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Fix cost evaluation. (chain product for integral power)

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Chen-Pang He 2012-09-22 17:37:14 +08:00
parent 446d14f6ad
commit dd8034bd1c
2 changed files with 35 additions and 18 deletions
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30
unsupported/Eigen/src/MatrixFunctions/MatrixPower.h
View File

@ -157,7 +157,7 @@ typename MatrixType::RealScalar MatrixPower<MatrixType>::modfAndInit(RealScalar
*intpart = std::floor(x); *intpart = std::floor(x);
RealScalar res = x - *intpart; RealScalar res = x - *intpart;
if (!m_init && res) { // !init && res if (!m_init && res) {
const ComplexSchur<MatrixType> schurOfA(m_A); const ComplexSchur<MatrixType> schurOfA(m_A);
m_T = schurOfA.matrixT(); m_T = schurOfA.matrixT();
m_U = schurOfA.matrixU(); m_U = schurOfA.matrixU();
@ -209,29 +209,41 @@ template<typename MatrixType>
template<typename PlainObject, typename ResultType> template<typename PlainObject, typename ResultType>
void MatrixPower<MatrixType>::computeIntPower(const PlainObject& b, ResultType& res, RealScalar p) void MatrixPower<MatrixType>::computeIntPower(const PlainObject& b, ResultType& res, RealScalar p)
{ {
if (b.cols() > m_A.cols()) { if (b.cols() >= m_A.cols()) {
m_tmp2 = MatrixType::Identity(m_A.rows(),m_A.cols()); m_tmp2 = MatrixType::Identity(m_A.rows(),m_A.cols());
computeIntPower(m_tmp2, p); computeIntPower(m_tmp2, p);
res.noalias() = m_tmp2 * b; res.noalias() = m_tmp2 * b;
} else { }
else {
RealScalar pp = std::abs(p); RealScalar pp = std::abs(p);
int cost = internal::binary_powering_cost(pp); int squarings, applyings = internal::binary_powering_cost(pp, &squarings);
bool init = false; bool init = false;
if (p==0) { if (p==0) {
res = b; res = b;
return; return;
} }
if (p<0) m_tmp1 = m_A.inverse(); else if (p>0) {
else m_tmp1 = m_A; m_tmp1 = m_A;
}
else if (b.cols() * (pp - applyings) <= m_A.cols() * squarings) {
PartialPivLU<MatrixType> A(m_A);
res = A.solve(b);
for (--pp; pp >= 1; --pp)
res = A.solve(res);
return;
}
else {
m_tmp1 = m_A.inverse();
}
while (b.cols()*pp > m_A.cols()*cost) { while (b.cols() * (pp - applyings) > m_A.cols() * squarings) {
if (std::fmod(pp, 2) >= 1) { if (std::fmod(pp, 2) >= 1) {
apply(b, res, init); apply(b, res, init);
--cost; --applyings;
} }
m_tmp1 *= m_tmp1; m_tmp1 *= m_tmp1;
--cost; --squarings;
pp /= 2; pp /= 2;
} }
for (; pp >= 1; --pp) for (; pp >= 1; --pp)

