19-Tanzanite

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How to count sign changes in a vector/matrix and at what positions is there a sign change?

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Hello,

1. I would like to know how many sign changes there are in this vector viewed as a matrix.

There are 8 sign changes as far as we can see:

So, here I would like a function that shows me 8 as output (the number 8 being the number of sign changes).

2. I would like a function that tells me that at column 0 and between lines 1 and 2 is a change of sign, that at column 0 and between lines 2 and 3 there is a change of sign, etc. :

1_Untitled1_P9.zip

Werner_EAnswer

25-Diamond I

Here are Lucs functions modified for option 1 or option 2 as explained above. I would vote for option 1 (ignoring the zeros)

L

LucMeekes

23-Emerald IV

Here you go:

Note that you have to supply the argument to the functions as an array, a vector to be specific. I abused an undocumented trick in the attached file: added an evaluation (=) to the end of the definition of the range.

Success!

Luc

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1_LM_20230926_SignChanges.zip

C

Cornel

Author

19-Tanzanite

@Werner_E

How to think in the case of complex numbers? Does have sense in the case of complex numbers to view sign changes? Or is not possible for complex numbers this thing? Can be included also complex numbers in this counting of sign changes and locations?

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L

LucMeekes

23-Emerald IV

There are three 'sign' functions: sign(), signum() and csgn(). Look them up in help.

Success!
Luc

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Werner_E

25-Diamond I

How would you deal with a zero in the vector. Needs definition!

Lets say the vector is (3, 1, 0, 0, 0, -4. -5, 0, 0, -3)^T. How many sign changes and at which positions?

Basically I see two options:

Option 1: If we treat zero as indifferent, neither pos nor neg, then I would say we have just one sign change (ignoring all zeros), but I could not say at which position - somewhere around 2,3,4? Maybe we say position 1 as being the last positive value?

Option 2: If we treat zero as a third case of sign, then we would have 4 sign changes. probably at 1,4,6 and 8.

As usual in math its just a matter of definition 😉

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