of dimension 80 over Rational Field Inner product matrix: sage: %time VectorSpace(QQ, 1000, inner_product_matrix=matrix.identity(1000)) CPU times: user 1.44 s, sys: 34.4 ms, total: 1.47 s Wall time: 1.48 s Ambient quadratic space of dimension 1000 over Rational Field Inner product matrix: ... sage: for n in 5, 80, 1000, 4000: print("n = {}".format(n)); print("Construction: ", timeit("V = VectorSpace(QQ, {}, inner_product_matrix=matrix.identity({}))".format(n, n),number=1,repeat=1)); u = [ x for x in range(n) ]; v = [ x + 1 for x in range(n) ]; V = VectorSpace(QQ, n, inner_product_matrix=matrix.identity(n)); print("Distance: ", timeit("t = V(u)V(v); sqrt(t.inner_product(t))")) n = 5 Construction: 1 loop, best of 1: 61.9 ms per loop Distance: 625 loops, best of 3: 49.4 μs per loop n = 80 Construction: 1 loop, best of 1: 9.75 ms per loop Distance: 625 loops, best of 3: 243 μs per loop n = 1000 Construction: 1 loop, best of 1: 1.51 s per loop Distance: 25 loops, best of 3: 14.4 ms per loop n = 4000 Construction: 1 loop, best of 1: 23.8 s per loop Distance: 5 loops, best of 3: 225 ms per loop
NB: It is not in the category MetricSpaces
, and thus the element methods dist
and abs
(?!) are missing... The methods __abs__
, norm
, and dot_product
are unrelated to the inner product matrix; only inner_product
uses inner_product_matrix
.
sage: EuclideanSpace(5).category() Category of smooth manifolds over Real Field with 53 bits of precision sage: %time EuclideanSpace(5) CPU times: user 177 ms, sys: 10.4 ms, total: 187 ms Wall time: 196 ms 5dimensional Euclidean space E^5 sage: %time EuclideanSpace(80) CPU times: user 32.8 s, sys: 758 ms, total: 33.6 s Wall time: 31.5 s 80dimensional Euclidean space E^80 sage: %time EuclideanSpace(1000) (timeout)
With this ticket (and its dependencies #30065, #30074):
sage: %time EuclideanSpace(5) CPU times: user 4.87 ms, sys: 372 µs, total: 5.24 ms Wall time: 4.93 ms 5dimensional Euclidean space E^5 sage: %time EuclideanSpace(80) CPU times: user 106 ms, sys: 4.52 ms, total: 110 ms Wall time: 92 ms 80dimensional Euclidean space E^80 sage: %time EuclideanSpace(1000) CPU times: user 1.04 s, sys: 33.5 ms, total: 1.07 s Wall time: 986 ms
Some caching is happening too. The second time:
sage: %time EuclideanSpace(1000) CPU times: user 207 ms, sys: 5.63 ms, total: 213 ms Wall time: 212 ms 1000dimensional Euclidean space E^1000
Scalar product without a space:
sage: %time DiagonalQuadraticForm(QQ, [1]*5) CPU times: user 60 µs, sys: 1e+03 ns, total: 61 µs Wall time: 62.9 µs Quadratic form in 5 variables over Rational Field with coefficients: [ 1 0 0 0 0 ] [ * 1 0 0 0 ] [ * * 1 0 0 ] [ * * * 1 0 ] [ * * * * 1 ] sage: %time DiagonalQuadraticForm(QQ, [1]*80) CPU times: user 1.35 ms, sys: 31 µs, total: 1.39 ms Wall time: 1.44 ms Quadratic form in 80 variables over Rational Field with coefficients: sage: %time DiagonalQuadraticForm(QQ, [1]*1000) CPU times: user 144 ms, sys: 2.85 ms, total: 147 ms Wall time: 147 ms Quadratic form in 1000 variables over Rational Field with coefficients:
Change History (70)
comment:1 Changed 8 months ago by
comment:2 followups: ↓ 3 ↓ 4 Changed 8 months ago by
EuclideanSpace(n)
creates the following objects:
 a real smooth manifold
E
of dimensionn
 a chart
X
onE
, representing the Cartesian coordinates  the coordinate vector frame associated with
X
 a Riemannian metric
g
onE
, with its components w.r.t.X
initialized todiag(1,1,...,1)
 the LeviCivita connection associated with
g
, with its components w.r.t.X
initialized to0
Most of the CPU time is spent in step 2, actually in creating the symbolic variables (elements of SR
) representing the Cartesian coordinates. The latter operation is equivalent to
sage: def create_coords(n): ....: coords = SR.var(["x{}".format(i) for i in range(n)], domain='real') ....: for x in coords: ....: assume(x, 'real')
and we have:
sage: %time EuclideanSpace(5) CPU times: user 345 ms, sys: 28 ms, total: 373 ms Wall time: 373 ms 5dimensional Euclidean space E^5 sage: %time create_coords(5) CPU times: user 456 ms, sys: 338 µs, total: 456 ms Wall time: 402 ms
sage: %time EuclideanSpace(20) CPU times: user 3.66 s, sys: 58.9 ms, total: 3.72 s Wall time: 3.48 s 20dimensional Euclidean space E^20 sage: %time create_coords(20) CPU times: user 3.38 s, sys: 75.3 ms, total: 3.45 s Wall time: 3.21 s
