[with patch, positive review] mpmath support

[fredrik.johansson]

Patch description:

Adds sage.libs.mpmath which provides wrapper functions and monkey patches some internal mpmath functions for speed. Mpmath functions can be called from Sage as follows (with forward and backward conversions handled automatically):

sage: import sage.libs.mpmath.all as a
sage: a.call(a.hyp2f1, 2, 2/3, -1/2, 3+4*I)
-0.111907858412569 - 0.536467867510390*I
sage: a.call(a.hyp2f1, 2, 2/3, -1/2, 3+4*I, prec=100)
-0.11190785841256900204178259859 - 0.53646786751038954277574814099*I

Some partial support for direct conversion from Sage -> mpmath is also implemented (this is not completely working yet).

Also providing a preliminary spkg (with current mpmath trunk) in this issue.

[ncalexan]

I am interested in using mpmath for numerical integration, but unfortunately I get major build errors with 4.0.2.alpha0. See  http://pastebin.com/d13f03d03 for details. Any thoughts?

[mhansen]

I put an spkg at  http://sage.math.washington.edu/home/mhansen/mpmath-0.12.spkg

[ncalexan]

Apply all patches.

[ncalexan]

Positive review for me. Change status after my tiny patch is refereed.

[mhansen]

Nick's changes look good.

[boothby]

Doctest failures:

sage -t -long devel/sage/sage/rings/real_mpfr.pyx
**********************************************************************
File "/space/boothby/sage-4.0.3/devel/sage-main/sage/rings/real_mpfr.pyx", line 2284:
    sage: RR(-1.5)._mpmath_()
Exception raised:
    Traceback (most recent call last):
      File "/space/boothby/sage-4.0.3/local/bin/ncadoctest.py", line 1231, in run_one_test
        self.run_one_example(test, example, filename, compileflags)
      File "/space/boothby/sage-4.0.3/local/bin/sagedoctest.py", line 38, in run_one_example
        OrigDocTestRunner.run_one_example(self, test, example, filename, compileflags)
      File "/space/boothby/sage-4.0.3/local/bin/ncadoctest.py", line 1172, in run_one_example
        compileflags, 1) in test.globs
      File "<doctest __main__.example_65[2]>", line 1, in <module>
        RR(-RealNumber('1.5'))._mpmath_()###line 2284:
    sage: RR(-1.5)._mpmath_()
      File "real_mpfr.pyx", line 2289, in sage.rings.real_mpfr.RealNumber._mpmath_ (sage/rings/real$
        from sage.libs.mpmath.all import make_mpf
      File "/space/boothby/sage-4.0.3/local/lib/python2.5/site-packages/sage/libs/mpmath/all.py", l$
        import mpmath
    ImportError: No module named mpmath
**********************************************************************
1 items had failures:
   1 of   3 in __main__.example_65
***Test Failed*** 1 failures.

sage -t -long devel/sage/sage/rings/complex_number.pyx
**********************************************************************
File "/space/boothby/sage-4.0.3/devel/sage-main/sage/rings/complex_number.pyx", line 484:
    sage: CC(1,2)._mpmath_()
Exception raised:
    Traceback (most recent call last):
      File "/space/boothby/sage-4.0.3/local/bin/ncadoctest.py", line 1231, in run_one_test
        self.run_one_example(test, example, filename, compileflags)
      File "/space/boothby/sage-4.0.3/local/bin/sagedoctest.py", line 38, in run_one_example
        OrigDocTestRunner.run_one_example(self, test, example, filename, compileflags)
      File "/space/boothby/sage-4.0.3/local/bin/ncadoctest.py", line 1172, in run_one_example
        compileflags, 1) in test.globs
      File "<doctest __main__.example_15[2]>", line 1, in <module>
        CC(Integer(1),Integer(2))._mpmath_()###line 484:
    sage: CC(1,2)._mpmath_()
      File "complex_number.pyx", line 489, in sage.rings.complex_number.ComplexNumber._mpmath_ (sag$
        from sage.libs.mpmath.all import make_mpc
      File "/space/boothby/sage-4.0.3/local/lib/python2.5/site-packages/sage/libs/mpmath/all.py", l$
        import mpmath
    ImportError: No module named mpmath
**********************************************************************
1 items had failures:
   1 of   3 in __main__.example_15
***Test Failed*** 1 failures.

