NAG Library Function Document

nag_dger (f16pmc)

1  Purpose

2  Specification

3  Description

4  References

5  Arguments

1:    $\mathbf{order}$ – Nag_OrderTypeInput

On entry: the order argument specifies the two-dimensional storage scheme being used, i.e., row-major ordering or column-major ordering. C language defined storage is specified by $\mathbf{order}=\mathrm{Nag\_RowMajor}$. See Section 2.3.1.3 in How to Use the NAG Library and its Documentation for a more detailed explanation of the use of this argument.

Constraint: $\mathbf{order}=\mathrm{Nag\_RowMajor}$ or $\mathrm{Nag\_ColMajor}$.

2:    $\mathbf{conj}$ – Nag_ConjTypeInput

On entry: the argument conj is not referenced if $x$ and $y$ are real vectors. It is suggested that you set $\mathbf{conj}=\mathrm{Nag\_NoConj}$ where the elements $y_i$ are not conjugated.

Constraint: $\mathbf{conj}=\mathrm{Nag\_NoConj}$.

3:    $\mathbf{m}$ – IntegerInput

On entry: $m$, the number of rows of the matrix $A$.

Constraint: $\mathbf{m}\ge 0$.

4:    $\mathbf{n}$ – IntegerInput

On entry: $n$, the number of columns of the matrix $A$.

Constraint: $\mathbf{n}\ge 0$.

5:    $\mathbf{alpha}$ – doubleInput

On entry: the scalar $\alpha$.

6:    $\mathbf{x}\left[\mathit{dim}\right]$ – const doubleInput

Note: the dimension, dim, of the array x must be at least $\max \left(1,1+\left(\mathbf{n}-1\right)\left|\mathbf{incx}\right|\right)$.

On entry: the $n$-element vector $x$.

If $\mathbf{incx}>0$, $x_{\mathit{i}}$ must be stored in $\mathbf{x}\left[\left(\mathit{i}-1\right)\times \mathbf{incx}\right]$, for $\mathit{i}=1,2,\dots ,\mathbf{m}$.

If $\mathbf{incx}<0$, $x_{\mathit{i}}$ must be stored in $\mathbf{x}\left[\left(\mathbf{m}-\mathit{i}\right)\times \left|\mathbf{incx}\right|\right]$, for $\mathit{i}=1,2,\dots ,\mathbf{m}$.

Intermediate elements of x are not referenced. If $\mathbf{m}=0$, x is not referenced and may be NULL.

7:    $\mathbf{incx}$ – IntegerInput

On entry: the increment in the subscripts of x between successive elements of $x$.

Constraint: $\mathbf{incx}\ne 0$.

8:    $\mathbf{y}\left[\mathit{dim}\right]$ – const doubleInput

Note: the dimension, dim, of the array y must be at least $\max \left(1,1+\left(\mathbf{n}-1\right)\left|\mathbf{incy}\right|\right)$.

On entry: the $n$-element vector $y$.

If $\mathbf{incy}>0$, $y_{\mathit{i}}$ must be stored in $\mathbf{y}\left[\left(\mathit{i}-1\right)\times \mathbf{incy}\right]$, for $\mathit{i}=1,2,\dots ,\mathbf{n}$.

If $\mathbf{incy}<0$, $y_{\mathit{i}}$ must be stored in $\mathbf{y}\left[\left(\mathbf{n}-\mathit{i}\right)\times \left|\mathbf{incy}\right|\right]$, for $\mathit{i}=1,2,\dots ,\mathbf{n}$.

Intermediate elements of y are not referenced. If $\alpha =0.0$ or $\mathbf{n}=0$, y is not referenced and may be NULL.

9:    $\mathbf{incy}$ – IntegerInput

On entry: the increment in the subscripts of y between successive elements of $y$.

Constraint: $\mathbf{incy}\ne 0$.

10:  $\mathbf{beta}$ – doubleInput

On entry: the scalar $\beta$.

11:  $\mathbf{a}\left[\mathit{dim}\right]$ – doubleInput/Output

Note: the dimension, dim, of the array a must be at least

• $\max \left(1,\mathbf{pda}\times \mathbf{n}\right)$ when $\mathbf{order}=\mathrm{Nag\_ColMajor}$;
• $\max \left(1,\mathbf{m}\times \mathbf{pda}\right)$ when $\mathbf{order}=\mathrm{Nag\_RowMajor}$.

If $\mathbf{order}=\mathrm{Nag\_ColMajor}$, $A_{ij}$ is stored in $\mathbf{a}\left[\left(j-1\right)\times \mathbf{pda}+i-1\right]$.

If $\mathbf{order}=\mathrm{Nag\_RowMajor}$, $A_{ij}$ is stored in $\mathbf{a}\left[\left(i-1\right)\times \mathbf{pda}+j-1\right]$.

On entry: the $m$ by $n$ matrix $A$.

On exit: the updated matrix $A$.

12:  $\mathbf{pda}$ – IntegerInput

On entry: the stride separating row or column elements (depending on the value of order) in the array a.

Constraints:

• if $\mathbf{order}=\mathrm{Nag\_ColMajor}$, $\mathbf{pda}\ge \max \left(1,\mathbf{m}\right)$;
• if $\mathbf{order}=\mathrm{Nag\_RowMajor}$, $\mathbf{pda}\ge \mathbf{n}$.

13:  $\mathbf{fail}$ – NagError *Input/Output

The NAG error argument (see Section 2.7 in How to Use the NAG Library and its Documentation).

6  Error Indicators and Warnings

NE_ALLOC_FAIL

Dynamic memory allocation failed.
See Section 2.3.1.2 in How to Use the NAG Library and its Documentation for further information.

NE_BAD_PARAM

On entry, argument $〈\mathit{\text{value}}〉$ had an illegal value.

NE_INT

On entry, $\mathbf{incx}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{incx}\ne 0$.

On entry, $\mathbf{incy}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{incy}\ne 0$.

On entry, $\mathbf{m}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{m}\ge 0$.

On entry, $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{n}\ge 0$.

NE_INT_2

On entry, $\mathbf{pda}=〈\mathit{\text{value}}〉$, $\mathbf{m}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{pda}\ge \max \left(1,\mathbf{m}\right)$.

On entry, $\mathbf{pda}=〈\mathit{\text{value}}〉$ and $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{pda}\ge \mathbf{n}$.

NE_INTERNAL_ERROR

An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.

An unexpected error has been triggered by this function. Please contact NAG.
See Section 2.7.6 in How to Use the NAG Library and its Documentation for further information.

NE_NO_LICENCE

Your licence key may have expired or may not have been installed correctly.
See Section 2.7.5 in How to Use the NAG Library and its Documentation for further information.

7  Accuracy

8  Parallelism and Performance

9  Further Comments

10  Example

10.1  Program Text

Program Text (f16pmce.c)

10.2  Program Data

Program Data (f16pmce.d)

10.3  Program Results

Program Results (f16pmce.r)