// Calculate the roots of the approximation
int AlgRemez::root() {
long i,j;
bigfloat x,dx=0.05;
bigfloat upper=1, lower=-100000;
bigfloat tol = 1e-20;
bigfloat *poly = new bigfloat[neq+1];
// First find the numerator roots
for (i=0; i<=n; i++) poly[i] = param[i];
//for (i=0; i<=n; i++) printf("%d %e\n", i, (double)poly[i]);
for (i=n-1; i>=0; i--) {
roots[i] = rtnewt(poly,i+1,lower,upper,tol);
//printf("root[%d] = %e\n", i, (double)roots[i]);
if (roots[i] == 0.0) {
printf("Failure to converge on root %d/%d\n", i+1, n);
return 0;
}
poly[0] = -poly[0]/roots[i];
for (j=1; j<=i; j++) poly[j] = (poly[j-1] - poly[j])/roots[i];
}
// Now find the denominator roots
poly[d] = 1l;
for (i=0; i<d; i++) poly[i] = param[n+1+i];
//for (i=0; i<=d; i++) printf("%d %e\n", i, (double)poly[i]);
for (i=d-1; i>=0; i--) {
poles[i]=rtnewt(poly,i+1,lower,upper,tol);
//printf("pole[%d] = %e\n", i, (double)poles[i]);
if (poles[i] == 0.0) {
printf("Failure to converge on pole %d/%d\n", i+1, d);
return 0;
}
poly[0] = -poly[0]/poles[i];
for (j=1; j<=i; j++) poly[j] = (poly[j-1] - poly[j])/poles[i];
}
norm = param[n];
//printf("Normalisation constant is %e\n",(double)norm);
//for (i=0; i<n; i++) printf("%ld root = %e\n",i,(double)roots[i]);
//for (i=0; i<d; i++) printf("%ld pole = %e\n",i,(double)poles[i]);
delete [] poly;
return 1;
}
// Calculate the roots of the approximation
int AlgRemez::root() {
char *fname = "root()";
// VRB.Func(cname,fname);
long i,j;
bigfloat x,dx=0.05;
bigfloat upper=1, lower=-100000;
bigfloat tol = 1e-20;
bigfloat *poly = new bigfloat[neq+1];
if(poly == 0) ERR.Pointer(cname,fname,"poly");
VRB.Smalloc(cname,fname,"poly",poly,(n+d+2) * sizeof(bigfloat));
// First find the numerator roots
for (i=0; i<=n; i++) poly[i] = param[i];
for (i=n-1; i>=0; i--) {
roots[i] = rtnewt(poly,i+1,lower,upper,tol);
if (roots[i] == 0.0) {
VRB.Warn(cname,fname,"Failure to converge on root\n");
return 0;
}
poly[0] = -poly[0]/roots[i];
for (j=1; j<=i; j++) poly[j] = (poly[j-1] - poly[j])/roots[i];
}
// Now find the denominator roots
poly[d] = 1l;
for (i=0; i<d; i++) poly[i] = param[n+1+i];
for (i=d-1; i>=0; i--) {
poles[i]=rtnewt(poly,i+1,lower,upper,tol);
if (poles[i] == 0.0) {
VRB.Warn(cname,fname,"Failure to converge on root");
return 0;
}
poly[0] = -poly[0]/poles[i];
for (j=1; j<=i; j++) poly[j] = (poly[j-1] - poly[j])/poles[i];
}
norm = param[n];
VRB.Result(cname,fname,"Normalisation constant is %0.14e\n",(double)norm);
for (i=0; i<n; i++) VRB.Result(cname,fname,"%ld root = %0.14e\n",i,(Float)roots[i]);
for (i=0; i<d; i++) VRB.Result(cname,fname,"%ld pole = %0.14e\n",i,(Float)poles[i]);
VRB.Sfree(cname,fname, "poly",poly);
delete [] poly;
return 1;
}
/******************************************************************************
* @brief Iterate to find actual shear stress during saltation.
*****************************************************************************/
void
shear_stress(double U10,
double ZO,
double *ushear,
double *Zo_salt,
double utshear)
{
double umin, umax, xacc;
double fl, fh, df;
/* Find min & max shear stress to bracket value. */
umin = utshear;
umax = CONST_KARMAN * U10;
xacc = 0.10 * umin;
/* Check to see if value is bracketed. */
get_shear(umin, &fl, &df, U10, 10.);
get_shear(umax, &fh, &df, U10, 10.);
if (fl < 0.0 && fh < 0.0) {
log_err("Solution surpasses upper boundary."
"fl(%f)=%f, fh(%f)=%f", umin, fl, umax, fh);
}
if (fl > 0.0 && fh > 0.0) {
*Zo_salt = ZO;
*ushear = CONST_KARMAN * U10 / log(10. / ZO);
}
else {
/* Iterate to find actual shear stress. */
*ushear = rtnewt(umin, umax, xacc, U10, 10.);
*Zo_salt = 0.12 * (*ushear) * (*ushear) / (2. * CONST_G);
}
}
void shear_stress(double U10, double ZO,double *ushear, double *Zo_salt, double utshear)
{
double umin, umax, xacc;
double fl, fh, df;
/* Find min & max shear stress to bracket value. */
umin = utshear;
umax = von_K*U10;
xacc = 0.10*umin;
/* Check to see if value is bracketed. */
get_shear(umin,&fl,&df, U10, 10.);
get_shear(umax,&fh,&df, U10, 10.);
if(fl < 0.0 && fh < 0.0) {
fprintf(stderr, "Solution in rtnewt surpasses upper boundary.\n");
fprintf(stderr, "fl(%f)=%f, fh(%f)=%f\n",umin, fl, umax, fh);
exit(0);
}
if(fl > 0.0 && fh > 0.0) {
// fprintf(stderr, "No solution possible that exceeds utshear.\n");
// fprintf(stderr, "utshear=%f, u10=%f\n",utshear, U10);
*Zo_salt = ZO;
*ushear = von_K * U10 / log(10./ZO);
}
else {
/* Iterate to find actual shear stress. */
*ushear = rtnewt (umin, umax, xacc, U10, 10.);
*Zo_salt = 0.12 *(*ushear) * (*ushear) / (2.* G_STD);
}
}