NAG Library Function Document

nag_ztfsm (f16zlc)

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:    $\mathbf{transr}$ – Nag_RFP_StoreInput

On entry: specifies whether the normal RFP representation of $A$ or its conjugate transpose is stored.

$\mathbf{transr}=\mathrm{Nag\_RFP\_Normal}$

The matrix $A$ is stored in normal RFP format.

$\mathbf{transr}=\mathrm{Nag\_RFP\_ConjTrans}$

The conjugate transpose of the RFP representation of the matrix $A$ is stored.

Constraint: $\mathbf{transr}=\mathrm{Nag\_RFP\_Normal}$ or $\mathrm{Nag\_RFP\_ConjTrans}$.

3:    $\mathbf{side}$ – Nag_SideTypeInput

On entry: specifies whether $B$ is operated on from the left or the right, or similarly whether $A$ (or its transpose) appears to the left or right of the solution matrix in the linear system to be solved.

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

$B$ is pre-multiplied from the left. The system to be solved has the form $AX=\alpha B$ or $A^{\mathrm{T}}X=\alpha B$.

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

$B$ is post-multiplied from the right. The system to be solved has the form $XA=\alpha B$ or $X{A}^{\mathrm{T}}=\alpha B$.

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

4:    $\mathbf{uplo}$ – 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 $\mathrm{Nag\_Lower}$.

5:    $\mathbf{trans}$ – Nag_TransTypeInput

On entry: specifies whether the operation involves $A^{-1}$ or $A^{-\mathrm{H}}$, i.e., whether or not $A$ is transpose conjugated in the linear system to be solved.

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

The operation involves $A^{-1}$, i.e., $A$ is not transpose conjugated.

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

The operation involves $A^{-\mathrm{H}}$, i.e., $A$ is transpose conjugated.

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

6:    $\mathbf{diag}$ – Nag_DiagTypeInput

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

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

The diagonal elements of $A$ are stored explicitly.

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

The diagonal elements of $A$ are assumed to be $1$, the corresponding elements of ar are not referenced.

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

7:    $\mathbf{m}$ – IntegerInput

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

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

8:    $\mathbf{n}$ – IntegerInput

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

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

9:    $\mathbf{alpha}$ – ComplexInput

On entry: the scalar $\alpha$.

10:  $\mathbf{ar}\left[\mathit{dim}\right]$ – const ComplexInput

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

• $\max \left(1,\mathbf{m}\times \left(\mathbf{m}+1\right)/2\right)$ when $\mathbf{side}=\mathrm{Nag\_LeftSide}$;
• $\max \left(1,\mathbf{n}\times \left(\mathbf{n}+1\right)/2\right)$ when $\mathbf{side}=\mathrm{Nag\_RightSide}$.

On entry: the $m$ by $m$ triangular matrix $A$ if $\mathbf{side}=\mathrm{Nag\_LeftSide}$ or the $n$ by $n$ triangular matrix $A$ if $\mathbf{side}=\mathrm{Nag\_RightSide}$, stored in RFP format (as specified by transr). The storage format is described in detail in Section 3.3.3 in the f07 Chapter Introduction. If $\mathbf{alpha}=0.0$, ar is not referenced.

11:  $\mathbf{b}\left[\mathit{dim}\right]$ – 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 $\mathbf{order}=\mathrm{Nag\_RowMajor}$.

On entry: the $m$ by $n$ matrix $B$.

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

On exit: the updated matrix $B$, or similarly the solution matrix $X$.

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

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 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, $\mathbf{m}=〈\mathit{\text{value}}〉$.
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.

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 (f16zlce.c)

10.2  Program Data

Program Data (f16zlce.d)

10.3  Program Results

Program Results (f16zlce.r)