# mkl_ddiasv

Solves a system of linear equations for a sparse matrix in the diagonal format with one-based indexing .

## Syntax

Fortran:

call mkl_ddiasv(transa, m, alpha, matdescra, val, lval, idiag, ndiag, x, y)

C:

mkl_ddiasv(&transa, &m, &alpha, matdescra, val, &lval, idiag, &ndiag, x, y);

## Description

The mkl_ddiasv routine solves a system of linear equations with matrix-vector operations for a sparse matrix stored in the diagonal format:
`y := alpha*inv(A)*x`

or
`y := alpha*inv(A')* x,`

where:

alpha is scalar, 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.

transa

  CHARACTER*1. Specifies the system of linear equations.

  If `transa = 'N'` or 'n', then `y := alpha*inv(A)*x`

  If `transa = 'T'` or 't' or 'C' or 'c', then `y := alpha*inv(A')*x`,

m

  INTEGER. Number of rows of the matrix A.

alpha

  REAL*8. Specifies the scalar alpha.

matdescra

  CHARACTER. Array of six elements, specifies properties of the matrix used for operation. Only first four array elements are used, their possible values are given in the “Possible Values of the Parameter matdescra (descra)”.

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 Scheme for 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 at least m.

  On entry, the array x must contain the vector x. The elements are accessed with unit increment.

y

  REAL*8.

  Array, DIMENSION at least m.

  On entry, the array y must contain the vector y. The elements are accessed with unit increment.

## Output Parameters

y

  Contains solution vector x.

## Interfaces

## FORTRAN 77:

SUBROUTINE mkl_ddiasv(transa, m, alpha, matdescra, val, lval, idiag, ndiag, x, y)

CHARACTER*1 transa

CHARACTER matdescra(*)

INTEGER m, lval, ndiag

INTEGER indiag(*)

REAL*8 alpha

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

## C:

void mkl_ddiasv(char *transa, int *m, double *alpha, char *matdescra,

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

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