NAG Toolbox: nag_zeros_quadratic_complex (c02ah)

Purpose

Syntax

Description

References

Parameters

Compulsory Input Parameters

1:     $\mathrm{ar}$ – double scalar

2:     $\mathrm{ai}$ – double scalar

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

3:     $\mathrm{br}$ – double scalar

4:     $\mathrm{bi}$ – double scalar

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

5:     $\mathrm{cr}$ – double scalar

6:     $\mathrm{ci}$ – double scalar

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

Optional Input Parameters

None.

Output Parameters

1:     $\mathrm{zsm}\left(2\right)$ – double array

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.

2:     $\mathrm{zlg}\left(2\right)$ – double array

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.

3:     $\mathrm{ifail}$ – int64int32nag_int scalar

$\mathbf{ifail}=\mathbf{0}$ unless the function detects an error (see Error Indicators and Warnings).

Error Indicators and Warnings

Cases prefixed with W are classified as warnings and do not generate an error of type NAG:error_n. See nag_issue_warnings.

W  $\mathbf{ifail}=1$

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 nag_machine_real_largest (x02al)) 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 nag_machine_real_largest (x02al)) 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.

   $\mathbf{ifail}=-399$

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

   $\mathbf{ifail}=-999$

Dynamic memory allocation failed.

Accuracy

Further Comments

Example

Open in the MATLAB editor: c02ah_example

function c02ah_example


fprintf('c02ah example results\n\n');

ar =  1;  ai = 0;
br = -3;  bi = 1;
cr =  8;  ci = 1;
[zsm, zlg, ifail] = c02ah(ar, ai, br, bi, cr, ci);

disp('Roots of the quadratic equation:');
z(1) = zsm(1) + i*zsm(2);
z(2) = zlg(1) + i*zlg(2);
disp(z');

c02ah example results

Roots of the quadratic equation:
   1.0000 - 2.0000i
   2.0000 + 3.0000i