CL_mean

Description

• Computes the mean value by quadrature.

  Assuming that the implicit (evenly spaced) abscissas are t1 .. tn, the mean value is defined by:

  xmean = Integral from t1 to tn of x(t), divided by tn-t1 (integral approximated by quadrature).

  The mean value can be computed on the rows (rc = "r") or on the columns (rc = "c"), exactly as the function "mean" does. If rc = "r", the result is a row vector. If rc = "c", the result is a column vector.

  Three methods are available:

  - trap: integral evaluated by trapezoidal method

  - simp: integral evaluated by Simpson's rule

  - boole: integral evaluated by Boole's rule

  The required number of values depends on the method used:

  - trap: any number

  - simp: odd number (e.g. 1, 3, 5, 7...)

  - boole: multiple of 4 plus 1 (e.g. 1, 5, 9, 13...)

  Notes:

  - rc can be omitted for a row vector or a column vector. The result is then a real number.

Parameters

x:

Matrix of real values (PxN)

meth:

(string) Method used: "trap", "simp", "boole" (1x1)

rc:

(string, optional) Direction: "r": mean computed on rows or "c": mean computed on columns. For default, see above.

xmean:

Mean value (Px1) or (1xN)

Authors

• CNES - DCT/SB

Examples

t = linspace(0, %pi, 101); CL_mean(sin(t), "trap") - 2/%pi CL_mean(sin(t), "simp") - 2/%pi CL_mean(sin(t), "boole") - 2/%pi