3dpcp/.svn/pristine/5c/5c0a6b3cc1d208e8fc4b49cf1ab9fa37c438f828.svn-base
2012-09-16 14:33:11 +02:00

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//$$jacobi.cpp jacobi eigenvalue analysis
// Copyright (C) 1991,2,3,4: R B Davies
//#define WANT_STREAM
#define WANT_MATH
#include "include.h"
#include "newmatap.h"
#include "precisio.h"
#include "newmatrm.h"
#ifdef use_namespace
namespace NEWMAT {
#endif
#ifdef DO_REPORT
#define REPORT { static ExeCounter ExeCount(__LINE__,18); ++ExeCount; }
#else
#define REPORT {}
#endif
void Jacobi(const SymmetricMatrix& X, DiagonalMatrix& D, SymmetricMatrix& A,
Matrix& V, bool eivec)
{
Real epsilon = FloatingPointPrecision::Epsilon();
Tracer et("Jacobi");
REPORT
int n = X.Nrows(); DiagonalMatrix B(n), Z(n); D.ReSize(n); A = X;
if (eivec) { REPORT V.ReSize(n,n); D = 1.0; V = D; }
B << A; D = B; Z = 0.0; A.Inject(Z);
bool converged = false;
for (int i=1; i<=50; i++)
{
Real sm=0.0; Real* a = A.Store(); int p = A.Storage();
while (p--) sm += fabs(*a++); // have previously zeroed diags
if (sm==0.0) { REPORT converged = true; break; }
Real tresh = (i<4) ? 0.2 * sm / square(n) : 0.0; a = A.Store();
for (p = 0; p < n; p++)
{
Real* ap1 = a + (p*(p+1))/2;
Real& zp = Z.element(p); Real& dp = D.element(p);
for (int q = p+1; q < n; q++)
{
Real* ap = ap1; Real* aq = a + (q*(q+1))/2;
Real& zq = Z.element(q); Real& dq = D.element(q);
Real& apq = A.element(q,p);
Real g = 100 * fabs(apq); Real adp = fabs(dp); Real adq = fabs(dq);
if (i>4 && g < epsilon*adp && g < epsilon*adq) { REPORT apq = 0.0; }
else if (fabs(apq) > tresh)
{
REPORT
Real t; Real h = dq - dp; Real ah = fabs(h);
if (g < epsilon*ah) { REPORT t = apq / h; }
else
{
REPORT
Real theta = 0.5 * h / apq;
t = 1.0 / ( fabs(theta) + sqrt(1.0 + square(theta)) );
if (theta<0.0) { REPORT t = -t; }
}
Real c = 1.0 / sqrt(1.0 + square(t)); Real s = t * c;
Real tau = s / (1.0 + c); h = t * apq;
zp -= h; zq += h; dp -= h; dq += h; apq = 0.0;
int j = p;
while (j--)
{
g = *ap; h = *aq;
*ap++ = g-s*(h+g*tau); *aq++ = h+s*(g-h*tau);
}
int ip = p+1; j = q-ip; ap += ip++; aq++;
while (j--)
{
g = *ap; h = *aq;
*ap = g-s*(h+g*tau); *aq++ = h+s*(g-h*tau);
ap += ip++;
}
if (q < n-1) // last loop is non-empty
{
int iq = q+1; j = n-iq; ap += ip++; aq += iq++;
for (;;)
{
g = *ap; h = *aq;
*ap = g-s*(h+g*tau); *aq = h+s*(g-h*tau);
if (!(--j)) break;
ap += ip++; aq += iq++;
}
}
if (eivec)
{
REPORT
RectMatrixCol VP(V,p); RectMatrixCol VQ(V,q);
Rotate(VP, VQ, tau, s);
}
}
}
}
B = B + Z; D = B; Z = 0.0;
}
if (!converged) Throw(ConvergenceException(X));
if (eivec) SortSV(D, V, true);
else SortAscending(D);
}
void Jacobi(const SymmetricMatrix& X, DiagonalMatrix& D)
{ REPORT SymmetricMatrix A; Matrix V; Jacobi(X,D,A,V,false); }
void Jacobi(const SymmetricMatrix& X, DiagonalMatrix& D, SymmetricMatrix& A)
{ REPORT Matrix V; Jacobi(X,D,A,V,false); }
void Jacobi(const SymmetricMatrix& X, DiagonalMatrix& D, Matrix& V)
{ REPORT SymmetricMatrix A; Jacobi(X,D,A,V,true); }
#ifdef use_namespace
}
#endif