# Re: Vectorization question

```Pavel Romashkin <promashkin@cmdl.noaa.gov> writes:

> Hi Liam,
> I came up with a different approach. For short arrays in a loop, it is 3
> times slower than your method, Liam. However, with A being 1,000,000 and
> both X and B 100,000 elements long, your method could not allocate
> memory on my machine, while mine ran in 0.07 s. Check out the code
> below. The loops were put in to get runtime extimates.
> I run 5.3 on PowerMac G4, 192 MB total RAM, 64 MB allocated to IDL.
> Cheers,
> Pavel

Here is my belated entry.  Getting the repeats right is the trick.  My
technique does use HISTOGRAM, but is thinking outside the box a little
bit by iterating over the number of hits in the histogram rather than
the reverse index array.

I use this technique some in my own work and it's fairly fast.  I use
it to place values known at semi-regularly spaced times onto a regular
grid.  Unfortunately I can't use these new-fangled VALUE_LOCATE() or
TOTAL(...,/CUMULATIVE) functions since I am staying compatible with
earlier versions of IDL.  We don't even have IDL 5.3 yet, so I can't
even test against any others.  Pavel, can you compare?  :-)

n = n_elements(a)
hh = histogram(x, min=0, max=n-1, reverse=rr)
wh = where(hh GT 0) & mx = max(hh(wh), min=mn)
for i = mn, mx do begin
wh = wh(where(hh(wh) GE i, ct))   ;; Get X cells with GE i entries
a(wh) = a(wh) + b(rr(rr(wh)+i-1)) ;; Add into the total
endfor

Below are my array setups, and the functions I used.  The pavel
function is slightly modified for practicality reasons.

Craig

a = lonarr(1000000)
b = long(randomu(seed,100000)*1000000)
x = long(randomu(seed,100000)*1000000)

pro craig, a, b, x, iter=iter
start = systime(1)
if n_elements(iter) EQ 0 then iter = 1
start = systime(1)
for j = 0, iter-1 do begin
n = n_elements(a)
hh = histogram(x, min=0, max=n-1, reverse=rr)
wh = where(hh GT 0) & mx = max(hh(wh), min=mn)
for i = mn, mx do begin
wh = wh(where(hh(wh) GE i, ct))
a(wh) = a(wh) + b(rr(rr(wh)+i-1))
endfor
endfor
print, systime(1) - start
end

pro pavel, a, b, x, iter=iter
start = systime(1)
if n_elements(iter) EQ 0 then iter = 1
out = a
start = systime(1)
for i = 0, iter-1 do begin
ind = x[uniq(x, sort(x))]
loc = value_locate(x, ind)
sum_b = total(b, /cumulative)
res = [0, sum_b[loc], 0]
a_values = (res-shift(res, 1))[1:n_elements(res)-2]
out[ind] = a_values
endfor
print, systime(1) - start
end

pro liam, a, b, x, iter=iter
start = systime(1)
if n_elements(iter) EQ 0 then iter = 1
out = a
start = systime(1)
for i = 0, iter-1 do begin
tmp = intarr(n_elements(a), n_elements(x))
tmp[x, indgen(n_elements(x))] = b
out = a + total(tmp, 2)
endfor
print, systime(1) - start
end

>
> pro pavel, a, b, x
> out = a
> start = systime(1)
> ;for i =0, 10000 do begin
> ind = x[uniq(x, sort(x))]
> loc = value_locate(x, ind)
> sum_b = total(b, /cumulative)
> res = [0, sum_b[loc], 0]
> a_values = (res-shift(res, 1))[1:n_elements(res)-2]
> out[ind] = a_values
> ;endfor
> print, systime(1) - start
> ;print, out, format='(10i4)'
> end
>
> pro liam, a, b, x
> out = a
> start = systime(1)
> ;for i =0, 10000 do begin
> tmp = intarr(n_elements(a), n_elements(x))
> tmp[x, indgen(n_elements(x))] = b
> out = a + total(tmp, 2)
> ;endfor
> print, systime(1) - start
> ;print,  out, format='(10i4)'
> end

--
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Craig B. Markwardt, Ph.D.         EMAIL:    craigmnet@cow.physics.wisc.edu
Astrophysics, IDL, Finance, Derivatives | Remove "net" for better response
--------------------------------------------------------------------------

```