Matrix oriented computing

On Fri, 2005-08-26 at 15:25 +0200, Peter Dalgaard wrote:

Marc Schwartz <MSchwartz at mn.rr.com> writes:

x <- c(0.005, 0.010, 0.025, 0.05, 0.1, 0.5, 0.9,
       0.95, 0.975, 0.99, 0.995)

df <- c(1:100)

mat <- sapply(x, qchisq, df)

dim(mat)

[1] 100  11

str(mat)

 num [1:100, 1:11] 3.93e-05 1.00e-02 7.17e-02 2.07e-01 4.12e-01 ...

outer() is perhaps a more natural first try... It does give the
transpose of the sapply approach, though.

round(t(outer(x,df,qchisq)),2)

should be close. You should likely add dimnames.

What I find interesting, is that I would have intuitively expected
outer() to be faster than sapply().  However:

 system.time(mat <- sapply(x, qchisq, df), gcFirst = TRUE)

[1] 0.01 0.00 0.01 0.00 0.00

 system.time(mat1 <- round(t(outer(x, df, qchisq)), 2),

              gcFirst = TRUE)
[1] 0.01 0.00 0.01 0.00 0.00

# No round() or t() to test for overhead

 system.time(mat2 <- outer(x, df, qchisq), gcFirst = TRUE)

[1] 0.01 0.00 0.02 0.00 0.00


# Bear in mind the round() on mat1 above

all.equal(mat, mat1)

[1] "Mean relative  difference: 4.905485e-05"

all.equal(mat, t(mat2))

[1] TRUE


Even when increasing the size of 'df' to 1:1000:

 system.time(mat <- sapply(x, qchisq, df), gcFirst = TRUE)

[1] 0.16 0.01 0.16 0.00 0.00

 system.time(mat1 <- round(t(outer(x, df, qchisq)), 2), gcFirst =

TRUE)
[1] 0.16 0.00 0.18 0.00 0.00

 # No round() or t() to test for overhead
 system.time(mat2 <- outer(x, df, qchisq), gcFirst = TRUE)

[1] 0.16 0.01 0.17 0.00 0.00



It also seems that, at least in this case, t() and round() do not add
much overhead.

n <- 1000
system.time(for (i in 1:n) mat <- sapply(x, qchisq, df), gcFirst = TRUE)

system.time(for(i in 1:n) mat2 <- outer(x, df, qchisq), gcFirst = TRUE)