internal virtual double z_abs(doublecomplex z)
{
double temp, real, imag;
real = z.r;
imag = z.i;
if (real < 0)
{
real = -real;
}
if (imag < 0)
{
imag = -imag;
}
if (imag > real)
{
temp = real;
real = imag;
imag = temp;
}
if ((real + imag) == real)
{
return(real);
}
temp = imag / real;
temp = real * Math.Sqrt(1.0 + temp * temp);
return(temp);
}
internal virtual void aberth_(int n, int j, doublecomplex[] root, doublecomplex abcorr)
{
int i__1, i__2;
doublecomplex z__1 = dc(), z__2 = dc();
int i;
doublecomplex z = dc(), zj = dc();
abcorr.r = 0.0;
abcorr.i = 0.0;
i__1 = j;
zj.r = root[i__1 - 1].r;
zj.i = root[i__1 - 1].i;
i__1 = j - 1;
for (i = 1; i <= i__1; ++i)
{
i__2 = i;
z__1.r = zj.r - root[i__2 - 1].r;
z__1.i = zj.i - root[i__2 - 1].i;
z.r = z__1.r;
z.i = z__1.i;
z_div(z__2, c_b35, z);
z__1.r = abcorr.r + z__2.r;
z__1.i = abcorr.i + z__2.i;
abcorr.r = z__1.r;
abcorr.i = z__1.i;
}
i__1 = n;
for (i = j + 1; i <= i__1; ++i)
{
i__2 = i;
z__1.r = zj.r - root[i__2 - 1].r;
z__1.i = zj.i - root[i__2 - 1].i;
z.r = z__1.r;
z.i = z__1.i;
z_div(z__2, c_b35, z);
z__1.r = abcorr.r + z__2.r;
z__1.i = abcorr.i + z__2.i;
abcorr.r = z__1.r;
abcorr.i = z__1.i;
}
}
internal virtual void z_div(doublecomplex c, doublecomplex a, doublecomplex b)
{
double ratio, den;
double abr, abi, cr;
if ((abr = b.r) < 0.0)
{
abr = -abr;
}
if ((abi = b.i) < 0.0)
{
abi = -abi;
}
if (abr <= abi)
{
if (abi == 0)
{
PrintError("complex division by zero");
c.r = 1.0;
c.i = 1.0;
return;
}
ratio = b.r / b.i;
den = b.i * (1 + ratio * ratio);
cr = (a.r * ratio + a.i) / den;
c.i = (a.i * ratio - a.r) / den;
}
else
{
ratio = b.i / b.r;
den = b.r * (1 + ratio * ratio);
cr = (a.r + a.i * ratio) / den;
c.i = (a.i - a.r * ratio) / den;
}
c.r = cr;
}
internal virtual int start_(int n, double[] a, doublecomplex[] y, double[] radius, int[] nz, double theSmall, double big, bool[] h)
{
int i__1, i__2, i__3;
double d__1, d__2;
doublecomplex z__1 = dc(), z__2 = dc(), z__3 = dc();
int iold;
double xbig, temp;
int i, j;
double r = 0.0;
int jj;
double th, xsmall;
int nzeros;
double ang;
xsmall = JMath.log(theSmall);
xbig = JMath.log(big);
nz[0] = 0;
i__1 = n + 1;
for (i = 1; i <= i__1; ++i)
{
if (a[i - 1] != 0.0)
{
a[i - 1] = JMath.log(a[i - 1]);
}
else
{
a[i - 1] = -1e30;
}
}
i__1 = n + 1;
cnvex_(i__1, a, h);
iold = 1;
th = 6.2831853071796 / n;
i__1 = n + 1;
for (i = 2; i <= i__1; ++i)
{
if (h[i - 1])
{
nzeros = i - iold;
temp = (a[iold - 1] - a[i - 1]) / nzeros;
if (temp < -xbig && temp >= xsmall)
{
nz[0] += nzeros;
r = 1.0 / big;
}
if (temp < xsmall)
{
nz[0] += nzeros;
}
if (temp > xbig)
{
r = big;
nz[0] += nzeros;
}
d__1 = -xbig;
if (temp <= xbig && temp > Math.Max(d__1, xsmall))
{
r = JMath.exp(temp);
}
ang = 6.2831853071796 / nzeros;
i__2 = i - 1;
for (j = iold; j <= i__2; ++j)
{
jj = j - iold + 1;
if (r <= 1.0 / big || r == big)
{
radius[j - 1] = -1.0;
}
i__3 = j;
d__1 = Math.Cos(ang * jj + th * i + .7);
d__2 = Math.Sin(ang * jj + th * i + .7);
z__3.r = d__2 * (float)0.0;
z__3.i = d__2 * (float)1.0;
z__2.r = d__1 + z__3.r;
z__2.i = z__3.i;
z__1.r = r * z__2.r;
z__1.i = r * z__2.i;
y[i__3 - 1].r = z__1.r;
