297 lines
9.3 KiB
C++
297 lines
9.3 KiB
C++
//$$evalue.cpp eigen-value decomposition
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// Copyright (C) 1991,2,3,4: R B Davies
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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 "newmatrm.h"
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#include "precisio.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__,17); ++ExeCount; }
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#else
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#define REPORT {}
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#endif
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static void tred2(const SymmetricMatrix& A, DiagonalMatrix& D,
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DiagonalMatrix& E, Matrix& Z)
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{
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Tracer et("Evalue(tred2)");
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REPORT
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Real tol =
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FloatingPointPrecision::Minimum()/FloatingPointPrecision::Epsilon();
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int n = A.Nrows(); Z.ReSize(n,n); Z.Inject(A);
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D.ReSize(n); E.ReSize(n);
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Real* z = Z.Store(); int i;
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for (i=n-1; i > 0; i--) // i=0 is excluded
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{
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Real f = Z.element(i,i-1); Real g = 0.0;
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int k = i-1; Real* zik = z + i*n;
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while (k--) g += square(*zik++);
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Real h = g + square(f);
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if (g <= tol) { REPORT E.element(i) = f; h = 0.0; }
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else
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{
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REPORT
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g = sign(-sqrt(h), f); E.element(i) = g; h -= f*g;
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Z.element(i,i-1) = f-g; f = 0.0;
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Real* zji = z + i; Real* zij = z + i*n; Real* ej = E.Store();
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int j;
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for (j=0; j<i; j++)
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{
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*zji = (*zij++)/h; g = 0.0;
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Real* zjk = z + j*n; zik = z + i*n;
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k = j; while (k--) g += *zjk++ * (*zik++);
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k = i-j;
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if (k) for(;;)
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{ g += *zjk * (*zik++); if (!(--k)) break; zjk += n; }
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*ej++ = g/h; f += g * (*zji); zji += n;
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}
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Real hh = f / (h + h); zij = z + i*n; ej = E.Store();
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for (j=0; j<i; j++)
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{
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f = *zij++; g = *ej - hh * f; *ej++ = g;
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Real* zjk = z + j*n; Real* zik = z + i*n;
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Real* ek = E.Store(); k = j+1;
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while (k--) *zjk++ -= ( f*(*ek++) + g*(*zik++) );
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}
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}
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D.element(i) = h;
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}
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D.element(0) = 0.0; E.element(0) = 0.0;
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for (i=0; i<n; i++)
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{
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if (D.element(i) != 0.0)
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{
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REPORT
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for (int j=0; j<i; j++)
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{
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Real g = 0.0;
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Real* zik = z + i*n; Real* zkj = z + j;
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int k = i;
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if (k) for (;;)
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{ g += *zik++ * (*zkj); if (!(--k)) break; zkj += n; }
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Real* zki = z + i; zkj = z + j;
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k = i;
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if (k) for (;;)
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{ *zkj -= g * (*zki); if (!(--k)) break; zkj += n; zki += n; }
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}
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}
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Real* zij = z + i*n; Real* zji = z + i;
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int j = i;
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if (j) for (;;)
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{ *zij++ = 0.0; *zji = 0.0; if (!(--j)) break; zji += n; }
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D.element(i) = *zij; *zij = 1.0;
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}
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}
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static void tql2(DiagonalMatrix& D, DiagonalMatrix& E, Matrix& Z)
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{
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Tracer et("Evalue(tql2)");
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REPORT
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Real eps = FloatingPointPrecision::Epsilon();
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int n = D.Nrows(); Real* z = Z.Store(); int l;
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for (l=1; l<n; l++) E.element(l-1) = E.element(l);
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Real b = 0.0; Real f = 0.0; E.element(n-1) = 0.0;
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for (l=0; l<n; l++)
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{
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int i,j;
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Real& dl = D.element(l); Real& el = E.element(l);
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Real h = eps * ( fabs(dl) + fabs(el) );
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if (b < h) { REPORT b = h; }
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int m;
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for (m=l; m<n; m++) if (fabs(E.element(m)) <= b) break;
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bool test = false;
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for (j=0; j<30; j++)
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{
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if (m==l) { REPORT test = true; break; }
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Real& dl1 = D.element(l+1);
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Real g = dl; Real p = (dl1-g) / (2.0*el); Real r = sqrt(p*p + 1.0);
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dl = el / (p < 0.0 ? p-r : p+r); Real h = g - dl; f += h;
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Real* dlx = &dl1; i = n-l-1; while (i--) *dlx++ -= h;
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p = D.element(m); Real c = 1.0; Real s = 0.0;
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for (i=m-1; i>=l; i--)
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{
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Real ei = E.element(i); Real di = D.element(i);
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Real& ei1 = E.element(i+1);
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g = c * ei; h = c * p;
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if ( fabs(p) >= fabs(ei))
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{
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REPORT
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c = ei / p; r = sqrt(c*c + 1.0);
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ei1 = s*p*r; s = c/r; c = 1.0/r;
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}
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else
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{
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REPORT
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c = p / ei; r = sqrt(c*c + 1.0);
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ei1 = s * ei * r; s = 1.0/r; c /= r;
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}
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p = c * di - s*g; D.element(i+1) = h + s * (c*g + s*di);
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Real* zki = z + i; Real* zki1 = zki + 1; int k = n;
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if (k) for (;;)
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{
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REPORT
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h = *zki1; *zki1 = s*(*zki) + c*h; *zki = c*(*zki) - s*h;
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if (!(--k)) break;
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zki += n; zki1 += n;
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}
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}
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el = s*p; dl = c*p;
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if (fabs(el) <= b) { REPORT; test = true; break; }
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}
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if (!test) Throw ( ConvergenceException(D) );
