DERIV Function

Standard Library function that calculates the first derivative of a function in x and y.

result = DERIV([x,] y)

x (optional) The vector of independent x-coordinates of the data (i.e., the variable with respect to which the function should be differentiated). Must be a one-dimensional array (a vector).

y The vector of dependent y-coordinates at which the derivative of function f is evaluated. Must be a one-dimensional array (a vector).

result The first derivative of the vector y, with respect to the independent variable x. The result has the same size as y.

None.

The numerical differentiation algorithm for DERIV uses a three-point Lagrangian interpolation.

The vector of x-coordinates, x, is optional. The conditions set on this vector are given below:

• If you specify x, then both x and y must be one-dimensional and have the same number of elements. Selecting this option allows you to define the spacing along the x-axis, for the case where the independent data is not monotonically increasing.

• If you don't specify x, then it is automatically provided with even spacing, using a unit of one, along the x-axis. (In other words, x(i) = i, where i = 0, 1, 2, 3, ... n.)

x = FINDGEN(10)
xx = x^2
d = DERIV(xx)
PRINT, d
PLOT, xx
OPLOT, d, Linestyle=2

x = FINDGEN(100) * 10 * !Dtor

; Create an array that contains values 0, 10, 20 ... and multiply these
; by !Dtor (which equals 0.0174533) to convert the values from
; degrees to radians.

sin_x = SIN(x)
d_sin_x = DERIV(x, sin_x)
PLOT, sin_x
OPLOT, d_sin_x, Linestyle=2

For an example of the three-point Lagrangian interpolation used in DERIV, see the Introduction to Numerical Analysis by F. B. Hildebrand, Dover Publishing, New York, 1987.