NAG FL Interface
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) array Output

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) array Output

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: $\mathbf{ifail}$ – Integer Input/Output

On entry: ifail must be set to $0$, $-1$ or $1$ to set behaviour on detection of an error; these values have no effect when no error is detected.

A value of $0$ causes the printing of an error message and program execution will be halted; otherwise program execution continues. A value of $-1$ means that an error message is printed while a value of $1$ means that it is not.

If halting is not appropriate, the value $-1$ or $1$ is recommended. If message printing is undesirable, then the value $1$ is recommended. Otherwise, the value $0$ is recommended. When the value $-\mathbf{1}$ 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, $(\mathbf{ar},\mathbf{ai})=(0,0)$.

$\mathbf{ifail}=2$

On entry, $(\mathbf{ar},\mathbf{ai})=(0,0)$ and $(\mathbf{br},\mathbf{bi})=(0,0)$.

$\mathbf{ifail}=3$

On entry, $(\mathbf{ar},\mathbf{ai})=(0,0)$ and the root $-(\mathbf{cr},\mathbf{ci})/(\mathbf{br},\mathbf{bi})$ overflows: $\mathbf{ar}=⟨\mathit{\text{value}}⟩$, $\mathbf{cr}=⟨\mathit{\text{value}}⟩$, $\mathbf{br}=⟨\mathit{\text{value}}⟩$, $\mathbf{ai}=⟨\mathit{\text{value}}⟩$, $\mathbf{ci}=⟨\mathit{\text{value}}⟩$ and $\mathbf{bi}=⟨\mathit{\text{value}}⟩$.

$\mathbf{ifail}=4$

On entry, $(\mathbf{cr},\mathbf{ci})=(0,0)$ and the root $-(\mathbf{br},\mathbf{bi})/(\mathbf{ar},\mathbf{ai})$ overflows: $\mathbf{cr}=⟨\mathit{\text{value}}⟩$, $\mathbf{br}=⟨\mathit{\text{value}}⟩$, $\mathbf{ar}=⟨\mathit{\text{value}}⟩$, $\mathbf{ci}=⟨\mathit{\text{value}}⟩$, $\mathbf{bi}=⟨\mathit{\text{value}}⟩$ and $\mathbf{ai}=⟨\mathit{\text{value}}⟩$.

$\mathbf{ifail}=5$

On entry, $B$ is so large that $B^2$ is indistinguishable from $(B^2-4\times A\times C)$ and the root $-(\mathbf{br},\mathbf{bi})/(\mathbf{ar},\mathbf{ai})$ overflows: $B=\max (\left|\mathbf{br}\right|,\left|\mathbf{bi}\right|)=⟨\mathit{\text{value}}⟩$, $A=\max (\left|\mathbf{ar}\right|,\left|\mathbf{ai}\right|)=⟨\mathit{\text{value}}⟩$, $C=\max (\left|\mathbf{cr}\right|,\left|\mathbf{ci}\right|)=⟨\mathit{\text{value}}⟩$, $\mathbf{br}=⟨\mathit{\text{value}}⟩$, $\mathbf{bi}=⟨\mathit{\text{value}}⟩$, $\mathbf{ar}=⟨\mathit{\text{value}}⟩$ and $\mathbf{ai}=⟨\mathit{\text{value}}⟩$.

$\mathbf{ifail}=-99$

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

See Section 7 in the Introduction to the NAG Library FL Interface for further information.

$\mathbf{ifail}=-399$

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

See Section 8 in the Introduction to the NAG Library FL Interface for further information.

$\mathbf{ifail}=-999$

Dynamic memory allocation failed.

See Section 9 in the Introduction to the NAG Library FL Interface for further information.

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results