Parameters

trans

Type: System..::..String

On entry: specifies the operation to be performed.

$\mathbf{trans}=\text{"N"}$

$y\leftarrow \alpha Ax+\beta y$.

$\mathbf{trans}=\text{"T"}$ or $\text{"C"}$

$y\leftarrow \alpha A^{\mathrm{T}}x+\beta y$.

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: $\mathrm{dim1}\ge \max \left(1,\mathbf{m}\right)$

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 $\max \left(1,1+\left(\mathbf{n}-1\right)\times \left|\mathbf{incx}\right|\right)$ if $\mathbf{trans}=\text{"N"}$ and at least $\max \left(1,1+\left(\mathbf{m}-1\right)\times \left|\mathbf{incx}\right|\right)$ 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 $\mathbf{x}\left[1+\left(\mathit{i}-1\right)\times \mathbf{incx}-1\right]$, for $\mathit{i}=1,2,\dots ,\mathbf{n}$;
• if $\mathbf{incx}<0$, $x_{\mathit{i}}$ must be stored in $\mathbf{x}\left[1-\left(\mathbf{n}-\mathit{i}\right)\times \mathbf{incx}-1\right]$, 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 $\mathbf{x}\left[1+\left(\mathit{i}-1\right)\times \mathbf{incx}-1\right]$, for $\mathit{i}=1,2,\dots ,\mathbf{m}$;
• if $\mathbf{incx}<0$, $x_{\mathit{i}}$ must be stored in $\mathbf{x}\left[1-\left(\mathbf{m}-\mathit{i}\right)\times \mathbf{incx}-1\right]$, 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 $\max \left(1,1+\left(\mathbf{m}-1\right)\times \left|\mathbf{incy}\right|\right)$ if $\mathbf{trans}=\text{"N"}$ and at least $\max \left(1,1+\left(\mathbf{n}-1\right)\times \left|\mathbf{incy}\right|\right)$ 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 $\mathbf{y}\left[1+\left(\mathit{i}-1\right)\times \mathbf{incy}-1\right]$, for $\mathit{i}=1,2,\dots ,\mathbf{m}$;
• if $\mathbf{incy}<0$, $y_{\mathit{i}}$ must be stored in $\mathbf{y}\left[1-\left(\mathbf{m}-\mathit{i}\right)\times \mathbf{incy}-1\right]$, 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 $\mathbf{y}\left[1+\left(\mathit{i}-1\right)\times \mathbf{incy}-1\right]$, for $\mathit{i}=1,2,\dots ,\mathbf{n}$;
• if $\mathbf{incy}<0$, $y_{\mathit{i}}$ must be stored in $\mathbf{y}\left[1-\left(\mathbf{n}-\mathit{i}\right)\times \mathbf{incy}-1\right]$, 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]).