NAG CL Interfacef01vkc (ztpttf)

Settings help

CL Name Style:

1Purpose

f01vkc copies a complex triangular matrix, stored in a standard packed format array, to a Rectangular Full Packed (RFP) format array.

2Specification

 #include
 void f01vkc (Nag_OrderType order, Nag_RFP_Store transr, Nag_UploType uplo, Integer n, const Complex ap[], Complex ar[], NagError *fail)
The function may be called by the names: f01vkc, nag_matop_ztpttf or nag_ztpttf.

3Description

f01vkc copies a complex $n×n$ triangular matrix, $A$, stored in packed format, to RFP format. This function is intended for possible use in conjunction with functions from Chapters F06, F07 and F16 where some functions that use triangular matrices store them in RFP format. The RFP storage format is described in Section 3.4.3 in the F07 Chapter Introduction and the packed storage format is described in Section 3.4.2 in the F07 Chapter Introduction.

4References

Gustavson F G, Waśniewski J, Dongarra J J and Langou J (2010) Rectangular full packed format for Cholesky's algorithm: factorization, solution, and inversion ACM Trans. Math. Software 37, 2

5Arguments

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: $\mathbf{transr}$Nag_RFP_Store Input
On entry: specifies whether the normal RFP representation of $A$ or its conjugate transpose is stored.
${\mathbf{transr}}=\mathrm{Nag_RFP_Normal}$
The RFP representation of the matrix $A$ is stored.
${\mathbf{transr}}=\mathrm{Nag_RFP_ConjTrans}$
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: $\mathbf{uplo}$Nag_UploType Input
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: $\mathbf{n}$Integer Input
On entry: $n$, the order of the matrix $A$.
Constraint: ${\mathbf{n}}\ge 0$.
5: $\mathbf{ap}\left[\mathit{dim}\right]$const Complex Input
Note: the dimension, dim, of the array ap must be at least ${\mathbf{n}}×\left({\mathbf{n}}+1\right)/2$.
On entry: the $n×n$ triangular matrix $A$, packed by rows or columns depending on order.
The storage of elements ${A}_{ij}$ depends on the order and uplo arguments as follows:
if ${\mathbf{order}}=\mathrm{Nag_ColMajor}$ and ${\mathbf{uplo}}=\mathrm{Nag_Upper}$,
${A}_{ij}$ is stored in ${\mathbf{ap}}\left[\left(j-1\right)×j/2+i-1\right]$, for $i\le j$;
if ${\mathbf{order}}=\mathrm{Nag_ColMajor}$ and ${\mathbf{uplo}}=\mathrm{Nag_Lower}$,
${A}_{ij}$ is stored in ${\mathbf{ap}}\left[\left(2n-j\right)×\left(j-1\right)/2+i-1\right]$, for $i\ge j$;
if ${\mathbf{order}}=\mathrm{Nag_RowMajor}$ and ${\mathbf{uplo}}=\mathrm{Nag_Upper}$,
${A}_{ij}$ is stored in ${\mathbf{ap}}\left[\left(2n-i\right)×\left(i-1\right)/2+j-1\right]$, for $i\le j$;
if ${\mathbf{order}}=\mathrm{Nag_RowMajor}$ and ${\mathbf{uplo}}=\mathrm{Nag_Lower}$,
${A}_{ij}$ is stored in ${\mathbf{ap}}\left[\left(i-1\right)×i/2+j-1\right]$, for $i\ge j$.
6: $\mathbf{ar}\left[{\mathbf{n}}×\left({\mathbf{n}}+1\right)/2\right]$Complex Output
On exit: the upper or lower $n×n$ triangular matrix $A$ (as specified by uplo) in either normal or transposed RFP format (as specified by transr). The storage format is described in Section 3.4.3 in the F07 Chapter Introduction.
7: $\mathbf{fail}$NagError * Input/Output
The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).

6Error 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.
On entry, argument $⟨\mathit{\text{value}}⟩$ had an illegal value.
NE_INT
On entry, ${\mathbf{n}}=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{n}}\ge 0$.
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.
See Section 7.5 in the Introduction to the NAG Library CL Interface for further information.
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.

Not applicable.

8Parallelism and Performance

f01vkc is not threaded in any implementation.

None.

10Example

This example reads in a triangular matrix in packed format and copies it to RFP format.

10.1Program Text

Program Text (f01vkce.c)

10.2Program Data

Program Data (f01vkce.d)

10.3Program Results

Program Results (f01vkce.r)