naginterfaces.library.matop.complex_​addsub

naginterfaces.library.matop.complex_addsub(transa, transb, m, n, alpha, a, beta, b)

complex_addsub adds two complex matrices, each one optionally transposed and multiplied by a scalar.

For full information please refer to the NAG Library document for f01cw

https://www.nag.com/numeric/nl/nagdoc_29.3/flhtml/f01/f01cwf.html

Parameters

transastr, length 1

$transa$ and $transb$ must specify whether or not the matrix $A$ and the matrix $B$, respectively, are to be transposed before addition.

$transa$ or $transb=\text{'N'}$

The matrix will not be transposed.

$transa$ or $transb=\text{'T'}$

The matrix will be transposed.

$transa$ or $transb=\text{'C'}$

The matrix will be transposed and conjugated.

transbstr, length 1

$transa$ and $transb$ must specify whether or not the matrix $A$ and the matrix $B$, respectively, are to be transposed before addition.

$transa$ or $transb=\text{'N'}$

The matrix will not be transposed.

$transa$ or $transb=\text{'T'}$

The matrix will be transposed.

$transa$ or $transb=\text{'C'}$

The matrix will be transposed and conjugated.

mint

$m$, the number of rows of the matrices $A$ and $B$ or their transposes. Also the number of rows of the matrix $C$.

nint

$n$, the number of columns of the matrices $A$ and $B$ or their transposes. Also the number of columns of the matrix $C$.

alphacomplex

The scalar $\alpha$, by which matrix $A$ is multiplied before addition.

acomplex, array-like, shape $(:,:)$

Note: the required extent for this argument in dimension 1 is determined as follows: if $transa=\text{'N'}$: $m$; otherwise: $n$.

Note: the required extent for this argument in dimension 2 is determined as follows: if $alpha\ne 0\text{and}transa=\text{'N'}$: $n$; if $alpha\ne 0\text{and}transa\text{in}(\text{'T'},\text{'C'})$: $m$; if $alpha=0$: $1$; otherwise: $0$.

The matrix $A$. If $\alpha =0$, the array $a$ is not referenced.

betacomplex

The scalar $\beta$, by which matrix $B$ is multiplied before addition.

bcomplex, array-like, shape $(:,:)$

Note: the required extent for this argument in dimension 1 is determined as follows: if $transb=\text{'N'}$: $m$; otherwise: $n$.

Note: the required extent for this argument in dimension 2 is determined as follows: if $beta\ne 0\text{and}transb=\text{'N'}$: $n$; if $beta\ne 0\text{and}transb\text{in}(\text{'T'},\text{'C'})$: $m$; if $beta=0$: $1$; otherwise: $0$.

The matrix $B$. If $\beta =0$, the array $b$ is not referenced.

Returns

ccomplex, ndarray, shape $(m,n)$

The elements of the $m\times n$ matrix $C$.

Raises

NagValueError

(errno $1$)

On entry, $transb=⟨value⟩$.

Constraint: $transb=\text{'N'}$, $\text{'T'}$ or $\text{'C'}$.

(errno $1$)

On entry, $transa=⟨value⟩$.

Constraint: $transa=\text{'N'}$, $\text{'T'}$ or $\text{'C'}$.

(errno $2$)

On entry, $m=⟨value⟩$ and $n=⟨value⟩$.

Constraint: $m\ge 0$ and $n\ge 0$.

(errno $3$)

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

Constraint: if $transa=⟨value⟩$, $\text{lda}\ge max(1,n)$.

(errno $3$)

On entry, $\text{lda}=⟨value⟩$ and $m=⟨value⟩$.

Constraint: if $transa=⟨value⟩$, $\text{lda}\ge max(1,m)$.

(errno $4$)

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

Constraint: if $transb=⟨value⟩$, $\text{ldb}\ge max(1,n)$.

(errno $4$)

On entry, $\text{ldb}=⟨value⟩$ and $m=⟨value⟩$.

Constraint: if $transb=⟨value⟩$, $\text{ldb}\ge max(1,m)$.

Notes

No equivalent traditional C interface for this routine exists in the NAG Library.

complex_addsub performs one of the operations

$C:=\alpha A+\beta B$,

$C:=\alpha A^T+\beta B$,

$C:=\alpha A^H+\beta B$,

$C:=\alpha A+\beta B^T$,

$C:=\alpha A^T+\beta B^T$,

$C:=\alpha A^H+\beta B^T$,

$C:=\alpha A+\beta B^H$,

$C:=\alpha A^T+\beta B^H$ or

$C:=\alpha A^H+\beta B^H$,

where $A$, $B$ and $C$ are matrices, $\alpha$ and $\beta$ are scalars, $T$ denotes transposition and $H$ denotes conjugate transposition. For efficiency, the function contains special code for the cases when one or both of $\alpha$, $\beta$ is equal to zero, unity or minus unity. The matrices, or their transposes, must be compatible for addition. $A$ and $B$ are either $m\times n$ or $n\times m$ matrices, depending on whether they are to be transposed before addition. $C$ is an $m\times n$ matrix.