mkl_?bsrtrsv

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_?bsrtrsv

Triangular solver with simplified interface for a sparse matrix stored in the BSR format (3-array variation) with one-based indexing (deprecated).

Syntax

call mkl_sbsrtrsv(uplo, transa, diag, m, lb, a, ia, ja, x, y)

call mkl_dbsrtrsv(uplo, transa, diag, m, lb, a, ia, ja, x, y)

call mkl_cbsrtrsv(uplo, transa, diag, m, lb, a, ia, ja, x, y)

call mkl_zbsrtrsv(uplo, transa, diag, m, lb, a, ia, ja, x, y)

Include Files

mkl.fi

Description

This routine is deprecated. Use mkl_sparse_?_trsvfrom the Intel® oneAPI Math Kernel Library Inspector-executor Sparse BLAS interface instead.

The mkl_?bsrtrsv routine solves a system of linear equations with matrix-vector operations for a sparse matrix stored in the BSR format (3-array variation) :

y := A*x

y := A^T*x,

where:

x and y are vectors,

A is a sparse upper or lower triangular matrix with unit or non-unit main diagonal, A^T is the transpose of A.

NOTE:

This routine supports only one-based indexing of the input arrays.

Input Parameters

Parameter descriptions are common for all implemented interfaces with the exception of data types that refer here to the FORTRAN 77 standard types. Data types specific to the different interfaces are described in the section "Interfaces" below.

uplo

CHARACTER*1. Specifies the upper or low triangle of the matrix A is used.

If uplo = 'U' or 'u', then the upper triangle of the matrix A is used.

If uplo = 'L' or 'l', then the low triangle of the matrix A is used.

transa

CHARACTER*1. Specifies the operation.

If transa = 'N' or 'n', then the matrix-vector product is computed as y := A*x

If transa = 'T' or 't' or 'C' or 'c', then the matrix-vector product is computed as y := A^T*x.

diag

CHARACTER*1. Specifies whether A is a unit triangular matrix.

If diag = 'U' or 'u', then A is a unit triangular.

If diag = 'N' or 'n', then A is not a unit triangular.

m

INTEGER. Number of block rows of the matrix A.

lb

INTEGER. Size of the block in the matrix A.

a

REAL for mkl_sbsrtrsv.

DOUBLE PRECISION for mkl_dbsrtrsv.

COMPLEX for mkl_cbsrtrsv.

DOUBLE COMPLEX for mkl_zbsrtrsv.

Array containing elements of non-zero blocks of the matrix A. Its length is equal to the number of non-zero blocks in the matrix A multiplied by lb*lb. Refer to values array description in BSR Format for more details.

NOTE:

The non-zero elements of the given row of the matrix must be stored in the same order as they appear in the row (from left to right).

No diagonal element can be omitted from a sparse storage if the solver is called with the non-unit indicator.

ia

INTEGER. Array of length (m + 1), containing indices of block in the array a, such that ia(I) is the index in the array a of the first non-zero element from the row I. The value of the last element ia(m + 1) is equal to the number of non-zero blocks plus one. Refer to rowIndex array description in BSR Format for more details.

ja

INTEGER.

Array containing the column indices for each non-zero block in the matrix A.

Its length is equal to the number of non-zero blocks of the matrix A. Refer to columns array description in BSR Format for more details.

x

REAL for mkl_sbsrtrsv.

DOUBLE PRECISION for mkl_dbsrtrsv.

COMPLEX for mkl_cbsrtrsv.

DOUBLE COMPLEX for mkl_zbsrtrsv.

Array, size (m*lb).

On entry, the array x must contain the vector x.

Output Parameters

y

REAL for mkl_sbsrtrsv.

DOUBLE PRECISION for mkl_dbsrtrsv.

COMPLEX for mkl_cbsrtrsv.

DOUBLE COMPLEX for mkl_zbsrtrsv.

Array, size at least (m*lb).

On exit, the array y must contain the vector y.

Interfaces

FORTRAN 77:

SUBROUTINE mkl_sbsrtrsv(uplo, transa, diag, m, lb, a, ia, ja, x, y)

   CHARACTER*1  uplo, transa, diag

   INTEGER      m, lb

   INTEGER      ia(*), ja(*)

   REAL          a(*), x(*), y(*)

SUBROUTINE mkl_dbsrtrsv(uplo, transa, diag, m, lb, a, ia, ja, x, y)

   CHARACTER*1  uplo, transa, diag

   INTEGER      m, lb

   INTEGER      ia(*), ja(*)

   DOUBLE PRECISION       a(*), x(*), y(*)

SUBROUTINE mkl_cbsrtrsv(uplo, transa, diag, m, lb, a, ia, ja, x, y)

   CHARACTER*1  uplo, transa, diag

   INTEGER      m, lb

   INTEGER      ia(*), ja(*)

   COMPLEX       a(*), x(*), y(*)

SUBROUTINE mkl_zbsrtrsv(uplo, transa, diag, m, lb, a, ia, ja, x, y)

   CHARACTER*1  uplo, transa, diag

   INTEGER      m, lb

   INTEGER      ia(*), ja(*)

   DOUBLE COMPLEX       a(*), x(*), y(*)

Parent topic: Sparse BLAS Level 2 and Level 3 Routines.

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

mkl_?bsrtrsv

FORTRAN 77: