NAG Library Routine Document

F01FDF

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     UPLO – CHARACTER(1)Input

On entry: if $\mathbf{UPLO}=\text{'U'}$, the upper triangle of the matrix $A$ is stored.

If $\mathbf{UPLO}=\text{'L'}$, the lower triangle of the matrix $A$ 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 $\mathbf{N}$.

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: if $\mathbf{IFAIL}=\mathbf{0}$, the upper or lower triangular part of the $n$ by $n$ matrix exponential, $e^A$.

4:     LDA – INTEGERInput

On entry: the first dimension of the array A as declared in the (sub)program from which F01FDF is called.

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

5:     IFAIL – INTEGERInput/Output

On entry: IFAIL must be set to $0$, $-1\text{ or }1$. If you are unfamiliar with this parameter you should refer to Section 3.3 in the Essential Introduction for details.

For environments where it might be inappropriate to halt program execution when an error is detected, the value $-1\text{ or }1$ is recommended. If the output of error messages is undesirable, then the value $1$ is recommended. Otherwise, if you are not familiar with this parameter, the recommended value is $0$. When the value $-\mathbf{1}\text{ or }\mathbf{1}$ is used it is essential to test the value of IFAIL on exit.

On exit: $\mathbf{IFAIL}=\mathbf{0}$ unless the routine detects an error or a warning has been flagged (see Section 6).

6  Error Indicators and Warnings

$\mathbf{IFAIL}<0\text{ and }\mathbf{IFAIL}\ne -999$

If $\mathbf{IFAIL}=-\mathit{i}$, the $i$th argument had an illegal value.

$\mathbf{IFAIL}=-999$

Allocation of memory failed. The INTEGER allocatable memory required is N, the real allocatable memory required is N and the complex allocatable memory required is approximately $\left(\mathbf{N}+\mathit{nb}+1\right)\times \mathbf{N}$, where nb is the block size required by F08FNF (ZHEEV).

$\mathbf{IFAIL}=i\text{ and }\mathbf{IFAIL}>0$

The algorithm to compute the spectral factorization failed to converge; $i$ off-diagonal elements of an intermediate tridiagonal form did not converge to zero (see F08FNF (ZHEEV)).

Note: this failure is unlikely to occur.

7  Accuracy

8  Further Comments

9  Example

9.1  Program Text

Program Text (f01fdfe.f90)

9.2  Program Data

Program Data (f01fdfe.d)

9.3  Program Results

Program Results (f01fdfe.r)