sage: %time EuclideanSpace(40) CPU times: user 12.6 s, sys: 253 ms, total: 12.8 s Wall time: 11.9 s 40dimensional EuclideanSR.var(["x{}".format(i) for i in range(n)], space E^40 sage: %time create_coords(40) CPU times: user 12.2 s, sys: 226 ms, total: 12.5 s Wall time: 11.4 s
Actually, it turns out that what takes most of CPU time is demanding that the symbolic variables are real. Indeed, if we skip domain='real'
and assume(x, 'real')
(each uses roughly half of the CPU time and, although they look redundant, both are actually necessary for efficient simplifications), we get very small times:
sage: %time coords = SR.var(["x{}".format(i) for i in range(40)]) CPU times: user 336 µs, sys: 9 µs, total: 345 µs Wall time: 350 µs
I don't know why SR.var('x', domain='real')
and assume(x, 'real')
are so slow...
NB: in the current setting, chart coordinates are stored as SR variables; but since SymPy can be used as the symbolic backend on manifolds, via
sage: E = EuclideanSpace(5) sage: E.set_calculus_method('sympy')
chart coordinates could be stored as SymPy variables, instead of SR ones.
comment:3 in reply to: ↑ 2 Changed 8 months ago by
Thanks very much for the explanation and analysis!
Replying to egourgoulhon:
I don't know why
SR.var('x', domain='real')
andassume(x, 'real')
are so slow...
I have created #30065 for this
comment:4 in reply to: ↑ 2 ; followup: ↓ 6 Changed 8 months ago by
Replying to egourgoulhon:
in the current setting, chart coordinates are stored as SR variables; but since SymPy can be used as the symbolic backend on manifolds, via
sage: E = EuclideanSpace(5) sage: E.set_calculus_method('sympy')chart coordinates could be stored as SymPy variables, instead of SR ones.
Thanks, I'll try this.
Actually, would it make sense (at least for simple cases) to have a calculus method that only uses Sage's rational functions?
comment:5 followup: ↓ 7 Changed 8 months ago by
In a related direction, would it be of interest to have a category of "algebraic" differential manifolds, as a differential geometry view on real varieties and semialgebraic sets (and their boundaries)?
comment:6 in reply to: ↑ 4 ; followups: ↓ 8 ↓ 10 Changed 8 months ago by
Replying to mkoeppe:
Replying to egourgoulhon:
in the current setting, chart coordinates are stored as SR variables; but since SymPy can be used as the symbolic backend on manifolds, via
sage: E = EuclideanSpace(5) sage: E.set_calculus_method('sympy')chart coordinates could be stored as SymPy variables, instead of SR ones.
Thanks, I'll try this.
Actually, would it make sense (at least for simple cases) to have a calculus method that only uses Sage's rational functions?
Yes, as soon as you don't have to take a square root, as for instance in evaluating the volume nform on a pseudoRiemannian manifold (aka LeviCivita tensor). In particular, this would forbid the computation of the triple scalar product within spherical coordinates in the Euclidean 3space.
Actually, it should be relatively easy to add a new calculus method, in addition to the two ones already implemented (SR and SymPy), via the classes CalculusMethod and ChartFunction.
comment:7 in reply to: ↑ 5 ; followup: ↓ 9 Changed 8 months ago by
Replying to mkoeppe:
In a related direction, would it be of interest to have a category of "algebraic" differential manifolds, as a differential geometry view on real varieties and semialgebraic sets (and their boundaries)?
Yes, I think so.
comment:8 in reply to: ↑ 6 Changed 8 months ago by
Replying to egourgoulhon:
Actually, would it make sense (at least for simple cases) to have a calculus method that only uses Sage's rational functions?
Yes, as soon as you don't have to take a square root, as for instance in evaluating the volume nform on a pseudoRiemannian manifold (aka LeviCivita tensor). In particular, this would forbid the computation of the triple scalar product within spherical coordinates in the Euclidean 3space.
Actually, it should be relatively easy to add a new calculus method, in addition to the two ones already implemented (SR and SymPy), via the classes CalculusMethod and ChartFunction.
