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RealSchur: use makeHouseholder() to construct the transformation.

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This commit is contained in:
Jitse Niesen 2010-04-07 10:27:27 +01:00
parent cc57df9bea
commit b6829e1d5b
1 changed files with 50 additions and 50 deletions
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100
Eigen/src/Eigenvalues/RealSchur.h
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@ -93,11 +93,13 @@ template<typename _MatrixType> class RealSchur
EigenvalueType m_eivalues; EigenvalueType m_eivalues;
bool m_isInitialized; bool m_isInitialized;
typedef Matrix<Scalar,3,1> Vector3s;
Scalar computeNormOfT(); Scalar computeNormOfT();
int findSmallSubdiagEntry(int n, Scalar norm); int findSmallSubdiagEntry(int n, Scalar norm);
void computeShift(Scalar& x, Scalar& y, Scalar& w, int iu, Scalar& exshift, int iter); void computeShift(Scalar& x, Scalar& y, Scalar& w, int iu, Scalar& exshift, int iter);
void findTwoSmallSubdiagEntries(Scalar x, Scalar y, Scalar w, int l, int& m, int iu, Scalar& p, Scalar& q, Scalar& r); void findTwoSmallSubdiagEntries(Scalar x, Scalar y, Scalar w, int il, int& m, int iu, Vector3s& firstHouseholderVector);
void doFrancisStep(int l, int m, int iu, Scalar p, Scalar q, Scalar r, Scalar x, Scalar* workspace); void doFrancisStep(int il, int m, int iu, const Vector3s& firstHouseholderVector, Scalar* workspace);
void splitOffTwoRows(int iu, Scalar exshift); void splitOffTwoRows(int iu, Scalar exshift);
}; };
@ -147,12 +149,13 @@ void RealSchur<MatrixType>::compute(const MatrixType& matrix)
} }
else // No convergence yet else // No convergence yet
{ {
Scalar p = 0, q = 0, r = 0, x, y, w; Scalar x, y, w;
Vector3s firstHouseholderVector;
computeShift(x, y, w, iu, exshift, iter); computeShift(x, y, w, iu, exshift, iter);
iter = iter + 1; // (Could check iteration count here.) iter = iter + 1; // (Could check iteration count here.)
int m; int m;
findTwoSmallSubdiagEntries(x, y, w, il, m, iu, p, q, r); findTwoSmallSubdiagEntries(x, y, w, il, m, iu, firstHouseholderVector);
doFrancisStep(il, m, iu, p, q, r, x, workspace); doFrancisStep(il, m, iu, firstHouseholderVector, workspace);
} // check convergence } // check convergence
} // while (iu >= 0) } // while (iu >= 0)
@ -265,8 +268,10 @@ inline void RealSchur<MatrixType>::computeShift(Scalar& x, Scalar& y, Scalar& w,
// Look for two consecutive small sub-diagonal elements // Look for two consecutive small sub-diagonal elements
template<typename MatrixType> template<typename MatrixType>
inline void RealSchur<MatrixType>::findTwoSmallSubdiagEntries(Scalar x, Scalar y, Scalar w, int il, int& m, int iu, Scalar& p, Scalar& q, Scalar& r) inline void RealSchur<MatrixType>::findTwoSmallSubdiagEntries(Scalar x, Scalar y, Scalar w, int il, int& m, int iu, Vector3s& firstHouseholderVector)
{ {
Scalar p = 0, q = 0, r = 0;
m = iu-2; m = iu-2;
while (m >= il) while (m >= il)
{ {
@ -298,64 +303,59 @@ inline void RealSchur<MatrixType>::findTwoSmallSubdiagEntries(Scalar x, Scalar y
