find_local_maximum/minimum() fails with expressions containing complex numbers

[rwst]

sage: find_local_maximum(abs(x+I),-1,1)
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
<ipython-input-3-f0919e050ec5> in <module>()
----> 1 find_local_maximum(abs(x+I),-Integer(1),Integer(1))

/home/ralf/sage/src/sage/misc/lazy_import.pyx in sage.misc.lazy_import.LazyImport.__call__ (build/cythonized/sage/misc/lazy_import.c:3703)()
    352             True
    353         """
--> 354         return self.get_object()(*args, **kwds)
    355 
    356     def __repr__(self):

/home/ralf/sage/local/lib/python2.7/site-packages/sage/numerical/optimize.pyc in find_local_maximum(f, a, b, tol, maxfun)
    143     """
    144     try:
--> 145         return f.find_local_maximum(a=a, b=b, tol=tol, maxfun=maxfun)
    146     except AttributeError:
    147         pass

/home/ralf/sage/src/sage/symbolic/expression.pyx in sage.symbolic.expression.Expression.find_local_maximum (build/cythonized/sage/symbolic/expression.cpp:66056)()
  11680             (0.561090323458081..., 0.857926501456...)
  11681         """
> 11682         minval, x = (-self).find_local_minimum(a, b, var=var, tol=tol,
  11683                                                      maxfun=maxfun)
  11684         return -minval, x

/home/ralf/sage/src/sage/symbolic/expression.pyx in sage.symbolic.expression.Expression.find_local_minimum (build/cythonized/sage/symbolic/expression.cpp:66379)()
  11739         if var is None:
  11740             var = self.default_variable()
> 11741         return find_local_minimum(self._fast_float_(var),
  11742                                         a=a, b=b, tol=tol, maxfun=maxfun )
  11743 

/home/ralf/sage/src/sage/symbolic/expression.pyx in sage.symbolic.expression.Expression._fast_float_ (build/cythonized/sage/symbolic/expression.cpp:66543)()
  11762         """
  11763         from sage.symbolic.expression_conversions import fast_float
> 11764         return fast_float(self, *vars)
  11765 
  11766     def _fast_callable_(self, etb):

/home/ralf/sage/local/lib/python2.7/site-packages/sage/symbolic/expression_conversions.pyc in fast_float(ex, *vars)
   1572         1.4142135623730951
   1573     """
-> 1574     return FastFloatConverter(ex, *vars)()
   1575 
   1576 #################

/home/ralf/sage/local/lib/python2.7/site-packages/sage/symbolic/expression_conversions.pyc in __call__(self, ex)
    215             if getattr(self, 'use_fake_div', False) and (operator is _operator.mul or operator is mul_vararg):
    216                 div = self.get_fake_div(ex)
--> 217                 return self.arithmetic(div, div.operator())
    218             return self.arithmetic(ex, operator)
    219         elif operator in relation_operators:

/home/ralf/sage/local/lib/python2.7/site-packages/sage/symbolic/expression_conversions.pyc in arithmetic(self, ex, operator)
   1513         operands = ex.operands()
   1514         if operator is _operator.neg:
-> 1515             return operator(self(operands[0]))
   1516 
   1517         from sage.rings.all import Rational

/home/ralf/sage/local/lib/python2.7/site-packages/sage/symbolic/expression_conversions.pyc in __call__(self, ex)
    224             return self.tuple(ex)
    225         else:
--> 226             return self.composition(ex, operator)
    227 
    228     def get_fake_div(self, ex):

/home/ralf/sage/local/lib/python2.7/site-packages/sage/symbolic/expression_conversions.pyc in composition(self, ex, operator)
   1547         """
   1548         f = operator
-> 1549         g = [self(_) for _ in ex.operands()]
   1550         try:
   1551             return f(*g)

/home/ralf/sage/local/lib/python2.7/site-packages/sage/symbolic/expression_conversions.pyc in __call__(self, ex)
    216                 div = self.get_fake_div(ex)
    217                 return self.arithmetic(div, div.operator())
--> 218             return self.arithmetic(ex, operator)
    219         elif operator in relation_operators:
    220             return self.relation(ex, operator)

/home/ralf/sage/local/lib/python2.7/site-packages/sage/symbolic/expression_conversions.pyc in arithmetic(self, ex, operator)
   1519             from sage.functions.all import sqrt
   1520             return sqrt(self(operands[0]))
-> 1521         fops = map(self, operands)
   1522         if operator == add_vararg:
   1523             operator = _operator.add

/home/ralf/sage/local/lib/python2.7/site-packages/sage/symbolic/expression_conversions.pyc in __call__(self, ex)
    206         except TypeError as err:
    207             if 'self must be a numeric expression' not in err.args:
--> 208                 raise err
    209 
    210         operator = ex.operator()

TypeError: unable to coerce to a real number

The rethrown error comes from an attempt to do float(I).