Thanks! I have created #30070 for this.
comment:9 in reply to: ↑ 7 ; followup: ↓ 11 Changed 8 months ago by
Replying to egourgoulhon:
Replying to mkoeppe:
In a related direction, would it be of interest to have a category of "algebraic" differential manifolds, as a differential geometry view on real varieties and semialgebraic sets (and their boundaries)?
Yes, I think so.
OK, I have created #30069 for the case of real algebraic manifolds.
Does sagemanifolds currently implement manifolds with boundary, or is it planned to implement them?
comment:10 in reply to: ↑ 6 Changed 8 months ago by
Replying to egourgoulhon:
Replying to mkoeppe:
Actually, would it make sense (at least for simple cases) to have a calculus method that only uses Sage's rational functions?
Yes, as soon as you don't have to take a square root, as for instance in evaluating the volume nform on a pseudoRiemannian manifold (aka LeviCivita tensor). In particular, this would forbid the computation of the triple scalar product within spherical coordinates in the Euclidean 3space.
Actually, for spherical coordinates, there is already some issue with rational functions at the level of the metric tensor itself, since the components of the Euclidean metric involve the sine function.
comment:11 in reply to: ↑ 9 ; followup: ↓ 18 Changed 8 months ago by
comment:12 Changed 8 months ago by
sage: %prun EuclideanSpace(1000) 53513603 function calls (53508842 primitive calls) in 37.037 seconds Ordered by: internal time ncalls tottime percall cumtime percall filename:lineno(function) 2002006 4.658 0.000 4.786 0.000 tensorfield.py:684(_del_restrictions) 3003010 3.263 0.000 3.766 0.000 tensorfield.py:667(_del_derived) 2002000 3.076 0.000 18.325 0.000 free_module_tensor.py:1191(_set_comp_unsafe) 2002000 3.047 0.000 25.990 0.000 tensorfield_paral.py:820(set_comp) 2002000 2.571 0.000 22.942 0.000 free_module_tensor.py:1263(set_comp) 2002000 2.478 0.000 7.194 0.000 comp.py:864(__setitem__) 2002000 2.147 0.000 2.147 0.000 free_module_tensor.py:1474(del_other_comp) 2003000 2.029 0.000 2.398 0.000 comp.py:616(_check_indices) 2002000 1.825 0.000 20.150 0.000 tensorfield_paral.py:730(_set_comp_unsafe) 2002006 1.697 0.000 9.256 0.000 tensorfield_paral.py:708(_del_derived) 1 1.532 1.532 36.171 36.171 free_module_basis.py:566(__init__) 1002000 1.095 0.000 1.108 0.000 scalarfield.py:1154(is_trivial_zero) 1001003 0.931 0.000 7.942 0.000 vectorfield.py:1612(_del_derived) 8071534 0.813 0.000 0.813 0.000 {builtin method builtins.isinstance} 1 0.722 0.722 15.342 15.342 free_module_basis.py:375(__init__) 1001003 0.675 0.000 0.675 0.000 vectorfield.py:292(_del_dependencies) 2004002 0.656 0.000 0.656 0.000 finite_rank_free_module.py:2037(irange) 1001000 0.603 0.000 5.144 0.000 diff_form.py:1241(_del_derived) 6800 0.532 0.000 0.598 0.000 maxima_lib.py:412(_eval_line) 2045310 0.378 0.000 0.378 0.000 {builtin method builtins.hasattr} 1001003 0.335 0.000 5.137 0.000 multivectorfield.py:966(_del_derived) 5005023 0.334 0.000 0.334 0.000 {method 'clear' of 'dict' objects}
comment:13 followup: ↓ 16 Changed 8 months ago by
 Cc tscrim added
 Description modified (diff)
 Summary changed from EuclideanSpace constructor is slow to Constructing Euclidean spaces, many variants
comment:14 Changed 8 months ago by
 Description modified (diff)
comment:15 Changed 8 months ago by
 Description modified (diff)
comment:16 in reply to: ↑ 13 Changed 8 months ago by
Replying to mkoeppe:
Regarding the new ticket description, I would not say that the first three examples, namely VectorSpace(QQ, 5)
, CombinatorialFreeModule(QQ, range(5))
and AffineSpace(RR, 5)
do construct an Euclidean space, because their ouputs are not endowed with a scalar product, are they?
comment:17 Changed 8 months ago by
 Description modified (diff)
Of course, I agree. The summary already showed the categories of the spaces, but I've added two headers to emphasize this point.
comment:18 in reply to: ↑ 11 Changed 8 months ago by
Replying to egourgoulhon:
Replying to mkoeppe:
Does sagemanifolds currently implement manifolds with boundary, or is it planned to implement them?
