NAG Library Routine Document

F08FSF (ZHETRD)

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:     A(LDA,$*$) – COMPLEX (KIND=nag_wp) arrayInput/Output

Note: the second dimension of the array A must be at least $\max \left(1,\mathbf{N}\right)$.

On entry: the $n$ by $n$ Hermitian matrix $A$.

• If $\mathbf{UPLO}=\text{'U'}$, the upper triangular part of $A$ must be stored and the elements of the array below the diagonal are not referenced.
• If $\mathbf{UPLO}=\text{'L'}$, the lower triangular part of $A$ must be stored and the elements of the array above the diagonal are not referenced.

On exit: A is overwritten by the tridiagonal matrix $T$ and details of the unitary matrix $Q$ as specified by UPLO.

4:     LDA – INTEGERInput

On entry: the first dimension of the array A as declared in the (sub)program from which F08FSF (ZHETRD) is called.

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

5:     D($*$) – REAL (KIND=nag_wp) arrayOutput

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

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

6:     E($*$) – REAL (KIND=nag_wp) arrayOutput

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

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

7:     TAU($*$) – COMPLEX (KIND=nag_wp) arrayOutput

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

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

8:     WORK($\max \left(1,\mathbf{LWORK}\right)$) – COMPLEX (KIND=nag_wp) arrayWorkspace

On exit: if $\mathbf{INFO}=\mathbf{0}$, the real part of $\mathbf{WORK}\left(1\right)$ contains the minimum value of LWORK required for optimal performance.

9:     LWORK – INTEGERInput

On entry: the dimension of the array WORK as declared in the (sub)program from which F08FSF (ZHETRD) is called.

If $\mathbf{LWORK}=-1$, a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued.

Suggested value: for optimal performance, $\mathbf{LWORK}\ge \mathbf{N}\times \mathit{nb}$, where $\mathit{nb}$ is the optimal block size.

Constraint: $\mathbf{LWORK}\ge 1$ or $\mathbf{LWORK}=-1$.

10:   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 ZUNGTR(UPLO,N,A,LDA,TAU,WORK,LWORK,INFO)

CALL ZUNMTR('Left',UPLO,'No Transpose',N,P,A,LDA,TAU,C,LDC, &
              WORK,LWORK,INFO)

9  Example

9.1  Program Text

Program Text (f08fsfe.f90)

9.2  Program Data

Program Data (f08fsfe.d)

9.3  Program Results

Program Results (f08fsfe.r)