DERIV Function

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

Usage

result = DERIV([x,] y)

Input Parameters

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).

Returned Value

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

Keywords

None.

Discussion

Note: DERIV does not support complex numbers.

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.)

Example 1

x = FINDGEN(10)
xx = x^2
d = DERIV(xx)
PRINT, d
; PV-WAVE prints:
;        1.00000       2.00000       4.00000
;       6.00000       8.00000
;       10.0000       12.0000       14.0000
;       16.0000       17.0000
PLOT, xx
OPLOT, d, Linestyle=2

Example 2

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

x = FINDGEN(100) * 10 * !Dtor
sin_x = SIN(x)
d_sin_x = DERIV(x, sin_x)
PLOT, sin_x
OPLOT, d_sin_x, Linestyle=2