# mkl_dcsrtrsv

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

## Syntax

Fortran:

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

C:

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

## Description

The mkl_dcsrtrsv routine solves a system of linear equations with matrix-vector operations for a sparse matrix stored in the CSR format (3 array variation):
`A*y = x`

or
`A'*y = 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 whether 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 system of linear equations.

  If `transa = 'N'` or 'n', then `A*y = x`

  If `transa = 'T'` or 't' or 'C' or 'c', then `A'*y = x`,

diag

  CHARACTER*1. Specifies whether A is unit triangular.

  If `diag = 'U'` or 'u', then A is aunit triangular.

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

m

  INTEGER. Number of rows of the matrix A.

a

  REAL*8. Array containing non-zero elements of the matrix A. Its length is equal to the number of non-zero elements in the matrix A. Refer to values array description in Sparse Matrix Storage Formats for more details.

ia

  INTEGER. Array of length `m + 1`, containing indices of elements 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-zeros plus one. Refer to rowIndex array description in Sparse Matrix Storage Formats for more details.

ja

  REAL*8. Array containing the column indices for each non-zero element of the matrix A.

  Its length is equal to the length of the array a. Refer to columns array description in Sparse Matrix Storage Formats for more details.

  ### Note

  Column indices must be sorted in increasing order for each row.

x

  REAL*8.

  Array, DIMENSION is m.

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

## Output Parameters

y

  REAL*8.

  Array, DIMENSION at least m.

  Contains the vector y.

## Interfaces

## FORTRAN 77:

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

CHARACTER*1 uplo, transa, diag

INTEGER m

INTEGER ia(*), ja(*)

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

## C:

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

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

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