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https://gitlab.com/libeigen/eigen.git
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Cleaning in BDCSVD (formating, handling of transpose case, remove some for loops)
This commit is contained in:
Gael Guennebaud
parent
a96f3d629c
commit
c82dc227f1
@ -267,7 +267,6 @@ void SVDBase<Derived>::_solve_impl(const RhsType &rhs, DstType &dst) const
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Matrix<Scalar, Dynamic, RhsType::ColsAtCompileTime, 0, MatrixType::MaxRowsAtCompileTime, RhsType::MaxColsAtCompileTime> tmp;
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Index l_rank = rank();
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tmp.noalias() = m_matrixU.leftCols(l_rank).adjoint() * rhs;
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tmp = m_singularValues.head(l_rank).asDiagonal().inverse() * tmp;
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dst = m_matrixV.leftCols(l_rank) * tmp;
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@ -19,10 +19,6 @@
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#ifndef EIGEN_BDCSVD_H
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#define EIGEN_BDCSVD_H
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#define EPSILON 0.0000000000000001
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#define ALGOSWAP 16
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namespace Eigen {
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template<typename _MatrixType> class BDCSVD;
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@ -88,7 +84,7 @@ public:
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* The default constructor is useful in cases in which the user intends to
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* perform decompositions via BDCSVD::compute(const MatrixType&).
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*/
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BDCSVD() : algoswap(ALGOSWAP), m_numIters(0)
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BDCSVD() : m_algoswap(16), m_numIters(0)
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{}
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@ -99,7 +95,7 @@ public:
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* \sa BDCSVD()
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*/
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BDCSVD(Index rows, Index cols, unsigned int computationOptions = 0)
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: algoswap(ALGOSWAP), m_numIters(0)
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: m_algoswap(16), m_numIters(0)
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{
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allocate(rows, cols, computationOptions);
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}
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@ -115,7 +111,7 @@ public:
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* available with the (non - default) FullPivHouseholderQR preconditioner.
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*/
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BDCSVD(const MatrixType& matrix, unsigned int computationOptions = 0)
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: algoswap(ALGOSWAP), m_numIters(0)
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: m_algoswap(16), m_numIters(0)
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{
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compute(matrix, computationOptions);
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}
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@ -150,35 +146,7 @@ public:
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void setSwitchSize(int s)
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{
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eigen_assert(s>3 && "BDCSVD the size of the algo switch has to be greater than 3");
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algoswap = s;
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}
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const MatrixUType& matrixU() const
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{
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eigen_assert(this->m_isInitialized && "SVD is not initialized.");
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if (isTranspose){
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eigen_assert(this->computeV() && "This SVD decomposition didn't compute U. Did you ask for it?");
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return this->m_matrixV;
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}
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else
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{
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eigen_assert(this->computeU() && "This SVD decomposition didn't compute U. Did you ask for it?");
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return this->m_matrixU;
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}
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}
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const MatrixVType& matrixV() const
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{
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eigen_assert(this->m_isInitialized && "SVD is not initialized.");
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if (isTranspose){
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eigen_assert(this->computeU() && "This SVD decomposition didn't compute V. Did you ask for it?");
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return this->m_matrixU;
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}
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else
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{
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eigen_assert(this->computeV() && "This SVD decomposition didn't compute V. Did you ask for it?");
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return this->m_matrixV;
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}
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m_algoswap = s;
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}
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private:
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@ -194,15 +162,26 @@ private:
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void deflation43(Index firstCol, Index shift, Index i, Index size);
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void deflation44(Index firstColu , Index firstColm, Index firstRowW, Index firstColW, Index i, Index j, Index size);
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void deflation(Index firstCol, Index lastCol, Index k, Index firstRowW, Index firstColW, Index shift);
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void copyUV(const typename internal::UpperBidiagonalization<MatrixX>::HouseholderUSequenceType& householderU,
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const typename internal::UpperBidiagonalization<MatrixX>::HouseholderVSequenceType& householderV);
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template<typename HouseholderU, typename HouseholderV, typename NaiveU, typename NaiveV>
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void copyUV(const HouseholderU &householderU, const HouseholderV &householderV, const NaiveU &naiveU, const NaiveV &naivev);
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protected:
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MatrixXr m_naiveU, m_naiveV;
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MatrixXr m_computed;
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Index nRec;
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int algoswap;
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bool isTranspose, compU, compV;
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Index m_nRec;
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int m_algoswap;
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bool m_isTranspose, m_compU, m_compV;
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using Base::m_singularValues;
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using Base::m_diagSize;
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using Base::m_computeFullU;
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using Base::m_computeFullV;
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using Base::m_computeThinU;
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using Base::m_computeThinV;
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using Base::m_matrixU;
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using Base::m_matrixV;
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using Base::m_isInitialized;
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using Base::m_nonzeroSingularValues;
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public:
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int m_numIters;
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@ -213,50 +192,35 @@ public:
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template<typename MatrixType>
