Opened 11 years ago

Last modified 8 years ago

#9706 closed enhancement

New Version of orthogonal Polynomials — at Version 37

Reported by: maldun Owned by: burcin, maldun
Priority: major Milestone: sage-6.1
Component: symbolics Keywords: orthogonal polynomials, symbolics
Cc: fredrik.johansson, fstan, kcrisman Merged in:
Authors: Stefan Reiterer Reviewers: Burcin Erocal
Report Upstream: N/A Work issues:
Branch: Commit:
Dependencies: Stopgaps:

Status badges

Description (last modified by tscrim)

The current implementation of orthogonal polynomials is just a wrapper around maxima. (see http://wiki.sagemath.org/symbolics/) This update holds the following changes:

  • using of the pynac class for symbolic functions.
  • faster evaluation in general
  • evaluation of special values
  • mpmath for numeric evaluation

Remarks:

  • The current patch needs scipy-0.8. One has to install it before testing (see #9808 for spkg's and installation instructions)
  • Some of the old doctests in the old file don't work any more, due to coercion problems with pynac (see #9769)
  • Some doctests in Sage change, due to the fact that new BuiltIn? functions are added. symbolic.random_test.py had output changes since the random expression creation changed of course. The tests in pynac.pyx also changed, but this has a strange behavior (see below).

Apply:

Change History (48)

Changed 11 years ago by maldun

A new version of the orthogonal_polys.py file.

Changed 11 years ago by maldun

Newer version, with legendre_P, and faster evaluation of symbolic expressions

Changed 11 years ago by maldun

Version from 10. August 2010

Changed 11 years ago by maldun

Latest version. It holds classes of all polys (but not all completed yet)

comment:1 follow-up: Changed 11 years ago by maldun

All Polys now have their own class. Much faster evaluation is added. Numerical evaluation is provided. Except for legendre_Q, gen_legendre_P, and gen_legendre_Q these aren't ready yet

comment:2 in reply to: ↑ 1 Changed 11 years ago by maldun

Replying to maldun:

All Polys now have their own class. Much faster evaluation is added. Numerical evaluation is provided. Except for legendre_Q, gen_legendre_P, and gen_legendre_Q these aren't ready yet

orthogonal_polys4.py hold all changes but is not a patch yet, because it holds old code fragments, which I have to clean up...

comment:3 Changed 11 years ago by fredrik.johansson

  • Cc fredrik.johansson added

comment:4 Changed 11 years ago by maldun

I added in the latest patch (and orthogonal_polys.4.py contains these changes also) a new symbolic evaluation method for the orthogonal polynomials: Instead of call Maxima or use of the recursion, the polynomial is evaluated just using explicit formulas from Abramowitz and Stegun. This is an O(n) algorithm of course.

a little comparison on my machine: old version:

sage: time chebyshev_T(10,x); CPU times: user 0.01 s, sys: 0.00 s, total: 0.01 s Wall time: 0.04 s sage: time chebyshev_T(100,x); CPU times: user 0.13 s, sys: 0.01 s, total: 0.14 s Wall time: 0.23 s sage: time chebyshev_T(1000,x); CPU times: user 5.01 s, sys: 0.01 s, total: 5.02 s Wall time: 6.98 s sage time chebyshev_T(5000,x); ??? (I got no output her after 2min)

sage: time gegenbauer(10,5,x); CPU times: user 0.01 s, sys: 0.00 s, total: 0.01 s Wall time: 0.05 s sage: time gegenbauer(100,5,x); CPU times: user 0.19 s, sys: 0.00 s, total: 0.19 s Wall time: 0.29 s sage: time gegenbauer(1000,5,x); CPU times: user 5.46 s, sys: 0.02 s, total: 5.48 s Wall time: 7.79 s

