NAG Library Routine Document

F08GSF (ZHPTRD)

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     UPLO – CHARACTER(1)Input

On entry: indicates whether the upper or lower triangular part of $A$ is stored.

$\mathbf{UPLO}=\text{'U'}$

The upper triangular part of $A$ is stored.

$\mathbf{UPLO}=\text{'L'}$

The lower triangular part of $A$ is stored.

Constraint: $\mathbf{UPLO}=\text{'U'}$ or $\text{'L'}$.

2:     N – INTEGERInput

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

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

3:     AP($*$) – COMPLEX (KIND=nag_wp) arrayInput/Output

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

On entry: the upper or lower triangle of the $n$ by $n$ Hermitian matrix $A$, packed by columns.

More precisely,

• if $\mathbf{UPLO}=\text{'U'}$, the upper triangle of $A$ must be stored with element $A_{ij}$ in $\mathbf{AP}\left(i+j\left(j-1\right)/2\right)$ for $i\le j$;
• if $\mathbf{UPLO}=\text{'L'}$, the lower triangle of $A$ must be stored with element $A_{ij}$ in $\mathbf{AP}\left(i+\left(2n-j\right)\left(j-1\right)/2\right)$ for $i\ge j$.

On exit: AP is overwritten by the tridiagonal matrix $T$ and details of the unitary matrix $Q$.

4:     D(N) – REAL (KIND=nag_wp) arrayOutput

On exit: the diagonal elements of the tridiagonal matrix $T$.

5:     E($\mathbf{N}-1$) – REAL (KIND=nag_wp) arrayOutput

On exit: the off-diagonal elements of the tridiagonal matrix $T$.

6:     TAU($\mathbf{N}-1$) – COMPLEX (KIND=nag_wp) arrayOutput

On exit: further details of the unitary matrix $Q$.

7:     INFO – INTEGEROutput

On exit: $\mathbf{INFO}=0$ unless the routine detects an error (see Section 6).

6  Error Indicators and Warnings

$\mathbf{INFO}<0$

If $\mathbf{INFO}=-i$, argument $i$ had an illegal value. An explanatory message is output, and execution of the program is terminated.

7  Accuracy

8  Further Comments

CALL ZUPGTR(UPLO,N,AP,TAU,Q,LDQ,WORK,INFO)

CALL ZUPMTR('Left',UPLO,'No Transpose',N,P,AP,TAU,C,LDC,WORK, &
              INFO)

9  Example

9.1  Program Text

Program Text (f08gsfe.f90)

9.2  Program Data

Program Data (f08gsfe.d)

9.3  Program Results

Program Results (f08gsfe.r)