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