I'm trying to use the condition 0<0.01 in while loop, but it is never true in Matlab. Apparently 0 is always equal to 0.01.
How can I work around this?
I need to do:
c1= 0;eps = .01while c1<epsdo something endMATLAB: Is 0<0.01
comparesmall numbers
Related Solutions
To sort the eigenvalues to be increasing in magnitude, use the following:
[U, d] = eig(k, m, 'vector');[d, ind] = sort(d);U = U(:, ind);The eig function doesn't sort the eigenvalues it returns, for two reasons:
1) This is not needed for many applications, and would slow down the computation time for these cases. 2) For non-symmetric eigenvalue problems, the eigenvalues are complex, and none of the sorting methods for complex values are very satisfactory.
For symmetric problems (for the generalized case, this means both matrices are symmetric, and the second matrix is also positive definite), the eigenvalues are typically returned in ascending order by eig, but this is not a guarantee.
MATLAB does not represent numbers with fractions in decimal (not even in the Symbolic toolbox, but you have to push hard to prove that for the Symbolic toolbox).
MATLAB itself represents most numbers in IEEE 754 Double Precision, which is a representation that uses one sign bit, 11 bits of binary exponent, and 52 bits of binary fraction. For technical reasons, this gives 53 bits of precision: numbers are effectively represented as a 53 bit integer times a power of 2 (that might be negative). The only fractions that can be exactly represented are those involving powers of 2. It is like having an unreduced fraction in which the denominator is always 2^53. Other denominators such as 10 are only possible if they are powers of 2: for example the system can exactly represent 16ths, but never 3rds or 10ths, not exactly.
This system has exactly the same variety of limitations that sticking strictly to a fixed number of decimal places would have. For example if you pick any fixed number of decimal places, you can never exactly represent 1/3 or 1/7, and instead those end up in decimal being infinite repeating decimals, just like how 1/3 in decimal starts 0.333333333333333 but continues on infinitely. Now in decimal, take that number and multiply it by 3 again, and what you get is 0.999999999999999 rather than exactly 1.
Just so, in binary, 1/10 is an infinite repeating number, and if you truncate it to any finite number of decimal places, and multiply by 10 you do not get exactly 1 back.
Now, with some multiples of 1/10 in binary, when you multiply by 10, the result rounds to the representation of an integer, but that is not the case for all multiples of 1/10 in finite binary: for some of them, after multiplication you get a number that is 1 bit different than an exact integer, just like the 0.99999999999999 is 1 trailing decimal place different from an exact decimal integer.
So 0.34/0.001 with both numbers expressed in finite binary approximation ends up rounding to an exact integer but 0.35/0.001 with both numbers expressed in finite binary approximation ends up rounding to one bit different from an exact integer.
The moral of the story is: Don't Do That!! Avoid using fractions to calculate integer indices, because fractions are only approximations.
Example: instead of
for f=0.01:0.01:1 G(100*f)=f.^2;endYou can use
for fi = 1:100 f=fi/100; G(fi) = f.^2; end
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