mkl_sparse_?_qr

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_rsolve

Second stage of the solving step of the SPARSE QR solver.

Syntax

stat mkl_sparse_d_qr_rsolve ( operation, A, layout, x, columns, ldx, b, ldb )

stat mkl_sparse_s_qr_rsolve ( operation, A, layout, x, columns, ldx, b, ldb )

Include Files

mkl_sparse_qr.f90

Description

The mkl_sparse_?_qr_rsolve routine implements the second step for computing the solution of \(A\cdot x = b\) using the QR-decomposition, \(Q\cdot R\cdot x = b\). In particular, it performs the triangular solve with \(R\),

\[R \cdot x = b\]

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

where \(R\) is a sparse upper triangular matrix factor, \(b\) is now the right hand side matrix after first step ( mkl_sparse_?_qr_qmult) is applied and \(x\) is the solution matrix to be computed.

NOTE:

Currently, mkl_sparse_?_qr_rsolve 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 for the system: \(op(A)\cdot x = b\) to be solved using the QR-decomposition.

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.

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_rsolve`
`C_DOUBLE`	for `mkl_sparse_d_qr_rsolve`

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_rsolve`
`C_DOUBLE`	for `mkl_sparse_d_qr_rsolve`

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_rsolve`
`C_DOUBLE`	for `mkl_sparse_d_qr_rsolve`

Contains the solution of the upper triangular system \(R\cdot x = b\) .

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_rsolve

Syntax

Include Files

Description

Input Parameters

Output Parameters

Return Values