f06pa computes the matrix-vector product for a real general matrix or its transpose.

# Syntax

C#
```public static void f06pa(
string trans,
int m,
int n,
double alpha,
double[,] a,
double[] x,
int incx,
double beta,
double[] y,
int incy,
out int ifail
)```
Visual Basic
```Public Shared Sub f06pa ( _
trans As String, _
m As Integer, _
n As Integer, _
alpha As Double, _
a As Double(,), _
x As Double(), _
incx As Integer, _
beta As Double, _
y As Double(), _
incy As Integer, _
<OutAttribute> ByRef ifail As Integer _
)```
Visual C++
```public:
static void f06pa(
String^ trans,
int m,
int n,
double alpha,
array<double,2>^ a,
array<double>^ x,
int incx,
double beta,
array<double>^ y,
int incy,
[OutAttribute] int% ifail
)```
F#
```static member f06pa :
trans : string *
m : int *
n : int *
alpha : float *
a : float[,] *
x : float[] *
incx : int *
beta : float *
y : float[] *
incy : int *
ifail : int byref -> unit
```

#### Parameters

trans
Type: System..::..String
On entry: specifies the operation to be performed.
${\mathbf{trans}}=\text{"N"}$
$y←\alpha Ax+\beta y$.
${\mathbf{trans}}=\text{"T"}$ or $\text{"C"}$
$y←\alpha {A}^{\mathrm{T}}x+\beta y$.
Constraint: ${\mathbf{trans}}=\text{"N"}$, $\text{"T"}$ or $\text{"C"}$.
m
Type: System..::..Int32
On entry: $m$, the number of rows of the matrix $A$.
Constraint: ${\mathbf{m}}\ge 0$.
n
Type: System..::..Int32
On entry: $n$, the number of columns of the matrix $A$.
Constraint: ${\mathbf{n}}\ge 0$.
alpha
Type: System..::..Double
On entry: the scalar $\alpha$.
a
Type: array<System..::..Double,2>[,](,)[,][,]
An array of size [dim1, dim2]
Note: dim1 must satisfy the constraint: $\mathrm{dim1}\ge \mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{m}}\right)$
Note: the second dimension of the array a must be at least ${\mathbf{n}}$.
On entry: the $m$ by $n$ matrix $A$.
x
Type: array<System..::..Double>[]()[][]
An array of size [dim1]
Note: the dimension of the array x must be at least $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,1+\left({\mathbf{n}}-1\right)×\left|{\mathbf{incx}}\right|\right)$ if ${\mathbf{trans}}=\text{"N"}$ and at least $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,1+\left({\mathbf{m}}-1\right)×\left|{\mathbf{incx}}\right|\right)$ if ${\mathbf{trans}}=\text{"T"}$ or $\text{"C"}$.
On entry: the vector $x$.
If ${\mathbf{trans}}=\text{"N"}$,
• if ${\mathbf{incx}}>0$, ${x}_{\mathit{i}}$ must be stored in ${\mathbf{x}}\left[1+\left(\mathit{i}-1\right)×{\mathbf{incx}}-1\right]$, for $\mathit{i}=1,2,\dots ,{\mathbf{n}}$;
• if ${\mathbf{incx}}<0$, ${x}_{\mathit{i}}$ must be stored in ${\mathbf{x}}\left[1-\left({\mathbf{n}}-\mathit{i}\right)×{\mathbf{incx}}-1\right]$, for $\mathit{i}=1,2,\dots ,{\mathbf{n}}$.
If ${\mathbf{trans}}=\text{"T"}$ or $\text{"C"}$,
• if ${\mathbf{incx}}>0$, ${x}_{\mathit{i}}$ must be stored in ${\mathbf{x}}\left[1+\left(\mathit{i}-1\right)×{\mathbf{incx}}-1\right]$, for $\mathit{i}=1,2,\dots ,{\mathbf{m}}$;
• if ${\mathbf{incx}}<0$, ${x}_{\mathit{i}}$ must be stored in ${\mathbf{x}}\left[1-\left({\mathbf{m}}-\mathit{i}\right)×{\mathbf{incx}}-1\right]$, for $\mathit{i}=1,2,\dots ,{\mathbf{m}}$.
incx
Type: System..::..Int32
On entry: the increment in the subscripts of x between successive elements of $x$.