sage -t -long devel/sage/sage/structure/element.pyx
**********************************************************************
File "/space/boothby/sage-4.0.3/devel/sage-main/sage/structure/element.pyx", line 426:
    sage: from sage.libs.mpmath.all import mp, mpmathify
Exception raised:
    Traceback (most recent call last):
      File "/space/boothby/sage-4.0.3/local/bin/ncadoctest.py", line 1231, in run_one_test
        self.run_one_example(test, example, filename, compileflags)
      File "/space/boothby/sage-4.0.3/local/bin/sagedoctest.py", line 38, in run_one_example
        OrigDocTestRunner.run_one_example(self, test, example, filename, compileflags)
      File "/space/boothby/sage-4.0.3/local/bin/ncadoctest.py", line 1172, in run_one_example
        compileflags, 1) in test.globs
      File "<doctest __main__.example_13[2]>", line 1, in <module>
        from sage.libs.mpmath.all import mp, mpmathify###line 426:
    sage: from sage.libs.mpmath.all import mp, mpmathify
      File "/space/boothby/sage-4.0.3/local/lib/python2.5/site-packages/sage/libs/mpmath/all.py", l$
        import mpmath
    ImportError: No module named mpmath
**********************************************************************
File "/space/boothby/sage-4.0.3/devel/sage-main/sage/structure/element.pyx", line 427:
    sage: mp.dps = 30
Exception raised:
    Traceback (most recent call last):
      File "/space/boothby/sage-4.0.3/local/bin/ncadoctest.py", line 1231, in run_one_test
        self.run_one_example(test, example, filename, compileflags)
      File "/space/boothby/sage-4.0.3/local/bin/sagedoctest.py", line 38, in run_one_example
        OrigDocTestRunner.run_one_example(self, test, example, filename, compileflags)
      File "/space/boothby/sage-4.0.3/local/bin/ncadoctest.py", line 1172, in run_one_example
        compileflags, 1) in test.globs
      File "<doctest __main__.example_13[3]>", line 1, in <module>
        mp.dps = Integer(30)###line 427:
    sage: mp.dps = 30
    NameError: name 'mp' is not defined
**********************************************************************
File "/space/boothby/sage-4.0.3/devel/sage-main/sage/structure/element.pyx", line 428:
    sage: 25._mpmath_(53)
Exception raised:
    Traceback (most recent call last):
      File "/space/boothby/sage-4.0.3/local/bin/ncadoctest.py", line 1231, in run_one_test
        self.run_one_example(test, example, filename, compileflags)
      File "/space/boothby/sage-4.0.3/local/bin/sagedoctest.py", line 38, in run_one_example
        OrigDocTestRunner.run_one_example(self, test, example, filename, compileflags)
      File "/space/boothby/sage-4.0.3/local/bin/ncadoctest.py", line 1172, in run_one_example
        compileflags, 1) in test.globs

...

sage -t -long devel/sage/sage/libs/mpmath/utils.pyx
**********************************************************************
File "/space/boothby/sage-4.0.3/devel/sage-main/sage/libs/mpmath/utils.pyx", line 27:
    sage: from mpmath.libmpf import from_man_exp
Exception raised:
    Traceback (most recent call last):
      File "/space/boothby/sage-4.0.3/local/bin/ncadoctest.py", line 1231, in run_one_test
        self.run_one_example(test, example, filename, compileflags)
      File "/space/boothby/sage-4.0.3/local/bin/sagedoctest.py", line 38, in run_one_example
        OrigDocTestRunner.run_one_example(self, test, example, filename, compileflags)
      File "/space/boothby/sage-4.0.3/local/bin/ncadoctest.py", line 1172, in run_one_example
        compileflags, 1) in test.globs
      File "<doctest __main__.example_0[2]>", line 1, in <module>
        from mpmath.libmpf import from_man_exp###line 27:
    sage: from mpmath.libmpf import from_man_exp
    ImportError: No module named mpmath.libmpf
**********************************************************************
File "/space/boothby/sage-4.0.3/devel/sage-main/sage/libs/mpmath/utils.pyx", line 28:
    sage: from_man_exp(-6, -1)
Exception raised:
    Traceback (most recent call last):
      File "/space/boothby/sage-4.0.3/local/bin/ncadoctest.py", line 1231, in run_one_test
        self.run_one_example(test, example, filename, compileflags)
      File "/space/boothby/sage-4.0.3/local/bin/sagedoctest.py", line 38, in run_one_example
        OrigDocTestRunner.run_one_example(self, test, example, filename, compileflags)
      File "/space/boothby/sage-4.0.3/local/bin/ncadoctest.py", line 1172, in run_one_example
        compileflags, 1) in test.globs
...

[ncalexan]

There's an spkg; this looks a lot like you didn't install it. I did *exactly* the same thing with malb's singular spkg update when I was release manager. Maybe we need sage -merge to yell if it sees certain things, like spkgs?

[boothby]

Oh damn. Thanks, Nick.

[mvngu]

The milestone for this ticket should be 4.1. I can't change it, since I don't have admin privileges on trac.