New Version sage: time chebyshev_T(10,x); CPU times: user 0.01 s, sys: 0.00 s, total: 0.01 s Wall time: 0.01 s sage: time chebyshev_T(100,x); CPU times: user 0.06 s, sys: 0.00 s, total: 0.06 s Wall time: 0.08 s sage: time chebyshev_T(1000,x); CPU times: user 1.22 s, sys: 0.00 s, total: 1.22 s Wall time: 1.22 s sage: time chebyshev_T(5000,x); CPU times: user 27.17 s, sys: 0.15 s, total: 27.32 s Wall time: 27.46 s

sage: time gegenbauer(10,5,x); CPU times: user 0.01 s, sys: 0.00 s, total: 0.01 s Wall time: 0.01 s sage: time gegenbauer(100,5,x); CPU times: user 0.03 s, sys: 0.00 s, total: 0.03 s Wall time: 0.04 s sage: time gegenbauer(1000,5,x); CPU times: user 1.08 s, sys: 0.01 s, total: 1.09 s Wall time: 1.11 s

A little bit faster :) I also don't need to spawn an instance of maxima which makes the initialisation faster.

And now also wider symbolic evaluation is possible:

old version: sage: var('a') a sage: gegenbauer(3,a,x) ... NameError?: name 'a' is not defined

new version: sage: var('a') a sage: gegenbauer(3,a,x) 4/3*x3*gamma(a + 3) - 2*x*gamma(a + 2)

The code needs now some cleanup, especially the documentations. The complete versions for legendre_Q, gen_legendre_P, and gen_legendre_Q will not be finished soon since the mpmath functions, don't seem to work correctly... I only provide a call function for maxima for them now.

comment:5 follow-up: Changed 11 years ago by fredrik.johansson

The complete versions for legendre_Q, gen_legendre_P, and gen_legendre_Q will not be finished soon since the mpmath functions, don't seem to work correctly...

Care to elaborate?

Changed 11 years ago by maldun

Latest version from 12. August 2010 (with bugfix in legendre_P)

comment:6 Changed 11 years ago by maldun

Killed bug in legendre_P

comment:7 in reply to: ↑ 5 Changed 11 years ago by maldun

Replying to fredrik.johansson:

The complete versions for legendre_Q, gen_legendre_P, and gen_legendre_Q will not be finished soon since the mpmath functions, don't seem to work correctly...

Care to elaborate?

Sorry for the late answer, I was on holidays.

In mpmath I have probs with the legenp and legenq functions. For some inputs I get this error:

sage: mpmath.call(mpmath.legenp,5,1,2)
---------------------------------------------------------------------------
OverflowError                             Traceback (most recent call last)

/home/maldun/prog/sage/ortho/<ipython console> in <module>()

/home/maldun/sage/sage-4.5.1/local/lib/python2.6/site-packages/sage/libs/mpmath/utils.so in sage.libs.mpmath.utils.call (sage/libs/mpmath/utils.c:5021)()

/home/maldun/sage/sage-4.5.1/local/lib/python2.6/site-packages/mpmath/functions/hypergeometric.pyc in legenp(ctx, n, m, z, type, **kwargs)
   1481             T = [1+z, 1-z], [g, -g], [], [1-m], [-n, n+1], [1-m], 0.5*(1-z)
   1482             return (T,)
-> 1483         return ctx.hypercomb(h, [n,m], **kwargs)
   1484     if type == 3:
   1485         def h(n,m):

/home/maldun/sage/sage-4.5.1/local/lib/python2.6/site-packages/mpmath/functions/hypergeometric.pyc in hypercomb(ctx, function, params, discard_known_zeros, **kwargs)
    125                     [ctx.gamma(a) for a in alpha_s] + \
    126                     [ctx.rgamma(b) for b in beta_s] + \
--> 127                     [ctx.power(w,c) for (w,c) in zip(w_s,c_s)])
    128                 if verbose:
    129                     print "    Value:", v

/home/maldun/sage/sage-4.5.1/local/lib/python2.6/site-packages/mpmath/ctx_base.pyc in power(ctx, x, y)
    417             3.16470269330255923143453723949e+12978188
    418         """
--> 419         return ctx.convert(x) ** ctx.convert(y)
    420 
    421     def _zeta_int(ctx, n):

/home/maldun/sage/sage-4.5.1/local/lib/python2.6/site-packages/sage/libs/mpmath/ext_main.so in sage.libs.mpmath.ext_main.mpnumber.__pow__ (sage/libs/mpmath/ext_main.c:13946)()

/home/maldun/sage/sage-4.5.1/local/lib/python2.6/site-packages/sage/libs/mpmath/ext_main.so in sage.libs.mpmath.ext_main.binop (sage/libs/mpmath/ext_main.c:4588)()

