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

Estimating Quantiles

You can use the Summary Statistics routines to compute quantiles for a matrix of observations. The computation routine can calculate more than one quantile at a time. Quantile orders belonging to the interval (0,1) are packed and passed into the library as an array. You should allocate enough memory to hold results of the calculations. The size of the array should provide storage for at least d*p elements, where

  1. p is the dimension of the task.

  2. d is the number of the requested quantiles.

Quantiles in the array are packed component by component, starting from the first component of the random vector and following the quantile orders.

See the Mathematical Notation and Definitions chapter in the Summary Statistics section of [MKLMan] for additional information.

The example below illustrates quantile-related calculations:

#include "mkl_vsl.h"
#include <stdio.h>
#define DIM 3      /* dimension of the task */
#define N   1000   /* number of observations */
#define M   100    /* number of quantiles to compute */
 
int main()
{
   int i, status;
   VSLSSTaskPtr task;
   float x[DIM][N];      /* matrix of observations */
   float order_stats[N]; /* matrix to store order statistics */
   float q_order[M], quants[M];
   MKL_INT q_order_n;
   MKL_INT p, n, xstorage, ostatstorage;
   unsigned long long estimates;
   int indices[DIM]={1,0,0}; /* the first vector component is processed */
 
   /* Parameters of the task and initialization */
   p = DIM;
   n = N;
   q_order_n = M;
   xstorage  = VSL_SS_MATRIX_STORAGE_ROWS;
   ostatstorage = VSL_SS_MATRIX_STORAGE_ROWS;
 
   /* Calculate percentiles */
   for ( i = 0; i < M; i++ ) q_order[i] = (float)i / (float)M;
  
   /* Create a task */
   status = vslsSSNewTask( &task, &p, &n,
                           &xstorage, (float*)x, 0, indices );
 
   /* Initialize the task parameters */
   status = vslsSSEditQuantiles( task, &q_order_n, q_order,
                                 quants, order_stats, &ostatstorage );
 
   /* Compute the percentiles and order statistics */
   estimates = VSL_SS_QUANTS|VSL_SS_ORDER_STATS;
   status = vslsSSCompute( task, estimates, VSL_SS_METHOD_FAST );
 
   /* Deallocate the task resources */
   status = vslSSDeleteTask( &task );
 
   return 0;
}
Parent topic: Algorithms and Interfaces in Summary Statistics
Level Two Title