naginterfaces.library.sparse.real_​symm_​matvec

naginterfaces.library.sparse.real_symm_matvec(a, irow, icol, x, check='N')

real_symm_matvec computes a matrix-vector product involving a real sparse symmetric matrix stored in symmetric coordinate storage format.

For full information please refer to the NAG Library document for f11xe

https://support.nag.com/numeric/nl/nagdoc_30.3/flhtml/f11/f11xef.html

Parameters

afloat, array-like, shape $\left(\text{nnz}\right)$

The nonzero elements in the lower triangular part of the matrix $A$, ordered by increasing row index, and by increasing column index within each row. Multiple entries for the same row and column indices are not permitted. The function real_symm_sort() may be used to order the elements in this way.

irowint, array-like, shape $\left(\text{nnz}\right)$

The row indices of the nonzero elements supplied in array $a$.

icolint, array-like, shape $\left(\text{nnz}\right)$

The column indices of the nonzero elements supplied in array $a$.

xfloat, array-like, shape $\left(n\right)$

The vector $x$.

checkstr, length 1, optional

Specifies whether or not the SCS representation of the matrix $A$, values of $\text{n}$, $\text{nnz}$, $irow$ and $icol$ should be checked.

$check=\text{'C'}$

Checks are carried out on the values of $\text{n}$, $\text{nnz}$, $irow$ and $icol$.

$check=\text{'N'}$

None of these checks are carried out.

See also Further Comments.

Returns

yfloat, ndarray, shape $\left(n\right)$

The vector $y$.

Raises

NagValueError

(errno $1$)

On entry, $check=⟨value⟩$.

Constraint: $check=\text{'C'}$ or $\text{'N'}$.

(errno $2$)

On entry, $\text{nnz}=⟨value⟩$ and $n=⟨value⟩$.

Constraint: $\text{nnz}\le n\times (n+1)/2$.

(errno $2$)

On entry, $\text{nnz}=⟨value⟩$.

Constraint: $\text{nnz}\ge 1$.

(errno $2$)

On entry, $n=⟨value⟩$.

Constraint: $n\ge 1$.

(errno $3$)

On entry, the location ($irow[\text{I}-1],icol[\text{I}-1]$) is a duplicate: $\text{I}=⟨value⟩$.

(errno $3$)

On entry, $a[i-1]$ is out of order: $i=⟨value⟩$.

(errno $3$)

On entry, $\text{I}=⟨value⟩$, $icol[\text{I}-1]=⟨value⟩$ and $irow[\text{I}-1]=⟨value⟩$.

Constraint: $icol[\text{I}-1]\ge 1$ and $icol[\text{I}-1]\le irow[\text{I}-1]$.

(errno $3$)

On entry, $i=⟨value⟩$, $irow[i-1]=⟨value⟩$ and $n=⟨value⟩$.

Constraint: $irow[i-1]\ge 1$ and $irow[i-1]\le n$.

Notes

real_symm_matvec computes the matrix-vector product

$$y=Ax$$

where $A$ is an $n\times n$ symmetric sparse matrix, of arbitrary sparsity pattern, stored in symmetric coordinate storage (SCS) format (see the F11 Introduction). The array $a$ stores all nonzero elements in the lower triangular part of $A$, while arrays $irow$ and $icol$ store the corresponding row and column indices respectively.

It is envisaged that a common use of real_symm_matvec will be to compute the matrix-vector product required in the application of real_symm_basic_solver() to sparse symmetric linear systems. An illustration of this usage appears in real_symm_precon_ssor_solve().