How to delete arbitrary numbers of columns from a matrix in mathematica [duplicate]

This question already has an answer here:

Say I have a matrix of random integers, which is given by

A=RandomInteger[25, 9, 11]


How can specific columns of this matrix (say 4th and 7th columns) be deleted?

EDIT

It is really surprising that some people has found this question duplicate. I have asked for two specific columns, but it can be extended to any numbers of columns. Say I have a matrix of (985 x 1123), and I want to delete column no. 18, 37, 54, 85, 305, 564 and 1029 from the original matrix to get a new matrix of size (985 x 1116).

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

Delete[Transpose@A, 4, 7] // Transpose

mA[[All, Complement[Range[11], 4, 7]]]

7 Answers
7

I am confused by the complexity of many of these responses. The single command

Drop[A, None, 4,7,3]

Drop[A, None, 4,7,3]

is sufficient to remove columns $4$ and $7$, in steps of $3$ (so as not to remove columms $5$ and $6$). If you wanted to remove more than two columns that are not separated by an equal number of columns, then you would need to use Drop more than once, starting from the rightmost column to be removed; e.g., to remove columns $1$, $3$, and $9$, you could just do

Drop

Drop[Drop[A, None, 9], None, 1,3,2]

Drop[Drop[A, None, 9], None, 1,3,2]

or equivalently,

Drop[Drop[A, None, 3,9,6], None, 1]

Drop[Drop[A, None, 3,9,6], None, 1]

If you had an arbitrary sorted list of column indices to remove, which we might call c, then Fold is trivially applied:

c

Fold

Fold[Drop[#1, None, #2]&, A, Reverse[c]]

Fold[Drop[#1, None, #2]&, A, Reverse[c]]

Drop

Part

Drop

I learned this method long time ago from Mr Wizard answer, it works well. But there are many other ways

a = RandomInteger[25, 9, 11];
a // MatrixForm


ReplacePart[a, _, 4, _, 7 :> Sequence];
MatrixForm[%]


(## &)

Sequence

Nothing

The fasted way to do this is to use Part and construct the indices you need to take using Complement:

Part

Complement

dropColumns[mat_?MatrixQ, columns : __Integer] := With[
columnsToTake = Complement[
Range[Dimensions[mat][[2]]],
columns
]
,
mat[[All, columnsToTake]]
];
a = RandomInteger[25, 9, 11];
a // MatrixForm
dropColumns[a, 2, 5] // MatrixForm


A = RandomInteger[25, 9, 11];
A // MatrixForm
DeleteCol[Matrix_, indexlist_] :=
Block[internalMatrix = Matrix, i, k = 0,
internallist = SortBy[indexlist, Smaller],
For[i = 1, i <= Length[internallist], i++,
internalMatrix =
Delete[Transpose[internalMatrix], internallist[[i]] - k];
internalMatrix = Transpose[internalMatrix];
k++;
];
internalMatrix
];
DeleteCol[A, 4, 7];
% // MatrixForm
DeleteCol[A, 7, 4];
% // MatrixForm


Here is another way to do it. I assume that columns you want delete is ordered. i.e. 4,7 will work but 7,4 won't.

4,7

7,4

SeedRandom@2;
A = RandomInteger[25, 9, 11];
MatrixForm@A


$A=left(
beginarrayccccccccccc
23 & 3 & 18 & 11 & 10 & 17 & 8 & 3 & 8 & 0 & 19 \
9 & 23 & 25 & 24 & 14 & 4 & 3 & 4 & 12 & 12 & 8 \
8 & 18 & 6 & 3 & 1 & 14 & 21 & 4 & 14 & 10 & 20 \
22 & 8 & 10 & 20 & 19 & 1 & 9 & 12 & 0 & 19 & 11 \
25 & 10 & 8 & 7 & 18 & 7 & 9 & 23 & 1 & 6 & 15 \
12 & 1 & 0 & 14 & 19 & 12 & 2 & 5 & 3 & 7 & 5 \
23 & 24 & 1 & 14 & 3 & 2 & 22 & 16 & 21 & 4 & 11 \
4 & 2 & 3 & 20 & 24 & 8 & 10 & 3 & 6 & 12 & 19 \
20 & 24 & 6 & 1 & 13 & 10 & 8 & 21 & 5 & 6 & 21 \
endarray
right)$

deleteColumns[mat_?MatrixQ, col_] :=
With[column = col - Range[0, Length@col - 1],
Fold[Delete[#, #2] &, Transpose@A, column] // Transpose]
deleteColumns[A, 4, 7, 10] // MatrixForm


