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has been superseded by fast_callable()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, old=None, expect_one_var=False, *vars)#
Tries to create a function that evaluates f quickly using floating-point numbers, if possible. There are two implementations of fast_float in Sage; by default we use the newer, which is slightly faster on most tests.
On failure, returns the input unchanged.
INPUT:
f
– an expressionvars
– the names of the argumentsold
– deprecated, do not useexpect_one_var
– don’t give deprecation warning ifvars
is 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
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
- sage.ext.fast_eval.is_fast_float(x)#