if (i > m+2) if (i > m+2)
m_matT.coeffRef(i,i-3) = 0.0; m_matT.coeffRef(i,i-3) = 0.0;
} }
firstHouseholderVector << p, q, r;
} }
// Double QR step involving rows il:iu and columns m:iu // Double QR step involving rows il:iu and columns m:iu
template<typename MatrixType> template<typename MatrixType>
inline void RealSchur<MatrixType>::doFrancisStep(int il, int m, int iu, Scalar p, Scalar q, Scalar r, Scalar x, Scalar* workspace) inline void RealSchur<MatrixType>::doFrancisStep(int il, int m, int iu, const Vector3s& firstHouseholderVector, Scalar* workspace)
{ {
assert(m >= il);
assert(m <= iu-2);
const int size = m_matU.cols(); const int size = m_matU.cols();
for (int k = m; k <= iu-1; ++k) for (int k = m; k <= iu-2; ++k)
{ {
int notlast = (k != iu-1); bool firstIteration = (k == m);
if (k != m) {
p = m_matT.coeff(k,k-1);
q = m_matT.coeff(k+1,k-1);
r = notlast ? m_matT.coeff(k+2,k-1) : Scalar(0);
x = ei_abs(p) + ei_abs(q) + ei_abs(r);
if (x != 0.0)
{
p = p / x;
q = q / x;
r = r / x;
}
}
if (x == 0.0) Vector3s v;
break; if (firstIteration)
v = firstHouseholderVector;
else
v = m_matT.template block<3,1>(k,k-1);
Scalar s = ei_sqrt(p * p + q * q + r * r); Scalar tau, beta;
Matrix<Scalar, 2, 1> ess;
if (p < 0) v.makeHouseholder(ess, tau, beta);
s = -s;
if (beta != Scalar(0)) // if v is not zero
if (s != 0)
{ {
if (k != m) if (firstIteration && k > il)
m_matT.coeffRef(k,k-1) = -s * x;
else if (il != m)
m_matT.coeffRef(k,k-1) = -m_matT.coeff(k,k-1); m_matT.coeffRef(k,k-1) = -m_matT.coeff(k,k-1);
else if (!firstIteration)
m_matT.coeffRef(k,k-1) = beta;
p = p + s; // These Householder transformations form the O(n^3) part of the algorithm
m_matT.block(k, k, 3, size-k).applyHouseholderOnTheLeft(ess, tau, workspace);
m_matT.block(0, k, std::min(iu,k+3) + 1, 3).applyHouseholderOnTheRight(ess, tau, workspace);
m_matU.block(0, k, size, 3).applyHouseholderOnTheRight(ess, tau, workspace);
}
}
if (notlast) Matrix<Scalar, 2, 1> v = m_matT.template block<2,1>(iu-1, iu-2);
{ Scalar tau, beta;
Matrix<Scalar, 2, 1> ess(q/p, r/p); Matrix<Scalar, 1, 1> ess;
m_matT.block(k, k, 3, size-k).applyHouseholderOnTheLeft(ess, p/s, workspace); v.makeHouseholder(ess, tau, beta);
m_matT.block(0, k, std::min(iu,k+3) + 1, 3).applyHouseholderOnTheRight(ess, p/s, workspace);
m_matU.block(0, k, size, 3).applyHouseholderOnTheRight(ess, p/s, workspace); if (beta != Scalar(0)) // if v is not zero
} {
else m_matT.coeffRef(iu-1, iu-2) = beta;
{ m_matT.block(iu-1, iu-1, 2, size-iu+1).applyHouseholderOnTheLeft(ess, tau, workspace);
Matrix<Scalar, 1, 1> ess; m_matT.block(0, iu-1, iu+1, 2).applyHouseholderOnTheRight(ess, tau, workspace);
ess.coeffRef(0) = q/p; m_matU.block(0, iu-1, size, 2).applyHouseholderOnTheRight(ess, tau, workspace);
m_matT.block(k, k, 2, size-k).applyHouseholderOnTheLeft(ess, p/s, workspace); }
m_matT.block(0, k, std::min(iu,k+3) + 1, 2).applyHouseholderOnTheRight(ess, p/s, workspace);
m_matU.block(0, k, size, 2).applyHouseholderOnTheRight(ess, p/s, workspace);
}
} // (s != 0)
} // k loop
} }
#endif // EIGEN_REAL_SCHUR_H #endif // EIGEN_REAL_SCHUR_H