/home/maldun/sage/sage-4.5.1/local/lib/python2.6/site-packages/mpmath/libmp/libelefun.pyc in mpf_pow(s, t, prec, rnd)
    340     # General formula: s**t = exp(t*log(s))
    341     # TODO: handle rnd direction of the logarithm carefully
--> 342     c = mpf_log(s, prec+10, rnd)
    343     return mpf_exp(mpf_mul(t, c), prec, rnd)
    344 

/home/maldun/sage/sage-4.5.1/local/lib/python2.6/site-packages/mpmath/libmp/libelefun.pyc in mpf_log(x, prec, rnd)
    725     # optimal between 1000 and 100,000 digits.
    726     if wp <= LOG_TAYLOR_PREC:
--> 727         m = log_taylor_cached(lshift(man, wp-bc), wp)
    728         if mag:
    729             m += mag*ln2_fixed(wp)

/home/maldun/sage/sage-4.5.1/local/lib/python2.6/site-packages/mpmath/libmp/libelefun.pyc in log_taylor_cached(x, prec)
    643     else:
    644         a = n << (cached_prec - LOG_TAYLOR_SHIFT)
--> 645         log_a = log_taylor(a, cached_prec, 8)
    646         log_taylor_cache[n, cached_prec] = (a, log_a)
    647     a >>= dprec

/home/maldun/sage/sage-4.5.1/local/lib/python2.6/site-packages/mpmath/libmp/libelefun.pyc in log_taylor(x, prec, r)
    607     """
    608     for i in xrange(r):
--> 609         x = isqrt_fast(x<<prec)
    610     one = MPZ_ONE << prec
    611     v = ((x-one)<<prec)//(x+one)

/home/maldun/sage/sage-4.5.1/local/lib/python2.6/site-packages/mpmath/libmp/libintmath.pyc in isqrt_fast_python(x)
    240                     y = (y + x//y) >> 1
    241         return y
--> 242     bc = bitcount(x)
    243     guard_bits = 10
    244     x <<= 2*guard_bits

/home/maldun/sage/sage-4.5.1/local/lib/python2.6/site-packages/mpmath/libmp/libintmath.pyc in python_bitcount(n)
     78     if bc != 300:
     79         return bc
---> 80     bc = int(math.log(n, 2)) - 4
     81     return bc + bctable[n>>bc]
     82 

OverflowError: cannot convert float infinity to integer
Last edited 8 years ago by jdemeyer (previous) (diff)

comment:8 follow-ups: Changed 11 years ago by fredrik.johansson

That looks strange. I get:

sage: import sage.libs.mpmath.all as mpmath
sage: mpmath.call(mpmath.legenp, 5,1,2)
-2.96434298694874e-22 - 912.574269237852*I
sage: mpmath.call(mpmath.legenp, 5,1,2, prec=100)
-2.1062923756778274648015607872e-36 - 912.57426923785222402727329118*I

comment:9 in reply to: ↑ 8 Changed 11 years ago by maldun

Replying to fredrik.johansson:

That looks strange. I get:

sage: import sage.libs.mpmath.all as mpmath
sage: mpmath.call(mpmath.legenp, 5,1,2)
-2.96434298694874e-22 - 912.574269237852*I
sage: mpmath.call(mpmath.legenp, 5,1,2, prec=100)
-2.1062923756778274648015607872e-36 - 912.57426923785222402727329118*I

Hm strange. Today I install the new Sage version, perhaps it will then work again

comment:10 in reply to: ↑ 8 Changed 11 years ago by maldun

Replying to fredrik.johansson:

That looks strange. I get:

sage: import sage.libs.mpmath.all as mpmath
sage: mpmath.call(mpmath.legenp, 5,1,2)
-2.96434298694874e-22 - 912.574269237852*I
sage: mpmath.call(mpmath.legenp, 5,1,2, prec=100)
-2.1062923756778274648015607872e-36 - 912.57426923785222402727329118*I

It was the old version!a Thanx for pointing that out, I will continue soon =)

Changed 11 years ago by maldun

Version from 19. August 2010

comment:11 follow-ups: Changed 11 years ago by maldun

So now a "beta" is ready with full support of all classes.