The find_local functions use FastFloatConverter to compute values.

CC: @orlitzky

Component: symbolics

Author: Michael Orlitzky

Branch/Commit: 1fe5795

Reviewer: Matthias Koeppe

Issue created by migration from https://trac.sagemath.org/ticket/24536

[rwst]

Description changed:

--- 
+++ 
@@ -1,7 +1,7 @@
 
 ```
 sage: from sage.symbolic.expression_conversions import FastFloatConverter
-sage: f = FastFloatConverter(I)
+sage: f = FastFloatConverter(x + I)
 /home/ralf/sage/src/bin/sage-ipython:1: DeprecationWarning: Substitution using function-call syntax and unnamed arguments is deprecated and will be removed from a future release of Sage; you can use named arguments instead, like EXPR(x=..., y=...)
 See http://trac.sagemath.org/5930 for details.
   #!/usr/bin/env python
@@ -16,3 +16,4 @@
 
 TypeError: unable to coerce to a real number
 ```
+There is an expression() call somewhere intending substitution which should be replaced in this ticket, as well.

[rwst]

comment:2

Apparently "Float" literally means Python (real) "float" not floating-point. Of course then expressions containing I raise errors, even if the outcome is real. The original case was the usage by find_local_maximum---so that never worked, and the restriction was undocumented.

[rwst]

Description changed:

