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.