Hey there, community!

I have two matrices of floating point numbers, I'll call them simply A and B. Now, A is of size 700x5, and B is of size 300x2. I know that the 300 pairs of numbers that B represents are a subset of the 700 pairs of numbers given by the second and third column of A (i.e. A[[;;,2;;3]]).

I need to do the following: for each row in B, find a row in A where the second and third element match the ones in B, and create a new matrix where the rows of matrix B have been replaced by the corresponding rows of A. So, say that the matrices A and B are as follows:

A= {{0, 0.5, 1, 1.5, 2}, {1, 1.5, 2, 2.5, 3}, {3, 4.5, 6, 5, 2}};
B = {{4.5, 6}, {1.5, 2}};

Then the output should be the following:

Out: {{3, 4.5, 6, 5, 2}, {1, 1.5, 2, 2.5, 3}}

Some additional details:

• B may contain the same pair several times, and so can A. However, if A has the same pair twice, then their respective rows are equal, so it doesn't matter which of these rows is "found".

• Since I am working with floating points, I cannot guarantee that the numbers will match exactly -- I expect they will, but I'd rather avoid any bugs caused by rounding errors. However, any numbers that differ from each other by less than 10^-8, say, can be treated as equal. This is actually the main reason I'm asking this question, because I could probably work out how to do the rest but I'm unsure about what kind of issues the floating point numbers may cause.

• As can be seen from the example above, the output matrix should have the same order as the matrix B; in other words, if we call the output C, then the matrix C[[;;,2;;3]] should be the same as B.

Thanks in advance for any help!

-Jonatan