--- 
+++ 
@@ -1,12 +1,95 @@
 
 ```
-sage: from sage.symbolic.expression_conversions import FastFloatConverter
-sage: f = FastFloatConverter(x + I)
-/home/ralf/sage/src/bin/sage-ipython:1: DeprecationWarning: Substitution using function-call syntax and unnamed arguments is deprecated and will be removed from a future release of Sage; you can use named arguments instead, like EXPR(x=..., y=...)
-See http://trac.sagemath.org/5930 for details.
-  #!/usr/bin/env python
-<sage.symbolic.expression_conversions.FastFloatConverter object at 0x7fdec25cf110>
-sage: f()
+sage: find_local_maximum(abs(x+I),-1,1)
+---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+<ipython-input-3-f0919e050ec5> in <module>()
+----> 1 find_local_maximum(abs(x+I),-Integer(1),Integer(1))
+
+/home/ralf/sage/src/sage/misc/lazy_import.pyx in sage.misc.lazy_import.LazyImport.__call__ (build/cythonized/sage/misc/lazy_import.c:3703)()
+    352             True
+    353         """
+--> 354         return self.get_object()(*args, **kwds)
+    355 
+    356     def __repr__(self):
+
+/home/ralf/sage/local/lib/python2.7/site-packages/sage/numerical/optimize.pyc in find_local_maximum(f, a, b, tol, maxfun)
+    143     """
+    144     try:
+--> 145         return f.find_local_maximum(a=a, b=b, tol=tol, maxfun=maxfun)
+    146     except AttributeError:
+    147         pass
+
+/home/ralf/sage/src/sage/symbolic/expression.pyx in sage.symbolic.expression.Expression.find_local_maximum (build/cythonized/sage/symbolic/expression.cpp:66056)()
+  11680             (0.561090323458081..., 0.857926501456...)
+  11681         """
+> 11682         minval, x = (-self).find_local_minimum(a, b, var=var, tol=tol,
+  11683                                                      maxfun=maxfun)
+  11684         return -minval, x
+
+/home/ralf/sage/src/sage/symbolic/expression.pyx in sage.symbolic.expression.Expression.find_local_minimum (build/cythonized/sage/symbolic/expression.cpp:66379)()
+  11739         if var is None:
+  11740             var = self.default_variable()
+> 11741         return find_local_minimum(self._fast_float_(var),
+  11742                                         a=a, b=b, tol=tol, maxfun=maxfun )
+  11743 
+
+/home/ralf/sage/src/sage/symbolic/expression.pyx in sage.symbolic.expression.Expression._fast_float_ (build/cythonized/sage/symbolic/expression.cpp:66543)()
+  11762         """
+  11763         from sage.symbolic.expression_conversions import fast_float
+> 11764         return fast_float(self, *vars)
+  11765 
+  11766     def _fast_callable_(self, etb):
+
+/home/ralf/sage/local/lib/python2.7/site-packages/sage/symbolic/expression_conversions.pyc in fast_float(ex, *vars)
+   1572         1.4142135623730951
+   1573     """
+-> 1574     return FastFloatConverter(ex, *vars)()
+   1575 
+   1576 #################
+
+/home/ralf/sage/local/lib/python2.7/site-packages/sage/symbolic/expression_conversions.pyc in __call__(self, ex)
+    215             if getattr(self, 'use_fake_div', False) and (operator is _operator.mul or operator is mul_vararg):
+    216                 div = self.get_fake_div(ex)
+--> 217                 return self.arithmetic(div, div.operator())
+    218             return self.arithmetic(ex, operator)
+    219         elif operator in relation_operators:
+
+/home/ralf/sage/local/lib/python2.7/site-packages/sage/symbolic/expression_conversions.pyc in arithmetic(self, ex, operator)
+   1513         operands = ex.operands()
+   1514         if operator is _operator.neg:
+-> 1515             return operator(self(operands[0]))
+   1516 
+   1517         from sage.rings.all import Rational
+
+/home/ralf/sage/local/lib/python2.7/site-packages/sage/symbolic/expression_conversions.pyc in __call__(self, ex)
+    224             return self.tuple(ex)
+    225         else:
+--> 226             return self.composition(ex, operator)
+    227 
+    228     def get_fake_div(self, ex):
+
+/home/ralf/sage/local/lib/python2.7/site-packages/sage/symbolic/expression_conversions.pyc in composition(self, ex, operator)
+   1547         """
+   1548         f = operator
+-> 1549         g = [self(_) for _ in ex.operands()]
+   1550         try:
+   1551             return f(*g)
+
+/home/ralf/sage/local/lib/python2.7/site-packages/sage/symbolic/expression_conversions.pyc in __call__(self, ex)
+    216                 div = self.get_fake_div(ex)
+    217                 return self.arithmetic(div, div.operator())
+--> 218             return self.arithmetic(ex, operator)
+    219         elif operator in relation_operators:
+    220             return self.relation(ex, operator)
+
+/home/ralf/sage/local/lib/python2.7/site-packages/sage/symbolic/expression_conversions.pyc in arithmetic(self, ex, operator)
+   1519             from sage.functions.all import sqrt
+   1520             return sqrt(self(operands[0]))
+-> 1521         fops = map(self, operands)
+   1522         if operator == add_vararg:
+   1523             operator = _operator.add
+
 /home/ralf/sage/local/lib/python2.7/site-packages/sage/symbolic/expression_conversions.pyc in __call__(self, ex)
     206         except TypeError as err:
     207             if 'self must be a numeric expression' not in err.args:
@@ -16,4 +99,6 @@
 
 TypeError: unable to coerce to a real number
 ```
-There is an expression() call somewhere intending substitution which should be replaced in this ticket, as well.
+The rethrown error comes from an attempt to do `float(I)`.
+
+The find_local functions use `FastFloatConverter` to compute values.

[rwst]

comment:4

The documentation of fast_float states

def fast_float(ex, *vars):
    """
    Returns an object which provides fast floating point evaluation of
    the symbolic expression *ex*.

but

sage: from sage.symbolic.expression_conversions import fast_float
sage: ff = fast_float(abs(x+I))
/home/ralf/sage/local/lib/python2.7/site-packages/sage/symbolic/expression_conversions.py:1574: DeprecationWarning: Substitution using function-call syntax and unnamed arguments is deprecated and will be removed from a future release of Sage; you can use named arguments instead, like EXPR(x=..., y=...)
See http://trac.sagemath.org/5930 for details.
  return FastFloatConverter(ex, *vars)()

gives the ticket error.

[rwst]

comment:5

Relevant: #5572. Somewhat related: #13559, #16899.

[johanrosenkilde]

comment:6

Note that changing the call from find_local_maximum(abs(x+I),-1,1) to

find_local_maximum(lambda x: abs(x+I),-1,1)

Then everything works fine.

[mkoeppe]

Dependencies: #32234

[orlitzky]

comment:8

The fix for this will be similar to the one in #8450. After #32234, we're using fast_callable() on these expressions with domain=float, which converts all intermediate expression-evaluation results to float. Obviously that causes problems with the x+I in abs(x+I). To work around that, we can probably just run the computation with domain=CDF and then convert the answer to float if its imaginary part is small enough. (But we don't want to return NaN if the end result has a nontrivial imaginary part, like we do when plotting.)

[orlitzky]

comment:9

I'll deal with it once the prereqs start to settle.