### 2.4 Sorting ¶

The function `sort` returns an index list:

    list = sort(x);

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:

    list = sort(yield/input);
    yield = yield(list);
    input = input(list);
    mass = mass(list);

The inverse list, which will return them to their orginal order, is:

    invlist = list;  /* faster than  array(0, dimsof(list)) */
    invlist(list) = indgen(numberof(list));

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.