No, manifolds with boundary are not implemented yet; it would be nice to have them.
I have created #30080 for this
comment:19 Changed 8 months ago by
 Description modified (diff)
comment:20 Changed 8 months ago by
 Dependencies set to #30065, #30074
comment:21 followup: ↓ 22 Changed 8 months ago by
For further speedups of EuclideanSpace(1000)
, it seems one would need to work on
sage.tensor.modules.free_module_basis.FreeModuleCoBasis.__init__
and FreeModuleBasis.__init__
. They dominate the computation now, using nonsparse operations, calling sage.manifolds.differentiable.tensorfield_paral.TensorFieldParal.set_comp
1000^{2} times. Does it make sense to make this sparse in some way? Would major speedups be expected from cythonizing this module?
comment:22 in reply to: ↑ 21 Changed 8 months ago by
Replying to mkoeppe:
For further speedups of
EuclideanSpace(1000)
, it seems one would need to work onsage.tensor.modules.free_module_basis.FreeModuleCoBasis.__init__
andFreeModuleBasis.__init__
. They dominate the computation now, using nonsparse operations, callingsage.manifolds.differentiable.tensorfield_paral.TensorFieldParal.set_comp
1000^{2} times. Does it make sense to make this sparse in some way?
Yes, actually in the current framework, any uninitialized component of a vector/tensor is considered to be zero. So in FreeModuleBasis.__init__
, we could skip the loop initializing the components of the basis vector to zero:
for i in fmodule.irange():
v = fmodule.element_class(fmodule)
 for j in fmodule.irange():
 v.set_comp(self)[j] = fmodule._ring.zero()
v.set_comp(self)[i] = fmodule._ring.one()
vl.append(v)
This would make the number of calls to TensorFieldParal.set_comp
to be 1000, instead in of 1000^{2} !
Similarly in FreeModuleCoBasis.__init_
:
for i in self._fmodule.irange(): v = self._fmodule.linear_form()  for j in self._fmodule.irange():  v.set_comp(basis)[j] = 0  v.set_comp(basis)[i] = 1 + v.set_comp(basis)[i] = self._fmodule._ring.one() vl.append(v)
The above unnecessary initializations to zero have been implemented at the early stage of the manifolds project, when we were not certain to keep the storage convention of having uninitialized components to be zero. Given the heavy use of that convention now, it's pretty safe to remove these lines.
comment:23 followup: ↓ 26 Changed 8 months ago by
 Branch set to public/manifolds/init_module_basis30061
 Commit set to fccbf438290e2404a79a4c7a650721120157a6c0
The changes suggested in comment:22 are implemented in the above branch.
New commits:
fccbf43  Improve initialization of elements of a free module basis

comment:24 Changed 8 months ago by
 Commit changed from fccbf438290e2404a79a4c7a650721120157a6c0 to 3ce0c15fc9b3d71842946ad6a0b0449771b1ada7
Branch pushed to git repo; I updated commit sha1. New commits:
134da39  sage.symbolic.assumptions.GenericDeclaration.assume: Validate against cached valid features first

1fbfb68  Update instead of overwriting

a99aa3f  Merge branch 't/30065/faster_maxima_assumptions' into t/30061/public/manifolds/init_module_basis30061

8b31261  sage.symbolic.assumptions.GenericDeclaration: Make it a UniqueRepresentation

51ea23d  sage.symbolic.assumptions.GenericDeclaration.assume: Check first if already in _assumptions

9119e82  sage.symbolic.assumptions._assumptions: Change from list to OrderDict

cda81ff  sage.symbolic.assumptions.GenericDeclaration: Make it hashable by inheriting comparisons from UniqueRepresentation

642836d  sage.symbolic.assumptions: Use dict instead of OrderedDict for _assumptions

3ce0c15  Merge branch 't/30074/even_faster_maxima_assumptions' into t/30061/public/manifolds/init_module_basis30061

comment:25 Changed 8 months ago by
Merged in the tickets listed as dependencies
comment:26 in reply to: ↑ 23 Changed 8 months ago by
Replying to egourgoulhon:
The changes suggested in comment:22 are implemented in the above branch.
