down sampling a vector keeping the order of elements values

I have a vector of u with size of 45X1.

I want to down sampling it to u_new with size of 7X1. u here is the velocity profile in a tube. So I'd like to have 7 points of them instead of 45 points to plot it with 7 points. when moving from the start and end points of the vector toward the center, data values are increasing. I need to keep this order for 7 bins as well.

what would be the best way to do this?

u=

0.0182

0.0253

0.0324

0.0404

0.0487

0.0552

0.0603

0.0643

0.0674

0.0699

0.0718

0.0732

0.0743

0.0751

0.0757

0.0762

0.0767

0.0770

0.0772

0.0773

0.0774

0.0775

0.0775

0.0775

0.0774

0.0772

0.0770

0.0767

0.0764

0.0760

0.0755

0.0749

0.0740

0.0730

0.0716

0.0699

0.0676

0.0646

0.0608

0.0559

0.0495

0.0416

0.0341

0.0273

0.0199

Answer 1

[Voss]

u=[
    0.0182
    0.0253
    0.0324
    0.0404
    0.0487
    0.0552
    0.0603
    0.0643
    0.0674
    0.0699
    0.0718
    0.0732
    0.0743
    0.0751
    0.0757
    0.0762
    0.0767
    0.0770
    0.0772
    0.0773
    0.0774
    0.0775
    0.0775
    0.0775
    0.0774
    0.0772
    0.0770
    0.0767
    0.0764
    0.0760
    0.0755
    0.0749
    0.0740
    0.0730
    0.0716
    0.0699
    0.0676
    0.0646
    0.0608
    0.0559
    0.0495
    0.0416
    0.0341
    0.0273
    0.0199
    ];

x = 1:numel(u);
plot(x,u)
hold on

x_new = linspace(x(1),x(end),7);
u_new = interp1(x,u,x_new);

plot(x_new,u_new,'-o')

[Ham Man]

thank you so much for replying. what I'm looking for is:

• the first and last bins(1 &7) which are the average of some points should locate somewhere higher than the original value.

[Voss]

Something like this? The only difference is x_new.

u=[
    0.0182
    0.0253
    0.0324
    0.0404
    0.0487
    0.0552
    0.0603
    0.0643
    0.0674
    0.0699
    0.0718
    0.0732
    0.0743
    0.0751
    0.0757
    0.0762
    0.0767
    0.0770
    0.0772
    0.0773
    0.0774
    0.0775
    0.0775
    0.0775
    0.0774
    0.0772
    0.0770
    0.0767
    0.0764
    0.0760
    0.0755
    0.0749
    0.0740
    0.0730
    0.0716
    0.0699
    0.0676
    0.0646
    0.0608
    0.0559
    0.0495
    0.0416
    0.0341
    0.0273
    0.0199
    ];

x = 1:numel(u);
plot(x,u)
hold on

x_new = linspace(x(4),x(end-3),7); % change this line until you get something you like
u_new = interp1(x,u,x_new);

plot(x_new,u_new,'-o')

[Ham Man]

something like this, but keeping all data in, without ignoring some part of data (here: the first 3 and last data are excluded).

averaging the first 7 data, then 8th to 14th, and so on so forth, then finally get a vector of seven points.

[Voss]

u=[
    0.0182
    0.0253
    0.0324
    0.0404
    0.0487
    0.0552
    0.0603
    0.0643
    0.0674
    0.0699
    0.0718
    0.0732
    0.0743
    0.0751
    0.0757
    0.0762
    0.0767
    0.0770
    0.0772
    0.0773
    0.0774
    0.0775
    0.0775
    0.0775
    0.0774
    0.0772
    0.0770
    0.0767
    0.0764
    0.0760
    0.0755
    0.0749
    0.0740
    0.0730
    0.0716
    0.0699
    0.0676
    0.0646
    0.0608
    0.0559
    0.0495
    0.0416
    0.0341
    0.0273
    0.0199
    ];

x = 1:numel(u);
plot(x,u)
hold on

nu = numel(u);
npts = 7;

idx = (1:npts:nu)+(0:npts-1).'

idx = 7×7

1 8 15 22 29 36 43 2 9 16 23 30 37 44 3 10 17 24 31 38 45 4 11 18 25 32 39 46 5 12 19 26 33 40 47 6 13 20 27 34 41 48 7 14 21 28 35 42 49

% in case nu is not a multiple of npts (e.g., 45 is not a multiple of 7),
% add some NaNs to the end of u, which will not affect the average except
% the last bin will have fewer non-NaN points than the other bins

if idx(end) > nu
    bad_idx = idx > nu;
    u_temp = [u; NaN(idx(end)-nu,1)];
else
    bad_idx = [];
    u_temp = u;
end

% average value of each group of npts values:
u_new = mean(u_temp(idx),1,'omitnan')

u_new = 1×7

0.0401 0.0709 0.0768 0.0773 0.0745 0.0586 0.0271

% average index of each group of npts values:
idx(bad_idx) = NaN;
x_new = mean(idx,1,'omitnan')

x_new = 1×7

4 11 18 25 32 39 44

plot(x_new,u_new,'-o')