Column Operation - Subtract part of nested list from part of another nested list [duplicate]

Question

I have two lists with x- and y-coordinates with different z-coordinates of the form

{{x0, y0, z0_1}, {x1, y1, z1_1}, ..., {xn, yn, zn_1}}  

and

{{x0, y0, z0_2}, {x1, y1, z1_2}, ..., {xn, yn, zn_2}}.  

I want to construct the list

{{x0, y0, z0_1 - z0_2}, {x1, y1, z1_1 - z1_2}, ..., {xn, yn, zn_1 - zn_2}}  

i.e. construct a list containing the difference of only the z-coordinates, for each x- and y-coordinate.

Is it possible to do this with a few simple commands, or should I construct a loop and create a new list from scratch?

Answer 1

lis1 = {{x0, y0, z01}, {x1, y1, z11}, {xn, yn, zn1}};
lis2 = {{x0, y0, z02}, {x1, y1, z12}, {xn, yn, zn2}};

If you first define this function:

f[{x_, y_, z_}, {x_, y_, u_}] := {x, y, z - u}

You can then easily do:

f @@@ Transpose[{lis1, lis2}]

{{x0, y0, z01 - z02}, {x1, y1, z11 - z12}, {xn, yn, zn1 - zn2}}

Answer 2

Consider:

a = {{x0, y0, z0}, {x1, y1, z1}, {xn, yn, zn}};
b = {{x0, y0, Z0}, {x1, y1, Z1}, {xn, yn, Zn}};  (* note capital Z *)

c = a;
c[[All, 3]] -= b[[All, 3]];
c

{{x0, y0, z0 - Z0}, {x1, y1, z1 - Z1}, {xn, yn, zn - Zn}}

See: Elegant operations on matrix rows and columns

You can use a Module if you wish to make this a self-contained function.

Another option (looks better in a Notebook):

{#, #2, #3 - b[[All, 3]]}\[Transpose] & @@ (a\[Transpose])