defuzz
Replaces entries that are extremely close to being integral with the integers they approximate.
Syntax
-
defuzz(x[, ε])-
xis a number, a vector, or a matrix -
εis a positive number
-
Description
If x is a number, a vector, or a matrix, then defuzz(x, ε) returns x with all entries that are extremely close to being integral replaced by the integers they approximate. The required closeness is specified by the ε parameter, which defaults to 1E−8 if omitted.
Examples
A ≔ ❨❨4, 1, 2, 3❩, ❨0, −2, 1, 5❩, ❨1, 0, 2, 2❩, ❨6, 1, 0, 2❩❩
⎛ 4 1 2 3⎞ ⎜ 0 −2 1 5⎟ ⎜ 1 0 2 2⎟ ⎝ 6 1 0 2⎠
Λ, U ≔ eigenvectors(A);
U ⋅ diag(Λ) ⋅ U^−1
⎛ 4 − 2.93249699516⋅10^−18⋅i 1 − 6.7735386976⋅10^−19⋅i 2 + 5.21897174135⋅10^−20⋅i 3 + 5.6676363145⋅10^−21⋅i⎞ ⎜−2.23074596989⋅10^−17 + 3.91940438539⋅10^−18⋅i −2 + 1.1917654819⋅10^−18⋅i 1 − 2.81257201536⋅10^−18⋅i 5 − 4.7883868275⋅10^−18⋅i⎟ ⎜ 1 − 8.33908275002⋅10^−19⋅i 1.21972744405⋅10^−19 − 1.51585575754⋅10^−19⋅i 2 − 3.33358238173⋅10^−19⋅i 2 − 4.65069351146⋅10^−19⋅i⎟ ⎝ 6 − 1.47707544878⋅10^−18⋅i 1 − 1.22688894046⋅10^−19⋅i 5.96311194867⋅10^−19 − 8.62051771278⋅10^−19⋅i 2 − 1.37030513329⋅10^−18⋅i⎠
defuzz(ans)
⎛ 4 1 2 3⎞ ⎜ 0 −2 1 5⎟ ⎜ 1 0 2 2⎟ ⎝ 6 1 0 2⎠