[?] Check entries and return output if condition is satisfied?

Questions
1

I would be grateful if someone could help me with this code.

I want to check whether all the entries in any column of the generated table is equal to one
If the condition is satisfied in any column, the result shall be the column’s heading.
If the condition is not satisfied in all columns, the result shall be none.

For example, I am attaching a file that outputs a table. This table contains no columns with all values are equal to one, so I am expecting the result to be none.

Trial-Modified path matrix - Second order.nb (202 KB)

2

Here is one way

{rows, columns} = Dimensions@colmat

(* Create list of column number and number of ones in the column *)
onesCount = 
 Table[{i, Flatten@Tally[Select[colmat[[All, i]], # == 1 &]]}, {i, 1, columns}]

(* Select the ones that have a count equal to the number of rows *)
onesCount // Select[Length@#[[2]] > 0 && #[[2, 2]] == rows &]

(* {} *}

(* Columns that have one value not equal to one *)
onesCount // Select[Length@#[[2]] > 0 && #[[2, 2]] == rows - 1 &]

(* {{1, {1, 43}}, {2, {1, 43}}, {62, {1, 43}}, {82, {1, 43}}, {96, {1, 43}}} *)
3

I think you didn’t understand me well. I am searching for the index of columns with all its values equal to one. In the attached example, actually there doesn’t exist any column that contains all its elements equal to one.

4

I don’t want to know the position of ones in terms of (row, column)

5

Yes. I believe I satisfied your requirements.

onesCount // Select[Length@#[[2]] > 0 && #[[2, 2]] == rows &]

Returns an empty list, as I showed above, because no columns satisfy the condition.

In the second example

onesCount // Select[Length@#[[2]] > 0 && #[[2, 2]] == rows - 1 &]
(* {{1, {1, 43}}, {2, {1, 43}}, {62, {1, 43}}, {82, {1, 43}}, {96, {1, 43}}} *)

The first element of each sub-list is the index of the column that has one value not equal to one.

So columns 1, 2, 62, 82, 96 satisfy that condition, they all have 43 1’s

e.g. column 96 has 43 1’s and one 0

colmat[[All, 96]] // Tally
(* {{1, 43}, {0, 1}} *)
6

Yeah I got it now. I understood your comment. Thanks a million:) One last question please if we could re-shape the output to be only 1, 2, 62, 82, 96 without the number of ones in each column.
couldn’t thank you more. You really saved my day.

7

Check entries and return output if condition is satisfied

8

Sure

onesCount // Select[Length@#[[2]] > 0 && #[[2, 2]] == rows - 1 &] // Map[First]
(* {1, 2, 62, 82, 96} *)

With some helper functions

countsOf[n_, matrix_] := 
 Table[{i, Flatten@Tally[Select[matrix[[All, i]], # == n &]]}, {i, 1, Last@Dimensions@matrix}]

withCount[n_] := 
 Select[Length@#[[2]] > 0 && #[[2, 2]] == n &] /* Map[First]

Index of columns in colmat that have 10 2’s

countsOf[2, colmat] // withCount[10]
(* {97, 100, 110, 129, 139, 143, 149, 150, 153, 174, 205} *)