How to find positions of certain matrix elements in one matrix and, based upon these positions, delete elements in a different matrix of the same size

Question

I have a matrix m

m={{10,2},{20,3},{30,4},{40,5},{50,6}}

I also have a list n

list1={1,2,3,4,5}

and another matrix

p={{25,-23},{64,33},{77,74},{99,5},{200,68}}

I can find certain elements in matrix m with this statement

list2=Select[m,(10 < #[[1]] < 50 ) && (#[[2]] < 6) &]

and I get

{20,3},{30,4},{40,5}

I can also use

list2=DeleteCases[m , _?(10 < #[[1]] < 50 && #[[2]] < 6 &)];

Now, how can I get the position of those deleted items (or selected items) so I can use that information to trim down both the list1 and other matrix p to yield

{2,3,4}

and from matrix p

p={{64,33},{77,74},{99,5}}

I've tried to obtain position information about the deleted items using:

list3 = Position[m, _?(10 < #[[1]] < 50) && (#[[2]] < 6) &]

and

list3 = Position[m, (10 < #[[1]] < 50) && (#[[2]] < 6) &]

but I'm getting empty set all the time.

Thanks,

Answer 1

One way:

selected = 10 < #[[1]] < 50 && #[[2]] < 6 & /@ m;
Pick[p, selected]

{{64, 33}, {77, 74}, {99, 5}}

Pick[list1, selected]

{2, 3, 4}

Of course, you can also use this on m: Pick[m, selected].

To make your approach work you have to change a few things. As Edmund said, the & needs to go inside the parenthesis. Then you need another set of parenthesis to surround the And statement. You also need to set Heads -> False or it will try to match your pattern with the heads of subexpressions, in this case List. That will give errors because List doesn't have a first and a second part. Finally you also need to specify at what level the subexpressions exist. All in all:

selected = Position[m, _?((10 < #[[1]] < 50) && (#[[2]] < 6) &), {1}, Heads -> False]
Extract[p, selected]

{{64, 33}, {77, 74}, {99, 5}}

Of course, this is based on the premise that you want to use the pattern in the question. As Edmund has shown, there are more appropriate patterns.

Answer 2

You may use a named Pattern with a Condition to get the Positions.The use Extract to collect them from p.

pos = Position[m, (v : {a_, b_}) /; (10 < a < 50 && b < 6)]

{{2}, {3}, {4}}

Then

Extract[p, pos]

{{64, 33}, {77, 74}, {99, 5}}

Hope this helps.