L_ISUNIFORM

=L_ISUNIFORM(vector, [precision_n])

Description

L_ISUNIFORM returns {TRUE;step} if the values in the vector are evenly spaced (all steps are identical). If FALSE, it returns {FALSE; MAX(step)-MIN(step)}.

You can set the precision_n parameter to be a number of decimal places (such as 10), and the step size will be rounded to that number of decimal places prior to testing for uniformity.

Purpose of precision_n: In some cases, precision errors in Excel may cause this function to return FALSE when you might otherwise consider the uniformity to be "close enough." For example, if MAX(step)-MIN(step) is a number smaller than 1E-10, it might be a precision error, and you might determine that a difference in step size smaller than 1E-10 is sufficient to consider the vector uniform.

In Excel, make the function return only a single value by using the @ symbol in front of the function: =@L_ISUNIFORM(...).

Lambda Formula

This code for using L_ISUNIFORM in Excel is provided under the License as part of the LAMBDA Library, but to use just this function, you may copy the following code directly into your spreadsheet.

Name: L_ISUNIFORM
Comment: Returns {TRUE;step} if the vector is uniformly spaced
Refers To:

=LAMBDA(vector,[precision_n],
LET(doc,"https://www.vertex42.com/lambda/isuniform.html",
    rows,ROWS(vector),cols,COLUMNS(vector),
    vector,TAKE(IF(AND(cols>1,rows=1),TRANSPOSE(vector),vector),,1),
    steps,DROP(vector,1)-DROP(vector,-1),
    unique_steps,UNIQUE(IF(ISOMITTED(precision_n),steps,ROUND(steps,precision_n))),
    IF(ROWS(unique_steps)=1,
        TRUE,
        VSTACK(FALSE,MAX(unique_steps)-MIN(unique_steps))
    )
))

/**
* Returns {TRUE;step} if the vector is uniformly spaced (all the
* steps are identical to a precision of n decimal places)
* If FALSE, returns {FALSE, MAX(steps)-MIN(steps)}
*/
L_ISUNIFORM = LAMBDA(vector,[precision_n],
LET(doc,"https://www.vertex42.com/lambda/isuniform.html",
    rows,ROWS(vector),cols,COLUMNS(vector),
    vector,TAKE(IF(AND(cols>1,rows=1),TRANSPOSE(vector),vector),,1),
    steps,DROP(vector,1)-DROP(vector,-1),
    unique_steps,UNIQUE(IF(ISOMITTED(precision_n),steps,ROUND(steps,precision_n))),
    IF(ROWS(unique_steps)=1,
        TRUE,
        VSTACK(FALSE,MAX(unique_steps)-MIN(unique_steps))
    )
));

Name: L_ISUNIFORM
Description: Returns {TRUE;step} if the vector is uniformly spaced (steps are identical). If FALSE, returns {FALSE, MAX(steps)-MIN(steps)}
Arguments: vector, precision_n
Function:

LET(doc,"https://www.vertex42.com/lambda/isuniform.html",
    r,ROWS(vector),
    steps,ARRAYFORMULA(CHOOSEROWS(vector,SEQUENCE(r-1,1,2))-CHOOSEROWS(vector,SEQUENCE(r-1,1,1))),    unique_steps,UNIQUE(IF(ISBLANK(precision_n),steps,ARRAYFORMULA(ROUND(steps,precision_n)))),
    ret,IF(ROWS(unique_steps)=1,TRUE,VSTACK(FALSE,MAX(unique_steps)-MIN(unique_steps))),
    ret
)

L_ISUNIFORM Examples

Test: Copy and Paste this LET function into a cell
=LET(
    vector, L_LINSPACE(1,2,4),
    L_ISUNIFORM(vector)
)

Result: TRUE

=LET(
    vector, {1; 1.333333; 1.666667; 2},
    L_ISUNIFORM(vector)
)

Result: {FALSE; 1E-6}

Test: Copy and Paste this LET function into a cell
=LET(
    logseq, L_LOGSPACE(1,2,5),
    L_ISUNIFORM(LOG10(logseq))
)

Result: {FALSE; 4.4409E-16}

SE, LINSPACE, LOGSPACE, RESCALE, ISUNIFORM