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void BDCSVD<MatrixType>::allocate(Index rows, Index cols, unsigned int computationOptions)
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{
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isTranspose = (cols > rows);
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if (Base::allocate(rows, cols, computationOptions)) return;
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m_computed = MatrixXr::Zero(this->m_diagSize + 1, this->m_diagSize );
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if (isTranspose){
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compU = this->computeU();
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compV = this->computeV();
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}
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else
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{
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compV = this->computeU();
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compU = this->computeV();
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}
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if (compU) m_naiveU = MatrixXr::Zero(this->m_diagSize + 1, this->m_diagSize + 1 );
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else m_naiveU = MatrixXr::Zero(2, this->m_diagSize + 1 );
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m_isTranspose = (cols > rows);
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if (Base::allocate(rows, cols, computationOptions))
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return;
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if (compV) m_naiveV = MatrixXr::Zero(this->m_diagSize, this->m_diagSize);
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m_computed = MatrixXr::Zero(m_diagSize + 1, m_diagSize );
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m_compU = computeV();
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m_compV = computeU();
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if (m_isTranspose)
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std::swap(m_compU, m_compV);
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//should be changed for a cleaner implementation
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if (isTranspose){
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bool aux;
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if (this->computeU()||this->computeV()){
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aux = this->m_computeFullU;
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this->m_computeFullU = this->m_computeFullV;
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this->m_computeFullV = aux;
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aux = this->m_computeThinU;
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this->m_computeThinU = this->m_computeThinV;
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this->m_computeThinV = aux;
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}
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}
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if (m_compU) m_naiveU = MatrixXr::Zero(m_diagSize + 1, m_diagSize + 1 );
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else m_naiveU = MatrixXr::Zero(2, m_diagSize + 1 );
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if (m_compV) m_naiveV = MatrixXr::Zero(m_diagSize, m_diagSize);
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}// end allocate
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// Methode which compute the BDCSVD for the int
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template<>
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BDCSVD<Matrix<int, Dynamic, Dynamic> >& BDCSVD<Matrix<int, Dynamic, Dynamic> >::compute(const MatrixType& matrix, unsigned int computationOptions) {
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BDCSVD<Matrix<int, Dynamic, Dynamic> >& BDCSVD<Matrix<int, Dynamic, Dynamic> >::compute(const MatrixType& matrix, unsigned int computationOptions)
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{
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allocate(matrix.rows(), matrix.cols(), computationOptions);
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this->m_nonzeroSingularValues = 0;
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m_nonzeroSingularValues = 0;
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m_computed = Matrix<int, Dynamic, Dynamic>::Zero(rows(), cols());
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for (int i=0; i<this->m_diagSize; i++) {
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this->m_singularValues.coeffRef(i) = 0;
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}
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if (this->m_computeFullU) this->m_matrixU = Matrix<int, Dynamic, Dynamic>::Zero(rows(), rows());
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if (this->m_computeFullV) this->m_matrixV = Matrix<int, Dynamic, Dynamic>::Zero(cols(), cols());
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this->m_isInitialized = true;
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m_singularValues.head(m_diagSize).setZero();
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if (m_computeFullU) m_matrixU.setZero(rows(), rows());
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if (m_computeFullV) m_matrixV.setZero(cols(), cols());
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m_isInitialized = true;
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return *this;
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}
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@ -268,59 +232,62 @@ BDCSVD<MatrixType>& BDCSVD<MatrixType>::compute(const MatrixType& matrix, unsign
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allocate(matrix.rows(), matrix.cols(), computationOptions);
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using std::abs;
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//**** step 1 Bidiagonalization isTranspose = (matrix.cols()>matrix.rows()) ;
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//**** step 1 Bidiagonalization m_isTranspose = (matrix.cols()>matrix.rows()) ;
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MatrixType copy;
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if (isTranspose) copy = matrix.adjoint();
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else copy = matrix;
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if (m_isTranspose) copy = matrix.adjoint();
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else copy = matrix;
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internal::UpperBidiagonalization<MatrixX> bid(copy);
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//**** step 2 Divide
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m_computed.topRows(this->m_diagSize) = bid.bidiagonal().toDenseMatrix().transpose();
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m_computed.topRows(m_diagSize) = bid.bidiagonal().toDenseMatrix().transpose();
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m_computed.template bottomRows<1>().setZero();
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divide(0, this->m_diagSize - 1, 0, 0, 0);
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divide(0, m_diagSize - 1, 0, 0, 0);
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//**** step 3 copy
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for (int i=0; i<this->m_diagSize; i++) {
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for (int i=0; i<m_diagSize; i++)
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{
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RealScalar a = abs(m_computed.coeff(i, i));
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this->m_singularValues.coeffRef(i) = a;
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if (a == 0){
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this->m_nonzeroSingularValues = i;
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this->m_singularValues.tail(this->m_diagSize - i - 1).setZero();
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m_singularValues.coeffRef(i) = a;
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if (a == 0)
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{
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m_nonzeroSingularValues = i;
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m_singularValues.tail(m_diagSize - i - 1).setZero();
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break;
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}
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else if (i == this->m_diagSize - 1)
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else if (i == m_diagSize - 1)
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{
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this->m_nonzeroSingularValues = i + 1;
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m_nonzeroSingularValues = i + 1;
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break;
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}
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}
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copyUV(bid.householderU(), bid.householderV());