Only the Legendre functions are still using Maxima.

some advances for the future:

-Zernike polys (this should be done in the next time, since explicit formulas are available) -support for numpy_eval. (But this will be done, when the scipy package is updated to 0.8, else it has no sense, because the current version of scipy does not support ortho polys well, but the newer can handle them)

Now I need some people for testing this out =)

comment:12 in reply to: ↑ 11 Changed 11 years ago by maldun

And there was an interisting bug:

the import of mpmath at the beginning of the file caused the whole trouble I had with the numeric evaluation of the legendre functions....

I think I should report this..

comment:13 Changed 11 years ago by maldun

  • Type changed from defect to enhancement

Changed 11 years ago by maldun

Added numpy support, eliminated some bugs (19.08.2010)

comment:14 in reply to: ↑ 11 Changed 11 years ago by maldun

-support for numpy_eval. (But this will be done, when the scipy package is updated to 0.8, else it has no sense, because the current version of scipy does not support ortho polys well, but the newer can handle them)

I decided to give at least some numpy support for compability reasons. But this is a bad hack...when scipy 0.8 comes I use scipy itself, I change this to a better version :)

comment:15 Changed 11 years ago by maldun

  • Status changed from new to needs_review

comment:16 Changed 11 years ago by maldun

  • Milestone set to sage-5.0

comment:17 Changed 11 years ago by maldun

Some of the old doctests fail. But it is not my fault, it seem's that it is a bug in the SymbolicFunction? class.

see: http://trac.sagemath.org/sage_trac/ticket/9769

comment:18 Changed 11 years ago by maldun

  • Milestone changed from sage-5.0 to sage-4.5.3

Changed 11 years ago by maldun

Latest version with some code cleanup (no program changes)

comment:19 Changed 11 years ago by maldun

  • Owner changed from burcin to burcin, maldun

comment:20 follow-up: Changed 11 years ago by burcin

Hi Stefan,

can you post a patch corresponding to attachment:orthogonal_polys.8.py for review?

Thanks,
Burcin

Changed 11 years ago by maldun

Patch for latest version with some code cleanup (no program changes)

comment:21 in reply to: ↑ 20 Changed 11 years ago by maldun

Replying to burcin:

Hi Stefan,

can you post a patch corresponding to attachment:orthogonal_polys.8.py for review?

Thanks,
Burcin

Done!

comment:22 follow-up: Changed 11 years ago by fredrik.johansson

Why is mpmath's precision used by default? Shouldn't the default be RR / CC precision? Actually, does _evalf_ ever get called without this information?

Some complex tests would be nice.

comment:23 in reply to: ↑ 22 ; follow-up: Changed 11 years ago by maldun

Replying to fredrik.johansson:

Why is mpmath's precision used by default? Shouldn't the default be RR / CC precision? Actually, does _evalf_ ever get called without this information?

Some complex tests would be nice.

This is a good point, and it shouldn't be a problem to change that. But I don't think it's a big deal, because the function takes the "parents" precision, which means, if my input is RR it evals it with RR's precision.

Of course can you call _evalf_ just with (), and then the default value is used.

I just sticked to the old's version tests, and expanded it. Of course it's possible to expand the tests. I hope I will find some time for it soon, since I have some other more urgent things todo also.

comment:24 in reply to: ↑ 23 Changed 11 years ago by maldun

Replying to maldun:

Replying to fredrik.johansson:

Why is mpmath's precision used by default? Shouldn't the default be RR / CC precision? Actually, does _evalf_ ever get called without this information?

Some complex tests would be nice.

This is a good point, and it shouldn't be a problem to change that. But I don't think it's a big deal, because the function takes the "parents" precision, which means, if my input is RR it evals it with RR's precision.

Of course can you call _evalf_ just with (), and then the default value is used.

Ok sorry, wrong explination: when your input are exact data types like ZZ ore QQ then the parent has no precision, then you need a default value

comment:25 Changed 11 years ago by maldun

Since it seems that numpy-1.4.1, and scipy 0.8 should work now (see #9808) I programmed a version which uses scipy itself to evaluate the orthogonal polys for numpy arrays. When the new versions of numpy/scipy become merged into sage I will provide a patch for these.

