mkl_sparse_?

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 4/28/2026

Version

Public

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, columns, x, 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

\[op(A) \cdot x = b\]

so that op(A) = \(Q \cdot R\) where Q is the orthogonal matrix and R is upper triangular, and calculates the solution:

\[x = R^{-1} \cdot Q^{T} \cdot b\]

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, with \(op(A)=A\), and single right-hand side.

Input Parameters

operation

C_INT

Specifies the operation to perform, solve \(op(A) \cdot x = b\).

NOTE:

Currently, the only supported value is SPARSE_OPERATION_NON_TRANSPOSE (non-transpose case; that is, \(A\cdot x = b\) 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.

sparse_matrix_type_t type

Specifies the type of a sparse matrix:

SPARSE_MATRIX_TYPE_GENERAL - The matrix is processed as is.

type

Specifies the type of sparse matrix in the descriptor.

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 where:

	`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 where:

	`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.

Return Values

See Output Parameter stat.

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

mkl_sparse_?_qr

Syntax

Include Files

Description

Input Parameters

Output Parameters

Return Values