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this->m_isInitialized = true;
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if(m_isTranspose) copyUV(bid.householderV(), bid.householderU(), m_naiveV, m_naiveU);
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else copyUV(bid.householderU(), bid.householderV(), m_naiveU, m_naiveV);
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m_isInitialized = true;
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return *this;
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}// end compute
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template<typename MatrixType>
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void BDCSVD<MatrixType>::copyUV(const typename internal::UpperBidiagonalization<MatrixX>::HouseholderUSequenceType& householderU,
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const typename internal::UpperBidiagonalization<MatrixX>::HouseholderVSequenceType& householderV)
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template<typename HouseholderU, typename HouseholderV, typename NaiveU, typename NaiveV>
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void BDCSVD<MatrixType>::copyUV(const HouseholderU &householderU, const HouseholderV &householderV, const NaiveU &naiveU, const NaiveV &naiveV)
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{
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// Note exchange of U and V: m_matrixU is set from m_naiveV and vice versa
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if (this->computeU()){
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Index Ucols = this->m_computeThinU ? this->m_nonzeroSingularValues : householderU.cols();
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this->m_matrixU = MatrixX::Identity(householderU.cols(), Ucols);
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Index blockCols = this->m_computeThinU ? this->m_nonzeroSingularValues : this->m_diagSize;
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this->m_matrixU.block(0, 0, this->m_diagSize, blockCols) =
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m_naiveV.template cast<Scalar>().block(0, 0, this->m_diagSize, blockCols);
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this->m_matrixU = householderU * this->m_matrixU;
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if (computeU())
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{
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Index Ucols = m_computeThinU ? m_nonzeroSingularValues : householderU.cols();
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m_matrixU = MatrixX::Identity(householderU.cols(), Ucols);
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Index blockCols = m_computeThinU ? m_nonzeroSingularValues : m_diagSize;
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m_matrixU.topLeftCorner(m_diagSize, blockCols) = naiveV.template cast<Scalar>().topLeftCorner(m_diagSize, blockCols);
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m_matrixU = householderU * m_matrixU;
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}
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if (this->computeV()){
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Index Vcols = this->m_computeThinV ? this->m_nonzeroSingularValues : householderV.cols();
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this->m_matrixV = MatrixX::Identity(householderV.cols(), Vcols);
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Index blockCols = this->m_computeThinV ? this->m_nonzeroSingularValues : this->m_diagSize;
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this->m_matrixV.block(0, 0, this->m_diagSize, blockCols) =
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m_naiveU.template cast<Scalar>().block(0, 0, this->m_diagSize, blockCols);
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this->m_matrixV = householderV * this->m_matrixV;
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if (computeV())
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{
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Index Vcols = m_computeThinV ? m_nonzeroSingularValues : householderV.cols();
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m_matrixV = MatrixX::Identity(householderV.cols(), Vcols);
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Index blockCols = m_computeThinV ? m_nonzeroSingularValues : m_diagSize;
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m_matrixV.topLeftCorner(m_diagSize, blockCols) = naiveU.template cast<Scalar>().topLeftCorner(m_diagSize, blockCols);
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m_matrixV = householderV * m_matrixV;
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}
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}
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@ -335,8 +302,7 @@ void BDCSVD<MatrixType>::copyUV(const typename internal::UpperBidiagonalization<
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//@param shift : Each time one takes the left submatrix, one must add 1 to the shift. Why? Because! We actually want the last column of the U submatrix
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// to become the first column (*coeff) and to shift all the other columns to the right. There are more details on the reference paper.
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template<typename MatrixType>
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void BDCSVD<MatrixType>::divide (Index firstCol, Index lastCol, Index firstRowW,
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Index firstColW, Index shift)
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void BDCSVD<MatrixType>::divide (Index firstCol, Index lastCol, Index firstRowW, Index firstColW, Index shift)
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{
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// requires nbRows = nbCols + 1;
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using std::pow;
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@ -351,21 +317,19 @@ void BDCSVD<MatrixType>::divide (Index firstCol, Index lastCol, Index firstRowW,
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MatrixXr l, f;
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// We use the other algorithm which is more efficient for small
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// matrices.
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if (n < algoswap){
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JacobiSVD<MatrixXr> b(m_computed.block(firstCol, firstCol, n + 1, n),
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ComputeFullU | (ComputeFullV * compV)) ;
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if (compU) m_naiveU.block(firstCol, firstCol, n + 1, n + 1).real() << b.matrixU();
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if (n < m_algoswap)
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{
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JacobiSVD<MatrixXr> b(m_computed.block(firstCol, firstCol, n + 1, n), ComputeFullU | (m_compV ? ComputeFullV : 0)) ;
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if (m_compU)
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m_naiveU.block(firstCol, firstCol, n + 1, n + 1).real() = b.matrixU();
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else
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{
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m_naiveU.row(0).segment(firstCol, n + 1).real() << b.matrixU().row(0);
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m_naiveU.row(1).segment(firstCol, n + 1).real() << b.matrixU().row(n);
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m_naiveU.row(0).segment(firstCol, n + 1).real() = b.matrixU().row(0);
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m_naiveU.row(1).segment(firstCol, n + 1).real() = b.matrixU().row(n);
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}
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if (compV) m_naiveV.block(firstRowW, firstColW, n, n).real() << b.matrixV();
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if (m_compV) m_naiveV.block(firstRowW, firstColW, n, n).real() = b.matrixV();
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m_computed.block(firstCol + shift, firstCol + shift, n + 1, n).setZero();
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for (int i=0; i<n; i++)
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{
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m_computed(firstCol + shift + i, firstCol + shift +i) = b.singularValues().coeffRef(i);
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}
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m_computed.diagonal().segment(firstCol + shift, n) = b.singularValues().head(n);
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return;
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}
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// We use the divide and conquer algorithm
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@ -376,7 +340,7 @@ void BDCSVD<MatrixType>::divide (Index firstCol, Index lastCol, Index firstRowW,
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// right submatrix before the left one.
