astds#

Purpose#

Computes the biased standard deviation of the elements across one dimension of an N-dimensional array.

Format#

y = astds(x, dim)#

Parameters:

x (N-dimensional array)
dim (scalar) – number of dimension to sum across.

Returns:

y (N-dimensional array) – standard deviation across specified dimension of x.

Examples#

a = areshape(25*rndn(16,1),4|2|2);
y = astds(a,3);

print "a = " a;
print "y = " y;

The code above produces the following output (due to the use of random data in this example your answers will be different):

a =

Plane [1,.,.]

  12.538  -56.786
 -40.283  -58.287

Plane [2,.,.]

   4.047   -0.325
  17.617   -9.248

Plane [3,.,.]

  17.908   40.048
   8.916  -37.247

Plane [4,.,.]

  -0.977   16.058
 -38.189    0.984

 y =

 Plane [1,.,.]

    7.321   35.659
   26.441   23.333

In this example, 16 standard Normal random variables are generated. They are multiplied by 25 and areshape()’d into a 4x2x2 array, and the standard deviation is computed across the third dimension of the array.

Remarks#

The output y, will have the same sizes of dimensions as x, except that the dimension indicated by dim will be collapsed to 1.

This function essentially computes:

\[\sigma = \sqrt{\frac{1}{n}×\Sigma_{i=1}^n(X_i − \mu)^2}\]

Thus, the divisor is N rather than N-1, where N is the number of elements being summed. See astd() for the alternate definition.