Another thing I have to mention are these 2 failde doctests:

  • sage -t -long "devel/sage/sage/symbolic/random_tests.py"
  • sage -t -long "devel/sage/sage/symbolic/pynac.pyx"
sage -t -long "devel/sage/sage/symbolic/random_tests.py"    
**********************************************************************
File "/home/maldun/sage/sage-4.5.2/devel/sage/sage/symbolic/random_tests.py", line 17:
    sage: [f for (one,f,arity) in _mk_full_functions()]
Expected:
    [Ei, abs, arccos, arccosh, arccot, arccoth, arccsc, arccsch,
    arcsec, arcsech, arcsin, arcsinh, arctan, arctan2, arctanh,
    binomial, ceil, conjugate, cos, cosh, cot, coth, csc, csch,
    dickman_rho, dilog, dirac_delta, elliptic_e, elliptic_ec,
    elliptic_eu, elliptic_f, elliptic_kc, elliptic_pi, erf, exp,
    factorial, floor, heaviside, imag_part, integrate,
    kronecker_delta, log, polylog, real_part, sec, sech, sgn, sin,
    sinh, tan, tanh, unit_step, zeta, zetaderiv]
Got:
    [Ei, abs, arccos, arccosh, arccot, arccoth, arccsc, arccsch, arcsec, arcsech, arcsin, arcsinh, arctan, arctan2, arctanh, binomial, ceil, chebyshev_T, chebyshev_U, conjugate, cos, cosh, cot, coth, csc, csch, dickman_rho, dilog, dirac_delta, elliptic_e, elliptic_ec, elliptic_eu, elliptic_f, elliptic_kc, elliptic_pi, erf, exp, factorial, floor, gegenbauer, gen_laguerre, gen_legendre_P, gen_legendre_Q, heaviside, hermite, imag_part, integrate, jacobi_P, kronecker_delta, laguerre, legendre_P, legendre_Q, log, polylog, real_part, sec, sech, sgn, sin, sinh, tan, tanh, unit_step, zeta, zetaderiv]
**********************************************************************
File "/home/maldun/sage/sage-4.5.2/devel/sage/sage/symbolic/random_tests.py", line 237:
    sage: random_expr(50, nvars=3, coeff_generator=CDF.random_element)
Expected:
    (euler_gamma - v3^(-e) + (v2 - factorial(-e/v2))^(((2.85879036573 - 1.18163393202*I)*v2 + (2.85879036573 - 1.18163393202*I)*v3)*pi - 0.247786879678 + 0.931826724898*I)*arccsc((0.891138386848 - 0.0936820840629*I)/v1) + (-0.553423153995 + 0.5481180572*I)*v3 + 0.149683576515 - 0.155746451854*I)*v1 + arccsch(pi + e)*elliptic_f(khinchin*v2, 1.4656989704 + 0.863754357069*I)
Got:
    -v1*e^((0.0666829501658 + 0.206976992303*I)/(v3 + e))/v3 + hermite(-(v3^(-0.48519994364 - 0.485764091302*I) - log((1.21734510331 - 1.22580558833*I)*pi*v1 + zeta((0.781366128261 + 0.957400336147*I)*v1*e + (-1.8919687109 + 0.753422167447*I)*elliptic_f(v1, v1))*arccsch(v3)))*v1, (-0.647983235144 + 1.20665952957*I)*v1 + (0.0909404921682 + 0.281538203756*I)/v3)
**********************************************************************
File "/home/maldun/sage/sage-4.5.2/devel/sage/sage/symbolic/random_tests.py", line 239:
    sage: random_expr(5, verbose=True)
Exception raised:
    Traceback (most recent call last):
      File "/home/maldun/sage/sage-4.5.2/local/bin/ncadoctest.py", line 1231, in run_one_test
        self.run_one_example(test, example, filename, compileflags)
      File "/home/maldun/sage/sage-4.5.2/local/bin/sagedoctest.py", line 38, in run_one_example
        OrigDocTestRunner.run_one_example(self, test, example, filename, compileflags)
      File "/home/maldun/sage/sage-4.5.2/local/bin/ncadoctest.py", line 1172, in run_one_example
        compileflags, 1) in test.globs
      File "<doctest __main__.example_5[5]>", line 1, in <module>
        random_expr(Integer(5), verbose=True)###line 239:
    sage: random_expr(5, verbose=True)
      File "/home/maldun/sage/sage-4.5.2/local/lib/python/site-packages/sage/symbolic/random_tests.py", line 254, in random_expr
        return random_expr_helper(size, internal, leaves, verbose)
      File "/home/maldun/sage/sage-4.5.2/local/lib/python/site-packages/sage/symbolic/random_tests.py", line 210, in random_expr_helper
        return r[1](*children)
      File "element.pyx", line 1529, in sage.structure.element.RingElement.__div__ (sage/structure/element.c:11992)
      File "coerce.pyx", line 713, in sage.structure.coerce.CoercionModel_cache_maps.bin_op (sage/structure/coerce.c:6126)
      File "element.pyx", line 1527, in sage.structure.element.RingElement.__div__ (sage/structure/element.c:11973)
      File "expression.pyx", line 2269, in sage.symbolic.expression.Expression._div_ (sage/symbolic/expression.cpp:11444)
    ZeroDivisionError: Symbolic division by zero
**********************************************************************
2 items had failures:
   1 of   4 in __main__.example_0
   2 of   6 in __main__.example_5
***Test Failed*** 3 failures.
For whitespace errors, see the file /home/maldun/.sage//tmp/.doctest_random_tests.py
         [7.7 s]
 
