f16 Chapter Contents
f16 Chapter Introduction
NAG Library Manual

# NAG Library Function Documentnag_dtr_copy (f16qec)

## 1  Purpose

nag_dtr_copy (f16qec) copies a real triangular matrix.

## 2  Specification

 #include #include
 void nag_dtr_copy (Nag_OrderType order, Nag_UploType uplo, Nag_TransType trans, Nag_DiagType diag, Integer n, const double a[], Integer pda, double b[], Integer pdb, NagError *fail)

## 3  Description

nag_dtr_copy (f16qec) performs the triangular matrix copy operations
 $B←A or B←AT$
where $A$ and $B$ are $n$ by $n$ real triangular matrices.

## 4  References

Basic Linear Algebra Subprograms Technical (BLAST) Forum (2001) Basic Linear Algebra Subprograms Technical (BLAST) Forum Standard University of Tennessee, Knoxville, Tennessee http://www.netlib.org/blas/blast-forum/blas-report.pdf

## 5  Arguments

1:     orderNag_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:     uploNag_UploTypeInput
On entry: specifies whether the upper or lower triangular part of $A$ is stored.
${\mathbf{uplo}}=\mathrm{Nag_Upper}$
The upper triangular part of $A$ is stored.
${\mathbf{uplo}}=\mathrm{Nag_Lower}$
The lower triangular part of $A$ is stored.
Constraint: ${\mathbf{uplo}}=\mathrm{Nag_Upper}$ or $\mathrm{Nag_Lower}$.
3:     transNag_TransTypeInput
On entry: specifies the operation to be performed.
${\mathbf{trans}}=\mathrm{Nag_NoTrans}$
$B←A$.
${\mathbf{trans}}=\mathrm{Nag_Trans}$ or $\mathrm{Nag_ConjTrans}$
$B←{A}^{\mathrm{T}}$.
Constraint: ${\mathbf{trans}}=\mathrm{Nag_NoTrans}$, $\mathrm{Nag_Trans}$ or $\mathrm{Nag_ConjTrans}$.
4:     diagNag_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 $\mathrm{Nag_UnitDiag}$.
5:     nIntegerInput
On entry: $n$, the order of the matrices $A$ and $B$.
Constraint: ${\mathbf{n}}\ge 0$.
6:     a[$\mathit{dim}$]const doubleInput
Note: the dimension, dim, of the array a must be at least $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{pda}}×{\mathbf{n}}\right)$.
On entry: the $n$ by $n$ triangular matrix $A$.
If ${\mathbf{order}}=\mathrm{Nag_ColMajor}$, ${A}_{ij}$ is stored in ${\mathbf{a}}\left[\left(j-1\right)×{\mathbf{pda}}+i-1\right]$.
If ${\mathbf{order}}=\mathrm{Nag_RowMajor}$, ${A}_{ij}$ is stored in ${\mathbf{a}}\left[\left(i-1\right)×{\mathbf{pda}}+j-1\right]$.
If ${\mathbf{uplo}}=\mathrm{Nag_Upper}$, the upper triangular part of $A$ must be stored and the elements of the array below the diagonal are not referenced.
If ${\mathbf{uplo}}=\mathrm{Nag_Lower}$, the lower triangular part of $A$ must be stored and the elements of the array above the diagonal are not referenced.
If ${\mathbf{diag}}=\mathrm{Nag_UnitDiag}$, the diagonal elements of $A$ are assumed to be $1$, and are not referenced.
7:     pdaIntegerInput
On entry: the stride separating row or column elements (depending on the value of order) of the matrix $A$ in the array a.
Constraint: ${\mathbf{pda}}\ge \mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{n}}\right)$.
8:     b[$\mathit{dim}$]doubleOutput
Note: the dimension, dim, of the array b must be at least $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{pdb}}×{\mathbf{n}}\right)$.
On exit: the $n$ by $n$ triangular matrix $B$.
If ${\mathbf{order}}=\mathrm{Nag_ColMajor}$, ${B}_{ij}$ is stored in ${\mathbf{b}}\left[\left(j-1\right)×{\mathbf{pdb}}+i-1\right]$.
If ${\mathbf{order}}=\mathrm{Nag_RowMajor}$, ${B}_{ij}$ is stored in ${\mathbf{b}}\left[\left(i-1\right)×{\mathbf{pdb}}+j-1\right]$.
If ${\mathbf{uplo}}=\mathrm{Nag_Upper}$ and ${\mathbf{trans}}=\mathrm{Nag_NoTrans}$ or if ${\mathbf{uplo}}=\mathrm{Nag_Lower}$ and ${\mathbf{trans}}=\mathrm{Nag_Trans}$ or ${\mathbf{trans}}=\mathrm{Nag_ConjTrans}$, $B$ is upper triangular and the elements of the array below the diagonal are not set.
If ${\mathbf{uplo}}=\mathrm{Nag_Lower}$ and ${\mathbf{trans}}=\mathrm{Nag_NoTrans}$ or if ${\mathbf{uplo}}=\mathrm{Nag_Upper}$ and ${\mathbf{trans}}=\mathrm{Nag_Trans}$ or ${\mathbf{trans}}=\mathrm{Nag_ConjTrans}$, $B$ is lower triangular and the elements of the array above the diagonal are not set.
9:     pdbIntegerInput
On entry: the stride separating row or column elements (depending on the value of order) in the array b.
Constraint: ${\mathbf{pdb}}\ge \mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{n}}\right)$.
10:   failNagError *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.
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_INT_2
On entry, ${\mathbf{pda}}=⟨\mathit{\text{value}}⟩$, ${\mathbf{n}}=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{pda}}\ge \mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{n}}\right)$.
On entry, ${\mathbf{pdb}}=⟨\mathit{\text{value}}⟩$, ${\mathbf{n}}=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{pdb}}\ge \mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{n}}\right)$.

## 7  Accuracy

The BLAS standard requires accurate implementations which avoid unnecessary over/underflow (see Section 2.7 of Basic Linear Algebra Subprograms Technical (BLAST) Forum (2001)).

Not applicable.

None.

## 10  Example

This example copys the lower triangular matrix $A$ to $B$ where
 $A = 1.0 0.0 0.0 0.0 2.0 2.0 0.0 0.0 3.0 3.0 3.0 0.0 4.0 4.0 4.0 4.0 .$

### 10.1  Program Text

Program Text (f16qece.c)

### 10.2  Program Data

Program Data (f16qece.d)

### 10.3  Program Results

Program Results (f16qece.r)