Opened 7 years ago
Closed 7 years ago
#17285 closed defect (fixed)
CIF is missing many functions
Reported by:  jdemeyer  Owned by:  

Priority:  major  Milestone:  sage6.6 
Component:  basic arithmetic  Keywords:  
Cc:  tmonteil, vdelecroix  Merged in:  
Authors:  Vincent Delecroix  Reviewers:  Jeroen Demeyer 
Report Upstream:  N/A  Work issues:  
Branch:  afccfe6 (Commits, GitHub, GitLab)  Commit:  afccfe62eac92dd2cea900f3bac44600e633aa7d 
Dependencies:  #17130  Stopgaps: 
Description (last modified by )
sage: CIF(cos(3/2))  TypeError Traceback (most recent call last) <ipythoninput314eae9038f0b3> in <module>() > 1 CIF(cos(Integer(3)/Integer(2))) /usr/local/src/sageconfig/local/lib/python2.7/sitepackages/sage/rings/complex_interval_field.pyc in __call__(self, x, im) 378 379 try: > 380 return x._complex_mpfi_( self ) 381 except AttributeError: 382 pass /usr/local/src/sageconfig/local/lib/python2.7/sitepackages/sage/symbolic/expression.so in sage.symbolic.expression.Expression._complex_mpfi_ (build/cythonized/sage/symbolic/expression.cpp:8043)()
The reason that this fails is:
sage: CIF(3/2).cos()  AttributeError Traceback (most recent call last) <ipythoninput1396dae572cb36> in <module>() > 1 CIF(Integer(3)/Integer(2)).cos() /usr/local/src/sageconfig/local/lib/python2.7/sitepackages/sage/structure/element.so in sage.structure.element.Element.__getattr__ (build/cythonized/sage/structure/element.c:4068)() /usr/local/src/sageconfig/local/lib/python2.7/sitepackages/sage/structure/misc.so in sage.structure.misc.getattr_from_other_class (build/cythonized/sage/structure/misc.c:1631)() AttributeError: 'sage.rings.complex_interval.ComplexIntervalFieldElement' object has no attribute 'cos'
This problem was also encoutered on this ask thread.
Change History (22)
comment:1 Changed 7 years ago by
 Component changed from symbolics to basic arithmetic
 Description modified (diff)
 Summary changed from CIF(cos(3/2)) fails to CIF is missing many functions
comment:2 followup: ↓ 3 Changed 7 years ago by
 Cc tmonteil added
 Description modified (diff)
comment:3 in reply to: ↑ 2 Changed 7 years ago by
Replying to tmonteil:
Are you working on this ?
No.
Is a solution involving the use of the (already defined)
.exp()
method acceptable on the short term (it may not lead to the thinest possible intervals), or do you think about some more accurate way of writing those ?
I think it's acceptable to rely on exp()
but instead, I would rather use the structure of the exp()
method: completely reduce the computation to a computation in RIF
.
comment:4 Changed 7 years ago by
For best accuracy, one should use cos(a+bi) = cos(a)*cosh(b) + sin(a)*sinh(b)*i
and sin(a+bi) = sin(a)*cosh(b) + cos(a)*sinh(b)*i
(if I got those formulas right).
There's a mpfi_sin_cos
but it looks like there's no mpfi_sinh_cosh
yet.
comment:5 Changed 7 years ago by
 Cc vdelecroix added
This is also responsible for
sage: a = RLF(cos(2/3)) sage: b = CLF(QQbar(2).sqrt()) sage: a + b <repr(<sage.rings.real_lazy.LazyBinop at 0x7fb7ffc28680>) failed: TypeError: unable to simplify to a complex interval approximation>
comment:6 Changed 7 years ago by
 Branch set to u/vdelecroix/17285
 Commit set to dd4cf4e61cbc44485985e1f74de201c87ad06bc9
 Status changed from new to needs_review
New commits:
dd4cf4e  Trac 17285: CIF trigonometric functions

