naginterfaces.library.sparse.complex_​gen_​matvec

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

complex_gen_matvec computes a matrix-vector or conjugate transposed matrix-vector product involving a complex sparse non-Hermitian matrix stored in coordinate storage format.

For full information please refer to the NAG Library document for f11xn

https://support.nag.com/numeric/nl/nagdoc_30.3/flhtml/f11/f11xnf.html

Parameters

transstr, length 1

Specifies whether or not the matrix $A$ is conjugate transposed.

$trans=\text{'N'}$

$y=Ax$ is computed.

$trans=\text{'T'}$

$y=A^{H}x$ is computed.

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

The nonzero elements in 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 complex_gen_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 $a$.

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

The vector $x$.

checkstr, length 1, optional

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

$check=\text{'C'}$

Checks are carried 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

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

The vector $y$.

Raises

NagValueError

(errno $1$)

On entry, $trans=⟨value⟩$.

Constraint: $trans=\text{'N'}$ or $\text{'T'}$.

(errno $1$)

On entry, $check=⟨value⟩$.

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

(errno $2$)

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

Constraint: $\text{nnz}\le n^2$.

(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, $i=⟨value⟩$, $icol[i-1]=⟨value⟩$ and $n=⟨value⟩$.

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

(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

complex_gen_matvec computes either the matrix-vector product $y=Ax$, or the conjugate transposed matrix-vector product $y=A^{H}x$, according to the value of the argument $trans$, where $A$ is a complex $n\times n$ sparse non-Hermitian matrix, of arbitrary sparsity pattern. The matrix $A$ is stored in coordinate storage (CS) format (see the F11 Introduction). The array $a$ stores all the nonzero elements of $A$, while arrays $irow$ and $icol$ store the corresponding row and column indices respectively.

It is envisaged that a common use of complex_gen_matvec will be to compute the matrix-vector product required in the application of complex_gen_basic_solver() to sparse complex linear systems.

See also

naginterfaces.library.examples.sparseig.feast_poly_gen_solve_ex.main()