# Write a row and column vector as matrix index

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rakesh kumar on 24 Jan 2023
Commented: rakesh kumar on 24 Jan 2023
I want to write a row vector [4 5 3] and column vector [4 5 3]' as (4, 4) (4,5) 4, 3) (5, 4) (5, 5) (5, 3) (3, 4) (3, 5) and (3, 3) so that i can use it as index of a matrix.
Stephen23 on 24 Jan 2023
"I want to write a row vector [4 5 3] and column vector [4 5 3]' as (4, 4) (4,5) 4, 3) (5, 4) (5, 5) (5, 3) (3, 4) (3, 5) and (3, 3) so that i can use it as index of a matrix."
Why do you need to "write" it like that to "use it as index of a matrix" ?
You can use those numeric vectors directly as indices:
A = rand(5,5)
A = 5×5
0.7590 0.3614 0.8548 0.3843 0.2101 0.5864 0.4088 0.1042 0.7392 0.7515 0.7229 0.3837 0.2563 0.8996 0.6743 0.8432 0.9548 0.7702 0.7944 0.3817 0.1770 0.8465 0.8390 0.8715 0.3211
X1 = [4,5,3];
X2 = [4,5,3];
B = A(X1,X2)
B = 3×3
0.7944 0.3817 0.7702 0.8715 0.3211 0.8390 0.8996 0.6743 0.2563

Torsten on 24 Jan 2023
a = [4 5 3];
% Generate index vectors A and B
[A,B] = ndgrid(a,a);
A = A(:)
A = 9×1
4 5 3 4 5 3 4 5 3
B = B(:)
B = 9×1
4 4 4 5 5 5 3 3 3
% Use A and B as index vectors for a matrix M
M = rand(10)
M = 10×10
0.7393 0.4634 0.5887 0.1407 0.1101 0.2377 0.3904 0.9721 0.7022 0.5305 0.4654 0.4633 0.4541 0.0660 0.8832 0.4376 0.1124 0.0514 0.7515 0.1212 0.1072 0.2151 0.8151 0.0369 0.0057 0.3753 0.1588 0.9982 0.6612 0.0060 0.0766 0.8351 0.3845 0.1705 0.2370 0.4290 0.2396 0.6795 0.1800 0.3630 0.1256 0.2626 0.1554 0.5475 0.3741 0.0379 0.8317 0.6551 0.3080 0.5904 0.7688 0.2174 0.4294 0.8774 0.3330 0.6635 0.2581 0.9678 0.5832 0.9380 0.0689 0.1080 0.3615 0.1752 0.9369 0.7941 0.9837 0.2153 0.0956 0.5375 0.6504 0.6525 0.4916 0.4062 0.4640 0.3774 0.1426 0.2489 0.0271 0.6749 0.2760 0.9112 0.9862 0.2613 0.0224 0.3852 0.8678 0.0309 0.0715 0.5662 0.1792 0.2675 0.8429 0.0210 0.9328 0.0579 0.6163 0.4985 0.1558 0.0611
S = M(sub2ind([10 10],A,B))
S = 9×1
0.1705 0.5475 0.0369 0.2370 0.3741 0.0057 0.3845 0.1554 0.8151

Benjamin Kraus on 24 Jan 2023
Edited: Benjamin Kraus on 24 Jan 2023
Is meshgrid or ndgrid what you are trying to do?
[X,Y] = meshgrid([4 5 3],[4 5 3])
X = 3×3
4 5 3 4 5 3 4 5 3
Y = 3×3
4 4 4 5 5 5 3 3 3
[X,Y] = ndgrid([4 5 3],[4 5 3])
X = 3×3
4 4 4 5 5 5 3 3 3
Y = 3×3
4 5 3 4 5 3 4 5 3
After calling either meshgrid or ndgrid you can then convert those matrices into vectors, although that isn't needed.
[X,Y] = meshgrid([4 5 3],[4 5 3]);
X = X(:);
Y = Y(:);
[X Y]
ans = 9×2
4 4 4 5 4 3 5 4 5 5 5 3 3 4 3 5 3 3
Both meshgrid and ndgrid do the same thing, but they swap the orientation of the first two dimensions. meshgrid works with "X" (the first input/output) along the columns and "Y" (the second input/output) along the rows. ndgrid works with "X" (the first input/output) along the rows, and "Y" (the second input/output) along the columns. It may help to understand the behavior of meshgrid and ndgrid (and the difference), if you use different vectors for the inputs, so for the sake of comparing the two:
[X,Y] = meshgrid(1:3,4:6)
X = 3×3
1 2 3 1 2 3 1 2 3
Y = 3×3
4 4 4 5 5 5 6 6 6
[X,Y] = ndgrid(1:3,4:6)
X = 3×3
1 1 1 2 2 2 3 3 3
Y = 3×3
4 5 6 4 5 6 4 5 6
Also, if the first two inputs are the same, you can use a shortcut and just provide one input:
[X,Y] = meshgrid([4 5 3])
X = 3×3
4 5 3 4 5 3 4 5 3
Y = 3×3
4 4 4 5 5 5 3 3 3
[X,Y] = ndgrid([4 5 3])
X = 3×3
4 4 4 5 5 5 3 3 3
Y = 3×3
4 5 3 4 5 3 4 5 3
rakesh kumar on 24 Jan 2023
thanks stephen

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