Accuracy of linspace using low integers...

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Kevin
Kevin 2013-7-9
Matlab Maci64 R2012a
This bothers me greatly. I am creating an evenly spaced array on the fly for several particles that I integrate using ode45. I then place the answer on an interpolated timeline so that i can easily align the particles for animations, etc...
After having collected a large data set, I noticed the following, linspace is not accurate, even when it really should be.
try this:
linspace(0,1,401)'
then
linspace(0,10,401)'
This is a problem as I tried using unique to help me determine the final number of interpolated steps I had generated using the solver, only to find that there were several values on my timeline which differed by 1e-15.
Why can't linspace behave? When dealing with fractions of low integers, it really should not introduce artifacts in the numbers. Of course, I can solve my problem in a number of other manners, but still, linspace should generate artifacts, or perhaps it should have an added option to place the numbers within a certain accuracy?
-Kevin Mcilhany

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回答（2 个）

Jan
Jan 2013-7-9
Welcome to the world of floating point numerics with limited precision. Please read one of the most frequently asked questions: FAQ: Why is 0.3-0.2-0.1 ~= 0
So linspace is behaving exactly as expected, but decimal numbers cannot be converted to the binary format without a distinct lack of accuracy.
Matt J
Matt J 2013-7-9
编辑：Matt J 2013-7-9
Never mind linspace. What about this:
>> format long;
>> 39.8
ans =
39.799999999999997
or this,
>> 9.8
ans =
9.800000000000001
  2 个评论
Kevin
Kevin 2013-7-9
Exactly! So instead, I use str2num and sprintf and I waste cpu cycles. Mathworks really needs to work on long format.
Matt J
Matt J 2013-7-9
I don't think it's an issue with long format. Compare,
>> 39.8-39.7
ans =
0.099999999999994
but,
>> 0.2-0.1
ans =
0.100000000000000

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