Summary Statistics Task Computation Routines

Developer Reference for Intel® oneAPI Math Kernel Library for C

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Date 12/16/2022

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Summary Statistics Task Computation Routines

Task computation routines calculate statistical estimates on the data provided and parameters held in the task descriptor. After you create the task and initialize its parameters, you can call the computation routines as many times as necessary. Table "Summary Statistics Estimates Obtained with vslSSCompute Routine" lists the respective statistical estimates.

NOTE:

The Summary Statistics computation routines do not signal floating-point errors, such as overflow or gradual underflow, or operations with NaNs (except for the missing values in the observations).

Summary Statistics Estimates Obtained with vslSSCompute Routine
Estimate	Support of Observations Available in Blocks	Description
VSL_SS_MEAN	Yes	Computes the array of means.
VSL_SS_SUM	Yes	Computes the array of sums.
VSL_SS_2R_MOM	Yes	Computes the array of the 2^nd order raw moments.
VSL_SS_2R_SUM	Yes	Computes the array of raw sums of the 2^nd order.
VSL_SS_3R_MOM	Yes	Computes the array of the 3^rd order raw moments.
VSL_SS_3R_SUM	Yes	Computes the array of raw sums of the 3^rd order.
VSL_SS_4R_MOM	Yes	Computes the array of the 4^th order raw moments.
VSL_SS_4R_SUM	Yes	Computes the array of raw sums of the 4^th order.
VSL_SS_2C_MOM	Yes	Computes the array of the 2^nd order central moments.
VSL_SS_2C_SUM	Yes	Computes the array of central sums of the 2^nd order.
VSL_SS_3C_MOM	Yes	Computes the array of the 3^rd order central moments.
VSL_SS_3C_SUM	Yes	Computes the array of central sums of the 3^rd order.
VSL_SS_4C_MOM	Yes	Computes the array of the 4^th order central moments.
VSL_SS_4C_SUM	Yes	Computes the array of central sums of the 4^th order.
VSL_SS_KURTOSIS	Yes	Computes the array of kurtosis values.
VSL_SS_SKEWNESS	Yes	Computes the array of skewness values.
VSL_SS_MIN	Yes	Computes the array of minimum values.
VSL_SS_MAX	Yes	Computes the array of maximum values.
VSL_SS_VARIATION	Yes	Computes the array of variation coefficients.
VSL_SS_COV	Yes	Computes a covariance matrix.
VSL_SS_COR	Yes	Computes a correlation matrix. The main diagonal of the correlation matrix holds variances of the random vector components.
VSL_SS_CP	Yes	Computes a cross-product matrix.
VSL_SS_POOLED_COV	No	Computes a pooled covariance matrix.
VSL_SS_POOLED_MEAN	No	Computes an array of pooled means.
VSL_SS_GROUP_COV	No	Computes group covariance matrices.
VSL_SS_GROUP_MEAN	No	Computes group means.
VSL_SS_QUANTS	No	Computes quantiles.
VSL_SS_ORDER_STATS	No	Computes order statistics.
VSL_SS_ROBUST_COV	No	Computes a robust covariance matrix.
VSL_SS_OUTLIERS	No	Detects outliers in the dataset.
VSL_SS_PARTIAL_COV	No	Computes a partial covariance matrix.
VSL_SS_PARTIAL_COR	No	Computes a partial correlation matrix.
VSL_SS_MISSING_VALS	No	Supports missing values in datasets.
VSL_SS_PARAMTR_COR	No	Computes a parameterized correlation matrix.
VSL_SS_STREAM_QUANTS	Yes	Computes quantiles for streaming data.
VSL_SS_MDAD	No	Computes median absolute deviation.
VSL_SS_MNAD	No	Computes mean absolute deviation.
VSL_SS_SORTED_OBSERV	No	Sorts the dataset by the components of the random vector ξ.

Table "Summary Statistics Computation Method"lists estimate calculation methods supported by Intel® oneAPI Math Kernel Library. See theIntel® oneAPI Math Kernel Library Summary Statistics Application Notes document [SS Notes] for a detailed description of the methods.

Summary Statistics Computation Method
Method	Description
VSL_SS_METHOD_FAST	Fast method for calculation of the estimates: raw/central moments/sums, skewness, kurtosis, variation, variance-covariance/correlation/cross-product matrix min/max/quantile/order statistics partial variance-covariance median/mean absolute deviation
VSL_SS_METHOD_FAST_USER_MEAN	Fast method for calculation of the estimates given user-defined mean: central moments/sums of 2-4 order, skewness, kurtosis, variation, variance-covariance/correlation/cross-product matrix, mean absolute deviation
VSL_SS_METHOD_1PASS	One-pass method for calculation of estimates: raw/central moments/sums, skewness, kurtosis, variation, variance-covariance/correlation/cross-product matrix pooled/group covariance matrix
VSL_SS_METHOD_TBS	TBS method for robust estimation of covariance and mean
VSL_SS_METHOD_BACON	BACON method for detection of multivariate outliers
VSL_SS_METHOD_MI	Multiple imputation method for support of missing values
VSL_SS_METHOD_SD	Spectral decomposition method for parameterization of a correlation matrix
VSL_SS_METHOD_SQUANTS_ZW	Zhang-Wang (ZW) method for quantile estimation for streaming data
VSL_SS_METHOD_SQUANTS_ZW_FAST	Fast ZW method for quantile estimation for streaming data
VSL_SS_METHOD_RADIX	Radix method for dataset sorting

You can calculate all requested estimates in one call of the routine. For example, to compute a kurtosis and covariance matrix using a fast method, pass a combination of the pre-defined parameters into the Compute routine as shown in the example below:

...
method = VSL_SS_METHOD_FAST;
task_params = VSL_SS_KURTOSIS|VSL_SS_COV;
…
status = vsldSSCompute( task, task_params, method );

To compute statistical estimates for the next block of observations, you can do one of the following:

copy the observations to memory, starting with the address available to the task
use one of the appropriate Editors to modify the pointer to the new dataset in the task.

The library does not detect your changes of the dataset and computed statistical estimates. To obtain statistical estimates for a new matrix, change the observations and initialize relevant arrays. You can follow this procedure to compute statistical estimates for observations that come in portions. See Table "Summary Statistics Estimates Obtained with vslSSCompute Routine"for information on such observations supported by the Intel® oneAPI Math Kernel Library Summary Statistics estimators.

To modify parameters of the task using the Task Editors, set the address of the targeted matrix of the observations or change the respective vector component indices. After you complete editing the task parameters, you can compute statistical estimates in the modified environment.

If the task completes successfully, the computation routine returns the zero status code. If an error is detected, the computation routine returns an error code. In particular, an error status code is returned in the following cases:

the task pointer is NULL
memory allocation has failed
the calculation has failed for some other reason

NOTE:

You can use the NULL task pointer in calls to editor routines. In this case, the routine is terminated and no system crash occurs.

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Developer Reference for Intel® oneAPI Math Kernel Library for C

Summary Statistics Task Computation Routines