Why linspace function and Colon (:) operator giving me different number of elements in creating a vector ?

I am using an Optimization algorithm and the lower and upperbound for time is in between 3.8 seconds to 6 seconds. I wanted to create only 10 element from StartTime to EndTime. Moreover, I wanted to know the successive difference between the element as I will use it later in my function.

StartTime = 3.81;
EndTime = 5.91612005426755; % random number generated from optimization algorithm
tvec = linspace(StartTime, EndTime, 10)

tvec = 1×10

3.8100 4.0440 4.2780 4.5120 4.7461 4.9801 5.2141 5.4481 5.6821 5.9161

Dtime = tvec(2)-tvec(1)

Dtime = 0.2340

% If I use Dtime to create the same vector, I am getting only 9 element
% this time.
StartTime:Dtime:EndTime

ans = 1×10

3.8100 4.0440 4.2780 4.5120 4.7461 4.9801 5.2141 5.4481 5.6821 5.9161

Answer 1

[Image Analyst]

linspace() gives you exactly 10 elements and scales the numbers to make sure that's true.

Colon steps along until the number is more than the ending number and quits without exceeding the ending number. So the 10th number is slightly more than 5.91612005426755 so it quits at 5.6821. So there will be a variable numbers and sometimes a little less than what you expected.

See the FAQ for why sometimes numbers don't add to what you think they should.

https://matlab.fandom.com/wiki/FAQ#Why_is_0.3_-_0.2_-_0.1_.28or_similar.29_not_equal_to_zero.3F

[Pushpendra Gupta]

Thank You so much. yes, it clears my doubt.

Is there any way to find the Dtime such that it always give me 10 elements? I think I have to write a short program to determine whether there are 10 elements or not ... If not then I can increase the last value, which might be helpful in maintaining 10 elements?

[Image Analyst]

For me, and online, I always get 10 (see below where I ran it from my browser)

StartTime = 3.81;
EndTime = 5.91612005426755; % random number generated from optimization algorithm
tvec = linspace(StartTime, EndTime, 10)

tvec = 1×10

3.8100 4.0440 4.2780 4.5120 4.7461 4.9801 5.2141 5.4481 5.6821 5.9161

Dtime = tvec(2)-tvec(1)

Dtime = 0.2340

% If I use Dtime to create the same vector, I am getting only 9 element
% this time.
t2 = StartTime : Dtime : EndTime

t2 = 1×10

3.8100 4.0440 4.2780 4.5120 4.7461 4.9801 5.2141 5.4481 5.6821 5.9161

I guess if you're still getting 9 elements, you could go a fraction of a Dtime past the end point:

t3 = StartTime : Dtime : (EndTime + 0.1 * Dtime)

t3 = 1×10

3.8100 4.0440 4.2780 4.5120 4.7461 4.9801 5.2141 5.4481 5.6821 5.9161

[Pushpendra Gupta]

Thank You so much for the help.

Answer 2

[Matt J]

The algorithm that linspace uses is,

function out=linspace(a,b,n)

   increment=(b-a)/(n-1);

   for i=1:n
     out(i)=a + increment*(i-1);
   end
   
end

The algorithm that colon uses is,

function out=colon(a,increment,b)

   n=floor((b-a)/increment)+1;
 
   out=linspace(a, a+(n-1)*increment, n);
   
end

In the case of colon, n must be computed from the inputs using floating point arithemtic. In your case, (b-a)/increm=9 in ideal math, but in floating point it can work out to 8.9999999... leading to floor((b-a)/increm)=8. When this happens, n will of course be one fewer than it should be in ideal math.