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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