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divide(k + 1 + firstCol, lastCol, k + 1 + firstRowW, k + 1 + firstColW, shift);
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divide(firstCol, k - 1 + firstCol, firstRowW, firstColW + 1, shift + 1);
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if (compU)
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if (m_compU)
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{
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lambda = m_naiveU(firstCol + k, firstCol + k);
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phi = m_naiveU(firstCol + k + 1, lastCol + 1);
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@ -386,9 +350,8 @@ void BDCSVD<MatrixType>::divide (Index firstCol, Index lastCol, Index firstRowW,
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lambda = m_naiveU(1, firstCol + k);
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phi = m_naiveU(0, lastCol + 1);
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}
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r0 = sqrt((abs(alphaK * lambda) * abs(alphaK * lambda))
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+ abs(betaK * phi) * abs(betaK * phi));
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if (compU)
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r0 = sqrt((abs(alphaK * lambda) * abs(alphaK * lambda)) + abs(betaK * phi) * abs(betaK * phi));
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if (m_compU)
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{
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l = m_naiveU.row(firstCol + k).segment(firstCol, k);
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f = m_naiveU.row(firstCol + k + 1).segment(firstCol + k + 1, n - k - 1);
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@ -398,7 +361,7 @@ void BDCSVD<MatrixType>::divide (Index firstCol, Index lastCol, Index firstRowW,
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l = m_naiveU.row(1).segment(firstCol, k);
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f = m_naiveU.row(0).segment(firstCol + k + 1, n - k - 1);
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}
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if (compV) m_naiveV(firstRowW+k, firstColW) = 1;
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if (m_compV) m_naiveV(firstRowW+k, firstColW) = 1;
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if (r0 == 0)
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{
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c0 = 1;
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@ -409,21 +372,18 @@ void BDCSVD<MatrixType>::divide (Index firstCol, Index lastCol, Index firstRowW,
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c0 = alphaK * lambda / r0;
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s0 = betaK * phi / r0;
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}
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if (compU)
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if (m_compU)
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{
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MatrixXr q1 (m_naiveU.col(firstCol + k).segment(firstCol, k + 1));
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// we shiftW Q1 to the right
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for (Index i = firstCol + k - 1; i >= firstCol; i--)
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{
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m_naiveU.col(i + 1).segment(firstCol, k + 1) << m_naiveU.col(i).segment(firstCol, k + 1);
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}
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m_naiveU.col(i + 1).segment(firstCol, k + 1) = m_naiveU.col(i).segment(firstCol, k + 1);
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// we shift q1 at the left with a factor c0
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m_naiveU.col(firstCol).segment( firstCol, k + 1) << (q1 * c0);
|
||||
m_naiveU.col(firstCol).segment( firstCol, k + 1) = (q1 * c0);
|
||||
// last column = q1 * - s0
|
||||
m_naiveU.col(lastCol + 1).segment(firstCol, k + 1) << (q1 * ( - s0));
|
||||
m_naiveU.col(lastCol + 1).segment(firstCol, k + 1) = (q1 * ( - s0));
|
||||
// first column = q2 * s0
|
||||
m_naiveU.col(firstCol).segment(firstCol + k + 1, n - k) <<
|
||||
m_naiveU.col(lastCol + 1).segment(firstCol + k + 1, n - k) *s0;
|
||||
m_naiveU.col(firstCol).segment(firstCol + k + 1, n - k) = m_naiveU.col(lastCol + 1).segment(firstCol + k + 1, n - k) * s0;
|
||||
// q2 *= c0
|
||||
m_naiveU.col(lastCol + 1).segment(firstCol + k + 1, n - k) *= c0;
|
||||
}
|
||||
@ -432,9 +392,7 @@ void BDCSVD<MatrixType>::divide (Index firstCol, Index lastCol, Index firstRowW,