$A=left(
beginarraycccccccc
23 & 3 & 18 & 10 & 17 & 3 & 8 & 19 \
9 & 23 & 25 & 14 & 4 & 4 & 12 & 8 \
8 & 18 & 6 & 1 & 14 & 4 & 14 & 20 \
22 & 8 & 10 & 19 & 1 & 12 & 0 & 11 \
25 & 10 & 8 & 18 & 7 & 23 & 1 & 15 \
12 & 1 & 0 & 19 & 12 & 5 & 3 & 5 \
23 & 24 & 1 & 3 & 2 & 16 & 21 & 11 \
4 & 2 & 3 & 24 & 8 & 3 & 6 & 19 \
20 & 24 & 6 & 13 & 10 & 21 & 5 & 21 \
endarray
right)$

MapThread[Delete, A, ConstantArray[4, 7, Length[A]]]


You can also use a combination of Fold and Drop:

Fold

Drop

ClearAll[dropCols1]
dropCols1 = Fold[Drop[#, None, #2] &, #, List /@ Reverse @ Sort[#2]] &;


Examples:

m = Array[Subscript[a, ##] &, 9, 9];

dropCols1[m, 4, 7] // MatrixForm // TeXForm


$smallleft(
beginarrayccccccc
a_1,1 & a_1,2 & a_1,3 & a_1,5 & a_1,6 & a_1,8 & a_1,9 \
a_2,1 & a_2,2 & a_2,3 & a_2,5 & a_2,6 & a_2,8 & a_2,9 \
a_3,1 & a_3,2 & a_3,3 & a_3,5 & a_3,6 & a_3,8 & a_3,9 \
a_4,1 & a_4,2 & a_4,3 & a_4,5 & a_4,6 & a_4,8 & a_4,9 \
a_5,1 & a_5,2 & a_5,3 & a_5,5 & a_5,6 & a_5,8 & a_5,9 \
a_6,1 & a_6,2 & a_6,3 & a_6,5 & a_6,6 & a_6,8 & a_6,9 \
a_7,1 & a_7,2 & a_7,3 & a_7,5 & a_7,6 & a_7,8 & a_7,9 \
a_8,1 & a_8,2 & a_8,3 & a_8,5 & a_8,6 & a_8,8 & a_8,9 \
a_9,1 & a_9,2 & a_9,3 & a_9,5 & a_9,6 & a_9,8 & a_9,9 \
endarray
right)$

dropCols1[m, 4, 7, 1] // MatrixForm // TeXForm


$smallleft(
beginarraycccccc
a_1,2 & a_1,3 & a_1,5 & a_1,6 & a_1,8 & a_1,9 \
a_2,2 & a_2,3 & a_2,5 & a_2,6 & a_2,8 & a_2,9 \
a_3,2 & a_3,3 & a_3,5 & a_3,6 & a_3,8 & a_3,9 \
a_4,2 & a_4,3 & a_4,5 & a_4,6 & a_4,8 & a_4,9 \
a_5,2 & a_5,3 & a_5,5 & a_5,6 & a_5,8 & a_5,9 \
a_6,2 & a_6,3 & a_6,5 & a_6,6 & a_6,8 & a_6,9 \
a_7,2 & a_7,3 & a_7,5 & a_7,6 & a_7,8 & a_7,9 \
a_8,2 & a_8,3 & a_8,5 & a_8,6 & a_8,8 & a_8,9 \
a_9,2 & a_9,3 & a_9,5 & a_9,6 & a_9,8 & a_9,9 \
endarray
right)$

Alternatively, (1) assign ##& (or Nothing in versions 10+) to the desired columns (dropCols2) or (2) use a combination of MapAt and ##&& (dropCols3):

##&

Nothing

dropCols2

MapAt

##&&

dropCols3

ClearAll[dropCols2, dropCols3]
dropCols2 = Module[a = #, a[[All, #2]] = ## &; a] &;
dropCols3 = MapAt[## & &, #, All, #2] &;

Equal @@ (#[m, 4, 7] & /@ dropCols1, dropCols2, dropCols3)


True

Equal @@ (#[m, 4, 7, 1] & /@ dropCols1, dropCols2, dropCols3)


True