How to repeat a value and find the minima

Question

If I have two variables x and y and for every value of x how I can repeat y values as what I did in ( xytab ) manually.

    x = Table[0.2712 - n (0.0003), {n, 0, 2}]
{0.2712, 0.2709, 0.2706}

y = Table[0.07784 - n (0.0003), {n, 0, 2}]
{0.07784, 0.07754, 0.07724}

xytab = {{0.2712`, 0.07784`}, {0.2709`, 0.07784`}, {0.2706`, 
0.07784`}, {0.2712`, 0.07754000000000001`}, {0.2706`, 
0.07754000000000001`}, {0.2709`, 0.07754000000000001`}, {0.2712`, 
0.07724`}, {0.2709`, 0.07724`}, {0.2706`, 0.07724`}};

Below I generated a table including the points(f)that are the result from another code:

       f = {-12.614324138097164`, -11.403557753606028`, 
  -11.972267934125227`, -13.95736964188886`, -15.160073023551389`, 
  -11.37937735952056`, -11.945532093596869`, -13.965637862424334`, 
  -16.013160208902804`}

    x1 = xytab[[All, 1]]
y1 = xytab[[All, 2]]

If my table is as below how I can find the minimum of the third column that means(f) for every value of y automatically

    tab = Table[{x1[[i]], y1[[i]], f[[i]]}, {i, 1, Length[x1]}];

{{0.2712, 0.07784, -12.6143}, {0.2709, 0.07784, -11.4036}, {0.2706, 
 0.07784, -11.9723}, {0.2712, 0.07754, -13.9574}, {0.2706, 
 0.07754, -15.1601}, {0.2709, 0.07754, -11.3794}, {0.2712, 
 0.07724, -11.9455}, {0.2709, 0.07724, -13.9656}, {0.2706, 
 0.07724, -16.0132}}

So, I need two things, first how to repeat value of y for every value of x and then how to find the minimum for every y automatically.

Thanks.

Answer 1

x = Table[0.2712 - n (0.0003), {n, 0, 2}];
y = Table[0.07784 - n (0.0003), {n, 0, 2}];

xytab = Outer[{#2, #1} &, y, x] // Flatten[#, 1] &

(* {{0.2712, 0.07784}, {0.2709, 0.07784}, {0.2706, 0.07784}, {0.2712, 
  0.07754}, {0.2709, 0.07754}, {0.2706, 0.07754}, {0.2712, 
  0.07724}, {0.2709, 0.07724}, {0.2706, 0.07724}} *)

f = {-12.614324138097164`, -11.403557753606028`, \
-11.972267934125227`, -13.95736964188886`, -15.160073023551389`, \
-11.37937735952056`, -11.945532093596869`, -13.965637862424334`, \
-16.013160208902804`};

x1 = xytab[[All, 1]];
y1 = xytab[[All, 2]];

tab = Transpose[{x1, y1, f}]

(* {{0.2712, 0.07784, -12.6143}, {0.2709, 0.07784, -11.4036}, {0.2706, 
  0.07784, -11.9723}, {0.2712, 0.07754, -13.9574}, {0.2709, 
  0.07754, -15.1601}, {0.2706, 0.07754, -11.3794}, {0.2712, 
  0.07724, -11.9455}, {0.2709, 0.07724, -13.9656}, {0.2706, 
  0.07724, -16.0132}} *)

MinimalBy[#, #[[3]] &] & /@ GatherBy[tab, #[[2]] &]

(* {{{0.2712, 0.07784, -12.6143}}, {{0.2709, 
   0.07754, -15.1601}}, {{0.2706, 0.07724, -16.0132}}} *)

Answer 2

Maybe this helps:

x = Table[0.2712 - n (0.0003), {n, 0, 2}];
y = Table[0.07784 - n (0.0003), {n, 0, 2}];
xytab = Flatten[Transpose[Outer[List, x, y, 1]], 1];
f = {-12.614324138097164`, -11.403557753606028`, \
-11.972267934125227`, -13.95736964188886`, -15.160073023551389`, \
-11.37937735952056`, -11.945532093596869`, -13.965637862424334`, \
-16.013160208902804`};
tab = Join[xytab, Partition[f, 1], 2]
Min[tab[[All, 3]]]

A minimal position can be found with

i=Ordering[tab[[All, 3]], 1][[1]];
tab[[i]]

{0.2706, 0.07724, -16.0132}

For getting the minimum for each fixed value of y and with data layout, you may use

fpartitioned = Partition[f, Length[x]];
Min /@ fpartitioned

and

i = Ordering[#, 1][[1]] & /@ fpartitioned

Answer 3

Maybe this will help for you.

tab = 
  {{0.2712,0.07784,-12.6143}, {0.2709,0.07784,-11.4036}, {0.2706,0.07784,-11.9723}, 
   {0.2712,0.07754,-13.9574}, {0.2706,0.07754,-15.1601}, {0.2709,0.07754,-11.3794}, 
   {0.2712,0.07724,-11.9455}, {0.2709,0.07724,-13.9656}, {0.2706,0.07724,-16.0132}};

MinimalBy[#[[3]] &] /@ SplitBy[tab, #[[2]] &]

{{{0.2712,0.07784,-12.6143}}, 
  {{0.2706,0.07754,-15.1601}}, 
  {{0.2706,0.07724,-16.0132}}}