series_moving_var_fl()

Applies to: ✅ Microsoft Fabric ✅ Azure Data Explorer ✅ Azure Monitor ✅ Microsoft Sentinel

Applies a moving variance filter on a series.

The function series_moving_var_fl() is a user-defined function (UDF) that takes an expression containing a dynamic numerical array as input and applies on it a moving variance filter.

Syntax

series_moving_var_fl(y_series, n [, center ])

Learn more about syntax conventions.

Parameters

Name	Type	Required	Description
y_series	dynamic	✔️	An array cell of numeric values.
n	int	✔️	The width of the moving variance filter.
center	bool		Indicates whether the moving variance is either applied symmetrically on a window before and after the current point or applied on a window from the current point backwards. By default, center is false.

Function definition

You can define the function by either embedding its code as a query-defined function, or creating it as a stored function in your database, as follows:

Query-defined

Define the function using the following let statement. No permissions are required.

Important

A let statement can't run on its own. It must be followed by a tabular expression statement. To run a working example of series_moving_var_fl(), see Example.

let series_moving_var_fl = (y_series:dynamic, n:int, center:bool=false)
{
    let ey = series_fir(y_series, repeat(1, n), true, center);
    let e2y = series_multiply(ey, ey);
    let y2 = series_multiply(y_series, y_series);
    let ey2 = series_fir(y2, repeat(1, n), true, center);
    let var_series = series_subtract(ey2, e2y);
    var_series
};
// Write your query to use the function here.

Stored

Define the stored function once using the following .create function. Database User permissions are required.

Important

You must run this code to create the function before you can use the function as shown in the Example.

.create-or-alter function with (folder = "Packages\\Series", docstring = "Calculate moving variance of specified width")
series_moving_var_fl(y_series:dynamic, n:int, center:bool=false)
{
    let ey = series_fir(y_series, repeat(1, n), true, center);
    let e2y = series_multiply(ey, ey);
    let y2 = series_multiply(y_series, y_series);
    let ey2 = series_fir(y2, repeat(1, n), true, center);
    let var_series = series_subtract(ey2, e2y);
    var_series
}

Example

The following example uses the invoke operator to run the function.

Query-defined

To use a query-defined function, invoke it after the embedded function definition.

Run the query

let series_moving_var_fl = (y_series:dynamic, n:int, center:bool=false)
{
    let ey = series_fir(y_series, repeat(1, n), true, center);
    let e2y = series_multiply(ey, ey);
    let y2 = series_multiply(y_series, y_series);
    let ey2 = series_fir(y2, repeat(1, n), true, center);
    let var_series = series_subtract(ey2, e2y);
    var_series
}
;
let sinewave=(x:double, period:double, gain:double=1.0, phase:double=0.0)
{
    gain*sin(2*pi()/period*(x+phase))
}
;
let n=128;
let T=10;
let window=T*2;
union
(range x from 0 to n-1 step 1 | extend y=sinewave(x, T)),
(range x from n to 2*n-1 step 1 | extend y=0.0),
(range x from 2*n to 3*n-1 step 1 | extend y=sinewave(x, T)),
(range x from 3*n to 4*n-1 step 1 | extend y=(x-3.0*n)/128.0),
(range x from 4*n to 5*n-1 step 1 | extend y=sinewave(x, T))
| order by x asc 
| summarize x=make_list(x), y=make_list(y)
| extend y_var=series_moving_var_fl(y, T, true)
| render linechart  

Stored

Important

For this example to run successfully, you must first run the Function definition code to store the function.

let sinewave=(x:double, period:double, gain:double=1.0, phase:double=0.0)
{
    gain*sin(2*pi()/period*(x+phase))
}
;
let n=128;
let T=10;
let window=T*2;
union
(range x from 0 to n-1 step 1 | extend y=sinewave(x, T)),
(range x from n to 2*n-1 step 1 | extend y=0.0),
(range x from 2*n to 3*n-1 step 1 | extend y=sinewave(x, T)),
(range x from 3*n to 4*n-1 step 1 | extend y=(x-3.0*n)/128.0),
(range x from 4*n to 5*n-1 step 1 | extend y=sinewave(x, T))
| order by x asc 
| summarize x=make_list(x), y=make_list(y)
| extend y_var=series_moving_var_fl(y, T, true)
| render linechart

Output