Great! Together with the merged tickets, this now gives:
sage: %time EuclideanSpace(5) CPU times: user 4.87 ms, sys: 372 µs, total: 5.24 ms Wall time: 4.93 ms 5dimensional Euclidean space E^5 sage: %time EuclideanSpace(80) CPU times: user 106 ms, sys: 4.52 ms, total: 110 ms Wall time: 92 ms 80dimensional Euclidean space E^80 sage: %time EuclideanSpace(1000) CPU times: user 1.04 s, sys: 33.5 ms, total: 1.07 s Wall time: 986 ms
comment:27 Changed 8 months ago by
And some caching is happening too. The second time:
sage: %time EuclideanSpace(1000) CPU times: user 207 ms, sys: 5.63 ms, total: 213 ms Wall time: 212 ms 1000dimensional Euclidean space E^1000
comment:28 Changed 8 months ago by
That's faster than VectorSpace(QQ, 1000, inner_product_matrix=matrix.identity(1000))
comment:29 Changed 8 months ago by
Most of the caching is coming from #30074. Making the realdeclared symbolic variables known to Maxima is costly the first time; after that, it's free.
comment:30 Changed 8 months ago by
First time:
sage: %prun EuclideanSpace(10000) 4614917 function calls (4585885 primitive calls) in 42.685 seconds Ordered by: internal time ncalls tottime percall cumtime percall filename:lineno(function) 80096 35.217 0.000 35.779 0.000 maxima_lib.py:412(_eval_line) 25 0.529 0.021 0.529 0.021 {builtin method sage.libs.ecl.ecl_eval} 10000 0.425 0.000 39.373 0.004 {method 'var' of 'sage.symbolic.ring.SymbolicRing' objects} 20000 0.377 0.000 38.550 0.002 assumptions.py:213(assume) 20048 0.323 0.000 0.382 0.000 maxima_lib.py:274(max_to_string) 20006 0.275 0.000 0.288 0.000 free_module_tensor.py:258(__init__) 20000 0.208 0.000 0.460 0.000 assumptions.py:396(preprocess_assumptions) 56 0.207 0.004 0.207 0.004 {builtin method _imp.create_dynamic} 50000 0.190 0.000 0.190 0.000 latex.py:463(__add__) 209119 0.165 0.000 0.165 0.000 {builtin method builtins.hasattr} 20007 0.164 0.000 0.180 0.000 tensorfield_paral.py:689(_init_derived) 10032/1 0.139 0.000 42.050 42.050 {sage.misc.classcall_metaclass.typecall} 10139 0.129 0.000 0.130 0.000 {builtin method builtins.repr} 20001 0.125 0.000 0.143 0.000 interface.py:620(__getattr__) 714 0.119 0.000 0.119 0.000 {builtin method marshal.loads} 546190 0.114 0.000 0.114 0.000 {builtin method builtins.isinstance} 1 0.102 0.102 39.733 39.733 chart.py:1610(_init_coordinates) 10003 0.091 0.000 0.107 0.000 chart_func.py:318(__init__) 10000 0.091 0.000 0.460 0.000 {method '_maxima_init_' of 'sage.structure.sage_object.SageObject' objects} 40024 0.090 0.000 0.099 0.000 interface.py:491(_next_var_name) 20000 0.087 0.000 13.550 0.001 interface.py:587(function_call) 40024 0.086 0.000 15.460 0.000 maxima_lib.py:492(set) 30024 0.086 0.000 13.245 0.000 interface.py:251(__call__) 30024 0.082 0.000 13.139 0.000 interface.py:706(__init__) 30000 0.080 0.000 0.237 0.000 scalarfield.py:1154(is_trivial_zero) 20000 0.079 0.000 3.032 0.000 interface.py:534(_convert_args_kwds) 20024 0.078 0.000 16.639 0.001 interface.py:981(__del__) 20000 0.077 0.000 0.416 0.000 free_module_tensor.py:1191(_set_comp_unsafe) 160195 0.074 0.000 0.074 0.000 {method 'find' of 'str' objects} 30000 0.069 0.000 0.126 0.000 chart_func.py:810(is_trivial_zero) 10000 0.065 0.000 0.118 0.000 diff_form.py:1241(_del_derived) 10001 0.061 0.000 0.069 0.000 interface.py:419(_relation_symbols) 20048 0.059 0.000 0.059 0.000 {method 'python' of 'sage.libs.ecl.EclObject' objects} 90434 0.057 0.000 0.057 0.000 {method 'split' of 'str' objects} 20006 0.051 0.000 0.053 0.000 tensorfield.py:684(_del_restrictions) 30024 0.051 0.000 13.056 0.000 maxima_lib.py:561(_create) 56/50 0.049 0.001 0.054 0.001 {builtin method _imp.exec_dynamic} 20000 0.045 0.000 0.045 0.000 infinity.py:1020(gen) 30010 0.044 0.000 0.051 0.000 tensorfield.py:667(_del_derived) 20000 0.044 0.000 21.876 0.001 interface.py:653(__call__) 20001 0.044 0.000 0.070 0.000 vectorfield_module.py:1765(dual_exterior_power) 20000 0.042 0.000 0.251 0.000 comp.py:864(__setitem__) 30000 0.042 0.000 0.050 0.000 comp.py:616(_check_indices) 20000 0.041 0.000 0.043 0.000 interface.py:603(_function_call_string) 10001 0.040 0.000 0.332 0.000 vectorfield.py:1533(__init__) 10000 0.040 0.000 0.224 0.000 expression_conversions.py:155(__call__) 20024 0.039 0.000 16.518 0.001 maxima_lib.py:516(clear)
