series_moving_var_fl()

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 ])

Parameters

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.

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.

.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.

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

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