Converting matrix operations in Matlab to R code

Question

I'm trying to convert Matlab code to R. I'm not familiar with Matlab matrix operations, and it appears the results from my R code do not match the results from Matlab, so any help would be greatly appreciated. The Matlab code I'm trying to convert is below (from this website):

% Mean Variance Optimizer

% S is matrix of security covariances
S = [185 86.5 80 20; 86.5 196 76 13.5; 80 76 411 -19; 20 13.5 -19 25]

% Vector of security expected returns
zbar = [14; 12; 15; 7]

% Unity vector..must have same length as zbar
unity = ones(length(zbar),1)

% Vector of security standard deviations
stdevs = sqrt(diag(S))

% Calculate Efficient Frontier
A = unity'*S^-1*unity
B = unity'*S^-1*zbar
C = zbar'*S^-1*zbar
D = A*C-B^2

% Efficient Frontier
mu = (1:300)/10;

% Plot Efficient Frontier
minvar = ((A*mu.^2)-2*B*mu+C)/D;
minstd = sqrt(minvar);

plot(minstd,mu,stdevs,zbar,'*')
title('Efficient Frontier with Individual Securities','fontsize',18)
ylabel('Expected Return (%)','fontsize',18)
xlabel('Standard Deviation (%)','fontsize',18)

Here is my attempt in R:

# S is matrix of security covariances
S <- matrix(c(185, 86.5, 80, 20, 86.5, 196, 76, 13.5, 80, 76, 411, -19, 20, 13.5, -19, 25), nrow=4, ncol=4, byrow=TRUE)

# Vector of security expected returns
zbar = c(14, 12, 15, 7)

# Unity vector..must have same length as zbar
unity <- rep(1, length(zbar))

# Vector of security standard deviations
stdevs <- sqrt(diag(S))

# Calculate Efficient Frontier
A <- unity*S^-1*unity
B <- unity*S^-1*zbar
C <- zbar*S^-1*zbar
D <- A*C-B^2

# Efficient Frontier
mu = (1:300)/10

# Plot Efficient Frontier
minvar = ((A*mu^2)-2*B*mu+C)/D
minstd = sqrt(minvar)

It appears that unity*S in Matlab is equivalent to colSums(S) in R. But I haven't been able to figure out how to calculate the equivalent of S^-1*unity in R. If I type this Matlab code in R (S^-1*unity), it calculates without error, but it gives a different answer. Because I don't understand the underlying Matlab calculation, I'm not sure how to translate it to R.

that is, `%*%` is standard matrix multiplication; `*` denotes an elementwise (Hadamard) product, equivalent to `.*` in MATLAB. — Ben Bolker, Oct 26 '14 at 19:03
@BenBolker I wasn't aware there's a name for elementwise product of matrices. I assumed it's called "common sense" product. :) — Roman Luštrik, Oct 26 '14 at 19:10
I think you will need a matrix inverse function as well (perhaps `solve`), at least assuming that `^-1` is a matrix inverse in Matlab. — IRTFM, Oct 26 '14 at 19:14

score 2 · Accepted Answer · answered Oct 26 '14 at 19:21

I used to do matlab -> R conversions quite a bit a few years ago.

My general suggestion is to open 2 terminals side by side and try to do everything going line-by-line. Then after each line you should check if what you got in MATLAB and R are equivalent.

This document should be handy: http://mathesaurus.sourceforge.net/octave-r.html

In your case these appear to be the commands that you should have in mind:

Matrix multiplication:

Matlab: A*B
R: A %*% B

Transpose:

Matlab: A'
R: t(A)

Matrix inverse:

Matlab: inv(A) or A^-1
R: solve(A)

Don't try to convert everything at once because you will run into trouble. When the results won't match you will not be able to tell where the error is.

Converting matrix operations in Matlab to R code

1 Answers1