mkl_sparse_?

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 12/16/2022

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mkl_sparse_?_qr

Computes the QR decomposition for the matrix of a sparse linear system and calculates the solution.

Syntax

stat = mkl_sparse_d_qr (operation, A, descr, layout, *columns, x, *ldx, b, ldb)

stat = mkl_sparse_s_qr (operation, A, descr, layout, x, columns, ldx, b, ldb)

Include Files

mkl_sparse_qr.f90

Description

The mkl_sparse_?_qr routine computes the QR decomposition for the matrix of a sparse linear system A*x = b, so that A = Q*R where Q is the orthogonal matrix and R is upper triangular, and calculates the solution.

NOTE:

Currently, mkl_sparse_?_qr supports only square and overdetermined systems. For underdetermined systems you can manually transpose the system matrix and use QR decomposition for A^T to get the minimum-norm solution for the original underdetermined system.

NOTE:

Currently, mkl_sparse_?_qr supports only CSR format for the input matrix, non-transpose operation, and single right-hand side.

Input Parameters

operation

C_INT

Specifies the operation to perform.

NOTE:

Currently, the only suppored value is SPARSE_OPERATION_NON_TRANSPOSE (non-transpose case; that is, A*x = b is solved).

A

SPARSE_MATRIX_T

Handle containing a sparse matrix in an internal data structure.

descr

MATRIX_DESCR

Structure specifying sparse matrix properties. Only the parameters listed here are currently supported.

type

Specifies the type of sparse matrix.

NOTE:

Currently, the only supported value is SPARSE_MATRIX_TYPE_GENERAL (the matrix is processed as-is).

layout

C_INT

Describes the storage scheme for the dense matrix:

`SPARSE_LAYOUT_COLUMN_MAJOR`	Storage of elements uses column-major layout.
`SPARSE_LAYOUT_ROW_MAJOR`	Storage of elements uses row-major layout.

x

C_FLOAT for mkl_sparse_s_qr; C_DOUBLE for mkl_sparse_d_qr

Array with a size of at least rows*cols:

	layout = `SPARSE_LAYOUT_COLUMN_MAJOR`	layout = `SPARSE_LAYOUT_ROW_MAJOR`
`rows` (number of rows in x)	ldx	Number of columns in A
`cols` (number of columns in x)	columns	ldx

columns

C_INT

Number of columns in matrix b.

ldx

C_INT

Specifies the leading dimension of matrix x.

b

C_FLOAT for mkl_sparse_s_qr; C_DOUBLE for mkl_sparse_d_qr

Array with a size of at least rows*cols:

	layout = `SPARSE_LAYOUT_COLUMN_MAJOR`	layout = `SPARSE_LAYOUT_ROW_MAJOR`
`rows` (number of rows in b)	ldb	Number of columns in A
`cols` (number of columns in b)	columns	ldb

ldb

C_INT

Specifies the leading dimension of matrix b.

Output Parameters

x

C_FLOAT for mkl_sparse_s_qr; C_DOUBLE for mkl_sparse_d_qr

Overwritten by the updated matrix y.

stat

INTEGER

Value indicating whether the operation was successful, and if not, why:

`SPARSE_STATUS_SUCCESS`	The operation was successful.
`SPARSE_STATUS_NOT_INITIALIZED`	The routine encountered an empty handle or matrix array.
`SPARSE_STATUS_ALLOC_FAILED`	Internal memory allocation failed.
`SPARSE_STATUS_INVALID_VALUE`	The input parameters contain an invalid value.
`SPARSE_STATUS_EXECUTION_FAILED`	Execution failed.
`SPARSE_STATUS_INTERNAL_ERROR`	An error in algorithm implementation occurred.
`SPARSE_STATUS_NOT_SUPPORTED`	The requested operation is not supported.

Parent topic: Sparse QR Routines

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

mkl_sparse_?_qr