On Aug 8, 2011, at 12:18 AM, Lei Liu wrote:
Hi there,
I have two questions on matrix manipulation. For the first one, I
want to calculate the product of each column of a matrix (say A)
with another vector (say b). That is, if A has 5 columns (a1, a2,
a3, a4, a5), I want to obtain a matrix with columns (a1*b, a2*b,
aA3*b, a4*b, a5*b). Can I do it directly, without using "for" loop?
b*A # arithmetic operations on matrices are column-wise and argument
recycling accomplishes the "loopless looping".
For the second one, I have a matrix A of dimension 2 by n (say
columns of a1, a2, ..., an), another matrix B of dimension 2 by 2. I
want to obtain the vector with elements (t(a1) %*% B %*% a1, t(a2) %*
% B %*% a2, ..., t(an) %*% B %*% an). Can I do it without using
"for" loop?
Perhaps:
B <- matrix(1:4, 2)
A <- matrix(1:10, 2)
apply(A, 2, function(x) x %*% B %*% x)
[1] 27 133 319 585 931
(Also not that this is only more compact than a loop. It should not be
expected to be more efficient since it is really a loop "underneath
the hood".)
Also noticed that this would yield the same result and it well could
be faster, despite the extraneous results that get discarded:
diag( crossprod( A, crossprod(B, A)) )
But other interpretations seem possible. Maybe next time you can heed
the admonitions in the Posting Guide and offer a reproducible example
and say what you think the answer should be?
--
Thanks a lot!
Lei Liu
Associate Professor
Division of Biostatistics
Department of Public Health Sciences
University of Virginia School of Medicine
http://people.virginia.edu/~ll9f/
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David Winsemius, MD
West Hartford, CT
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