Converting a matrix into another by a mapping table

Hello Matlab experts! May I ask a question?

I need to change the values of the matrix a, for example

a =

     3     4     2
     3     4     1
     4     1     2

Into the matrix, b

b =

     5     6     3
     5     6     2
     6     2     3

By applying the mapping matrix, for example c

c =

     1     2
     2     3
     3     5
     4     6

In other words, how do I convert matrix a, into matrix b, by using the mapping in c to substitute values.

For example, the first element of a(1,1), 3, becomes a 5 in b(1,1) via the mapping matrix c. Like a lookup table, the second element of a(1,2), 4, becomes a 6 in b(1,2) by looking it up in matrix c. Etc.

The matrix a may grow to 1000s of columns and up to a million rows.

I slightly prefer vectorization over looping if possible.

Thanks so much!

Answer 1

[Jan]

a = [3     4     2; ...
     3     4     1; ...
     4     1     2];

c = [1     2; ...
     2     3; ...
     3     5; ...
     4     6]

m      = c(:, 2);
Result = m(a)

This works if the first column of c does not matter, because it is 1:max(a(:)). Otherwise use this to create m:

m(c(:, 1)) = c(:, 2);

[Anthony Klinkert]

Thank you. I liked the simplicity of this approach.

Answer 2

[Image Analyst]

If the "a" and "c" are integers, you can use intlut() - a function meant for exactly this kind of operation. I show here for both cases: uint16 and uint8:

a = [3     4     2; ...
  3     4     1; ...
  4     1     2];

c = [1     2; ...
  2     3; ...
  3     5; ...
  4     6]

% If using uint16:
lut = uint16([0; c(:, 2); zeros(65535 - size(c, 1), 1)]);
output = intlut(uint16(a), lut)  % Or you can cast "a" to uint8 or int16

% If using uint8:
lut = uint8([0; c(:, 2); zeros(255 - size(c, 1), 1)]);
output = intlut(uint8(a), lut)  % Or you can cast "a" to uint8 or int16

[Anthony Klinkert]

Thanks so much! I will use this when I run into scaling issues.