NAG Library Function Document

nag_zupgtr (f08gtc)

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 Nag_ColMajor.

2:     uplo – Nag_UploTypeInput

On entry: this must be the same argument uplo as supplied to nag_zhptrd (f08gsc).

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

3:     n – IntegerInput

On entry: $n$, the order of the matrix $Q$.

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

4:     ap[$\mathit{dim}$] – const ComplexInput

Note: the dimension, dim, of the array ap must be at least $\max \left(1,\mathbf{n}\times \left(\mathbf{n}+1\right)/2\right)$.

On entry: details of the vectors which define the elementary reflectors, as returned by nag_zhptrd (f08gsc).

5:     tau[$\mathit{dim}$] – const ComplexInput

Note: the dimension, dim, of the array tau must be at least $\max \left(1,\mathbf{n}-1\right)$.

On entry: further details of the elementary reflectors, as returned by nag_zhptrd (f08gsc).

6:     q[$\mathit{dim}$] – ComplexOutput

Note: the dimension, dim, of the array q must be at least $\max \left(1,\mathbf{pdq}\times \mathbf{n}\right)$.

The $\left(i,j\right)$th element of the matrix $Q$ is stored in

• $\mathbf{q}\left[\left(j-1\right)\times \mathbf{pdq}+i-1\right]$ when $\mathbf{order}=\mathrm{Nag\_ColMajor}$;
• $\mathbf{q}\left[\left(i-1\right)\times \mathbf{pdq}+j-1\right]$ when $\mathbf{order}=\mathrm{Nag\_RowMajor}$.

On exit: the $n$ by $n$ unitary matrix $Q$.

7:     pdq – IntegerInput

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

Constraint: $\mathbf{pdq}\ge \max \left(1,\mathbf{n}\right)$.

8:     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_INT

On entry, $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{n}\ge 0$.

On entry, $\mathbf{pdq}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{pdq}>0$.

NE_INT_2

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

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  Further Comments

9  Example

9.1  Program Text

Program Text (f08gtce.c)

9.2  Program Data

Program Data (f08gtce.d)

9.3  Program Results

Program Results (f08gtce.r)