Taking weighted means over matrices with missing data

I have a matrix with some NaN entries. I want to calculate the weighted averages of each row, according to a supplied row vector of weights. Where a row has one or more missing values, I simply want to scale up the remaining weights. This is easy enough to do as a for loop over all rows; but I was wondering if there's a simple way to do so using just matrix operations.

Illustration: say my matrix is:

[4 NaN 1 NaN; 5 3 8 NaN; 1 6 2 4; 8 4 7 2]

The weight vector is:

[0.4 0.3 0.2 0.1]

I want to return the column vector:

[3; 5; 3; 6]

For the last row, 6 = 8*0.4 + 4*0.3 + 7*0.2 + 2*0.1. For the first row, 3 = (4*0.4 + 1*0.2)/(0.4 + 0.2). And so on.

Is this possible using matrix operations over the whole matrix at once, or will it have to be done row by row in a loop?

Answer 1

[Teja Muppirala]

M = [4 NaN 1 NaN; 5 3 8 NaN; 1 6 2 4; 8 4 7 2];
w = [0.4 0.3 0.2 0.1];

W = bsxfun(@times,~isnan(M),w);
W = bsxfun(@rdivide,W,sum(W,2));
M(isnan(M)) = 0;
sum(M.*W,2)

ans =
  3.0000
  5.0000
  3.0000
  6.0000

[Teja Muppirala]

A bit simpler:

W = bsxfun(@times,~isnan(M),w);
M(isnan(M)) = 0;
sum(M.*W,2)./sum(W,2)

Answer 2

[David Sanchez]

I think it is not possible, but you can write your own function to do it.

Answer 3

[Yao Li]

A=[4 NaN 1 NaN; 5 3 8 NaN; 1 6 2 4; 8 4 7 2];
A_u=A./A;
A(isnan(A))=0;
A_u(isnan(A_u))=0;
weight=[0.4 0.3 0.2 0.1];
y=weight*(A')./(weight*A_u')

[Teja Muppirala]

This will have some trouble if any of the elements in A are zero, because 0./0 equals NaN.

Answer 4

[Andrei Bobrov]

M = [4 NaN 1 NaN; 5 3 8 NaN; 1 6 2 4; 8 4 7 2];
w = [0.4 0.3 0.2 0.1]';

t = isnan(M);
M(t) = 0;
out = (M*w)./(~t*w);