I want to new vector with zero mean

I want to have mean of a vector zero.

for example I have a vector y=[12 -10 15 23];

I want a new vector (X) which has zero mean but each element of X should be less than each element of y.

This means x1 < 12, x2<-10, x3<13 and x4<23 ---------- with conditionation that mean(x1,x2,x3,x4) = 0;

Answer 1

[Priysha Aggarwal]

You can try x = y-mean(y).

However, the above solution wont work if you have a negative mean(y).

x=y-mean(y) will increase the value when mean is negative.

Solution :

if (mean(y) > 0)

x = y - mean(y)

else

x = y + mean(y)

Answer 2

[Image Analyst]

Hyder:

Here is a general solution that should work for any y:

y=[12 -10 15 23]
% Find out which indexes represent positive y.
indexesAbove = y > 0;
% Find out which indexes represent negative y.
indexesBelow = y < 0;
yAbove = y(indexesAbove)
yBelow = y(indexesBelow)
% Get sums above and below zero.
sumOfYAbove = sum(yAbove)
sumOfYBelow = sum(yBelow)
% Multiply yAbove by factor a to make them less than the positive y.
% Subtract b from yBelow to make it less than negative y.
% To get a mean of zero, you must have
% a * sumOfYAbove + (sumOfYBelow - b) = 0
% a * sumOfYAbove = b - sumOfYBelow
% So arbitrarily pick any a, say, a = 0.5 or whatever you want.
% Then determine b:
% b = a * sumOfYAbove + sumOfYBelow
a = 0.5
b = a * sumOfYAbove + sumOfYBelow
% Now construct new vectors
yNew = y; % Initialize.
yNew(indexesAbove) = a * yNew(indexesAbove);
yNew(indexesBelow) = yNew(indexesBelow) - b;
% Show new yMean in command window.
yNew
% Show (prove) that the new mean is zero:
newMean = mean(yNew)

It shows:

a =

0.5

b =

15

yNew =

6 -25 7.5 11.5

newMean =

0