Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

ID 766686
Date 3/22/2024
Public

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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 AT 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.