It seems that the find_minimum_on_interval and
find_maximum_on_interval functions do not work properly. I found some
posts about this and a ticket (http://trac.sagemath.org/sage_trac/
ticket/2607). Are there any alternatives built into sage that would
allow the numerical search for extreme values in a given interval?
Here is another example of something going horribly wrong (I actually
get that 'cannot coerce type...' message a lot when I try the
find_maximum... function):
-
| SAGE Version 3.1.1, Release Date: 2008-08-17 |
| Type notebook() for the GUI, and license() for information. |
----------------------------------------------------------------------
sage: find_minimum_on_interval(-x^2,-1,1)
(-0.99999992595132459, -0.999999962976)
sage: find_maximum_on_interval(-x^2,-1,1)
---------------------------------------------------------------------------
TypeError Traceback (most recent call
last)
/Users/sschym/Downloads/Free/sage-3.1.1/<ipython console> in
<module>()
/Users/sschym/Downloads/Free/sage-3.1.1/local/lib/python2.5/site-
packages/sage/numerical/optimize.py in find_maximum_on_interval(f, a,
b, tol, maxfun)
116 """
117 return -f(z)
--> 118 minval, x = find_minimum_on_interval(g, a=a, b=b, tol=tol,
maxfun=maxfun)
119 return -minval, x
120
/Users/sschym/Downloads/Free/sage-3.1.1/local/lib/python2.5/site-
packages/sage/numerical/optimize.py in find_minimum_on_interval(f, a,
b, tol, maxfun)
158 a = float(a); b = float(b)
159 import scipy.optimize
--> 160 xmin, fval, iter, funcalls = scipy.optimize.fminbound(f,
a, b, full_output=1, xtol=tol, maxfun=maxfun)
161 return fval, xmin
162
/Users/sschym/Downloads/Free/sage-3.1.1/local/lib/python2.5/site-
packages/scipy/optimize/optimize.py in fminbound(func, x1, x2, args,
xtol, maxfun, full_output, disp)
1307 si = numpy.sign(rat) + (rat == 0)
1308 x = xf + si*max([abs(rat), tol1])
-> 1309 fu = func(x,*args)
1310 num += 1
1311 fmin_data = (num, x, fu)
/Users/sschym/Downloads/Free/sage-3.1.1/local/lib/python2.5/site-
packages/sage/numerical/optimize.py in g(z)
115
116 """
--> 117 return -f(z)
118 minval, x = find_minimum_on_interval(g, a=a, b=b, tol=tol,
maxfun=maxfun)
119 return -minval, x
/Users/sschym/Downloads/Free/sage-3.1.1/local/lib/python2.5/site-
packages/sage/calculus/calculus.py in __call__(self, *args, **kwargs)
4607 new_ops.append( op )
4608 else:
-> 4609 new_ops.append( op(*[args[i] for i
in indices]) )
4610 except ValueError:
4611 new_ops.append( op )
/Users/sschym/Downloads/Free/sage-3.1.1/local/lib/python2.5/site-
packages/sage/calculus/calculus.py in __call__(self, *args, **kwargs)
4613 #Check to see if all of the new_ops are symbolic
constants
4614 #If so, then we should return a symbolic constant.
-> 4615 new_ops = map(SR, new_ops)
4616 is_constant = all(map(lambda x: isinstance(x,
SymbolicConstant), new_ops))
4617 if is_constant:
/Users/sschym/Downloads/Free/sage-3.1.1/local/lib/python2.5/site-
packages/sage/calculus/calculus.py in __call__(self, x)
449 msg, s, pos = err.args
450 raise TypeError, "%s: %s !!! %s" % (msg,
s[:pos], s[pos:])
--> 451 return self._coerce_impl(x)
452
453 def _coerce_impl(self, x):
/Users/sschym/Downloads/Free/sage-3.1.1/local/lib/python2.5/site-
packages/sage/calculus/calculus.py in _coerce_impl(self, x)
501 return self(x._sage_())
502 else:
--> 503 raise TypeError, "cannot coerce type '%s' into a
SymbolicExpression."%type(x)
504
505 def _repr_(self):
TypeError: cannot coerce type '<class
'sage.calculus.equations.SymbolicEquation'>' into a
SymbolicExpression.
sage:
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