y[i__3 - 1].i = z__1.i;
}
iold = i;
}
}
return(0);
}
internal virtual void newton_(int n, doublecomplex[] poly, double[] apoly, double[] apolyr, doublecomplex z, double theSmall, double[] radius, doublecomplex corr, bool[] again, int ik)
{
int i__1;
double d__1;
doublecomplex z__1 = dc(), z__2 = dc();
double absp;
doublecomplex ppsp = dc();
int i;
doublecomplex p = dc(), p1 = dc();
double ap, az;
doublecomplex zi = dc(), den = dc();
double azi;
az = z_abs(z);
if (az <= 1.0)
{
i__1 = n + 1;
p.r = poly[i__1 - 1].r;
p.i = poly[i__1 - 1].i;
ap = apoly[n + 1 - 1];
p1.r = p.r;
p1.i = p.i;
for (i = n; i >= 2; --i)
{
z__2.r = p.r * z.r - p.i * z.i;
z__2.i = p.r * z.i + p.i * z.r;
i__1 = i;
z__1.r = z__2.r + poly[i__1 - 1].r;
z__1.i = z__2.i + poly[i__1 - 1].i;
p.r = z__1.r;
p.i = z__1.i;
z__2.r = p1.r * z.r - p1.i * z.i;
z__2.i = p1.r * z.i + p1.i * z.r;
z__1.r = z__2.r + p.r;
z__1.i = z__2.i + p.i;
p1.r = z__1.r;
p1.i = z__1.i;
ap = ap * az + apoly[i - 1];
}
z__2.r = p.r * z.r - p.i * z.i;
z__2.i = p.r * z.i + p.i * z.r;
z__1.r = z__2.r + poly[1 - 1].r;
z__1.i = z__2.i + poly[1 - 1].i;
p.r = z__1.r;
p.i = z__1.i;
ap = ap * az + apoly[1 - 1];
z_div(z__1, p, p1);
corr.r = z__1.r;
corr.i = z__1.i;
absp = z_abs(p);
ap = ap;
again[ik] = (absp > theSmall + ap);
if (!again[ik])
{
radius[ik] = n * (absp + ap) / z_abs(p1);
}
return;
}
else
{
z_div(z__1, c_b35, z);
zi.r = z__1.r;
zi.i = z__1.i;
azi = 1 / az;
p.r = poly[1 - 1].r;
p.i = poly[1 - 1].i;
p1.r = p.r;
p1.i = p.i;
ap = apolyr[n + 1 - 1];
for (i = n; i >= 2; --i)
{
z__2.r = p.r * zi.r - p.i * zi.i;
z__2.i = p.r * zi.i + p.i * zi.r;
i__1 = n - i + 2;
z__1.r = z__2.r + poly[i__1 - 1].r;
z__1.i = z__2.i + poly[i__1 - 1].i;
p.r = z__1.r;
p.i = z__1.i;
z__2.r = p1.r * zi.r - p1.i * zi.i;
z__2.i = p1.r * zi.i + p1.i * zi.r;
z__1.r = z__2.r + p.r;
z__1.i = z__2.i + p.i;
p1.r = z__1.r;
p1.i = z__1.i;
ap = ap * azi + apolyr[i - 1];
}
z__2.r = p.r * zi.r - p.i * zi.i;
z__2.i = p.r * zi.i + p.i * zi.r;
i__1 = n + 1;
z__1.r = z__2.r + poly[i__1 - 1].r;
z__1.i = z__2.i + poly[i__1 - 1].i;
p.r = z__1.r;
p.i = z__1.i;
ap = ap * azi + apolyr[1 - 1];
absp = z_abs(p);
again[ik] = absp > theSmall + ap;
z__2.r = p.r * z.r - p.i * z.i;
z__2.i = p.r * z.i + p.i * z.r;
z_div(z__1, z__2, p1);
ppsp.r = z__1.r;
ppsp.i = z__1.i;
d__1 = (double)n;
z__2.r = d__1 * ppsp.r;
z__2.i = d__1 * ppsp.i;
z__1.r = z__2.r - 1;
z__1.i = z__2.i;
den.r = z__1.r;
den.i = z__1.i;
z_div(z__2, ppsp, den);
z__1.r = z.r * z__2.r - z.i * z__2.i;
z__1.i = z.r * z__2.i + z.i * z__2.r;
corr.r = z__1.r;
corr.i = z__1.i;
if (again[ik])
{
return;
}
radius[ik] = z_abs(ppsp) + ap * az / z_abs(p1);
radius[ik] = n * radius[ik] / z_abs(den);
radius[ik] *= az;
}
}
internal virtual void polzeros_(int n, doublecomplex[] poly, double eps, double big, double theSmall, int nitmax, doublecomplex[] root, double[] radius, bool[] err, int[] iter, double[] apoly, double[] apolyr)
{
int i__1, i__2, i__3, i__4;
double d__1, d__2;
doublecomplex z__1 = dc(), z__2 = dc(), z__3 = dc(), z__4 = dc();
double amax;
doublecomplex corr = dc();
int i;
doublecomplex abcorr = dc();
int[] nzeros = new int[1];
