Contents

Distributed Processing

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

Algorithm Parameters

The SVD algorithm in the distributed processing mode has the following parameters:

Algorithm Parameters for Singular Value Decomposition (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.

leftSingularMatrix

requiredInPackedForm

Specifies whether the matrix of left singular vectors is required. Can be:

  • notRequired - the matrix is not required

  • requiredInPackedForm - the matrix in the packed format is required

rightSingularMatrix

requiredInPackedForm

Specifies whether the matrix of right singular vectors is required. Can be:

  • notRequired - the matrix is not required

  • requiredInPackedForm - the matrix in the packed format is required

Use the three-step computation schema to compute SVD:

Step 1 - on Local Nodes

Singular Value Decomposition: Distributed Processing, Step 1 - on Local Nodes

In this step, SVD 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 Singular Value Decomposition (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

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

In this step, SVD 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 Singular Value Decomposition (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.

outputOfStep1ForStep3

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

Note

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

Step 2 - on Master Node

Singular Value Decomposition: Distributed Processing, Step 2 - on Master Node

In this step, SVD 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 Singular Value Decomposition (Distributed Processing, Step 2)

Input ID

Input

inputOfStep2FromStep1

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

Note

The 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, SVD calculates the results described below. Pass the Partial Result ID or Result ID as a parameter to the methods that access the results of your algorithm. For more details, see Algorithms.

Partial Results for Singular Value Decomposition (Distributed Processing, Step 2)

Partial Result ID

Result

outputOfStep2ForStep3

A collection that contains numeric tables to be split across local nodes to compute left singular vectors. Set to NULL if you do not need left singular vectors.

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 PackedSymmetricMatrix, PackedTriangularMatrix, and CSRNumericTable.
Output for Singular Value Decomposition (Distributed Processing, Step 2)

Result ID

Result

singularValues

Pointer to the \(1 \times p\) numeric table with singular values (the diagonal of the matrix \(\Sigma\)).

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 PackedSymmetricMatrix, PackedTriangularMatrix, and CSRNumericTable.

rightSingularMatrix

Pointer to the \(p \times p\) numeric table with right singular vectors (matrix \(V\)). Pass NULL if right singular vectors are not required.

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 PackedSymmetricMatrix, PackedTriangularMatrix, and CSRNumericTable.

Step 3 - on Local Nodes

Singular Value Decomposition: Distributed Processing, Step 3 - on Local Nodes

In this step, SVD 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 Singular Value Decomposition (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 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 PackedSymmetricMatrix and PackedTriangularMatrix.

In this step, SVD 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 Singular Value Decomposition (Distributed Processing, Step 3)

Result ID

Result

leftSingularMatrix

Pointer to the \(n \times p\) numeric table with left singular vectors (matrix \(U\)). Pass NULL if left singular vectors are not required.

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 PackedSymmetricMatrix, PackedTriangularMatrix, and CSRNumericTable.

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