----------------------------------------------------------------------
The following tests failed:


        sage -t -long "devel/sage/sage/symbolic/random_tests.py"
Total time for all tests: 7.8 seconds

I quite understand these, because we have introduced new functions, but I don't understand the exception in the last one

sage -t -long "devel/sage/sage/symbolic/pynac.pyx"          
**********************************************************************
File "/home/maldun/sage/sage-4.5.2/devel/sage/sage/symbolic/pynac.pyx", line 386:
    sage: get_sfunction_from_serial(i) == foo
Expected:
    True
Got:
    False
**********************************************************************
File "/home/maldun/sage/sage-4.5.2/devel/sage/sage/symbolic/pynac.pyx", line 388:
    sage: py_latex_function_pystring(i, (x,y^z))
Expected:
    'my args are: x, y^z'
Got:
    '\\mathrm{bar}\\left(x, y^{z}\\right)'
**********************************************************************
File "/home/maldun/sage/sage-4.5.2/devel/sage/sage/symbolic/pynac.pyx", line 478:
    sage: get_sfunction_from_serial(i) == foo
Expected:
    True
Got:
    False
**********************************************************************
File "/home/maldun/sage/sage-4.5.2/devel/sage/sage/symbolic/pynac.pyx", line 480:
    sage: py_print_fderivative(i, (0, 1, 0, 1), (x, y^z))
Expected:
    D[0, 1, 0, 1]func_with_args(x, y^z)
Got:
    D[0, 1, 0, 1](foo)(x, y^z)
**********************************************************************
File "/home/maldun/sage/sage-4.5.2/devel/sage/sage/symbolic/pynac.pyx", line 540:
    sage: get_sfunction_from_serial(i) == foo
Expected:
    True
Got:
    False
**********************************************************************
File "/home/maldun/sage/sage-4.5.2/devel/sage/sage/symbolic/pynac.pyx", line 542:
    sage: py_latex_fderivative(i, (0, 1, 0, 1), (x, y^z))
Expected:
    D[0, 1, 0, 1]func_with_args(x, y^z)
Got:
    D[0, 1, 0, 1]\left(\mathrm{bar}\right)\left(x, y^{z}\right)
**********************************************************************
3 items had failures:
   2 of  19 in __main__.example_14
   2 of  14 in __main__.example_16
   2 of  18 in __main__.example_18
***Test Failed*** 6 failures.
For whitespace errors, see the file /home/maldun/.sage//tmp/.doctest_pynac.py
         [7.3 s]
 
----------------------------------------------------------------------
The following tests failed:


        sage -t -long "devel/sage/sage/symbolic/pynac.pyx"
Total time for all tests: 7.3 seconds

And these are really strange, because when I type then into sage by hand everything works. wtf?? Can anyone have a look at these?

