The function sort returns an index list:
The list has the same length as the input vector x, and list(1) is the index of the smallest element of x, list(2) the index of the next smallest, and so on. Thus, x(list) will be x sorted into ascending order.
By returning an index list instead of the sorted array, sort simplifies the co-sorting of other arrays. For example, consider a series of elaborate experiments. On each experiment, thermonuclear yield and laser input energy are measured, as well as fuel mass. These might reasonably be stored in three vectors yield, input, and mass, each of which is a 1D array with as many elements as experiments performed. The order of the elements in the arrays maight naturally be the order in which the experiments were performed, so that yield(3), input(3), and mass(3) represent the third experiment. The experiments can be sorted into order of increasing gain (yield per unit input energy) as follows:
The inverse list, which will return them to their orginal order, is:
The sort function actually sorts along only one index of a multi-dimensional array. The dimensions of the returned list are the same as the dimensions of the input array; the values are indices relative to the beginning of the entire array, not indices for the dimension being sorted. Thus, x(sort(x)) is the array x sorted so that the elements along its first dimension are in ascending order. In order to sort along another dimension, pass sort a second argument -- x(sort(x,2)) will be x sorted into increasing order along its second dimension, x(sort(x,3)) along its third dimension, and so on.
A related function is median. It takes one or two arguments, just like sort, but its result -- which is, of course, the median values along the dimension being sorted -- has one fewer dimension than its input.