Module Romberg

Numerical integration using the Romberg method

Example:

 >>>from Scientific.Functions.Romberg import romberg
 >>>from Scientific.N import pi, tan
 >>>romberg(tan, (0.0, pi/3.0))

 yields '0.693147180562'

Parameters:

• function (callable) - a function of one variable
• interval (sequence of two floats) - the lower and upper limit of the integration interval
• accuracy (float) - convergence criterion (absolute error)

Returns: number

the numerical integral of the function over the interval

Numerical integration using the trapezoidal rule

Example:

 >>>from Scientific.Functions.Romberg import trapezoid
 >>>from Scientific.N import pi, tan
 >>>trapezoid(tan, (0.0, pi/3.0), 100)

 yields 0.69317459482518262

Parameters:

• function (callable) - a function of one variable
• interval (sequence of two floats) - the lower and upper limit of the integration interval
• numtraps (int) - the number of trapezoids

Returns: number

the numerical integral of the function over the interval