Version 5.0 The LEDA User Manual

5.17.2 Integration
double integrate function(double (∗f)(double), double l, double r,
double delta = 1.0e − 2)
Computes the integral of f in the interval [l, r] by forming
the sum delta∗ ∑ 0≤i 0.
template
double integrate function(const F & f, double l, double r, double delta = 1.0e − 2)
a more flexible version of the above. It is assumed that class
F offers the operator
double operator( )(double x). This operator is taken as the
function f.
5.17.3 Useful Numerical Functions
double binary entropy(double x)
returns the binary entropy of x, i.e., −x · log x − (1 − x) ·
log(1 − x).
Precondition: 0 ≤ x ≤ 1.
5.17.4 Root Finding
double zero of function(double (∗f)(double), double l, double r, double tol = 1.0e − 10)
returns a zero x of f. We have either |f(x)| ≤ 10 −10 or there
is an interval [x 0 , x 1 ] containing x such that f(x 0 )·f(x 1 ) ≤ 0
and x 1 − x 0 ≤ tol · max(1, |x 1 | + |x 1 |).
Precondition: l ≤ r and f(l) · f(r) ≤ 0.
template
double zero of function(const F & f, double l, double r, double tol = 1.0e − 10)
a more flexible version of the above. It is assumed that class
F offers the operator
double operator( )(double x). This operator is taken as the
function f.