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/* polrt.c
*
* Find roots of a polynomial
*
*
*
* SYNOPSIS:
*
* typedef struct
* {
* double r;
* double i;
* }cmplx;
*
* double xcof[], cof[];
* int m;
* cmplx root[];
*
* polrt( xcof, cof, m, root )
*
*
*
* DESCRIPTION:
*
* Iterative determination of the roots of a polynomial of
* degree m whose coefficient vector is xcof[]. The
* coefficients are arranged in ascending order; i.e., the
* coefficient of x**m is xcof[m].
*
* The array cof[] is working storage the same size as xcof[].
* root[] is the output array containing the complex roots.
*
*
* ACCURACY:
*
* Termination depends on evaluation of the polynomial at
* the trial values of the roots. The values of multiple roots
* or of roots that are nearly equal may have poor relative
* accuracy after the first root in the neighborhood has been
* found.
*
*/
/* polrt */
/* Complex roots of real polynomial */
/* number of coefficients is m + 1 ( i.e., m is degree of polynomial) */
#include <math.h>
/*
typedef struct
{
double r;
double i;
}cmplx;
*/
#ifdef ANSIPROT
extern double fabs ( double );
#else
double fabs();
#endif
int polrt( xcof, cof, m, root )
double xcof[], cof[];
int m;
cmplx root[];
{
register double *p, *q;
int i, j, nsav, n, n1, n2, nroot, iter, retry;
int final;
double mag, cofj;
cmplx x0, x, xsav, dx, t, t1, u, ud;
final = 0;
n = m;
if( n <= 0 )
return(1);
if( n > 36 )
return(2);
if( xcof[m] == 0.0 )
return(4);
n1 = n;
n2 = n;
nroot = 0;
nsav = n;
q = &xcof[0];
p = &cof[n];
for( j=0; j<=nsav; j++ )
*p-- = *q++; /* cof[ n-j ] = xcof[j];*/
xsav.r = 0.0;
xsav.i = 0.0;
nxtrut:
x0.r = 0.00500101;
x0.i = 0.01000101;
retry = 0;
tryagn:
retry += 1;
x.r = x0.r;
x0.r = -10.0 * x0.i;
x0.i = -10.0 * x.r;
x.r = x0.r;
x.i = x0.i;
finitr:
iter = 0;
while( iter < 500 )
{
u.r = cof[n];
if( u.r == 0.0 )
{ /* this root is zero */
x.r = 0;
n1 -= 1;
n2 -= 1;
goto zerrut;
}
u.i = 0;
ud.r = 0;
ud.i = 0;
t.r = 1.0;
t.i = 0;
p = &cof[n-1];
for( i=0; i<n; i++ )
{
t1.r = x.r * t.r - x.i * t.i;
t1.i = x.r * t.i + x.i * t.r;
cofj = *p--; /* evaluate polynomial */
u.r += cofj * t1.r;
u.i += cofj * t1.i;
cofj = cofj * (i+1); /* derivative */
ud.r += cofj * t.r;
ud.i -= cofj * t.i;
t.r = t1.r;
t.i = t1.i;
}
mag = ud.r * ud.r + ud.i * ud.i;
if( mag == 0.0 )
{
if( !final )
goto tryagn;
x.r = xsav.r;
x.i = xsav.i;
goto findon;
}
dx.r = (u.i * ud.i - u.r * ud.r)/mag;
x.r += dx.r;
dx.i = -(u.r * ud.i + u.i * ud.r)/mag;
x.i += dx.i;
if( (fabs(dx.i) + fabs(dx.r)) < 1.0e-6 )
goto lupdon;
iter += 1;
} /* while iter < 500 */
if( final )
goto lupdon;
if( retry < 5 )
goto tryagn;
return(3);
lupdon:
/* Swap original and reduced polynomials */
q = &xcof[nsav];
p = &cof[0];
for( j=0; j<=n2; j++ )
{
cofj = *q;
*q-- = *p;
*p++ = cofj;
}
i = n;
n = n1;
n1 = i;
if( !final )
{
final = 1;
if( fabs(x.i/x.r) < 1.0e-4 )
x.i = 0.0;
xsav.r = x.r;
xsav.i = x.i;
goto finitr; /* do final iteration on original polynomial */
}
findon:
final = 0;
if( fabs(x.i/x.r) >= 1.0e-5 )
{
cofj = x.r + x.r;
mag = x.r * x.r + x.i * x.i;
n -= 2;
}
else
{ /* root is real */
zerrut:
x.i = 0;
cofj = x.r;
mag = 0;
n -= 1;
}
/* divide working polynomial cof(z) by z - x */
p = &cof[1];
*p += cofj * *(p-1);
for( j=1; j<n; j++ )
{
*(p+1) += cofj * *p - mag * *(p-1);
p++;
}
setrut:
root[nroot].r = x.r;
root[nroot].i = x.i;
nroot += 1;
if( mag != 0.0 )
{
x.i = -x.i;
mag = 0;
goto setrut; /* fill in the complex conjugate root */
}
if( n > 0 )
goto nxtrut;
return(0);
}
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