extract a number N of equally spaced rows within a matrix

HI! I have a number N and a matrix with 100 rows and 2 columns.

How can I recover N rows of the matrix so that they are as equidistant from each other as possible?

For example:

• with N = 10 I will have 10 rows (row 1, 11, 21, 31,...)
• with N = 7 I will have 7 rows (row 1, 15, 29,...) In this case the steps are like 100/7 = 14.28 = 14.

a=1:1:100;
a=a';
b=0.1:0.1:10;
b=b';
M=[a,b]; % example matrix
N=10; % number of rows

step = height(M)/N;
step = 14; % round down
v = 1:step:height(M);
M_new = M(v,:);

Answer 1

[Fangjun Jiang]

M=repmat((1:100)',1,2);
N=7;
d=M(round(linspace(1,height(M),N)),:)

d = 7×2

1 1 18 18 34 34 51 51 67 67 84 84 100 100

Answer 2

[Dyuman Joshi]

You are on the right course -

a=(1:1:100)';
b=(0.1:0.1:10)';
M=[a,b]; % example matrix

N=7; % number of rows

step = height(M)/N

step = 14.2857

%Use floor to round down to nearest integer less than or equal to step
step = floor(step) % round down

step = 14

v = 1:step:height(M)

v = 1×8

1 15 29 43 57 71 85 99

M_new = M(v,:)

M_new = 8×2

1.0000 0.1000 15.0000 1.5000 29.0000 2.9000 43.0000 4.3000 57.0000 5.7000 71.0000 7.1000 85.0000 8.5000 99.0000 9.9000

[Alberto Acri]

ok, but the rows of the 'M_new' matrix are 8 and must be 7 (like N)!

[Dyuman Joshi]

I seem to have overlooked that constraint. In that case -

a=(1:1:100)';
b=(0.1:0.1:10)';
M=[a,b]; % example matrix

N=7; % number of rows

%Use floor to round down to nearest integer less than or equal to step
step = floor(height(M)/N)

step = 14

M_new = M(1:step:N*step,:)

M_new = 7×2

1.0000 0.1000 15.0000 1.5000 29.0000 2.9000 43.0000 4.3000 57.0000 5.7000 71.0000 7.1000 85.0000 8.5000

[Dyuman Joshi]

Also, @Alberto Acri, the accepted answer is incorrect -

M=repmat((1:100)',1,2);

d1=@(N) M(round(linspace(1,height(M),N)),:);

• with N = 10 I will have 10 rows (row 1, 11, 21, 31,...)

d1(10)

ans = 10×2

1 1 12 12 23 23 34 34 45 45 56 56 67 67 78 78 89 89 100 100

• with N = 7 I will have 7 rows (row 1, 15, 29,...) In this case the steps are like 100/7 = 14.28 = 14.

d1(7)

ans = 7×2

1 1 18 18 34 34 51 51 67 67 84 84 100 100

[Fangjun Jiang]

The issue is clear. It is impossible to do an "equally spaced" distribution for any value of N, because height(M)/N is more likely not an integer. Using linspace() is easier to deal with this.

Using this approach, the rounding error will pile up when N is large.

M=(1:1000)';
N=101;
step = height(M)/N

step = 9.9010

step_int=floor(step)

step_int = 9

M_new = M(1:step_int:N*step_int);
M_new(end)

ans = 901

d=M(round(linspace(1,height(M),N)));
d(end)

ans = 1000

[Dyuman Joshi]

I don't understand what your point is.

My point is that your answer does not produce the results OP wants.

[Fangjun Jiang]

when height(M) is 100 and N is 10, it is hard to say which one is the right answer.

d=1:10:100

d = 1×10

1 11 21 31 41 51 61 71 81 91

d1=1:11:100

d1 = 1×10

1 12 23 34 45 56 67 78 89 100

But when height(M) is 100 and N is 6, it is clear d is not the right answer while d1 still is right.

d=1:floor(100/6):6*floor(100/6)

d = 1×6

1 17 33 49 65 81

d1=round(linspace(1,100,6))

d1 = 1×6

1 21 41 60 80 100

In the resulting d, the even distance is 16. But the last value of d is 81. there is a bigger gap (19) to the last value of M, which is 100. So d is not evenly sampled from the rows of M. This becomes worse in previous example. The last value of d is 901 where the last value of M is 1000, and the "even distance" is 9.

Using round(linspace()) always gives the almost evenly distributed rows, just not the "exact" evenly distributed rows.

OP's numerical example has the same issue as a way to reflect "as equidistant from each other as possible".

[Dyuman Joshi]

"when height(M) is 100 and N is 10, it is hard to say which one is the right answer."

OP has specified what the expected outcome is and the logic behind it -

HI! I have a number N and a matrix with 100 rows and 2 columns.

How can I recover N rows of the matrix so that they are as equidistant from each other as possible?

For example:

• with N = 10 I will have 10 rows (row 1, 11, 21, 31,...)
• with N = 7 I will have 7 rows (row 1, 15, 29,...) In this case the steps are like 100/7 = 14.28 = 14.

[Alberto Acri]

Thanks for the replies!

@Fangjun Jiang Yes, it is actually impossible to make an "equally spaced" distribution for any value of N but your case is more useful for my purpose.

@Dyuman Joshi Your solution is certainly fine too. I gave an example to make it clear what I wanted to achieve as a final result. The distribution as you wrote it follows exactly what I wanted to obtain as a result in the question. But it was an example. You'll accept both as an answer but that's not possible.