NAG Library Function Document

nag_ztrsm (f16zjc)

1  Purpose

2  Specification

3  Description

4  References

5  Arguments

1:     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 3.2.1.3 in the Essential Introduction for a more detailed explanation of the use of this argument.

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

2:     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:     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:     trans – Nag_TransTypeInput

On entry: specifies the operation to be performed.

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

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

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

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

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

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

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

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

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

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

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

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

Constraints:

• $\mathbf{side}=\mathrm{Nag\_LeftSide}$ or $\mathrm{Nag\_RightSide}$;
• $\mathbf{trans}=\mathrm{Nag\_NoTrans}$ or $\mathrm{Nag\_Trans}$.

5:     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:     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:     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:     alpha – ComplexInput

On entry: the scalar $\alpha$.

9:     a[$\mathit{dim}$] – const ComplexInput

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:   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:   b[$\mathit{dim}$] – ComplexInput/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:   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:   fail – NagError *Input/Output

The NAG error argument (see Section 3.6 in the Essential Introduction).

6  Error Indicators and Warnings

NE_ALLOC_FAIL

Dynamic memory allocation failed.

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, $\mathbf{pda}=⟨\mathit{\text{value}}⟩$; $\mathbf{n}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{pda}\ge \max \left(1,\mathbf{n}\right)$.

On entry, $\mathbf{pdb}=⟨\mathit{\text{value}}⟩$; $\mathbf{m}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{pdb}\ge \max \left(1,\mathbf{m}\right)$.

On entry, $\mathbf{pdb}=⟨\mathit{\text{value}}⟩$, $\mathbf{m}=⟨\mathit{\text{value}}⟩$.
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.

7  Accuracy

8  Parallelism and Performance

9  Further Comments

10  Example

10.1  Program Text

Program Text (f16zjce.c)

10.2  Program Data

Program Data (f16zjce.d)

10.3  Program Results

Program Results (f16zjce.r)