Application Notes for Intel® oneAPI Math Kernel Library Summary Statistics

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Date 12/04/2020
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Document Table of Contents
Document Table of Contents x
Application Notes for Intel® oneAPI Math Kernel Library Summary Statistics
Application Notes for Intel® oneAPI Math Kernel Library Summary Statistics x
Legal Information About This Document About Summary Statistics Algorithms and Interfaces in Summary Statistics Common Usage Model of Summary Statistics Algorithms Processing Data in Blocks Detecting Outliers in Datasets Dealing with Missing Observations Computing Quantiles for Streaming Data Bibliography
About This Document x
Conventions and Symbols
Algorithms and Interfaces in Summary Statistics x
Estimating Raw and Central Moments and Sums, Skewness, Excess Kurtosis, Variation, and Variance-Covariance/Correlation/Cross-Product Matrix Computing Median Absolute Deviation Computing Mean Absolute Deviation Computing Minimum/Maximum Values Calculating Order Statistics Estimating Quantiles Estimating a Pooled/Group Variance-Covariance Matrices/Means Estimating a Partial Variance-Covariance Matrix Performing Robust Estimation of a Variance-Covariance Matrix Detecting Multivariate Outliers Handling Missing Values in Matrices of Observations Parameterizing a Correlation Matrix Sorting an Observation Matrix
Estimating Raw and Central Moments and Sums, Skewness, Excess Kurtosis, Variation, and Variance-Covariance/Correlation/Cross-Product Matrix x
Computing Estimations for Large Datasets Calculating Multiple Estimates
Estimating Quantiles x
Computing Quantiles for Streaming Data with VSL_SS_METHOD_SQUANTS_ZW
Handling Missing Values in Matrices of Observations x
Basic Assumptions for the MI Method Basic Components of the MI Method
Detecting Outliers in Datasets x
Using the BACON Algorithm for Outlier Detection Using Robust Methods
Application Notes for Intel® oneAPI Math Kernel Library Summary Statistics

Computing Minimum/Maximum Values

Use the VSL_SS_METHOD_FAST method to compute the minimum/maximum values in the datasets. The calculation is straightforward and follows the pattern of the example below:

#include "mkl_vsl.h"
 
#define DIM 3      /* dimension of the task */ 
#define N   1000   /* number of observations */
 
int main()
{
    VSLSSTaskPtr task;
    float x[DIM][N];  /* matrix of observations */
    float min_est[DIM], max_est[DIM];
    MKL_INT p, n, xstorage;
    int status;
  
    /* Parameters of the task and initialization */
    p = DIM;
    n = N;
    xstorage = VSL_SS_MATRIX_STORAGE_ROWS;
    for ( int i = 0; i < p; i++ ) min_est[i] = max_est[i] = x[i][0];
 
    /* Create a task */
    status = vslsSSNewTask( &task, &p, &n, &xstorage, (float*)x, 0, 0 );
 
    /* Initialize the task parameters */
    status = vslsSSEditTask( task, VSL_SS_ED_MIN, min_est );
    status = vslsSSEditTask( task, VSL_SS_ED_MAX, max_est );
 
    /* Compute the minimum and maximum values in observations */
    status = vslsSSCompute( task, VSL_SS_MIN|VSL_SS_MAX,
                                  VSL_SS_METHOD_FAST );
 
    /* Deallocate the task resources */
    status = vslSSDeleteTask( &task );
 
    return 0;
}

The size of the arrays to hold the minimum/maximum values should be sufficient for storing at least p values of each estimate, where p is the dimension of the task.

You can use the computation of these estimates to find the minimum/maximum values in the dataset available in blocks. In this case, the estimates computed for the previous data portion are used for processing the next block of the data array.

Before the first call to the Compute routine, initialize the initial values of the estimates with reasonable values, such as the values of the first observation.

Parent topic: Algorithms and Interfaces in Summary Statistics
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