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clean y. to tolerance of x. (default 1e_10) form: tolerance (default 1e_10) clean numbers sets values less than tolerance to 0 sum data columns of matrix by key form: key colsum mat sum data columns of matrix on key columns e.g. if column 2 of mat is age, then 2 colsum mat sums the remaining columns by age group indices of y. in x. Return group indices of elements of y. x. is an integer vector of the starting numbers of each group, assumed to be in ascending order. e.g. 0 0 0 1 1 1 2 2 = 0 3 6 groupndx i.8 i.e. <:@(+/@(<:/)) range from a to b [in steps of c] range a,b[,c] = range from a to b [in steps of c] solves recurrence r(i)=a(i)+r(i-1)*m(i-1) form: r = m recur a r(0) = a(0) r(i) = a(i)+r(i-1)*m(i-1) e.g 1.05 1.10 recur 100 100 100 100 205 325.5 round y. to nearest x. with bankers rounding round y. to nearest x. if y. is a mid point, it is rounded up if even, down if odd 0.1 roundbanker 1.23 2.15 2.25 2.35 2.45 1.2 2.2 2.2 2.4 2.4 round y. to nearest x. preserving total distributive rounding round y. to nearest x. preserving total to nearest x. e.g. 0.1 rounddist 6$0.45 0.5 0.4 0.5 0.4 0.5 0.4 steps from a to b in c steps form: steps a,b,c
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