Constraint: ${\mathbf{incx}}\ne 0$.
beta
Type: System..::..Double
On entry: the scalar $\beta$.
y
Type: array<System..::..Double>[]()[][]
An array of size [dim1]
Note: the dimension of the array y must be at least $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,1+\left({\mathbf{m}}-1\right)×\left|{\mathbf{incy}}\right|\right)$ if ${\mathbf{trans}}=\text{"N"}$ and at least $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,1+\left({\mathbf{n}}-1\right)×\left|{\mathbf{incy}}\right|\right)$ if ${\mathbf{trans}}=\text{"T"}$ or $\text{"C"}$.
On entry: the vector $y$, if ${\mathbf{beta}}=0.0$, y need not be set.
If ${\mathbf{trans}}=\text{"N"}$,
• if ${\mathbf{incy}}>0$, ${y}_{\mathit{i}}$ must be stored in ${\mathbf{y}}\left[1+\left(\mathit{i}-1\right)×{\mathbf{incy}}-1\right]$, for $\mathit{i}=1,2,\dots ,{\mathbf{m}}$;
• if ${\mathbf{incy}}<0$, ${y}_{\mathit{i}}$ must be stored in ${\mathbf{y}}\left[1-\left({\mathbf{m}}-\mathit{i}\right)×{\mathbf{incy}}-1\right]$, for $\mathit{i}=1,2,\dots ,{\mathbf{m}}$.
If ${\mathbf{trans}}=\text{"T"}$ or $\text{"C"}$,
• if ${\mathbf{incy}}>0$, ${y}_{\mathit{i}}$ must be stored in ${\mathbf{y}}\left[1+\left(\mathit{i}-1\right)×{\mathbf{incy}}-1\right]$, for $\mathit{i}=1,2,\dots ,{\mathbf{n}}$;
• if ${\mathbf{incy}}<0$, ${y}_{\mathit{i}}$ must be stored in ${\mathbf{y}}\left[1-\left({\mathbf{n}}-\mathit{i}\right)×{\mathbf{incy}}-1\right]$, for $\mathit{i}=1,2,\dots ,{\mathbf{n}}$.
On exit: the updated vector $y$ stored in the array elements used to supply the original vector $y$.
incy
Type: System..::..Int32
On entry: the increment in the subscripts of y between successive elements of $y$.
Constraint: ${\mathbf{incy}}\ne 0$.
ifail
Type: System..::..Int32%
On exit: $\mathbf{ifail}=0$ unless the method detects an error (see [Error Indicators and Warnings]).

# Description

f06pa performs one of the matrix-vector operations
 $y←αAx+βy, or y←αATx+βy,$
where $A$ is an $m$ by $n$ real matrix, $x$ and $y$ are real vectors, and $\alpha$ and $\beta$ are real scalars.
If $m=0$ or $n=0$, no operation is performed.

None.

# Error Indicators and Warnings

${\mathbf{ifail}}=-9000$
An error occured, see message report.
${\mathbf{ifail}}=-6000$
Invalid Parameters $〈\mathit{\text{value}}〉$
${\mathbf{ifail}}=-4000$
Invalid dimension for array $〈\mathit{\text{value}}〉$
${\mathbf{ifail}}=-8000$
Negative dimension for array $〈\mathit{\text{value}}〉$
${\mathbf{ifail}}=-6000$
Invalid Parameters $〈\mathit{\text{value}}〉$
${\mathbf{ifail}}=-6000$
Invalid Parameters $〈\mathit{\text{value}}〉$

Not applicable.

None.