Extract data from a given nested table

Question

Suppose I have a nested table given by:

t[i_, j_] := j^2 - i^2 - 1;

Table[{j, Table[{i, t[i, j]}, {i, 0, 4, 0.1}]}, {j, 1, 4, 0.1}]

I need to plot j v/s ic, where ic is the first (critical) point at which t[i,j] becomes negative. For example, for j = 1, ic = 0.1, for j = 1.1, ic = 0.5, for j = 1.2, ic = 0.7 and so on.

How can I extract the data from the above-nested table, satisfying the given condition?

Answer 1

As of version 10.0, FirstCase is able to be used.

t[i_, j_] := j^2 - i^2 - 1
data = Table[{j, Table[{i, t[i, j]}, {i, 0, 4, 0.1}]}, {j, 1, 4, 0.1}];

{#, FirstCase[#2, {i_, _?Negative} :> i]} & @@@ data

{{1., 0.1}, {1.1, 0.5}, {1.2, 0.7}, {1.3, 0.9}, {1.4, 1.}, {1.5, 1.2}, {1.6, 1.3}, {1.7, 1.4}, {1.8, 1.5}, {1.9, 1.7}, {2., 1.8}, {2.1, 1.9}, {2.2, 2.}, {2.3, 2.1}, {2.4, 2.2}, {2.5, 2.3}, {2.6, 2.4}, {2.7, 2.6}, {2.8, 2.7}, {2.9, 2.8}, {3., 2.9}, {3.1, 3.}, {3.2, 3.1}, {3.3, 3.2}, {3.4, 3.3}, {3.5, 3.4}, {3.6, 3.5}, {3.7, 3.6}, {3.8, 3.7}, {3.9, 3.8}, {4., 3.9}}

Answer 2

Try this:

t[i_, j_] := j^2 - i^2 - 1
data = Table[{j, Table[{i, t[i, j]}, {i, 0, 4, 0.1}]}, {j, 1, 4, 0.1}];
Map[Composition[#[[1 ;; 2]] &, Flatten], Table[{data[[k, 1]], First[Map[If[#[[2]] < 0, #, Nothing] &, Map[#[[-1]] &, data][[k]]]]}, {k, 1, Length[data]}]]
(*{{1., 0.1}, {1.1, 0.5}, {1.2, 0.7}, {1.3, 0.9}, {1.4, 1.}, {1.5, 1.2}, {1.6, 1.3}, {1.7, 1.4}, {1.8, 1.5}, {1.9, 1.7}, {2., 1.8}, {2.1, 1.9}, {2.2, 2.}, {2.3, 2.1}, {2.4, 2.2}, {2.5, 2.3}, {2.6, 2.4}, {2.7, 2.6}, {2.8, 2.7}, {2.9, 2.8}, {3., 2.9}, {3.1, 3.}, {3.2, 3.1}, {3.3, 3.2}, {3.4, 3.3}, {3.5, 3.4}, {3.6, 3.5}, {3.7, 3.6}, {3.8, 3.7}, {3.9, 3.8}, {4., 3.9}}*)

Answer 3

t[i_, j_] := j^2 - i^2 - 1;


data = Table[{j, Table[{i, t[i, j]}, {i, 0, 4, 0.1}]}, {j, 1, 4, 0.1}];

First positions of negative elements

p = Last @ FirstPosition[#, {_, _?Negative}] & /@ data

{2, 6, 8, 10, 11, 13, 14, 15, 16, 18, 19, 20, 21, 22, 23, 24, 25, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40}

Table[{data[[i, 1]], data[[i, 2, p[[i]], 1]]}, {i, Length[data]}]

{{1., 0.1}, {1.1, 0.5}, {1.2, 0.7}, {1.3, 0.9}, {1.4, 1.}, {1.5, 1.2}, {1.6, 1.3}, {1.7, 1.4}, {1.8, 1.5}, {1.9, 1.7}, {2., 1.8}, {2.1, 1.9}, {2.2, 2.}, {2.3, 2.1}, {2.4, 2.2}, {2.5, 2.3}, {2.6, 2.4}, {2.7, 2.6}, {2.8, 2.7}, {2.9, 2.8}, {3., 2.9}, {3.1, 3.}, {3.2, 3.1}, {3.3, 3.2}, {3.4, 3.3}, {3.5, 3.4}, {3.6, 3.5}, {3.7, 3.6}, {3.8, 3.7}, {3.9, 3.8}, {4., 3.9}}