comment:31 Changed 8 months ago by
Second time:
2221257 function calls (2221199 primitive calls) in 2.982 seconds Ordered by: internal time ncalls tottime percall cumtime percall filename:lineno(function) 50000 0.297 0.000 0.297 0.000 latex.py:463(__add__) 30010 0.243 0.000 0.251 0.000 tensorfield.py:667(_del_derived) 20006 0.214 0.000 0.226 0.000 free_module_tensor.py:258(__init__) 10000 0.178 0.000 0.266 0.000 {method 'var' of 'sage.symbolic.ring.SymbolicRing' objects} 10003 0.091 0.000 0.107 0.000 chart_func.py:318(__init__) 30000 0.086 0.000 0.254 0.000 scalarfield.py:1154(is_trivial_zero) 20000 0.085 0.000 0.656 0.000 free_module_tensor.py:1191(_set_comp_unsafe) 10000 0.077 0.000 0.136 0.000 diff_form.py:1241(_del_derived) 130046 0.075 0.000 0.075 0.000 {builtin method builtins.hasattr} 30000 0.074 0.000 0.134 0.000 chart_func.py:810(is_trivial_zero) 20007 0.073 0.000 0.090 0.000 tensorfield_paral.py:689(_init_derived) 20000 0.068 0.000 0.085 0.000 assumptions.py:396(preprocess_assumptions) 20006 0.055 0.000 0.057 0.000 tensorfield.py:684(_del_restrictions) 20001 0.049 0.000 0.076 0.000 vectorfield_module.py:1765(dual_exterior_power) 270213 0.048 0.000 0.048 0.000 {builtin method builtins.isinstance} 30000 0.045 0.000 0.054 0.000 comp.py:616(_check_indices) 1 0.044 0.044 0.412 0.412 chart.py:1610(_init_coordinates) 20000 0.044 0.000 0.271 0.000 comp.py:864(__setitem__) 10001 0.042 0.000 0.276 0.000 vectorfield.py:1533(__init__) 30001 0.040 0.000 0.040 0.000 chart_func.py:460(expr) 20000 0.034 0.000 0.714 0.000 free_module_tensor.py:1263(set_comp) 10001 0.034 0.000 0.243 0.000 diff_form.py:1137(__init__) 20000 0.033 0.000 0.746 0.000 tensorfield_paral.py:820(set_comp) 30000 0.033 0.000 0.033 0.000 {method '_latex_' of 'sage.symbolic.expression.Expression' objects} 10001 0.033 0.000 0.059 0.000 free_module_alt_form.py:298(_new_comp) 30000 0.033 0.000 0.033 0.000 free_module_tensor.py:923(set_name) 10001 0.028 0.000 0.054 0.000 free_module_element.py:230(_new_comp) 10000 0.027 0.000 0.065 0.000 comp.py:3061(_ordered_indices) 20000 0.026 0.000 0.026 0.000 free_module_tensor.py:1474(del_other_comp) 10001 0.026 0.000 0.026 0.000 chart.py:311(<genexpr>) 10000 0.025 0.000 0.178 0.000 comp.py:4784(__setitem__) 120055 0.025 0.000 0.042 0.000 {builtin method builtins.len} 10001 0.024 0.000 0.024 0.000 euclidean.py:858(<genexpr>) 30010 0.024 0.000 0.024 0.000 tensorfield.py:654(_init_derived) 10001 0.023 0.000 0.023 0.000 vectorframe.py:1764(<genexpr>) 10001 0.023 0.000 0.038 0.000 vectorfield_module.py:1709(exterior_power) 3 0.022 0.007 0.339 0.113 free_module_basis.py:208(set_name) 20005 0.022 0.000 0.052 0.000 comp.py:496(__init__) 1 0.022 0.022 1.688 1.688 free_module_basis.py:566(__init__) 20006 0.022 0.000 0.318 0.000 tensorfield_paral.py:708(_del_derived)
comment:32 Changed 8 months ago by
 Cc nbruin added
comment:33 Changed 8 months ago by
First time profile, filtered to methods in maxima_lib
and sage.libs.ecl
:
sage: %prun EuclideanSpace(5000) 40096 7.970 0.000 8.203 0.000 maxima_lib.py:412(_eval_line) 25 0.511 0.020 0.511 0.020 {builtin method sage.libs.ecl.ecl_eval} 10048 0.133 0.000 0.158 0.000 maxima_lib.py:274(max_to_string) 20024 0.037 0.000 3.505 0.000 maxima_lib.py:492(set) 15024 0.021 0.000 2.934 0.000 maxima_lib.py:561(_create) 10024 0.017 0.000 3.597 0.000 maxima_lib.py:516(clear) 40096 0.015 0.000 0.017 0.000 maxima_lib.py:463(<listcomp>) 5023 0.007 0.000 0.275 0.000 maxima_lib.py:541(get)
comment:34 followup: ↓ 35 Changed 8 months ago by
The time spent on maxima_lib
can probably still be reduced a little by using ECL objects directly for "context", but I will not work on this at the moment.
