# mkl_dbsrtrsv

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

## Syntax

Fortran:

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

C:

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

## Description

The mkl_dbsrtrsv 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`

or
`y := A'*x,`

where:

x and y are vectors,

A is a sparse upper or lower triangular matrix with unit or non-unit main diagonal, A' 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'*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*8. 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.

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

  REAL*8. 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*8.

  Array, DIMENSION `(m*lb)`.

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

## Output Parameters

y

  REAL*8.

  Array, DIMENSION at least `(m*lb)`.

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

## Interfaces

## FORTRAN 77:

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

CHARACTER*1 uplo, transa, diag

INTEGER m, lb

INTEGER ia(*), ja(*)

REAL*8 a(*), x(*), y(*)

## C:

void mkl_dbsrtrsv(char *uplo, char *transa, char *diag, int *m,

int *lb, double *a, int *ia, int *ja, double *x, double *y);

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