if (z_abs(poly[n]) == 0.0)
{
PrintError("Inconsistent data: the leading coefficient is zero");
return;
}
if (z_abs(poly[0]) == 0.0)
{
PrintError("The constant term is zero: deflate the polynomial");
return;
}
amax = 0.0;
i__1 = n + 1;
for (i = 1; i <= i__1; ++i)
{
apoly[i - 1] = z_abs(poly[i - 1]);
d__1 = amax;
d__2 = apoly[i - 1];
amax = Math.Max(d__1, d__2);
apolyr[i - 1] = apoly[i - 1];
}
if (amax >= big / (n + 1))
{
PrintError("WARNING: COEFFICIENTS TOO BIG, OVERFLOW IS LIKELY");
}
i__1 = n;
for (i = 1; i <= i__1; ++i)
{
radius[i - 1] = 0.0;
err[i - 1] = true;
}
start_(n, apolyr, root, radius, nzeros, theSmall, big, err);
i__1 = n + 1;
for (i = 1; i <= i__1; ++i)
{
apolyr[n - i + 2 - 1] = eps * apoly[i - 1] * ((n - i + 1) * (float)3.8 + 1);
apoly[i - 1] = eps * apoly[i - 1] * ((i - 1) * (float)3.8 + 1);
}
if (apoly[1 - 1] == 0.0 || apoly[n + 1 - 1] == 0.0)
{
PrintError("WARNING: THE COMPUTATION OF SOME INCLUSION RADIUS MAY FAIL. THIS IS REPORTED BY RADIUS=0");
}
i__1 = n;
for (i = 1; i <= i__1; ++i)
{
err[i - 1] = true;
if (radius[i - 1] == -1.0)
{
err[i - 1] = false;
}
}
i__1 = nitmax;
for (iter[0] = 1; iter[0] <= i__1; ++iter[0])
{
i__2 = n;
for (i = 1; i <= i__2; ++i)
{
if (err[i - 1])
{
newton_(n, poly, apoly, apolyr, root[i - 1], theSmall, radius, corr, err, i - 1);
if (err[i - 1])
{
aberth_(n, i, root, abcorr);
i__3 = i;
i__4 = i;
z__4.r = corr.r * abcorr.r - corr.i * abcorr.i;
z__4.i = corr.r * abcorr.i + corr.i * abcorr.r;
z__3.r = 1 - z__4.r;
z__3.i = -z__4.i;
z_div(z__2, corr, z__3);
z__1.r = root[i__4 - 1].r - z__2.r;
z__1.i = root[i__4 - 1].i - z__2.i;
root[i__3 - 1].r = z__1.r;
root[i__3 - 1].i = z__1.i;
}
else
{
++nzeros[0];
if (nzeros[0] == n)
{
return;
}
}
}
}
}
}
public static void aberth(double[] ar, double[] ai, bool[] err)
{
for (int i = 0; i < err.Length; i++)
{
err[i] = true;
}
if (ar.Length != ai.Length || ar.Length != err.Length)
{
return;
}
int n_zero = 0;
while (n_zero < ar.Length && ar[n_zero] == 0.0 && ai[n_zero] == 0.0)
{
n_zero++;
}
if (n_zero == ar.Length)
{
return;
}
doublecomplex[] poly = new doublecomplex[ar.Length - n_zero];
for (int i = 0; i < poly.Length; i++)
{
poly[i] = Pzeros.pz.dc(ar[i + n_zero], ai[i + n_zero]);
}
int n = poly.Length - 1;
double eps = 2.22044604925031e-16;
double big = double.MaxValue;
double theSmall = double.Epsilon;
int nitmax = 100;
doublecomplex[] root = new doublecomplex[n];
double[] radius = new double[n];
bool[] errs = new bool[n + 1];
for (int i = 0; i < n; i++)
{
root[i] = Pzeros.pz.dc();
radius[i] = 1.0;
errs[i] = true;
}
int[] iter = new int[1];
iter[0] = 0;
double[] apoly = new double[n + 1];
double[] apolyr = new double[n + 1];
for (int i = 0; i < n + 1; i++)
{
apoly[i] = 1.0;
apolyr[i] = 1.0;
}
Pzeros.pz.polzeros_(n, poly, eps, big, theSmall, nitmax, root, radius, errs, iter, apoly, apolyr);
for (int i = 0; i < n_zero; i++)
{
ar[i] = 0.0;
ai[i] = 0.0;
err[i] = false;
}
for (int i = n_zero; i < ar.Length - 1; i++)
{
ar[i] = root[i - n_zero].r;
ai[i] = root[i - n_zero].i;
err[i] = errs[i - n_zero];
}
return;
}
private void InitializeInstanceFields()
{
c_b35 = new doublecomplex(this, 1.0, 0.0);
}