|
||||
RealScalar q1 = (m_naiveU(0, firstCol + k));
|
||||
// we shift Q1 to the right
|
||||
for (Index i = firstCol + k - 1; i >= firstCol; i--)
|
||||
{
|
||||
m_naiveU(0, i + 1) = m_naiveU(0, i);
|
||||
}
|
||||
// we shift q1 at the left with a factor c0
|
||||
m_naiveU(0, firstCol) = (q1 * c0);
|
||||
// last column = q1 * - s0
|
||||
@ -447,8 +405,8 @@ void BDCSVD<MatrixType>::divide (Index firstCol, Index lastCol, Index firstRowW,
|
||||
m_naiveU.row(0).segment(firstCol + k + 1, n - k - 1).setZero();
|
||||
}
|
||||
m_computed(firstCol + shift, firstCol + shift) = r0;
|
||||
m_computed.col(firstCol + shift).segment(firstCol + shift + 1, k) << alphaK * l.transpose().real();
|
||||
m_computed.col(firstCol + shift).segment(firstCol + shift + k + 1, n - k - 1) << betaK * f.transpose().real();
|
||||
m_computed.col(firstCol + shift).segment(firstCol + shift + 1, k) = alphaK * l.transpose().real();
|
||||
m_computed.col(firstCol + shift).segment(firstCol + shift + k + 1, n - k - 1) = betaK * f.transpose().real();
|
||||
|
||||
|
||||
// Second part: try to deflate singular values in combined matrix
|
||||
@ -458,9 +416,9 @@ void BDCSVD<MatrixType>::divide (Index firstCol, Index lastCol, Index firstRowW,
|
||||
MatrixXr UofSVD, VofSVD;
|
||||
VectorType singVals;
|
||||
computeSVDofM(firstCol + shift, n, UofSVD, singVals, VofSVD);
|
||||
if (compU) m_naiveU.block(firstCol, firstCol, n + 1, n + 1) *= UofSVD;
|
||||
else m_naiveU.block(0, firstCol, 2, n + 1) *= UofSVD;
|
||||
if (compV) m_naiveV.block(firstRowW, firstColW, n, n) *= VofSVD;
|
||||
if (m_compU) m_naiveU.block(firstCol, firstCol, n + 1, n + 1) *= UofSVD; // FIXME this requires a temporary
|
||||
else m_naiveU.block(0, firstCol, 2, n + 1) *= UofSVD; // FIXME this requires a temporary, and exploit that there are 2 rows at compile time
|
||||
if (m_compV) m_naiveV.block(firstRowW, firstColW, n, n) *= VofSVD; // FIXME this requires a temporary
|
||||
m_computed.block(firstCol + shift, firstCol + shift, n, n).setZero();
|
||||
m_computed.block(firstCol + shift, firstCol + shift, n, n).diagonal() = singVals;
|
||||
}// end divide
|
||||
@ -468,7 +426,7 @@ void BDCSVD<MatrixType>::divide (Index firstCol, Index lastCol, Index firstRowW,
|
||||
// Compute SVD of m_computed.block(firstCol, firstCol, n + 1, n); this block only has non-zeros in
|
||||
// the first column and on the diagonal and has undergone deflation, so diagonal is in increasing
|
||||
// order except for possibly the (0,0) entry. The computed SVD is stored U, singVals and V, except
|
||||
// that if compV is false, then V is not computed. Singular values are sorted in decreasing order.
|
||||
// that if m_compV is false, then V is not computed. Singular values are sorted in decreasing order.
|
||||
//
|
||||
// TODO Opportunities for optimization: better root finding algo, better stopping criterion, better
|
||||
// handling of round-off errors, be consistent in ordering
|
||||
@ -483,7 +441,7 @@ void BDCSVD<MatrixType>::computeSVDofM(Index firstCol, Index n, MatrixXr& U, Vec
|
||||
// compute singular values and vectors (in decreasing order)
|
||||
singVals.resize(n);
|
||||
U.resize(n+1, n+1);
|
||||
if (compV) V.resize(n, n);
|
||||
if (m_compV) V.resize(n, n);
|
||||
|
||||
if (col0.hasNaN() || diag.hasNaN()) return;
|
||||
|
||||
@ -495,7 +453,7 @@ void BDCSVD<MatrixType>::computeSVDofM(Index firstCol, Index n, MatrixXr& U, Vec
|
||||
// Reverse order so that singular values in increased order
|
||||
singVals.reverseInPlace();
|
||||
U.leftCols(n) = U.leftCols(n).rowwise().reverse().eval();
|
||||
if (compV) V = V.rowwise().reverse().eval();
|
||||
if (m_compV) V = V.rowwise().reverse().eval();
|
||||
}
|
||||
|
||||
template <typename MatrixType>
|
||||
@ -504,10 +462,13 @@ void BDCSVD<MatrixType>::computeSingVals(const ArrayXr& col0, const ArrayXr& dia
|
||||
{
|
||||
using std::abs;
|
||||
using std::swap;
|
||||
using std::max;
|
||||
|
||||
Index n = col0.size();
|
||||
for (Index k = 0; k < n; ++k) {
|
||||
if (col0(k) == 0) {
|
||||
for (Index k = 0; k < n; ++k)
|
||||
{
|
||||
if (col0(k) == 0)
|
||||
{
|
||||
// entry is deflated, so singular value is on diagonal
|
||||
singVals(k) = diag(k);
|
||||
mus(k) = 0;
|
||||
@ -523,27 +484,29 @@ void BDCSVD<MatrixType>::computeSingVals(const ArrayXr& col0, const ArrayXr& dia
|
||||
RealScalar mid = left + (right-left) / 2;
|
||||
RealScalar fMid = 1 + (col0.square() / ((diag + mid) * (diag - mid))).sum();
|
||||
|
||||
RealScalar shift;
|
||||
if (k == n-1 || fMid > 0) shift = left;
|
||||
else shift = right;
|
||||
RealScalar shift = (k == n-1 || fMid > 0) ? left : right;
|
||||
|
||||
// measure everything relative to shift
|
||||
ArrayXr diagShifted = diag - shift;
|
||||
|
||||
