MATLAB: Stuck on a simple cumsum prob

cumsum

I have a variable x. I make a variable y. I now need to regenerate my variable xNew from y.

Its very close but not exact. Why not? what I have done wrong?

x = cumsum(randn(1000,1));
y = 0.5.*(x(3:end) - x(1:end-2));
xNew = cumsum(y);
plot(x(3:end)); hold all; plot(xNew);

Best Answer

y = 0.5.*(x(3:end) - x(1:end-2));

Is linear interpolation between point 1 and 3, then between 2 and 4 and so on.

You cannot recover x from the linearly interpolated y unless you are given x(1) and x(end).

EDIT

Suppose you have 5 points only (for simplicity), then:

y2* = (x3-x1)/2;
y3* = (x4-x2)/2;
y4* = (x5-x3)/2;

I assume you know the series of y, i.e. are numbers, but x is unobserved, then you can see that the system has 5 unknowns (x1,...x5) in three equations. Thus, you can have a unique solution only if you are given x1 and x5.

Now, if you are given the x series for comparison reasons, you can guess x1 and x5 then retrieve the rest of the series and compare the distance between xNew and the original one. In an iterative fashion you can then tweak the guess and comapre again the two series, if the distance has dimished then continue tweaking the guess in the same direction until you reach distance = 0.

EDIT#2 You don't need exactly x1 and x5 but any two xi.

Related Solutions

MATLAB: How to plot a summation vs the x

When you do sum(y), it sums each element and gives you a scalar value. I think what you want is;

H = cumsum(y);

MATLAB: Find four midpoints between each two nodes

This should work:

d = [1 1; 2 1; 2 2; 1 2];
givenMidpoints = [1.25 1; 1.5 1;1.75 1; 2 1; 2 1.25; 2 1.5; 2 1.75; 2 2; 1.75 2; 1.5 2; 1.25 2; 1 2]; % included as a check
% I like to use tables to keep track of what's in each column, but you don't have to
d = array2table(d);
d.Properties.VariableNames = {'x', 'y'};
%
midpoints = NaN(4*height(d), 2); % pre-allocate slightly oversized matrix
midpoints = array2table(midpoints);
midpoints.Properties.VariableNames = {'xm', 'ym'};
counter = 1;
for ii = 2:height(d)
	% get x
	x_new = linspace(d.x(ii-1), d.x(ii), 5);
	x_new(end) = [];
	x_new = x_new';
	% get y
	y_new = linspace( d.y(ii-1), d.y(ii), 5);
	y_new(end) = [];
	y_new = y_new';
	% put into pre-allocated matrix
	start_row = counter;
	end_row = counter + length(x_new) -1;
	midpoints.xm(start_row:end_row) = x_new;
	midpoints.ym(start_row:end_row) = y_new;
	counter = end_row + 1;
end
midpoints = rmmissing(midpoints); % get rid of the extra rows

Here's what it looks like:

Best Answer

Related Solutions

MATLAB: How to plot a summation vs the x

MATLAB: Find four midpoints between each two nodes

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