Fast Numerical Evaluation¶
For many applications such as numerical integration, differential equation approximation, plotting a 3d surface, optimization problems, monte-carlo simulations, etc., one wishes to pass around and evaluate a single algebraic expression many, many times at various floating point values. Doing this via recursive calls over a python representation of the object (even if Maxima or other outside packages are not involved) is extremely inefficient.
The solution implemented in this module, by Robert Bradshaw (2008-10),
has been superseded by fast_callable().
All that remains here is a compatible interface function fast_float().
AUTHORS:
- Robert Bradshaw (2008-10): Initial version 
- sage.ext.fast_eval.fast_float(f, expect_one_var=False, *vars)[source]¶
- Try to create a function that evaluates f quickly using floating-point numbers, if possible. - On failure, returns the input unchanged. - This is an alternative interface to - sage.ext.fast_callable.fast_callable(). Issue #32268 proposes to deprecate this function.- INPUT: - f– an expression
- vars– the names of the arguments
- expect_one_var– don’t give deprecation warning if- varsis omitted, as long as expression has only one var
 - EXAMPLES: - sage: from sage.ext.fast_eval import fast_float sage: x,y = var('x,y') # needs sage.symbolic sage: f = fast_float(sqrt(x^2+y^2), 'x', 'y') # needs sage.symbolic sage: f(3,4) # needs sage.symbolic 5.0 - >>> from sage.all import * >>> from sage.ext.fast_eval import fast_float >>> x,y = var('x,y') # needs sage.symbolic >>> f = fast_float(sqrt(x**Integer(2)+y**Integer(2)), 'x', 'y') # needs sage.symbolic >>> f(Integer(3),Integer(4)) # needs sage.symbolic 5.0 - Specifying the argument names is essential, as fast_float objects only distinguish between arguments by order. - sage: # needs sage.symbolic sage: f = fast_float(x-y, 'x','y') sage: f(1,2) -1.0 sage: f = fast_float(x-y, 'y','x') sage: f(1,2) 1.0 - >>> from sage.all import * >>> # needs sage.symbolic >>> f = fast_float(x-y, 'x','y') >>> f(Integer(1),Integer(2)) -1.0 >>> f = fast_float(x-y, 'y','x') >>> f(Integer(1),Integer(2)) 1.0