comment:35 in reply to: ↑ 34 Changed 8 months ago by
comment:36 Changed 8 months ago by
comment:37 Changed 8 months ago by
Next I think we can benchmark some other basic operations in the spaces
comment:38 Changed 8 months ago by
 Description modified (diff)
comment:39 Changed 8 months ago by
 Description modified (diff)
comment:40 followup: ↓ 41 Changed 8 months ago by
Does EuclideanSpace
know how to compute geodesics, and thus distances?
comment:41 in reply to: ↑ 40 ; followup: ↓ 44 Changed 8 months ago by
Replying to mkoeppe:
Does
EuclideanSpace
know how to compute geodesics, and thus distances?
Yes it does, via IntegratedGeodesic. Note however that for Euclidean spaces, geodesics are trivial (straight lines).
comment:42 Changed 8 months ago by
By the way, an overview of EuclideanSpace
capabilities is in this thematic tutorial; see also the associated notebooks and this section of the reference manual.
comment:43 Changed 8 months ago by
Thanks for the pointers. It's on my list of things to learn more systematically about sagemanifolds.
comment:44 in reply to: ↑ 41 ; followup: ↓ 45 Changed 8 months ago by
Replying to egourgoulhon:
Replying to mkoeppe:
Does
EuclideanSpace
know how to compute geodesics, and thus distances?Yes it does, via IntegratedGeodesic.
Should it (and presumably other manifold classes) be added to the category MetricSpaces
then (#30062)?
comment:45 in reply to: ↑ 44 ; followup: ↓ 47 Changed 8 months ago by
comment:46 Changed 8 months ago by
 Cc ghmwageringel added
comment:47 in reply to: ↑ 45 Changed 8 months ago by
Replying to egourgoulhon:
Replying to mkoeppe:
Should it (and presumably other manifold classes) be added to the category
MetricSpaces
then (#30062)?Yes. It will be easy to implement the distance function by means of the Cartesian chart.
Thanks. I have added this task to #30062.
comment:48 Changed 8 months ago by
 Cc ghmjungmath added
comment:49 followup: ↓ 52 Changed 8 months ago by
Should we set this ticket to "needs_review"?
comment:50 followup: ↓ 53 Changed 8 months ago by
Can you please briefly summarize in the description what has actually been done and what the new benefits are? It is very difficult for me to piece that all together just from the comments and cross references to other tickets. Thanks! :)
In general, I would wait until the dependent tickets are merged. However, I am a bad role model due to my impatience.
comment:51 Changed 8 months ago by
 Status changed from new to needs_review
comment:52 in reply to: ↑ 49 Changed 8 months ago by
comment:53 in reply to: ↑ 50 ; followup: ↓ 54 Changed 8 months ago by
Replying to ghmjungmath:
Can you please briefly summarize in the description what has actually been done and what the new benefits are? It is very difficult for me to piece that all together just from the comments and cross references to other tickets. Thanks! :)
The code added in this ticket is described in comment:22 and comment:23. The other code in the ticket branch arises from the dependencies tickets #30065 and #30074.
comment:54 in reply to: ↑ 53 Changed 8 months ago by
Replying to egourgoulhon:
The code added in this ticket is described in comment:22 and comment:23. The other code in the ticket branch arises from the dependencies tickets #30065 and #30074.
Thanks!
comment:55 Changed 8 months ago by
 Summary changed from Constructing Euclidean spaces, many variants to Speed up constructing highdimensional Euclidean spaces
comment:56 Changed 8 months ago by
 Description modified (diff)
comment:57 Changed 8 months ago by
 Description modified (diff)
comment:58 Changed 8 months ago by
 Description modified (diff)
comment:59 Changed 8 months ago by
 Description modified (diff)
comment:60 Changed 8 months ago by
 Reviewers set to Matthias Koeppe
 Status changed from needs_review to positive_review
comment:61 Changed 8 months ago by
 Status changed from positive_review to needs_work
Patchbot not green. The latest branch of #30074 has not been merged yet.
comment:62 followup: ↓ 63 Changed 8 months ago by
 Status changed from needs_work to positive_review
That is not a real error (the other patchbot also came back green). You don't need to have all of the other branches merged in.
comment:63 in reply to: ↑ 62 ; followup: ↓ 64 Changed 8 months ago by
Replying to tscrim:
That is not a real error (the other patchbot also came back green).