23
unsupported/Eigen/src/MatrixFunctions/MatrixPowerBase.h
View File

@ -34,15 +34,18 @@ struct traits<MatrixPowerProductBase<Derived> > : traits<Derived>
{ }; { };
template<typename T> template<typename T>
inline int binary_powering_cost(T p) inline int binary_powering_cost(T p, int* squarings)
{ {
int cost, tmp; int applyings=0, tmp;
frexp(p, &cost);
if (frexp(p, squarings) != 0.5);
--*squarings;
while (std::frexp(p, &tmp), tmp > 0) { while (std::frexp(p, &tmp), tmp > 0) {
p -= std::ldexp(static_cast<T>(0.5), tmp); p -= std::ldexp(static_cast<T>(0.5), tmp);
++cost; ++applyings;
} }
return cost; return applyings;
} }
inline int matrix_power_get_pade_degree(float normIminusT) inline int matrix_power_get_pade_degree(float normIminusT)
@ -145,7 +148,7 @@ void MatrixPowerTriangularAtomic<MatrixType,UpLo>::computePade(int degree, const
RealScalar p) const RealScalar p) const
{ {
int i = degree<<1; int i = degree<<1;
res = (p-(i>>1)) / ((i-1)<<1) * IminusT; res = (p-degree) / ((i-1)<<1) * IminusT;
for (--i; i; --i) { for (--i; i; --i) {
res = (MatrixType::Identity(m_T.rows(), m_T.cols()) + res).template triangularView<UpLo>() res = (MatrixType::Identity(m_T.rows(), m_T.cols()) + res).template triangularView<UpLo>()
.solve((i==1 ? -p : i&1 ? (-p-(i>>1))/(i<<1) : (p-(i>>1))/((i-1)<<1)) * IminusT).eval(); .solve((i==1 ? -p : i&1 ? (-p-(i>>1))/(i<<1) : (p-(i>>1))/((i-1)<<1)) * IminusT).eval();
@ -166,9 +169,11 @@ void MatrixPowerTriangularAtomic<MatrixType,UpLo>::compute2x2(MatrixType& res, R
res(i,i) = pow(m_T(i,i), p); res(i,i) = pow(m_T(i,i), p);
if (m_T(i-1,i-1) == m_T(i,i)) { if (m_T(i-1,i-1) == m_T(i,i)) {
res(i-1,i) = p * pow(m_T(i-1,i), p-1); res(i-1,i) = p * pow(m_T(i-1,i), p-1);
} else if (2*abs(m_T(i-1,i-1)) < abs(m_T(i,i)) || 2*abs(m_T(i,i)) < abs(m_T(i-1,i-1))) { }
else if (2*abs(m_T(i-1,i-1)) < abs(m_T(i,i)) || 2*abs(m_T(i,i)) < abs(m_T(i-1,i-1))) {
res(i-1,i) = m_T(i-1,i) * (res(i,i)-res(i-1,i-1)) / (m_T(i,i)-m_T(i-1,i-1)); res(i-1,i) = m_T(i-1,i) * (res(i,i)-res(i-1,i-1)) / (m_T(i,i)-m_T(i-1,i-1));
} else { }
else {
// computation in previous branch is inaccurate if abs(m_T(i,i)) \approx abs(m_T(i-1,i-1)) // computation in previous branch is inaccurate if abs(m_T(i,i)) \approx abs(m_T(i-1,i-1))
int unwindingNumber = std::ceil(((logTdiag[i]-logTdiag[i-1]).imag() - M_PI) / (2*M_PI)); int unwindingNumber = std::ceil(((logTdiag[i]-logTdiag[i-1]).imag() - M_PI) / (2*M_PI));
Scalar w = internal::atanh2(m_T(i,i)-m_T(i-1,i-1), m_T(i,i)+m_T(i-1,i-1)) + Scalar(0, M_PI*unwindingNumber); Scalar w = internal::atanh2(m_T(i,i)-m_T(i-1,i-1), m_T(i,i)+m_T(i-1,i-1)) + Scalar(0, M_PI*unwindingNumber);
@ -187,9 +192,9 @@ void MatrixPowerTriangularAtomic<MatrixType,UpLo>::computeBig(MatrixType& res, R
digits <= 64? 2.4471944416607995472e-1L: // extended precision digits <= 64? 2.4471944416607995472e-1L: // extended precision
digits <= 106? 1.1016843812851143391275867258512e-01: // double-double digits <= 106? 1.1016843812851143391275867258512e-01: // double-double
9.134603732914548552537150753385375e-02; // quadruple precision 9.134603732914548552537150753385375e-02; // quadruple precision
int degree, degree2, numberOfSquareRoots=0, numberOfExtraSquareRoots=0;
MatrixType IminusT, sqrtT, T=m_T; MatrixType IminusT, sqrtT, T=m_T;
RealScalar normIminusT; RealScalar normIminusT;
int degree, degree2, numberOfSquareRoots=0, numberOfExtraSquareRoots=0;
while (true) { while (true) {
IminusT = MatrixType::Identity(m_T.rows(), m_T.cols()) - T; IminusT = MatrixType::Identity(m_T.rows(), m_T.cols()) - T;