comment:7 Changed 7 years ago by
This is not the fastest and safest way possible (the obtained interval is sometimes too large). But at least, the given implementation has the feature that trigonometric functions preserve real and imaginary axes...
Vincent
comment:8 Changed 7 years ago by
Note: the link to the ask question is dead!
comment:9 followup: ↓ 10 Changed 7 years ago by
I don't like the added complexity of having 3 branches in every function. Why not just use the generic case everywhere?
comment:10 in reply to: ↑ 9 Changed 7 years ago by
Replying to jdemeyer:
I don't like the added complexity of having 3 branches in every function. Why not just use the generic case everywhere?
The main reason is to avoid numerical noise (I want the cosine of a real number to be a real number). You have
sage: a = CIF(2,0) sage: I = CIF.gen() sage: ((I*a).exp() + (I*a).exp()) / 2 0.4161468365471424? + 0.?e16*I
It should be fine to remove the imaginary branch, but then it would be less precise
sage: a = CIF(0,2) sage: b1 = CIF(0, a.imag().cosh()) sage: b1.diameter() 1.33393183261575e16 sage: b2 = ((I*a).exp() + (I*a).exp()) / 2 sage: b2.diameter() 2.36079803558624e16
Vincent
comment:11 Changed 7 years ago by
 Milestone changed from sage6.4 to sage6.6
 Status changed from needs_review to needs_work
For the sine and cosine, you can use the formula at the end of http://en.wikipedia.org/wiki/Trigonometric_functions#Relationship_to_exponential_function_and_complex_numbers which computes the real and imaginary part separately. Assuming that sinh(0) = 0 exactly, this formula will not introduce a fake imaginary part.
comment:12 Changed 7 years ago by
 Commit changed from dd4cf4e61cbc44485985e1f74de201c87ad06bc9 to 3f8cd4178d279dbb6e5ad87c3f4a1c9f5ac75548
Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:
3f8cd41  Trac 17285: CIF trigonometric functions

comment:13 Changed 7 years ago by
 Status changed from needs_work to needs_review
New implementation using other trigonometric identities (and much faster).
For tan
and tanh
this is certainly not the best possible.
Vincent
comment:14 Changed 7 years ago by
 Reviewers set to Jeroen Demeyer
 Status changed from needs_review to needs_work
You're not actually supposed to do this:
from sage.ext.interrupt cimport sig_on, sig_off
The official way is still include "sage/ext/interrupt.pxi"
(and this will even become mandatory after #18027)
comment:15 Changed 7 years ago by
I like the new code. However, a few comments:
 move the
# cos(x + yi) = ...
comments inside the docstring as anALGORITHM:
block.  move the
mpfi_init2()
andmpfi_clear()
outside thesig_on()
/sig_off()
(it's not really wrong to put them inside, but it's certainly safer outside)
comment:16 Changed 7 years ago by
 Commit changed from 3f8cd4178d279dbb6e5ad87c3f4a1c9f5ac75548 to afccfe62eac92dd2cea900f3bac44600e633aa7d
Branch pushed to git repo; I updated commit sha1. New commits:
afccfe6  Trac 17285: signal handling + doc

comment:17 Changed 7 years ago by
 Status changed from needs_work to needs_review
comment:18 Changed 7 years ago by
 Status changed from needs_review to positive_review
comment:19 followup: ↓ 20 Changed 7 years ago by
Thanks for the review.
Just one related question. With the current code, if a KeyboardInterrupt
happens in between the sig_on/sig_off
block, then the code mpfi_clear(tmp)
will never get called and hence the memory allocated to tmp
will not be freed. Is there a clean solution for that?
comment:20 in reply to: ↑ 19 Changed 7 years ago by
comment:21 Changed 7 years ago by
 Description modified (diff)
comment:22 Changed 7 years ago by
 Branch changed from u/vdelecroix/17285 to afccfe62eac92dd2cea900f3bac44600e633aa7d
 Resolution set to fixed
 Status changed from positive_review to closed
Are you working on this ?
Is a solution involving the use of the (already defined)
.exp()
method acceptable on the short term (it may not lead to the thinest possible intervals), or do you think about some more accurate way of writing those ?