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dl += f;
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}
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/*
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for (int i=0; i<n; i++)
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{
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int k = i; Real p = D.element(i);
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for (int j=i+1; j<n; j++)
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{ if (D.element(j) < p) { k = j; p = D.element(j); } }
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if (k != i)
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{
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D.element(k) = D.element(i); D.element(i) = p; int j = n;
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Real* zji = z + i; Real* zjk = z + k;
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if (j) for(;;)
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{
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p = *zji; *zji = *zjk; *zjk = p;
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if (!(--j)) break;
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zji += n; zjk += n;
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}
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}
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}
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*/
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}
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static void tred3(const SymmetricMatrix& X, DiagonalMatrix& D,
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DiagonalMatrix& E, SymmetricMatrix& A)
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{
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Tracer et("Evalue(tred3)");
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REPORT
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Real tol =
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FloatingPointPrecision::Minimum()/FloatingPointPrecision::Epsilon();
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int n = X.Nrows(); A = X; D.ReSize(n); E.ReSize(n);
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Real* ei = E.Store() + n;
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for (int i = n-1; i >= 0; i--)
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{
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Real h = 0.0; Real f = - FloatingPointPrecision::Maximum();
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Real* d = D.Store(); Real* a = A.Store() + (i*(i+1))/2; int k = i;
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while (k--) { f = *a++; *d++ = f; h += square(f); }
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if (h <= tol) { REPORT *(--ei) = 0.0; h = 0.0; }
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else
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{
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REPORT
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Real g = sign(-sqrt(h), f); *(--ei) = g; h -= f*g;
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f -= g; *(d-1) = f; *(a-1) = f; f = 0.0;
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Real* dj = D.Store(); Real* ej = E.Store(); int j;
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for (j = 0; j < i; j++)
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{
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Real* dk = D.Store(); Real* ak = A.Store()+(j*(j+1))/2;
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Real g = 0.0; k = j;
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while (k--) g += *ak++ * *dk++;
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k = i-j; int l = j;
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if (k) for (;;) { g += *ak * *dk++; if (!(--k)) break; ak += ++l; }
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g /= h; *ej++ = g; f += g * *dj++;
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}
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Real hh = f / (2 * h); Real* ak = A.Store();
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dj = D.Store(); ej = E.Store();
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for (j = 0; j < i; j++)
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{
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f = *dj++; g = *ej - hh * f; *ej++ = g;
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Real* dk = D.Store(); Real* ek = E.Store(); k = j+1;
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while (k--) { *ak++ -= (f * *ek++ + g * *dk++); }
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}
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}
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*d = *a; *a = h;
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}
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}
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static void tql1(DiagonalMatrix& D, DiagonalMatrix& E)
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{
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Tracer et("Evalue(tql1)");
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REPORT
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Real eps = FloatingPointPrecision::Epsilon();
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int n = D.Nrows(); int l;
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for (l=1; l<n; l++) E.element(l-1) = E.element(l);
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Real b = 0.0; Real f = 0.0; E.element(n-1) = 0.0;
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for (l=0; l<n; l++)
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{
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int i,j;
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Real& dl = D.element(l); Real& el = E.element(l);
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Real h = eps * ( fabs(dl) + fabs(el) );
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if (b < h) b = h;
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int m;
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for (m=l; m<n; m++) if (fabs(E.element(m)) <= b) break;
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bool test = false;
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for (j=0; j<30; j++)
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{
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if (m==l) { REPORT test = true; break; }
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Real& dl1 = D.element(l+1);
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Real g = dl; Real p = (dl1-g) / (2.0*el); Real r = sqrt(p*p + 1.0);
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dl = el / (p < 0.0 ? p-r : p+r); Real h = g - dl; f += h;
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Real* dlx = &dl1; i = n-l-1; while (i--) *dlx++ -= h;
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p = D.element(m); Real c = 1.0; Real s = 0.0;
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for (i=m-1; i>=l; i--)
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{
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Real ei = E.element(i); Real di = D.element(i);
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Real& ei1 = E.element(i+1);
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g = c * ei; h = c * p;
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if ( fabs(p) >= fabs(ei))
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{
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REPORT
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c = ei / p; r = sqrt(c*c + 1.0);
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ei1 = s*p*r; s = c/r; c = 1.0/r;
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}
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else
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{
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REPORT
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c = p / ei; r = sqrt(c*c + 1.0);
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ei1 = s * ei * r; s = 1.0/r; c /= r;
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}
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p = c * di - s*g; D.element(i+1) = h + s * (c*g + s*di);
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}
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el = s*p; dl = c*p;
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if (fabs(el) <= b) { REPORT test = true; break; }
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}
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if (!test) Throw ( ConvergenceException(D) );
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Real p = dl + f;
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test = false;
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for (i=l; i>0; i--)
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{
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if (p < D.element(i-1)) { REPORT D.element(i) = D.element(i-1); }
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else { REPORT test = true; break; }
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}
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if (!test) i=0;
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D.element(i) = p;
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}
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}
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void EigenValues(const SymmetricMatrix& A, DiagonalMatrix& D, Matrix& Z)
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{ REPORT DiagonalMatrix E; tred2(A, D, E, Z); tql2(D, E, Z); SortSV(D,Z,true); }
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void EigenValues(const SymmetricMatrix& X, DiagonalMatrix& D)
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{ REPORT DiagonalMatrix E; SymmetricMatrix A; tred3(X,D,E,A); tql1(D,E); }
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void EigenValues(const SymmetricMatrix& X, DiagonalMatrix& D,
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SymmetricMatrix& A)
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{ REPORT DiagonalMatrix E; tred3(X,D,E,A); tql1(D,E); }
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#ifdef use_namespace
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}
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#endif
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