// initial guess
|
||||
RealScalar muPrev, muCur;
|
||||
if (shift == left) {
|
||||
if (shift == left)
|
||||
{
|
||||
muPrev = (right - left) * 0.1;
|
||||
if (k == n-1) muCur = right - left;
|
||||
else muCur = (right - left) * 0.5;
|
||||
} else {
|
||||
else muCur = (right - left) * 0.5;
|
||||
}
|
||||
else
|
||||
{
|
||||
muPrev = -(right - left) * 0.1;
|
||||
muCur = -(right - left) * 0.5;
|
||||
}
|
||||
|
||||
RealScalar fPrev = 1 + (col0.square() / ((diagShifted - muPrev) * (diag + shift + muPrev))).sum();
|
||||
RealScalar fCur = 1 + (col0.square() / ((diagShifted - muCur) * (diag + shift + muCur))).sum();
|
||||
if (abs(fPrev) < abs(fCur)) {
|
||||
if (abs(fPrev) < abs(fCur))
|
||||
{
|
||||
swap(fPrev, fCur);
|
||||
swap(muPrev, muCur);
|
||||
}
|
||||
@ -551,7 +514,8 @@ void BDCSVD<MatrixType>::computeSingVals(const ArrayXr& col0, const ArrayXr& dia
|
||||
// rational interpolation: fit a function of the form a / mu + b through the two previous
|
||||
// iterates and use its zero to compute the next iterate
|
||||
bool useBisection = false;
|
||||
while (abs(muCur - muPrev) > 8 * NumTraits<RealScalar>::epsilon() * (std::max)(abs(muCur), abs(muPrev)) && fCur != fPrev && !useBisection) {
|
||||
while (abs(muCur - muPrev) > 8 * NumTraits<RealScalar>::epsilon() * (max)(abs(muCur), abs(muPrev)) && fCur != fPrev && !useBisection)
|
||||
{
|
||||
++m_numIters;
|
||||
|
||||
RealScalar a = (fCur - fPrev) / (1/muCur - 1/muPrev);
|
||||
@ -567,13 +531,17 @@ void BDCSVD<MatrixType>::computeSingVals(const ArrayXr& col0, const ArrayXr& dia
|
||||
}
|
||||
|
||||
// fall back on bisection method if rational interpolation did not work
|
||||
if (useBisection) {
|
||||
if (useBisection)
|
||||
{
|
||||
RealScalar leftShifted, rightShifted;
|
||||
if (shift == left) {
|
||||
if (shift == left)
|
||||
{
|
||||
leftShifted = 1e-30;
|
||||
if (k == 0) rightShifted = right - left;
|
||||
else rightShifted = (right - left) * 0.6; // theoretically we can take 0.5, but let's be safe
|
||||
} else {
|
||||
else rightShifted = (right - left) * 0.6; // theoretically we can take 0.5, but let's be safe
|
||||
}
|
||||
else
|
||||
{
|
||||
leftShifted = -(right - left) * 0.6;
|
||||
rightShifted = -1e-30;
|
||||
}
|
||||
@ -582,13 +550,17 @@ void BDCSVD<MatrixType>::computeSingVals(const ArrayXr& col0, const ArrayXr& dia
|
||||
RealScalar fRight = 1 + (col0.square() / ((diagShifted - rightShifted) * (diag + shift + rightShifted))).sum();
|
||||
assert(fLeft * fRight < 0);
|
||||
|
||||
while (rightShifted - leftShifted > 2 * NumTraits<RealScalar>::epsilon() * (std::max)(abs(leftShifted), abs(rightShifted))) {
|
||||
while (rightShifted - leftShifted > 2 * NumTraits<RealScalar>::epsilon() * (max)(abs(leftShifted), abs(rightShifted)))
|
||||
{
|
||||
RealScalar midShifted = (leftShifted + rightShifted) / 2;
|
||||
RealScalar fMid = 1 + (col0.square() / ((diagShifted - midShifted) * (diag + shift + midShifted))).sum();
|
||||
if (fLeft * fMid < 0) {
|
||||
if (fLeft * fMid < 0)
|
||||
{
|
||||
rightShifted = midShifted;
|
||||
fRight = fMid;
|
||||
} else {
|
||||
}
|
||||
else
|
||||
{
|
||||
leftShifted = midShifted;
|
||||
fLeft = fMid;
|
||||
}
|
||||
@ -615,13 +587,15 @@ void BDCSVD<MatrixType>::perturbCol0
|
||||
(const ArrayXr& col0, const ArrayXr& diag, const VectorType& singVals,
|
||||
const ArrayXr& shifts, const ArrayXr& mus, ArrayXr& zhat)
|
||||
{
|
||||
using std::sqrt;
|
||||
Index n = col0.size();
|
||||
for (Index k = 0; k < n; ++k) {
|
||||
for (Index k = 0; k < n; ++k)
|
||||
{
|
||||
if (col0(k) == 0)
|
||||
zhat(k) = 0;
|
||||
else {
|
||||
else
|
||||
{
|
||||
// see equation (3.6)
|
||||
using std::sqrt;
|
||||
RealScalar tmp =
|
||||
sqrt(
|
||||
(singVals(n-1) + diag(k)) * (mus(n-1) + (shifts(n-1) - diag(k)))
|
||||
@ -647,16 +621,21 @@ void BDCSVD<MatrixType>::computeSingVecs
|
||||
const ArrayXr& shifts, const ArrayXr& mus, MatrixXr& U, MatrixXr& V)
|
||||
{
|
||||
Index n = zhat.size();
|
||||
for (Index k = 0; k < n; ++k) {
|
||||
if (zhat(k) == 0) {
|
||||
for (Index k = 0; k < n; ++k)
|
||||
{
|
||||
if (zhat(k) == 0)
|
||||
{
|
||||
U.col(k) = VectorType::Unit(n+1, k);
|
||||
if (compV) V.col(k) = VectorType::Unit(n, k);
|
||||
} else {
|
||||
if (m_compV) V.col(k) = VectorType::Unit(n, k);
|
||||
}
|
||||
else
|
||||
{
|
||||
U.col(k).head(n) = zhat / (((diag - shifts(k)) - mus(k)) * (diag + singVals[k]));
|
||||
U(n,k) = 0;
|
||||
U.col(k).normalize();
|
||||
|
||||
if (compV) {
|
||||
if (m_compV)
|
||||
{
|
||||
V.col(k).tail(n-1) = (diag * zhat / (((diag - shifts(k)) - mus(k)) * (diag + singVals[k]))).tail(n-1);
|
||||
V(0,k) = -1;
|
||||
V.col(k).normalize();
|
||||
@ -671,15 +650,17 @@ void BDCSVD<MatrixType>::computeSingVecs
|
||||
// i >= 1, di almost null and zi non null.
