NAG Library Function Document

nag_dtrsm (f16yjc)

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 3.3.1.3 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:    $\mathbf{side}$ – Nag_SideTypeInput

On entry: specifies whether $B$ is operated on from the left or the right.

$\mathbf{side}=\mathrm{Nag\_LeftSide}$

$B$ is pre-multiplied from the left.

$\mathbf{side}=\mathrm{Nag\_RightSide}$

$B$ is post-multiplied from the right.

Constraint: $\mathbf{side}=\mathrm{Nag\_LeftSide}$ or $\mathrm{Nag\_RightSide}$.

3:    $\mathbf{uplo}$ – Nag_UploTypeInput

On entry: specifies whether $A$ is upper or lower triangular.

$\mathbf{uplo}=\mathrm{Nag\_Upper}$

$A$ is upper triangular.

$\mathbf{uplo}=\mathrm{Nag\_Lower}$

$A$ is lower triangular.

Constraint: $\mathbf{uplo}=\mathrm{Nag\_Upper}$ or $\mathrm{Nag\_Lower}$.

4:    $\mathbf{trans}$ – Nag_TransTypeInput

On entry: specifies the operation to be performed.

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

$B\leftarrow \alpha A^{-\mathrm{T}}B$.

$\mathbf{trans}=\mathrm{Nag\_NoTrans}$ and $\mathbf{side}=\mathrm{Nag\_LeftSide}$

$B\leftarrow \alpha A^{-1}B$.

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

$B\leftarrow \alpha B{A}^{-\mathrm{T}}$.

$\mathbf{trans}=\mathrm{Nag\_NoTrans}$ and $\mathbf{side}=\mathrm{Nag\_RightSide}$

$B\leftarrow \alpha B{A}^{-1}$.

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

5:    $\mathbf{diag}$ – Nag_DiagTypeInput

On entry: specifies whether $A$ has nonunit or unit diagonal elements.

$\mathbf{diag}=\mathrm{Nag\_NonUnitDiag}$

The diagonal elements are stored explicitly.

$\mathbf{diag}=\mathrm{Nag\_UnitDiag}$

The diagonal elements are assumed to be $1$ and are not referenced.

Constraint: $\mathbf{diag}=\mathrm{Nag\_NonUnitDiag}$ or $\mathrm{Nag\_UnitDiag}$.

6:    $\mathbf{m}$ – IntegerInput

On entry: $m$, the number of rows of the matrix $B$; the order of $A$ if $\mathbf{side}=\mathrm{Nag\_LeftSide}$.

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

7:    $\mathbf{n}$ – IntegerInput

On entry: $n$, the number of columns of the matrix $B$; the order of $A$ if $\mathbf{side}=\mathrm{Nag\_RightSide}$.

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

8:    $\mathbf{alpha}$ – doubleInput

On entry: the scalar $\alpha$.

9:    $\mathbf{a}\left[\mathit{dim}\right]$ – const doubleInput

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

• $\max \left(1,\mathbf{pda}\times \mathbf{m}\right)$ when $\mathbf{side}=\mathrm{Nag\_LeftSide}$;
• $\max \left(1,\mathbf{pda}\times \mathbf{n}\right)$ when $\mathbf{side}=\mathrm{Nag\_RightSide}$.

On entry: the triangular matrix $A$; $A$ is $m$ by $m$ if $\mathbf{side}=\mathrm{Nag\_LeftSide}$, or $n$ by $n$ if $\mathbf{side}=\mathrm{Nag\_RightSide}$.

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 $\mathbf{a}\left[\left(i-1\right)\times \mathbf{pda}+j-1\right]$.

If $\mathbf{uplo}=\mathrm{Nag\_Upper}$, $A$ is upper triangular and the elements of the array corresponding to the lower triangular part of $A$ are not referenced.

If $\mathbf{uplo}=\mathrm{Nag\_Lower}$, $A$ is lower triangular and the elements of the array corresponding to the upper triangular part of $A$ are not referenced.

If $\mathbf{diag}=\mathrm{Nag\_UnitDiag}$, the diagonal elements of $A$ are assumed to be $1$, and are not referenced.

10:  $\mathbf{pda}$ – IntegerInput

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

Constraints:

• if $\mathbf{side}=\mathrm{Nag\_LeftSide}$, $\mathbf{pda}\ge \max \left(1,\mathbf{m}\right)$;
• if $\mathbf{side}=\mathrm{Nag\_RightSide}$, $\mathbf{pda}\ge \max \left(1,\mathbf{n}\right)$.

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

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

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

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

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

On entry: the $m$ by $n$ matrix $B$.

If $\mathbf{alpha}=0$, b need not be set.

On exit: the updated matrix $B$.

12:  $\mathbf{pdb}$ – IntegerInput

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

Constraints:

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

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

The NAG error argument (see Section 3.7 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_ENUM_INT_2

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

On entry, $\mathbf{side}=〈\mathit{\text{value}}〉$, $\mathbf{pda}=〈\mathit{\text{value}}〉$, $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: if $\mathbf{side}=\mathrm{Nag\_RightSide}$, $\mathbf{pda}\ge \max \left(1,\mathbf{n}\right)$.

NE_INT

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

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

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.

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 (f16yjce.c)

10.2

Program Data

Program Data (f16yjce.d)

10.3

Program Results

Program Results (f16yjce.r)