It is a real error. Pyflakes is complaining about an unused import.
You don't need to have all of the other branches merged in.
Why is that? Wouldn't that cause a merge conflict later on?
comment:64 in reply to: ↑ 63 ; followup: ↓ 65 Changed 8 months ago by
Replying to ghmjungmath:
Replying to tscrim:
That is not a real error (the other patchbot also came back green).
It is a real error. Pyflakes is complaining about an unused import.
No, it is not. Pyflakes are not real errors (but they are good to clear).
You don't need to have all of the other branches merged in.
Why is that? Wouldn't that cause in a merge conflict later on?
There is no need to add unnecessary extra merge commits when there is no conflict or a need to have the latest branch. If later changes on the first branch are done to unrelated parts to the changes on this branch, there is no conflict.
Addendum  The pyflakes is handled on the later commits from #30074. So changing that here would cause a merge conflict and resolve a problem already fixed.
comment:65 in reply to: ↑ 64 ; followup: ↓ 66 Changed 8 months ago by
Replying to tscrim:
Replying to ghmjungmath:
Replying to tscrim:
That is not a real error (the other patchbot also came back green).
It is a real error. Pyflakes is complaining about an unused import.
No, it is not. Pyflakes are not real errors (but they are good to clear).
Okay, I see what you mean.
Replying to tscrim:
Addendum  The pyflakes is handled on the later commits from #30074. So changing that here would cause a merge conflict and resolve a problem already fixed.
Mh. Sorry, I don't get it. The #30074 will be merged into develop first because of the dependence, right? Afterwards, this ticket will be merged. If this ticket consists of an older version than #30074, this would cause a merge conflict, wouldn't it? Or, at least, the pyflakes error would be added again.
comment:66 in reply to: ↑ 65 ; followup: ↓ 67 Changed 8 months ago by
Replying to ghmjungmath:
Replying to tscrim:
Addendum  The pyflakes is handled on the later commits from #30074. So changing that here would cause a merge conflict and resolve a problem already fixed.
Mh. Sorry, I don't get it. The #30074 will be merged into develop first because of the dependence, right? Afterwards, this ticket will be merged. If this ticket consists of an older version than #30074, this would cause a merge conflict, wouldn't it? Or, at least, the pyflakes error would be added again.
No. The result will look like this:
B0XTM \ / 00H
where T
is this branch and H
is the head of #30074. So the #30074 branch will be merged first (all commits marked 0
starting from the latest beta B
and H
), then the commits from this branch (labelled X
and T
), which will result in the merge commit M
. This would be exactly the same as if you merged in the latest commits from #30074 because that would be doing the same thing. The only difference is you have an extra merge commit in where this branch is pointing to.
comment:67 in reply to: ↑ 66 ; followup: ↓ 68 Changed 8 months ago by
Replying to tscrim:
No. The result will look like this:
B0XTM \ / 00Hwhere
T
is this branch andH
is the head of #30074. So the #30074 branch will be merged first (all commits marked0
starting from the latest betaB
andH
), then the commits from this branch (labelledX
andT
), which will result in the merge commitM
. This would be exactly the same as if you merged in the latest commits from #30074 because that would be doing the same thing. The only difference is you have an extra merge commit in where this branch is pointing to.
Ah, I see. This is because the commit in #30074 is more recent, right?
comment:68 in reply to: ↑ 67 ; followup: ↓ 69 Changed 8 months ago by
Replying to ghmjungmath:
Ah, I see. This is because the commit in #30074 is more recent, right?
Yes, but it is still based off a common base commit.
comment:69 in reply to: ↑ 68 Changed 8 months ago by
Replying to tscrim:
Replying to ghmjungmath:
Ah, I see. This is because the commit in #30074 is more recent, right?
Yes, but it is still based off a common base commit.
Ah well. Thank you for explaining this, and sorry for delaying the process. This is good to know for future commits of mine.
comment:70 Changed 7 months ago by
 Branch changed from public/manifolds/init_module_basis30061 to 3ce0c15fc9b3d71842946ad6a0b0449771b1ada7
 Resolution set to fixed
 Status changed from positive_review to closed
Most of the time spent seems to come from SR (Maxima). Is it possible to speed things up for this easy special case, avoiding symbolic computation completely?