|
||||
// We use a rotation to zero out zi applied to the left of M
|
||||
template <typename MatrixType>
|
||||
void BDCSVD<MatrixType>::deflation43(Index firstCol, Index shift, Index i, Index size){
|
||||
void BDCSVD<MatrixType>::deflation43(Index firstCol, Index shift, Index i, Index size)
|
||||
{
|
||||
using std::abs;
|
||||
using std::sqrt;
|
||||
using std::pow;
|
||||
RealScalar c = m_computed(firstCol + shift, firstCol + shift);
|
||||
RealScalar s = m_computed(i, firstCol + shift);
|
||||
RealScalar r = sqrt(pow(abs(c), 2) + pow(abs(s), 2));
|
||||
if (r == 0){
|
||||
m_computed(i, i)=0;
|
||||
if (r == 0)
|
||||
{
|
||||
m_computed(i, i) = 0;
|
||||
return;
|
||||
}
|
||||
c/=r;
|
||||
@ -687,7 +668,8 @@ void BDCSVD<MatrixType>::deflation43(Index firstCol, Index shift, Index i, Index
|
||||
m_computed(firstCol + shift, firstCol + shift) = r;
|
||||
m_computed(i, firstCol + shift) = 0;
|
||||
m_computed(i, i) = 0;
|
||||
if (compU){
|
||||
if (m_compU)
|
||||
{
|
||||
m_naiveU.col(firstCol).segment(firstCol,size) =
|
||||
c * m_naiveU.col(firstCol).segment(firstCol, size) -
|
||||
s * m_naiveU.col(i).segment(firstCol, size) ;
|
||||
@ -703,7 +685,8 @@ void BDCSVD<MatrixType>::deflation43(Index firstCol, Index shift, Index i, Index
|
||||
// i,j >= 1, i != j and |di - dj| < epsilon * norm2(M)
|
||||
// We apply two rotations to have zj = 0;
|
||||
template <typename MatrixType>
|
||||
void BDCSVD<MatrixType>::deflation44(Index firstColu , Index firstColm, Index firstRowW, Index firstColW, Index i, Index j, Index size){
|
||||
void BDCSVD<MatrixType>::deflation44(Index firstColu , Index firstColm, Index firstRowW, Index firstColW, Index i, Index j, Index size)
|
||||
{
|
||||
using std::abs;
|
||||
using std::sqrt;
|
||||
using std::conj;
|
||||
@ -711,7 +694,8 @@ void BDCSVD<MatrixType>::deflation44(Index firstColu , Index firstColm, Index fi
|
||||
RealScalar c = m_computed(firstColm, firstColm + j - 1);
|
||||
RealScalar s = m_computed(firstColm, firstColm + i - 1);
|
||||
RealScalar r = sqrt(pow(abs(c), 2) + pow(abs(s), 2));
|
||||
if (r==0){
|
||||
if (r==0)
|
||||
{
|
||||
m_computed(firstColm + i, firstColm + i) = m_computed(firstColm + j, firstColm + j);
|
||||
return;
|
||||
}
|
||||
@ -720,7 +704,8 @@ void BDCSVD<MatrixType>::deflation44(Index firstColu , Index firstColm, Index fi
|
||||
m_computed(firstColm + i, firstColm) = r;
|
||||
m_computed(firstColm + i, firstColm + i) = m_computed(firstColm + j, firstColm + j);
|
||||
m_computed(firstColm + j, firstColm) = 0;
|
||||
if (compU){
|
||||
if (m_compU)
|
||||
{
|
||||
m_naiveU.col(firstColu + i).segment(firstColu, size) =
|
||||
c * m_naiveU.col(firstColu + i).segment(firstColu, size) -
|
||||
s * m_naiveU.col(firstColu + j).segment(firstColu, size) ;
|
||||
@ -729,7 +714,8 @@ void BDCSVD<MatrixType>::deflation44(Index firstColu , Index firstColm, Index fi
|
||||
(c + s*s/c) * m_naiveU.col(firstColu + j).segment(firstColu, size) +
|
||||
(s/c) * m_naiveU.col(firstColu + i).segment(firstColu, size);
|
||||
}
|
||||
if (compV){
|
||||
if (m_compV)
|
||||
{
|
||||
m_naiveV.col(firstColW + i).segment(firstRowW, size - 1) =
|
||||
c * m_naiveV.col(firstColW + i).segment(firstRowW, size - 1) +
|
||||
s * m_naiveV.col(firstColW + j).segment(firstRowW, size - 1) ;
|
||||
