Differences in QR decomposition of complex matrix in R and Matlab

Question

With the below matrix A, I get different matrices for R in its QR decomposition between [R] and Matlab. (The Q's are different as well, of course.)

A <- structure(c(1+0i, -0.75+0.75i, 0+0i, 0+0i, 1+0i, -0.75+0.75i, 
1+0i, -1.5+1.5i, 0-1i), .Dim = c(3L, 3L))

QR <- qr(A)
Q <- qr.Q(A)
R <- qr.R(QR)
R
            [,1]                  [,2]                   [,3]
[1,] -2.54951+0i  0.8825226+0.8825226i -1.27475488+0.0000000i
[2,]  0.00000+0i -0.7531983+0.0000000i -0.49787685+0.4978768i
[3,]  0.00000+0i  0.0000000+0.0000000i -0.06509446+0.0000000i

Whereas with Matlab:

[Q,R] = qr(A);
R =
  -1.4577 + 0.0000i   0.5145 + 0.5145i  -2.2295 - 0.0000i
   0.0000 + 0.0000i  -1.2632 + 0.0000i   0.8732 - 0.8732i
   0.0000 + 0.0000i   0.0000 + 0.0000i  -0.0679 + 0.0000i

Checking the decomposition from R software, I have to reorder the R matrix's columns to recreate my original matrix A using Q %*% R[, QR$pivot], but this of course destroys the upper triangular nature of R:

zapsmall(Q %*% R[, QR$pivot])
            [,1]        [,2]      [,3]
[1,]  1.00+0.00i  0.00+0.00i  1.0+0.0i
[2,] -0.75+0.75i  1.00+0.00i -1.5+1.5i
[3,]  0.00+0.00i -0.75+0.75i  0.0-1.0i

Whereas with Matlab, a straight Q * R works:

Q * R
ans = 
   1.0000 + 0.0000i   0.0000 + 0.0000i   1.0000 + 0.0000i
  -0.7500 + 0.7500i   1.0000 + 0.0000i  -1.5000 + 1.5000i
   0.0000 + 0.0000i  -0.7500 + 0.7500i   0.0000 - 1.0000i

I realise that a QR decomposition is not unique, but I need to get an upper triangular R matrix just like in Matlab which I can use subsequently without rearranging its columns, such that Q %*% R = A.

Any suggestions in the R software on how I might achieve this?

Update: A suggestion was made that question may be answered here, but that answer will only work with real matrices, whereas my query is for complex.