NAG Library Routine Document

c02ahf  (quadratic_complex)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:     $\mathbf{ar}$ – Real (Kind=nag_wp)Input

2:     $\mathbf{ai}$ – Real (Kind=nag_wp)Input

On entry: ar and ai must contain the real and imaginary parts respectively of $a$, the coefficient of $z^2$.

3:     $\mathbf{br}$ – Real (Kind=nag_wp)Input

4:     $\mathbf{bi}$ – Real (Kind=nag_wp)Input

On entry: br and bi must contain the real and imaginary parts respectively of $b$, the coefficient of $z$.

5:     $\mathbf{cr}$ – Real (Kind=nag_wp)Input

6:     $\mathbf{ci}$ – Real (Kind=nag_wp)Input

On entry: cr and ci must contain the real and imaginary parts respectively of $c$, the constant coefficient.

7:     $\mathbf{zsm}\left(2\right)$ – Real (Kind=nag_wp) arrayOutput

On exit: the real and imaginary parts of the smallest root in magnitude are stored in $\mathbf{zsm}\left(1\right)$ and $\mathbf{zsm}\left(2\right)$ respectively.

8:     $\mathbf{zlg}\left(2\right)$ – Real (Kind=nag_wp) arrayOutput

On exit: the real and imaginary parts of the largest root in magnitude are stored in $\mathbf{zlg}\left(1\right)$ and $\mathbf{zlg}\left(2\right)$ respectively.

9:     $\mathbf{ifail}$ – IntegerInput/Output

On entry: ifail must be set to $0$, $-1\text{ or }1$. If you are unfamiliar with this argument you should refer to Section 3.4 in How to Use the NAG Library and its Documentation 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 argument, 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, $\left(\mathbf{ar},\mathbf{ai}\right)=\left(0,0\right)$. In this case, $\mathbf{zsm}\left(1\right)$ and $\mathbf{zsm}\left(2\right)$ contain the real and imaginary parts respectively of the root $-c/b$.

$\mathbf{ifail}=2$

On entry, $\left(\mathbf{ar},\mathbf{ai}\right)=\left(0,0\right)$ and $\left(\mathbf{br},\mathbf{bi}\right)=\left(0,0\right)$. In this case, $\mathbf{zsm}\left(1\right)$ contains the largest machine representable number (see x02alf) and $\mathbf{zsm}\left(2\right)$ contains zero.

$\mathbf{ifail}=3$

On entry, $\left(\mathbf{ar},\mathbf{ai}\right)=\left(0,0\right)$ and the root $-c/b$ overflows. In this case, $\mathbf{zsm}\left(1\right)$ contains the largest machine representable number (see x02alf) and $\mathbf{zsm}\left(2\right)$ contains zero.

$\mathbf{ifail}=4$

On entry, $\left(\mathbf{cr},\mathbf{ci}\right)=\left(0,0\right)$ and the root $-b/a$ overflows. In this case, both $\mathbf{zsm}\left(1\right)$ and $\mathbf{zsm}\left(2\right)$ contain zero.

$\mathbf{ifail}=5$

On entry, $\tilde{b}$ is so large that ${\tilde{b}}^2$ is indistinguishable from ${\tilde{b}}^2-4\tilde{a}\tilde{c}$ and the root $-b/a$ overflows, where $\tilde{b}=\max \left(\left|\mathbf{br}\right|,\left|\mathbf{bi}\right|\right)$, $\tilde{a}=\max \left(\left|\mathbf{ar}\right|,\left|\mathbf{ai}\right|\right)$ and $\tilde{c}=\max \left(\left|\mathbf{cr}\right|,\left|\mathbf{ci}\right|\right)$. In this case, $\mathbf{zsm}\left(1\right)$ and $\mathbf{zsm}\left(2\right)$ contain the real and imaginary parts respectively of the root $-c/b$.

$\mathbf{ifail}=-99$

An unexpected error has been triggered by this routine. Please contact NAG.

See Section 3.9 in How to Use the NAG Library and its Documentation for further information.

$\mathbf{ifail}=-399$

Your licence key may have expired or may not have been installed correctly.

See Section 3.8 in How to Use the NAG Library and its Documentation for further information.

$\mathbf{ifail}=-999$

Dynamic memory allocation failed.

See Section 3.7 in How to Use the NAG Library and its Documentation for further information.

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example

10.1

Program Text

Program Text (c02ahfe.f90)

10.2

Program Data

Program Data (c02ahfe.d)

10.3

Program Results

Program Results (c02ahfe.r)