static void tred3(const SymmetricMatrix& X, DiagonalMatrix& D,
DiagonalMatrix& E, SymmetricMatrix& A)
{
Tracer et("Evalue(tred3)");
Real tol =
FloatingPointPrecision::Minimum()/FloatingPointPrecision::Epsilon();
int n = X.Nrows(); A = X; D.ReSize(n); E.ReSize(n);
Real* ei = E.Store() + n;
for (int i = n-1; i >= 0; i--)
{
Real h = 0.0; Real f;
Real* d = D.Store(); Real* a = A.Store() + (i*(i+1))/2; int k = i;
while (k--) { f = *a++; *d++ = f; h += square(f); }
if (h <= tol) { *(--ei) = 0.0; h = 0.0; }
else
{
Real g = sign(-sqrt(h), f); *(--ei) = g; h -= f*g;
f -= g; *(d-1) = f; *(a-1) = f; f = 0.0;
Real* dj = D.Store(); Real* ej = E.Store(); int j;
for (j = 0; j < i; j++)
{
Real* dk = D.Store(); Real* ak = A.Store()+(j*(j+1))/2;
Real g = 0.0; k = j;
while (k--) g += *ak++ * *dk++;
k = i-j; int l = j;
while (k--) { g += *ak * *dk++; ak += ++l; }
g /= h; *ej++ = g; f += g * *dj++;
}
Real hh = f / (2 * h); Real* ak = A.Store();
dj = D.Store(); ej = E.Store();
for (j = 0; j < i; j++)
{
f = *dj++; g = *ej - hh * f; *ej++ = g;
Real* dk = D.Store(); Real* ek = E.Store(); k = j+1;
while (k--) { *ak++ -= (f * *ek++ + g * *dk++); }
}
}
*d = *a; *a = h;
}
}
ReturnMatrix Cholesky(const SymmetricMatrix& S)
{
REPORT
Tracer trace("Cholesky");
int nr = S.Nrows();
LowerTriangularMatrix T(nr);
Real* s = S.Store(); Real* t = T.Store(); Real* ti = t;
for (int i=0; i<nr; i++)
{
Real* tj = t; Real sum; int k;
for (int j=0; j<i; j++)
{
Real* tk = ti; sum = 0.0; k = j;
while (k--) { sum += *tj++ * *tk++; }
*tk = (*s++ - sum) / *tj++;
}
sum = 0.0; k = i;
while (k--) { sum += square(*ti++); }
Real d = *s++ - sum;
if (d<=0.0) Throw(NPDException(S));
*ti++ = sqrt(d);
}
T.release(); return T.for_return();
}
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);
}
