# rearrange: Rearrange bootstrap axes by comparing to sample axes. In cabootcrs: Bootstrap Confidence Regions for Correspondence Analysis.

## Description

Compares one set of axes for row points and column points (from the bootstrap data matrix) to another (from the sample data matrix) by looking at all possible reorderings and reflections (only) of the bootstrap axes and picking the one which best matches the sample axes.

## Usage

 `1` ```rearrange(RS, RB, CS, CB, r) ```

## Arguments

 `RS` Sample axes for row points. `RB` Bootstrap axes for row points. `CS` Sample axes for column points. `CB` Bootstrap axes for column points. `r` Rank of bootstrap data matrix.

## Details

Used to find the ordering of the bootstrap axes which best matches the sample axes under reordering and reflection, but not rotation.

Only the first six axes at most of the sample and bootstrap solutions are considered, for speed and simplicity. It is assumed that users are usually only interested in the first 2-4 axes of the sample solution and that hence the only reorderings of axes between sample and resample that are of interest are among the first six. Hence variances for the 6th axis may be inaccurate because reordering has not been fully allowed for, while those for the 7th axis and above will be very inaccurate.

Note that the routine is very literal and unsubtle and considers every possible ordering. The for loop calculating the match values is usually the main computational burden in the whole program, and a better algorithm for finding the best permutation for the bootstrap eigenvectors to match the sample eigenvectors would speed the program substantially.

## Value

A list of items used in rearranging.

 `T` Matrix to postmultiply the bootstrap axes to match them to the sample axes. `numrearranged` Number of axes potentially rearranged = min(input rank,6). `match` Vector of values of the matching coefficient for each possible ordering. `same` TRUE if no reordering needed, FALSE otherwise.

## Note

Internal routine, not intended for direct call by users.

## Author(s)

T.J. Ringrose

`sca` , `cabootcrs`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68``` ```## Not intended for direct call by users. ## The function is currently defined as function (RS, RB, CS, CB, r) { if (r >= 1) { maxrearrange <- 6 numrearranged <- min(r, maxrearrange) switch(numrearranged, per <- matrix(1, 1, 1), per <- rbind(c(1, 2), c(2, 1)), per <- cbind(rep(1:3, each = 2), c(2, 3, 1, 3, 1, 2), c(3, 2, 3, 1, 2, 1)), { p <- cbind(rep(1:3, each = 2), c(2, 3, 1, 3, 1, 2), c(3, 2, 3, 1, 2, 1), 4) per <- rbind(p, p + 3 * (p == 1) - 3 * (p == 4), p + 2 * (p == 2) - 2 * (p == 4), p + (p == 3) - (p == 4)) }, { p <- cbind(rep(1:3, each = 2), c(2, 3, 1, 3, 1, 2), c(3, 2, 3, 1, 2, 1), 4) p <- rbind(p, p + 3 * (p == 1) - 3 * (p == 4), p + 2 * (p == 2) - 2 * (p == 4), p + (p == 3) - (p == 4)) p <- cbind(p, 5) per <- rbind(p, p + 4 * (p == 1) - 4 * (p == 5), p + 3 * (p == 2) - 3 * (p == 5), p + 2 * (p == 3) - 2 * (p == 5), p + (p == 4) - (p == 5)) }, { p <- cbind(rep(1:3, each = 2), c(2, 3, 1, 3, 1, 2), c(3, 2, 3, 1, 2, 1), 4) p <- rbind(p, p + 3 * (p == 1) - 3 * (p == 4), p + 2 * (p == 2) - 2 * (p == 4), p + (p == 3) - (p == 4)) p <- cbind(p, 5) p <- rbind(p, p + 4 * (p == 1) - 4 * (p == 5), p + 3 * (p == 2) - 3 * (p == 5), p + 2 * (p == 3) - 2 * (p == 5), p + (p == 4) - (p == 5)) p <- cbind(p, 6) per <- rbind(p, p + 5 * (p == 1) - 5 * (p == 6), p + 4 * (p == 2) - 4 * (p == 6), p + 3 * (p == 3) - 3 * (p == 6), p + 2 * (p == 4) - 2 * (p == 6), p + (p == 5) - (p == 6)) }) nper <- dim(per)[1] match <- matrix(0, nper, 1) for (i in 1:nper) { match[i] = sum(diag(abs(t(RS[, 1:numrearranged]) %*% RB[, per[i, ]] + t(CS[, 1:numrearranged]) %*% CB[, per[i, ]]))) } posn <- which.max(match) same <- posn == 1 I <- diag(rep(1, numrearranged)) T <- I[, per[posn, ]] t <- diag(t(RS[, 1:numrearranged]) %*% RB[, per[posn, ]] + t(CS[, 1:numrearranged]) %*% CB[, per[posn, ]]) T <- T %*% diag((t >= 0) - (t < 0), nrow = numrearranged, ncol = numrearranged) } else { T <- matrix(1, 1, 1) numrearranged <- 1 match <- 0 same <- 0 } list(T = T, numrearranged = numrearranged, match = match, same = same) } ```