Changed 11 years ago by maldun

ortho polys with scipy support

comment:26 Changed 11 years ago by maldun

  • Milestone changed from sage-4.6 to sage-5.0
  • Status changed from needs_review to needs_work

comment:27 Changed 11 years ago by kcrisman

Just cc:ing myself by commenting.

Also, there seems to be a lot of stuff in the latest Python file that is the same as the original one (in terms of explanation, not code). Maybe posting an updated patch (once the numpy/scipy-fest is over, which is hopefully the case) would help some of us figure this out. Thanks for working on this - there is still a lot of overhauling that symbolics could use, but this is a great step.

comment:28 Changed 11 years ago by maldun

  • Description modified (diff)
  • Status changed from needs_work to needs_review

@kcrisman thanks for paying attention. I added now an updated patch and extended instructions.

the doctest changes in symbolic.random_tests.py are easy to explain: new functions are involved -> new random expressions. But I had to change random_expr(50, nvars=3, coeff_generator=CDF.random_element) to random_expr(60, nvars=3, coeff_generator=CDF.random_element) or else one gets an expression generated where a division through zero occours.

As mentioned on sage-devel I repaired the doctests in symbolic.pynac.pyx, the trick is to enlarge the range of the for loop: for i in range(get_ginac_serial(), get_ginac_serial()+50): changed to for i in range(get_ginac_serial(), get_ginac_serial()+100): now it works. My explaination: since we have new functions we have longer to search, and then we reach our goal. What I can not explain is, that it works, when I type it in by hand.

All doctests pass now, so I think a review would be nice.

-maldun

comment:29 Changed 11 years ago by maldun

  • Description modified (diff)

Cleaned up discription of the ticket and some comments in the ortho polys file.

comment:30 follow-up: Changed 11 years ago by kcrisman

I don't have time to review this for a while, but did take a quick look - thanks for polishing that patch! I don't think we are allowed to import numpy or scipy like that anymore, but rather have to do it in an individual function (lest startup times get huge). I don't quite understand exactly how that works, but anyway such a blanket import statement probably isn't appropriate, the way I understand what others have said.

Changed 11 years ago by maldun

Latest version of orthogonal polys with scipy support, and changed doctests. Tested in sage-4.6.alpha3

comment:31 in reply to: ↑ 30 Changed 11 years ago by maldun

Replying to kcrisman:

I don't have time to review this for a while, but did take a quick look - thanks for polishing that patch! I don't think we are allowed to import numpy or scipy like that anymore, but rather have to do it in an individual function (lest startup times get huge). I don't quite understand exactly how that works, but anyway such a blanket import statement probably isn't appropriate, the way I understand what others have said.

But thanks for giving feedback! I know that this patch isn't easy for review because the code grew from 650 to about 2300 lines of code. But I'm happy to get at least some info.

You are right the imports didn't change since I started this ticket and importing the whole numpy and scipy packages is to much. This isn't a very good Idea if one thinks about performance either. I changed that now so that only functions that are really needed are importet. I did this also for mpmath but the problem with the global import remains. (see above). Also changed some errors in the discription I missed and repaired a wrong doctest.

PS: If diffs or more changelogs are needed let me know. I'm keeping track with git on my machine of the changes.

comment:32 Changed 11 years ago by burcin

  • Cc fstan added
  • Reviewers set to Burcin Erocal
  • Status changed from needs_review to needs_work

Great work Stefan. Your patch looks good overall, but it needs a lot of polish. Thank you very much for this.

Here are some quick comments after reading attachment:trac_9706_orthogonal_polys.patch. I didn't try to apply and run the code yet. It would be better if other people try this as well since I am really short on time these days.

  • I suggest you use your real name in the HG headers. This information is used for copyright/license issues as well. In the future it might cause a lot of trouble if people have to chase down maldun for copyright questions.
  • You shouldn't import any part of numpy at the module level. This slows down startup too much. See #3561 for example. I'd say the same holds for mpmath and scipy.
  • line 385-386 has this:
    Then after using one of these functions, it changes:: (The value is now  
    False for chebyshev_T because chebyshev_T uses clenshaw method instead...)
    
