NAG CL Interface
f16pbc (dgbmv)

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

1: $\mathbf{order}$ – Nag_OrderType Input

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 3.1.3 in the Introduction to the NAG Library CL Interface for a more detailed explanation of the use of this argument.

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

2: $\mathbf{trans}$ – Nag_TransType Input

On entry: specifies the operation to be performed.

$\mathbf{trans}=\mathrm{Nag\_NoTrans}$

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

$\mathbf{trans}=\mathrm{Nag\_Trans}$ or $\mathrm{Nag\_ConjTrans}$

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

Constraint: $\mathbf{trans}=\mathrm{Nag\_NoTrans}$, $\mathrm{Nag\_Trans}$ or $\mathrm{Nag\_ConjTrans}$.

3: $\mathbf{m}$ – Integer Input

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

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

4: $\mathbf{n}$ – Integer Input

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

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

5: $\mathbf{kl}$ – Integer Input

On entry: $k_l$, the number of subdiagonals within the band of $A$.

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

6: $\mathbf{ku}$ – Integer Input

On entry: $k_u$, the number of superdiagonals within the band of $A$.

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

7: $\mathbf{alpha}$ – double Input

On entry: the scalar $\alpha$.

8: $\mathbf{ab}\left[\mathit{dim}\right]$ – const double Input

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

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

On entry: the $m\times n$ band matrix $A$.

This is stored as a notional two-dimensional array with row elements or column elements stored contiguously. The storage of elements $A_{ij}$, for row $i=1,\dots ,m$ and column $j=\max (1,i-k_l),\dots ,\min (n,i+k_u)$, depends on the order argument as follows:

• if $\mathbf{order}=\mathrm{Nag\_ColMajor}$, $A_{ij}$ is stored as $\mathbf{ab}\left[(j-1)\times \mathbf{pdab}+\mathbf{ku}+i-j\right]$;
• if $\mathbf{order}=\mathrm{Nag\_RowMajor}$, $A_{ij}$ is stored as $\mathbf{ab}\left[(i-1)\times \mathbf{pdab}+\mathbf{kl}+j-i\right]$.

9: $\mathbf{pdab}$ – Integer Input

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

Constraint: $\mathbf{pdab}\ge \mathbf{kl}+\mathbf{ku}+1$.

10: $\mathbf{x}\left[\mathit{dim}\right]$ – const double Input

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

• $\max (1,1+(\mathbf{n}-1)\left|\mathbf{incx}\right|)$ when $\mathbf{trans}=\mathrm{Nag\_NoTrans}$;
• $\max (1,1+(\mathbf{m}-1)\left|\mathbf{incx}\right|)$ when $\mathbf{trans}=\mathrm{Nag\_Trans}$ or $\mathrm{Nag\_ConjTrans}$.

On entry: the vector $x$.

If $\mathbf{trans}=\mathrm{Nag\_NoTrans}$, then $x$ is an $n$-element vector.

• If $\mathbf{incx}>0$, $x_{\mathit{i}}$ must be stored in $\mathbf{x}\left[(\mathit{i}-1)\times \mathbf{incx}\right]$, for $\mathit{i}=1,2,\dots ,\mathbf{n}$.
• If $\mathbf{incx}<0$, $x_{\mathit{i}}$ must be stored in $\mathbf{x}\left[(\mathbf{n}-\mathit{i})\times \left|\mathbf{incx}\right|\right]$, for $\mathit{i}=1,2,\dots ,\mathbf{n}$.
• Intermediate elements of x are not referenced. If $\mathbf{n}=0$, x is not referenced and may be NULL.

Otherwise, $x$ is an $m$-element vector.

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

11: $\mathbf{incx}$ – Integer Input

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

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

12: $\mathbf{beta}$ – double Input

On entry: the scalar $\beta$.

13: $\mathbf{y}\left[\mathit{dim}\right]$ – double Input/Output

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

• $\max (1,1+(\mathbf{m}-1)\left|\mathbf{incy}\right|)$ when $\mathbf{trans}=\mathrm{Nag\_NoTrans}$;
• $\max (1,1+(\mathbf{n}-1)\left|\mathbf{incy}\right|)$ when $\mathbf{trans}=\mathrm{Nag\_Trans}$ or $\mathrm{Nag\_ConjTrans}$.

On entry: the vector $y$. See x for details of storage.

If $\mathbf{beta}=0$, y need not be set.

On exit: the updated vector $y$.

14: $\mathbf{incy}$ – Integer Input

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

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

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

The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).

6 Error Indicators and Warnings

NE_ALLOC_FAIL

Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface 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, $\mathbf{kl}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{kl}\ge 0$.

On entry, $\mathbf{ku}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{ku}\ge 0$.

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_3

On entry, $\mathbf{pdab}=⟨\mathit{\text{value}}⟩$, $\mathbf{kl}=⟨\mathit{\text{value}}⟩$, $\mathbf{ku}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{pdab}\ge \mathbf{kl}+\mathbf{ku}+1$.

NE_NO_LICENCE

Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library CL Interface for further information.

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results