Contents

Distributed Processing

This mode assumes that the data set is split into nblocks blocks across computation nodes.

Algorithm Parameters

QR decomposition in the distributed processing mode has the following parameters:

Algorithm Parameters for QR Decomposition without Pivoting (Distributed Processing)

Parameter

Default Valude

Description

computeStep

Not applicable

The parameter required to initialize the algorithm. Can be:

  • step1Local - the first step, performed on local nodes

  • step2Master - the second step, performed on a master node

  • step3Local - the final step, performed on local nodes

algorithmFPType

float

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

method

defaultDense

Performance-oriented computation method, the only method supported by the algorithm.

Use the three-step computation schema to compute QR decomposition:

Step 1 - on Local Nodes

QR Decomposition without Pivoting: Distributed Processing, Step 1 - on Local Nodes

In this step, QR decomposition 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 for QR Decomposition without Pivoting (Distributed Processing, Step 1)

Input ID

Input

data

Pointer to the \(n_i \times p\) numeric table that represents the \(i\)-th data block on the local node. Note that each data block must have sufficient size: \(n_i > p\).

Note

The input can be an object of any class derived from NumericTable.

In this step, QR decomposition calculates the results described below. Pass the Partial Result ID as a parameter to the methods that access the results of your algorithm. For more details, see Algorithms.

Partial Results for QR Decomposition without Pivoting (Distributed Processing, Step 1)

Partial Result ID

Result

outputOfStep1ForStep2

A collection that contains numeric tables each with the partial result to transmit to the master node for Step 2.

Note

By default, these tables are objects of the HomogenNumericTable class, but you can define them as objects of any class derived from NumericTable except the PackedSymmetricMatrix class, CSRNumericTable class, and PackedTriangularMatrix class with the lowerPackedTriangularMatrix layout.

outputOfStep1ForStep3

A collection that contains numeric tables each with the partial result to keep on the local node for Step 3.

Note

By default, these tables are objects of the HomogenNumericTable class, but you can define them as objects of any class derived from NumericTable except the PackedSymmetricMatrix, PackedTriangularMatrix, and CSRNumericTable.

Step 2 - on Master Node

QR Decomposition without Pivoting: Distributed Processing, Step 2 - on Master Node

In this step, QR decomposition accepts the input from each local node described below. Pass the Input ID as a parameter to the methods that provide input for your algorithm. For more details, see Algorithms.

Input for QR Decomposition without Pivoting (Distributed Processing, Step 2)

Input ID

Input

inputOfStep2FromStep1

A collection that contains results computed in Step 1 on local nodes (outputOfStep1ForStep2).

Note

This collection can contain objects of any class derived from NumericTable except the PackedSymmetricMatrix class and PackedTriangularMatrix class with the lowerPackedTriangularMatrix layout.

key

A key, a number of type int. Keys enable tracking the order in which partial results from Step 1 (inputOfStep2FromStep1) come to the master node, so that the partial results computed in Step 2 (outputOfStep2ForStep3) can be delivered back to local nodes in exactly the same order.

In this step, QR decomposition calculates the results described below. Pass the Result ID or Partial Result ID as a parameter to the methods that access the results of your algorithm. For more details, see Algorithms.

Partial Results for QR Decomposition without Pivoting (Distributed Processing, Step 2)

Partial Result ID

Result

outputOfStep2ForStep3

A collection that contains numeric tables to be split across local nodes to compute \(Q_1\).

Note

By default, these tables are objects of the HomogenNumericTable class, but you can define them as objects of any class derived from NumericTable except the PackedSymmetricMatrix class, CSRNumericTable class, and PackedTriangularMatrix class with the lowerPackedTriangularMatrix layout.
Output for QR Decomposition without Pivoting (Distributed Processing, Step 2)

Result ID

Result

matrixR

Pointer to the numeric table with the \(p \times p\) upper triangular matrix \(R_1\).

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 the PackedSymmetricMatrix class, CSRNumericTable class, and PackedTriangularMatrix class with the lowerPackedTriangularMatrix layout.

Step 3 - on Local Nodes

QR Decomposition without Pivoting: Distributed Processing, Step 3 - on Local Nodes

In this step, QR decomposition 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 for QR Decomposition without Pivoting (Distributed Processing, Step 3)

Input ID

Input

inputOfStep3FromStep1

A collection that contains results computed in Step 1 on local nodes (outputOfStep1ForStep3).

Note

The collection can contain objects of any class derived from NumericTable except the PackedSymmetricMatrix and PackedTriangularMatrix.

inputOfStep3FromStep2

A collection that contains results computed in Step 2 on local nodes (outputOfStep2ForStep3).

Note

The collection can contain objects of any class derived from NumericTable except the PackedSymmetricMatrix class and PackedTriangularMatrix class with the lowerPackedTriangularMatrix layout.

In this step, QR decomposition calculates the 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.

Output for QR Decomposition without Pivoting (Distributed Processing, Step 3)

Result ID

Result

matrixQ

Pointer to the numeric table with the \(n \times p\) matrix \(Q_1\).

Note

By default, the result 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.

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Pivoted QR Decomposition