123 lines
3.9 KiB
Text
123 lines
3.9 KiB
Text
//$$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
|
|
|