astds ============================================== Purpose ---------------- Computes the biased standard deviation of the elements across one dimension of an N-dimensional array. Format ---------------- .. function:: y = astds(x, dim) :param x: :type x: N-dimensional array :param dim: number of dimension to sum across. :type dim: scalar :return y: standard deviation across specified dimension of *x*. :rtype y: N-dimensional array 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 :func: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: .. math:: \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 :func:astd for the alternate definition. .. seealso:: Functions :func:astd, :func:stdsc