# mkl_ddiatrsv

Triangular solvers with simplified interface for a sparse matrix in the diagonal format with one-based indexing.

## Syntax

Fortran:

call mkl_ddiatrsv(uplo, transa, diag, m, val, lval, idiag, ndiag, x, y)

C:

mkl_ddiatrsv(&uplo, &transa, &diag, &m, val, &lval, idiag, &ndiag, x, y);

## Description

The mkl_ddiatrsv routine solves a system of linear equations with matrix-vector operations for a sparse matrix stored in the diagonal format:
`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 unit triangular.

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

m

  INTEGER. Number of rows of the matrix A.

val

  REAL*8. Two-dimensional array of size lval by ndiag, contains non-zero diagonals of the matrix A. Refer to values array description in Diagonal Storage Schemefor more details.

lval

  INTEGER. Leading dimension of val, `lval≥m`. Refer to lval description in Diagonal Storage Scheme for more details.

idiag

  INTEGER. Array of length ndiag, contains the distances between main diagonal and each non-zero diagonals in the matrix A.

  ### Note

  All elements of this array must be sorted in increasing order.

Refer to distance array description in Diagonal Storage Scheme for more details.

ndiag

  INTEGER. Specifies the number of non-zero diagonals of the matrix A.

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_ddiatrsv(uplo, transa, diag, m, val, lval, idiag, ndiag, x, y)

CHARACTER*1 uplo, transa, diag

INTEGER m, lval, ndiag

INTEGER indiag(*)

REAL*8 val(lval,*), x(*), y(*)

## C:

void mkl_ddiatrsv(char *uplo, char *transa, char *diag, int *m, double

*val, int *lval, int *idiag, int *ndiag, double *x, double *y);

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