An absolutely ascending sequence

How can I check if a sequence is absolutely ascending?

Answer 1

[Torsten]

x = 0:10;
all(diff(x)>0)

ans = logical
   1

Answer 2

[Steven Lord]

Those who have said there is no function for this are incorrect. The issorted function allows you to ask if an array is sorted and has options to control what "sorted" means (which direction, and whether or not ties are allowed.)

x1 = 1:5;
x2 = [1 2 3 3 4 5];
s1 = issorted(x1)

s1 = logical
   1

s2 = issorted(x2)

s2 = logical
   1

s3 = issorted(x1, 'strictascend')

s3 = logical
   1

s4 = issorted(x2, 'strictascend')

s4 = logical
   0

s5 = issorted(x1, 'descend')

s5 = logical
   0

s1, s2, and s3 are true. But because the third and fourth elements of x2 are the same, x2 is not strictly ascending and s4 is false. And since x1 is sorted in ascending order, s5 is also false.

[Umar]

Hi @Steven Lord,

I appreciate your insights on the issorted function. Your explanation effectively highlights its versatility in determining the sorted status of arrays in various contexts based on the documentation shared in your comments. After reviewing the documentation on issorted function myself, I understood that this function not only checks for standard ascending or descending order but also allows for strict conditions, which can be especially useful in data analysis where duplicates might affect outcomes.

To further clarify, as you have shown, when using issorted(x1, strictascend), it correctly identifies that x1 is strictly ascending, while x2 fails this test due to the repeated element 3. This distinction can be critical in scenarios such as algorithm design or data preprocessing where strict ordering is required.

Moreover, the ability to specify dimensions and comparison methods provides users with a powerful tool for more nuanced data validation. For example, using issorted(A, 2, descend) checks if each row in a matrix is sorted in descending order, which could have implications in statistical analyses or machine learning feature engineering.

Overall, your demonstration of the issorted function’s capabilities is a great reminder of how MATLAB's built-in functions can simplify complex data operations. Thank you for shedding light on this!

Answer 3

[Umar]

Hi @Amir Mahmoudi ,

To elaborate on checking if a sequence is absolutely ascending in MATLAB, you have to utilize logical comparisons and built-in functions as pointed out in example provided by @Torsten. To help you understand further, here is a simple MATLAB code snippet that checks if a sequence is absolutely ascending:

% Sample sequence
sequence = [1, 2, 3, 4, 5];

% Check if the sequence is absolutely ascending
isAscending = all(diff(sequence) > 0);

if isAscending
  disp('The sequence is absolutely ascending.');
else
  disp('The sequence is not absolutely ascending.');
end

Please see attached.

So, let me help you understand how these functions explained below help achieve your goal,

diff(sequence): This function calculates the difference between consecutive elements in the array. If the result is positive for all elements, it indicates that each element is greater than its predecessor.

all(...): This function checks if all elements of the array are true (non-zero). If diff(sequence) results in an array where all values are greater than zero, isAscending will be true.

Please let us know if you need further clarification or assistance. Hope this helps.