counts ============================================== Purpose ---------------- Counts the numbers of elements of a vector that fall into specified ranges. Format ---------------- .. function:: c = counts(x, v) :param x: the numbers to be counted :type x: Nx1 vector :param v: breakpoints specifying the ranges within which counts are to be made. The vector *v* MUST be sorted in ascending order. :type v: Px1 vector :return c: the counts of the elements of *x* that fall into the regions: .. math:: x \leq v[1],\\ v[1] < x \leq v[2],\\ \vdots\\ v[p-1] < x \leq v[p] :rtype c: Px1 vector Examples ---------------- Basic example +++++++++++++ Count the number of elements which are in a specific range. :: // Original data x = { 1.5, 3, 5, 4, 1, 3 }; // Break points v = { 0, 2, 4 }; // Get counts c = counts(x, v); :: 1.5 3 0 0 x = 5 v = 2 c = 2 4 4 3 1 3 Count integers ++++++++++++++ Count how many times each integer from 1 to 10 is present in a vector. :: x = { 9, 8, 9, 9, 6, 8, 6, 7 }; ints = seqa(1, 1, 10); c = counts(x, ints); :: 1 0 2 0 3 0 4 0 ints = 5 c = 0 6 2 7 1 8 2 9 3 10 0 Remarks ------- If the maximum value of *x* is greater than the last element (the maximum value) of *v*, the sum of the elements of the result, *c*, will be less than :math:N, the total number of elements in *x*. If :: 1 2 3 4 4 x = 5 v = 5 6 8 7 8 9 then :: 4 c = 1 3 The first category can be a missing value if you need to count missings directly. Also :math:+\infty or :math:-\infty are allowed as breakpoints. The missing value must be the first breakpoint if it is included as a breakpoint and infinities must be in the proper location depending on their sign. :math:-\infty must be in the :math:[2, 1] element of the breakpoint vector if there is a missing value as a category as well, otherwise it has to be in the :math:[1, 1] element. If :math:+\infty is included, it must be the last element of the breakpoint vector.