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This commit is contained in:
Gabriele Cosmo
2016-06-09 15:37:50 +02:00
parent a8e9364cea
commit 96c8bcd0af
6923 changed files with 198390 additions and 41849 deletions
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source/global/HEPNumerics/src/G4JTPolynomialSolver.cc
+43 -43
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@@ -23,8 +23,8 @@
// * acceptance of all terms of the Geant4 Software license. *
// ********************************************************************
//
// $Id: G4JTPolynomialSolver.cc,v 1.5 2006/06/29 19:00:18 gunter Exp $
// GEANT4 tag $Name: geant4-09-00 $
// $Id: G4JTPolynomialSolver.cc,v 1.6 2007/11/13 17:35:06 gcosmo Exp $
// GEANT4 tag $Name: geant4-09-01 $
//
// --------------------------------------------------------------------
// GEANT 4 class source file
@@ -52,7 +52,7 @@ G4JTPolynomialSolver::~G4JTPolynomialSolver()
{
}
G4int G4JTPolynomialSolver::FindRoots(G4double *op, G4int degree,
G4int G4JTPolynomialSolver::FindRoots(G4double *op, G4int degr,
G4double *zeror, G4double *zeroi)
{
G4double t=0.0, aa=0.0, bb=0.0, cc=0.0, factor=1.0;
@@ -67,7 +67,7 @@ G4int G4JTPolynomialSolver::FindRoots(G4double *op, G4int degree,
rot = 94.0*deg;
G4double cosr = std::cos(rot),
sinr = std::sin(rot);
n = degree;
n = degr;
// Algorithm fails if the leading coefficient is zero.
//
@@ -77,7 +77,7 @@ G4int G4JTPolynomialSolver::FindRoots(G4double *op, G4int degree,
//
while (!(op[n] != 0.0))
{
j = degree - n;
j = degr - n;
zeror[j] = 0.0;
zeroi[j] = 0.0;
n--;
@@ -86,14 +86,14 @@ G4int G4JTPolynomialSolver::FindRoots(G4double *op, G4int degree,
// Allocate buffers here
//
std::vector<G4double> temp(degree+1) ;
std::vector<G4double> pt(degree+1) ;
std::vector<G4double> temp(degr+1) ;
std::vector<G4double> pt(degr+1) ;
p.assign(degree+1,0) ;
qp.assign(degree+1,0) ;
k.assign(degree+1,0) ;
qk.assign(degree+1,0) ;
svk.assign(degree+1,0) ;
p.assign(degr+1,0) ;
qp.assign(degr+1,0) ;
k.assign(degr+1,0) ;
qk.assign(degr+1,0) ;
svk.assign(degr+1,0) ;
// Make a copy of the coefficients.
//
@@ -104,17 +104,17 @@ G4int G4JTPolynomialSolver::FindRoots(G4double *op, G4int degree,
{
if (n == 1) // Start the algorithm for one zero.
{
zeror[degree-1] = -p[1]/p[0];
zeroi[degree-1] = 0.0;
zeror[degr-1] = -p[1]/p[0];
zeroi[degr-1] = 0.0;
n -= 1;
return degree - n ;
return degr - n ;
}
if (n == 2) // Calculate the final zero or pair of zeros.
{
Quadratic(p[0],p[1],p[2],&zeror[degree-2],&zeroi[degree-2],
&zeror[degree-1],&zeroi[degree-1]);
Quadratic(p[0],p[1],p[2],&zeror[degr-2],&zeroi[degr-2],
&zeror[degr-1],&zeroi[degr-1]);
n -= 2;
return degree - n ;
return degr - n ;
}
// Find largest and smallest moduli of coefficients.
@@ -268,7 +268,7 @@ G4int G4JTPolynomialSolver::FindRoots(G4double *op, G4int degree,
// Deflate the polynomial, store the zero or zeros and
// return to the main algorithm.
//
j = degree - n;
j = degr - n;
zeror[j] = szr;
zeroi[j] = szi;
n -= nz;
@@ -297,7 +297,7 @@ G4int G4JTPolynomialSolver::FindRoots(G4double *op, G4int degree,
// Return with failure if no convergence with 20 shifts.
//
return degree - n;
return degr - n;
}
void G4JTPolynomialSolver::ComputeFixedShiftPolynomial(G4int l2, G4int *nz)
@@ -306,7 +306,7 @@ void G4JTPolynomialSolver::ComputeFixedShiftPolynomial(G4int l2, G4int *nz)
// in the linear or quadratic case. Initiates one of the variable shift
// iterations and returns with the number of zeros found.
G4double svu=0.0, svv=0.0, ui=0.0, vi=0.0, s=0.0;
G4double svu=0.0, svv=0.0, ui=0.0, vi=0.0, xs=0.0;
G4double betas=0.25, betav=0.25, oss=sr, ovv=v,
ss=0.0, vv=0.0, ts=1.0, tv=1.0;
G4double ots=0.0, otv=0.0;
@@ -328,7 +328,7 @@ void G4JTPolynomialSolver::ComputeFixedShiftPolynomial(G4int l2, G4int *nz)
ComputeNewEstimate(type,&ui,&vi);
vv = vi;
// Estimate s.
// Estimate xs.
//
ss = 0.0;
if (k[n-1] != 0.0) { ss = -p[n]/k[n-1]; }
@@ -343,7 +343,7 @@ void G4JTPolynomialSolver::ComputeFixedShiftPolynomial(G4int l2, G4int *nz)
continue;
}
// Compute relative measures of convergence of s and v sequences.
