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# numeric: numeric utilities
Name | Type | Description
baserep | verb | y. in base x.
clean | verb | clean y. to tolerance of x. (default 1e_10)
colsum | verb | sum data columns of matrix by key
groupndx | verb | group indices of y. in x.
int01 | verb | interval in n steps from 0 to 1 (= steps 0 1,n)
linsert | verb | linear insert x. (default 2) steps into y.
randomize | verb | sets a random value into random link
range | verb | range from a to b [in steps of c]
recur | verb | solves recurrence r(i)=a(i)+r(i-1)*m(i-1)
round | verb | round y. to nearest x. (e.g. 1000 round 12345)
roundbanker | verb | round y. to nearest x. with bankers rounding
rounddist | verb | round y. to nearest x. preserving total
rounddown | verb | round y. down to nearest x. (e.g. 1000 round 12345)
roundint | verb | round to nearest integer
roundup | verb | round y. up to nearest x. (e.g. 1000 round 12345)
steps | verb | steps from a to b in c steps
clean
    clean y. to tolerance of x. (default 1e_10)
    form: tolerance (default 1e_10) clean numbers
    sets values less than tolerance to 0
colsum
    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
groupndx
    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
    range from a to b [in steps of c]
    range a,b[,c] = range from a to b [in steps of c]
recur
    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
roundbanker
    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
rounddist
    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
    steps from a to b in c steps
    form: steps a,b,c
>> << Ndx Usr Pri Phr Dic Rel Voc !: wd Help User