# Online Processing¶

Online processing computation mode assumes that data arrives in blocks $$i = 1, 2, 3, \ldots \text{nblocks}$$.

Computation of correlation and variance-covariance matrices in the online processing mode follows the general computation schema for online processing described in Algorithms.

## Algorithm Input¶

The correlation and variance-covariance matrices algorithm in the online processing mode accepts the input described below. Pass the Input ID as a parameter to the methods that provide input for your algorithm. For more details, see Algorithms.

Input ID

Input

data

Pointer to the numeric table of size $$n_i \times p$$ that represents the current data block.

While the input for defaultDense, singlePassDense, or sumDense method can be an object of any class derived from NumericTable, the input for fastCSR, singlePassCSR, or sumCSR method can only be an object of the CSRNumericTable class.

## Algorithm Parameters¶

The correlation and variance-covariance matrices algorithm has the following parameters in the online processing mode:

Parameter

Default Valude

Description

algorithmFPType

float

The floating-point type that the algorithm uses for intermediate computations. Can be float or double.

method

defaultDense

Available methods for computation of correlation and variance-covariance matrices:

defaultDense

default performance-oriented method

singlePassDense

implementation of the single-pass algorithm proposed by D.H.D. West

sumDense

implementation of the algorithm in the cases where the basic statistics associated with the numeric table are pre-computed sums; returns an error if pre-computed sums are not defined

fastCSR

performance-oriented method for CSR numeric tables

singlePassCSR

implementation of the single-pass algorithm proposed by D.H.D. West; optimized for CSR numeric tables

sumCSR

implementation of the algorithm in the cases where the basic statistics associated with the numeric table are pre-computed sums; optimized for CSR numeric tables; returns an error if pre-computed sums are not defined

outputMatrixType

covarianceMatrix

The type of the output matrix. Can be:

• covarianceMatrix - variance-covariance matrix

• correlationMatrix - correlation matrix

initializationProcedure

Not applicable

The procedure for setting initial parameters of the algorithm in the online processing mode. By default, the algorithm sets the nObservations, sum, and crossProduct parameters to zero.

## Partial Results¶

The correlation and variance-covariance matrices algorithm in the online processing mode calculates partial results described below. Pass the Result ID as a parameter to the methods that access the results of your algorithm. For more details, see Algorithms.

Result ID

Result

nObservations

Pointer to the $$1 \times 1$$ numeric table that contains the number of observations processed so far.

Note

By default, this result is an object of the HomogenNumericTable class, but you can define the result as an object of any class derived from NumericTable except CSRNumericTable.

crossProduct

Pointer to $$p \times p$$ numeric table with the cross-product matrix computed so far.

Note

By default, this table is an object of the HomogenNumericTable class, but you can define the result as an object of any class derived from NumericTable except PackedSymmetricMatrix, PackedTriangularMatrix, and CSRNumericTable.

sum

Pointer to $$1 \times p$$ numeric table with partial sums computed so far.

Note

By default, this table is an object of the HomogenNumericTable class, but you can define the result as an object of any class derived from NumericTable except PackedSymmetricMatrix, PackedTriangularMatrix, and CSRNumericTable.

## Algorithm Output¶

The correlation and variance-covariance matrices algorithm calculates the result described below. Pass the Result ID as a parameter to the methods that access the results of your algorithm. For more details, see Algorithms.

Result ID

Result

covariance

Use when outputMatrixType=covarianceMatrix. Pointer to the numeric table with the $$p \times p$$ variance-covariance matrix.

Note

By default, this result is an object of the HomogenNumericTable class, but you can define the result as an object of any class derived from NumericTable except PackedTriangularMatrix and CSRNumericTable.

correlation

Use when outputMatrixType=correlationMatrix. Pointer to the numeric table with the $$p \times p$$ correlation matrix.

Note

By default, this result is an object of the HomogenNumericTable class, but you can define the result as an object of any class derived from NumericTable except PackedTriangularMatrix and CSRNumericTable.

mean

Pointer to the $$1 \times p$$ numeric table with means.

Note

By default, this result is an object of the HomogenNumericTable class, but you can define the result as an object of any class derived from NumericTable except PackedTriangularMatrix, PackedSymmetricMatrix, and CSRNumericTable.

Optimization Notice

Intel’s compilers may or may not optimize to the same degree for non-Intel microprocessors for optimizations that are not unique to Intel microprocessors. These optimizations include SSE2, SSE3, and SSSE3 instruction sets and other optimizations. Intel does not guarantee the availability, functionality, or effectiveness of any optimization on microprocessors not manufactured by Intel. Microprocessor-dependent optimizations in this product are intended for use with Intel microprocessors. Certain optimizations not specific to Intel microarchitecture are reserved for Intel microprocessors. Please refer to the applicable product User and Reference Guides for more information regarding the specific instruction sets covered by this notice.

Notice revision #20110804