// Compute relative measures of convergence of xs and v sequences.
//
if (vv != 0.0) { tv = std::fabs((vv-ovv)/vv); }
if (ss != 0.0) { ts = std::fabs((ss-oss)/ss); }
@@ -375,7 +375,7 @@ void G4JTPolynomialSolver::ComputeFixedShiftPolynomial(G4int l2, G4int *nz)
{
svk[i] = k[i];
}
s = ss;
xs = ss;
// Choose iteration according to the fastest converging sequence.
//
@@ -383,7 +383,7 @@ void G4JTPolynomialSolver::ComputeFixedShiftPolynomial(G4int l2, G4int *nz)
stry = 0;
if (spass && (!vpass) || tss < tvv)
{
RealPolynomialIteration(&s,nz,&iflag);
RealPolynomialIteration(&xs,nz,&iflag);
if (*nz > 0) { return; }
// Linear iteration has failed. Flag that it has been
@@ -396,8 +396,8 @@ void G4JTPolynomialSolver::ComputeFixedShiftPolynomial(G4int l2, G4int *nz)
// If linear iteration signals an almost double real
// zero attempt quadratic iteration.
//
ui = -(s+s);
vi = s*s;
ui = -(xs+xs);
vi = xs*xs;
}
_quadratic_iteration:
@@ -421,7 +421,7 @@ _quadratic_iteration:
{
k[i] = svk[i];
}
RealPolynomialIteration(&s,nz,&iflag);
RealPolynomialIteration(&xs,nz,&iflag);
if (*nz > 0) { return; }
// Linear iteration has failed. Flag that it has been
@@ -434,8 +434,8 @@ _quadratic_iteration:
// If linear iteration signals an almost double real
// zero attempt quadratic iteration.
//
ui = -(s+s);
vi = s*s;
ui = -(xs+xs);
vi = xs*xs;
}
while (iflag != 0);
@@ -582,8 +582,8 @@ RealPolynomialIteration(G4double *sss, G4int *nz, G4int *iflag)
G4double t=0.;
G4double omp=0.;
G4double pv=0.0, kv=0.0, s= *sss;
G4double ms=0.0, mp=0.0, ee=0.0;
G4double pv=0.0, kv=0.0, xs= *sss;
G4double mx=0.0, mp=0.0, ee=0.0;
G4int i=1, j=0;
*nz = 0;
@@ -595,23 +595,23 @@ RealPolynomialIteration(G4double *sss, G4int *nz, G4int *iflag)
{
pv = p[0];
// Evaluate p at s.
// Evaluate p at xs.
//
qp[0] = pv;
for (i=1;i<=n;i++)
{
pv = pv*s + p[i];
pv = pv*xs + p[i];
qp[i] = pv;
}
mp = std::fabs(pv);
// Compute a rigorous bound on the error in evaluating p.
//
ms = std::fabs(s);
mx = std::fabs(xs);
ee = (mre/(are+mre))*std::fabs(qp[0]);
for (i=1;i<=n;i++)
{
ee = ee*ms + std::fabs(qp[i]);
ee = ee*mx + std::fabs(qp[i]);
}
// Iteration has converged sufficiently if the polynomial
@@ -620,7 +620,7 @@ RealPolynomialIteration(G4double *sss, G4int *nz, G4int *iflag)
if (mp <= 20.0*((are+mre)*ee-mre*mp))
{
*nz = 1;
szr = s;
szr = xs;
szi = 0.0;
return;
}
@@ -631,13 +631,13 @@ RealPolynomialIteration(G4double *sss, G4int *nz, G4int *iflag)
if (j > 10) { return; }
if (j >= 2)
{
if (!(std::fabs(t) > 0.001*std::fabs(s-t) || mp < omp))
if (!(std::fabs(t) > 0.001*std::fabs(xs-t) || mp < omp))
{
// A cluster of zeros near the real axis has been encountered.
// Return with iflag set to initiate a quadratic iteration.
//
*iflag = 1;
*sss = s;
*sss = xs;
return;
} // Return if the polynomial value has increased significantly.
}
@@ -650,7 +650,7 @@ RealPolynomialIteration(G4double *sss, G4int *nz, G4int *iflag)
qk[0] = kv;
for (i=1;i<n;i++)
{
kv = kv*s + k[i];
kv = kv*xs + k[i];
qk[i] = kv;
}
if (std::fabs(kv) <= std::fabs(k[n-1])*10.0*eta) // Use unscaled form.
@@ -661,7 +661,7 @@ RealPolynomialIteration(G4double *sss, G4int *nz, G4int *iflag)
k[i] = qk[i-1];
}
}
else // Use the scaled form of the recurrence if k at s is nonzero.
else // Use the scaled form of the recurrence if k at xs is nonzero.
{
t = -pv/kv;
k[0] = qp[0];
@@ -673,11 +673,11 @@ RealPolynomialIteration(G4double *sss, G4int *nz, G4int *iflag)
kv = k[0];
for (i=1;i<n;i++)
{
kv = kv*s + k[i];
kv = kv*xs + k[i];
}
t = 0.0;
if (std::fabs(kv) > std::fabs(k[n-1]*10.0*eta)) { t = -pv/kv; }
s += t;
xs += t;
}
}