    I don't think this is valid Sphinx.
  • delete line 412
    #load /home/maldun/sage/sage-4.5.2/devel/sage-ortho/sage/functions/orthogonal_polys.py 
    
  • line 419: he -> the
  • There are no doctests for the OrthogonalPolynomial class, make sure your file passes sage -coverage
  • The commented timings in the docstring of OrthogonalPolynomial._clenshaw_method_() are confusing. It would be better if you provide a function in the same file that does these timings automatically and prints out the results. You should at least delete this from the documentation though.
  • In the docstring of OrthogonalPolynomial._eval_()
    • remove the empty first line (line 494) of
    • remove the commented out timings as well
    • you need an empty line after EXAMPLES::
    • the empty last line should be removed
  • add some comments to the OrthogonalPolynomial._eval_() method to indicate what you're trying to do with these tests.
    • lines 583-593 have a confusing comment and a bug
      try: 
          #s = maxima(self._maxima_init_evaled_(*args)) 
          #This above is very inefficient! The older 
          #methods were much faster... 
          return self._maxima_init_evaled_(*args) 
      except TypeError: 
          return None 
      if self._maxima_name in repr(s): 
          return None 
      else: 
          return s.sage() 
      
  • You don't need to state "Class for" on line 598, "The Chebyshev ..." is enough.
  • Why do you delete the chebyshev_T(2,x) test on line 371? You can just add the new ones after that.
  • line 626, EXAMPLES: -> EXAMPLES::
  • Don't use *args or **kwds when you don't need them. Name the arguments and be explicit. Remember the "Zen of Python", "Explicit is better than implicit."
  • OK, generally, fix the docstrings to conform to Sphinx standards. This should be documented somewhere in the developers guide.
  • line 673, _maxima_init_evaled_() doesn't have doctests.
  • line 678 - , _clenshaw_method_()
    • docstring is not indented properly.
    • It would be better to put the recursion formula in the docstring.
  • line 790 _clenshaw_method_() doesn't have doctests.
  • There is something wrong with the _maxima_init_evaled_() on line 821. Are you sure this function shouldn't just return a string to be run in maxima? How do we know that doctest actually calls this function? In any case, the right way to convert a maxima object to sage is to run .sage() on it. Never use sage_eval() on a string in the Sage library.
  • Calls to mpmath should be able to use the precision directly from the type of the argument now. Are you sure all this is necessary:
    try: 
        step_parent = kwds['parent'] 
    except KeyError: 
        step_parent = parent(args[-1]) 
    
    try: 
        precision = step_parent.prec() 
    except AttributeError: 
        precision = RR.prec() 
    
    See #9566.
  • line 924, change the error message to something more professional. "Derivative w.r.t. to the index is not supported, yet, and perhaps never will be..." is not acceptable. "Derivatives with respect to the index is not supported." would be enough.
  • Document the derivative formula in the docstring, using proper math notation
  • What needs to be discussed from the comments on line 968-974?
  • Same for lines 1058-1060?
  • no doctests for _clenshaw_method_() on line 1156.
  • no doctests for _maxima_init_evaled_() on line 1189.

I give up at this point. It seems that there are similar issues in the rest of the file as well.

After you clean up the code according to the comments above, perhaps a native English speaker like Karl-Dieter or Minh can help with the documentation.

Thanks again for all your work.

comment:33 Changed 10 years ago by kcrisman

  • Cc kcrisman added

comment:34 Changed 8 years ago by jdemeyer

  • Milestone changed from sage-5.11 to sage-5.12

comment:35 Changed 8 years ago by maldun

Hi!

I will now retry to build the new orthogonal polynomials. The last time I ran out of time due to my phd studies/theses this time i will split the changes up into several patches. So it will be easier to apply the changes step by step, and the review process gets simpler.

Hope this time everything will work out!

comment:36 Changed 8 years ago by maldun

  • Status changed from needs_work to needs_review

comment:37 Changed 8 years ago by tscrim

  • Description modified (diff)

Here is a review patch which does a bunch of documentation formatting tweaks. There are probably one or two other things that will need to be addressed, but I'd like to get the ball rolling on this again (and I need some sleep right now).

Best,
Travis

For patchbot:

Apply: trac_9706_chebyshev.patch​, trac_9706-review-ts.patch

Last edited 8 years ago by tscrim (previous) (diff)
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