Hi Justin - see below

I am working on implementing a small subset of the PLS analysis in R, as I do not have Matlab. I have a question regarding the appropriate manner in which to perform the Procrustes rotation when performing permutation tests and bootstrapping. I am following the introduction of the McIntosh & Lobaugh, 2004, Neuroimage paper. On the top of page S253, after a description of how to perform the rotation, there is a line that says "The singular values of the rotated matrix can be obtained by calculating the columnwise square root of the sum-of-squares". What I'm not clear about is, what columns are being referred to for calculation? Those of the rotated V_resamp or those of the rotated U_resamp? 

Either one would work since both are rescaled by the singular value when the rotation is applied.  Its probably more expedient to us V_resamp

A related question I have is, when calculating p-values for the singular values associated with different contrasts, it is stated (in McIntosh & Lobaugh, 2004) 'the numer of times the permuted singular values exceed the oserved singular values is calculated'. Does this mean if I'm looking at the first (largest) singular value I consider all permuted singular values in calculating the associated p-value or only the largest from the permutation tests, and a second singular value would only be compared against the second largest etc?

You are correct in how to map the permuted singular values.

Also, I was wondering if there was any test data in a generic form that I could use to ensure that I've implemented my code correctly. I'm mostly just looking for example X and Y matrices along with the appropriate bootstrap ratios and p-values for the different latent variables, as well as the U, delta, and V matrices. I see that there is some data in .mat form available on the website, but was looking for something in like a CSV file type format. I have tested my code against the matrices that are in one published paper (e.g., Krishnan et al, 2011, Neuroimage), but from what I can tell, there aren't any bootstrap ratios or p-values for permutation tests in that paper for comparison.

There is a small matlab file that has testdata plus the results for a mean-centred PLS analysis.  There are 5 subjects in 3 conditions with a four voxel brain :) 

If you don't have Matlab I can split the file into its pieces and post it for you

https://www.dropbox.com/s/psze4ahydht0xg8/testdata.mat?dl=0