How to find the rows of a floating point matrix that match another?

Questions
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1

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in A where the second and third element match the ones in B, and create a new matrix where the rows of matrix B have been replaced by the corresponding rows of A. So, say that the matrices A and B are as follows: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

2

To being with, I’m renaming A to matA and B to matB. User defined expressions and objects usually being with a lower case letter to separate them from the ones that come pre-defined. Also this gives us more information about what the objects are.

matA = {{0, 0.5, 1, 1.5, 2}, {1, 1.5, 2, 2.5, 3}, {3, 4.5, 6, 5, 2}};
matB = {{4.5, 6}, {1.5, 2}};

Given a row of B how can I find a corresponding row in A?

The function (#[[{2, 3}]] == row &) returns True with the 2nd and 3rd element of the input are equal (==) to row. Note that Equal (==) is not exact. Two floating point numbers that are very close for example will be considered equal when using Equal (==).

findReplacementInA[row_] := SelectFirst[matA, #[[{2, 3}]] == row &]

findReplacementInA[{4.5, 6}]
{3, 4.5, 6, 5, 2}

How can I apply this operation on every row of B?

Map[findReplacementInA, matB]
or
findReplacementInA /@ matB

3

Thank you very much, that’s exactly what I needed!