naginterfaces.library.matop.real_​addsub

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

real_addsub adds two float matrices, each one optionally transposed and multiplied by a scalar.

For full information please refer to the NAG Library document for f01ct

https://support.nag.com/numeric/nl/nagdoc_30.2/flhtml/f01/f01ctf.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 $transb=\text{'T'}$ or $\text{'C'}$

The matrix will be transposed.

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

The matrix will be transposed.

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 $C$.

alphafloat

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

afloat, 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 $transa=\text{'N'}$: $n$; otherwise: $m$.

If $\alpha =0.0$, the elements of array $a$ need not be assigned. If $\alpha \ne 0.0$, then if $transa=\text{'N'}$, the leading $m\times n$ part of $a$ must contain the matrix $A$, otherwise the leading $n\times m$ part of $a$ must contain the matrix $A$.

betafloat

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

bfloat, 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 $transb=\text{'N'}$: $n$; otherwise: $m$.

If $\beta =0.0$, the elements of array $b$ need not be assigned. If $\beta \ne 0.0$, then if $transa=\text{'N'}$, the leading $m\times n$ part of $b$ must contain the matrix $B$, otherwise the leading $n\times m$ part of $b$ must contain the matrix $B$.

Returns

cfloat, 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.

real_addsub performs one of the operations

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

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

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

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

where $A$, $B$ and $C$ are matrices, and $\alpha$ and $\beta$ are scalars. 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.