Application Notes for Intel® oneAPI Math Kernel Library Summary Statistics

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ID 772991
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 Mean Absolute Deviation

Summary Statistics offers two methods for computation of mean absolute deviation:

  1. Method VSL_SS_METHOD_FAST is a performance-oriented implementation of the algorithm.

  2. Method VSL_SS_METHOD_FAST_USER_MEAN is an implementation of the algorithm when a user-defined mean is provided.

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 mnad[DIM];
    MKL_INT p, n, xstorage;
    int status;
  
    /* Parameters of the task and initialization */
    p = DIM;
    n = N;
    xstorage = VSL_SS_MATRIX_STORAGE_ROWS;
  
    /* Create a task */
    status = vslsSSNewTask( &task, &p, &n, &xstorage, (float*)x, 0, 0 );
  
    /* Initialize the task parameters */
    status = vslsSSEditTask( task, VSL_SS_ED_MNAD, mnad );
  
    /* Compute median absolute deviation in observations */
    status = vslsSSCompute(task, VSL_SS_MNAD, VSL_SS_METHOD_FAST );
  
    /* Deallocate the task resources */
    status = vslSSDeleteTask( &task );
  
    return 0;
}

The size of the array to hold mean absolute deviations should be sufficient to hold at least p elements, where p is the dimension of the task.

Computation of mean absolute deviation is only possible for data arrays available at once, or in separate blocks of the dataset.

To achieve the best results, before you compute mean absolute deviation, provide the buffer for estimate of mean (or corresponding sum) even if you do not need this estimate.

Parent topic: Algorithms and Interfaces in Summary Statistics
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