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.
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.
f– an expression
vars– the names of the arguments
old– deprecated, do not use
expect_one_var– don’t give deprecation warning if
varsis omitted, as long as expression has only one var
sage: from sage.ext.fast_eval import fast_float sage: x,y = var('x,y') sage: f = fast_float(sqrt(x^2+y^2), 'x', 'y') sage: f(3,4) 5.0
Specifying the argument names is essential, as fast_float objects only distinguish between arguments by order.
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