NAG Library Routine Document

F03BNF

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     N – INTEGERInput

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

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

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

Note: the second dimension of the array A must be at least $\mathbf{N}$.

On entry: the $n$ by $n$ matrix $A$ in factorized form as returned by F07ARF (ZGETRF).

3:     LDA – INTEGERInput

On entry: the first dimension of the array A as declared in the (sub)program from which F03BNF is called.

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

4:     IPIV(N) – INTEGER arrayInput

On entry: the row interchanges used to factorize matrix $A$ as returned by F07ARF (ZGETRF).

5:     D – COMPLEX (KIND=nag_wp)Output

On exit: the mantissa of the real and imaginary parts of the determinant.

6:     ID($2$) – INTEGER arrayOutput

On exit: the exponents for the real and imaginary parts of the determinant. The determinant, $d=\left(d_r,d_i\right)$, is returned as $d_r=D_r\times 2^j$ and $d_i=D_i\times 2^k$, where $\mathbf{D}=\left(D_r,D_i\right)$ and $j$ and $k$ are stored in the first and second elements respectively of the array ID on successful exit.

7:     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

$\mathbf{IFAIL}=1$

On entry,

$\mathbf{N}<1$.

$\mathbf{IFAIL}=3$

On entry,

$\mathbf{LDA}<\mathbf{N}$.

$\mathbf{IFAIL}=4$

The matrix $A$ is approximately singular.

7  Accuracy

8  Further Comments

9  Example

9.1  Program Text

Program Text (f03bnfe.f90)

9.2  Program Data

Program Data (f03bnfe.d)

9.3  Program Results

Program Results (f03bnfe.r)