Numeric.GSL.Differentiation

Numerical differentiation.

http://www.gnu.org/software/gsl/manual/html_node/Numerical-Differentiation.html#Numerical-Differentiation

From the GSL manual: "The functions described in this chapter compute numerical derivatives by finite differencing. An adaptive algorithm is used to find the best choice of finite difference and to estimate the error in the derivative."

Documentation

derivCentral

Arguments

:: Double

initial step size

-> (Double -> Double)

function

-> Double

point where the derivative is taken

-> (Double, Double)

result and absolute error

Adaptive central difference algorithm, gsl_deriv_central. For example:

>>> let deriv = derivCentral 0.01
>>> deriv sin (pi/4)
(0.7071067812000676,1.0600063101654055e-10)
>>> cos (pi/4)
0.7071067811865476

derivForward

Arguments

:: Double

initial step size

-> (Double -> Double)

function

-> Double

point where the derivative is taken

-> (Double, Double)

result and absolute error

Adaptive forward difference algorithm, gsl_deriv_forward. The function is evaluated only at points greater than x, and never at x itself. The derivative is returned in result and an estimate of its absolute error is returned in abserr. This function should be used if f(x) has a discontinuity at x, or is undefined for values less than x. A backward derivative can be obtained using a negative step.

derivBackward

Arguments

:: Double

initial step size

-> (Double -> Double)

function

-> Double

point where the derivative is taken

-> (Double, Double)

result and absolute error

Adaptive backward difference algorithm, gsl_deriv_backward.