Variance (FPScript)

21.09.2021

Determines individual, moving or block variances for a data set.

Syntax

Variance(DataSet, [ Mode = PROCESS_COLUMNS ] [ , IntervalWidth ])

 

The syntax of the Variance function consists of the following parts:

Part

Description

DataSet

The data set to be evaluated.

All data structures are allowed. All numeric data types are permitted.

For complex data types the absolute value is formed.

If the argument is a list, then the function is executed for each element of the list and the result is also a list.

Mode

Specifies how data matrices and signal series are to be processed and whether individual, moving or block variances are to be determined.

The argument Mode can have the following values:

Constant

Meaning

PROCESS_COLUMNS

Data matrices and signal series are processed column by column. The result is a data series or a signal with one variance per column.

PROCESS_ROWS

Data matrices and signal series are processed row by row. The result is a data series or a signal with one variance per row.

PROCESS_COMPLETE

Data matrices and signal series are processed as a whole. The result is a scalar value with one variance for the entire data set.

...plus an optional constant, which determines the method of calculation:

Constant

Meaning

+ CALC_BLOCK

Block-by-block calculation. One value is calculated per interval.

+ CALC_MOVING

Moving calculation. For every value in the data set, a result is determined in the specified interval.

If the argument is a list, then the first element in the list is taken. If this is also a list, then the process is repeated.

If this argument is omitted, it will be set to the default value PROCESS_COLUMNS.

IntervalWidth

This argument is required for determining moving and block variances. The interval width then specifies the number of values to be examined. The width should be an odd number. Otherwise, the interval is asymmetrical, and one more value is included in the calculation to the right of the center as opposed to the left.

Permitted data structures are scalar value. All integral data types are permitted.

The value must be greater or equal to 1.

If the argument is a list, then the first element in the list is taken. If this is also a list, then the process is repeated.

Remarks

The result always has the data type 64-bit floating point.

The variance of a sample is defined as:

with the mean value

If DataSet is a scalar value, then 0 is always returned. For signals and signal series, the Y component is processed and the X or Z component is copied, if possible. When calculating moving and block variances, the data structure of the result corresponds to that of the argument. If, on the other hand, DataSet is a data series or a signal, the result is a scalar value with the variance searched for; otherwise, the result is a data series or a signal with one variance per column or row.

Available in

FlexPro View, Basic, Professional, Developer Suite

Examples

Variance({1, 3, 5, 2, 4})

Results in 2.5.

Variance({{1, 3, 5, 2, 4}, {2, 6, 10, 4, 8}})

Results in {2.5, 10}.

Variance({{1, 3, 5, 2, 4}, {2, 6, 10, 4, 8}}, PROCESS_ROWS)

Results in {0.5, 4.5, 12.5, 2, 8}.

Variance({1, 2, 3, 2, 1}, CALC_MOVING, 3)

Results in { 0.5, 1, 0.3333333333333339, 1, 0.5 }.

Variance({1, 2, 3, 4, 4.5, 5}, CALC_BLOCK, 3)

Results in {1, 0.25}.

See Also

Mean Function

Covariance Function

Statistical Quantity Analysis Object

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