@ -743,72 +729,56 @@ void BDCSVD<MatrixType>::deflation44(Index firstColu , Index firstColm, Index fi
|
||||
|
||||
// acts on block from (firstCol+shift, firstCol+shift) to (lastCol+shift, lastCol+shift) [inclusive]
|
||||
template <typename MatrixType>
|
||||
void BDCSVD<MatrixType>::deflation(Index firstCol, Index lastCol, Index k, Index firstRowW, Index firstColW, Index shift){
|
||||
void BDCSVD<MatrixType>::deflation(Index firstCol, Index lastCol, Index k, Index firstRowW, Index firstColW, Index shift)
|
||||
{
|
||||
//condition 4.1
|
||||
using std::sqrt;
|
||||
using std::abs;
|
||||
const Index length = lastCol + 1 - firstCol;
|
||||
RealScalar norm1 = m_computed.block(firstCol+shift, firstCol+shift, length, 1).squaredNorm();
|
||||
RealScalar norm2 = m_computed.block(firstCol+shift, firstCol+shift, length, length).diagonal().squaredNorm();
|
||||
RealScalar EPS = 10 * NumTraits<RealScalar>::epsilon() * sqrt(norm1 + norm2);
|
||||
if (m_computed(firstCol + shift, firstCol + shift) < EPS){
|
||||
m_computed(firstCol + shift, firstCol + shift) = EPS;
|
||||
}
|
||||
RealScalar epsilon = 10 * NumTraits<RealScalar>::epsilon() * sqrt(norm1 + norm2);
|
||||
if (m_computed(firstCol + shift, firstCol + shift) < epsilon)
|
||||
m_computed(firstCol + shift, firstCol + shift) = epsilon;
|
||||
|
||||
//condition 4.2
|
||||
for (Index i=firstCol + shift + 1;i<=lastCol + shift;i++){
|
||||
if (std::abs(m_computed(i, firstCol + shift)) < EPS){
|
||||
for (Index i=firstCol + shift + 1;i<=lastCol + shift;i++)
|
||||
if (abs(m_computed(i, firstCol + shift)) < epsilon)
|
||||
m_computed(i, firstCol + shift) = 0;
|
||||
}
|
||||
}
|
||||
|
||||
//condition 4.3
|
||||
for (Index i=firstCol + shift + 1;i<=lastCol + shift; i++){
|
||||
if (m_computed(i, i) < EPS){
|
||||
for (Index i=firstCol + shift + 1;i<=lastCol + shift; i++)
|
||||
if (m_computed(i, i) < epsilon)
|
||||
deflation43(firstCol, shift, i, length);
|
||||
}
|
||||
}
|
||||
|
||||
//condition 4.4
|
||||
|
||||
Index i=firstCol + shift + 1, j=firstCol + shift + k + 1;
|
||||
//we stock the final place of each line
|
||||
Index *permutation = new Index[length];
|
||||
Index *permutation = new Index[length]; // FIXME avoid repeated dynamic memory allocation
|
||||
|
||||
for (Index p =1; p < length; p++) {
|
||||
if (i> firstCol + shift + k){
|
||||
permutation[p] = j;
|
||||
j++;
|
||||
} else if (j> lastCol + shift)
|
||||
{
|
||||
permutation[p] = i;
|
||||
i++;
|
||||
}
|
||||
else
|
||||
{
|
||||
if (m_computed(i, i) < m_computed(j, j)){
|
||||
permutation[p] = j;
|
||||
j++;
|
||||
}
|
||||
else
|
||||
{
|
||||
permutation[p] = i;
|
||||
i++;
|
||||
}
|
||||
}
|
||||
for (Index p =1; p < length; p++)
|
||||
{
|
||||
if (i> firstCol + shift + k) permutation[p] = j++;
|
||||
else if (j> lastCol + shift) permutation[p] = i++;
|
||||
else if (m_computed(i, i) < m_computed(j, j)) permutation[p] = j++;
|
||||
else permutation[p] = i++;
|
||||
}
|
||||
//we do the permutation
|
||||
RealScalar aux;
|
||||
//we stock the current index of each col
|
||||
//and the column of each index
|
||||
Index *realInd = new Index[length];
|
||||
Index *realCol = new Index[length];
|
||||
for (int pos = 0; pos< length; pos++){
|
||||
Index *realInd = new Index[length]; // FIXME avoid repeated dynamic memory allocation
|
||||
Index *realCol = new Index[length]; // FIXME avoid repeated dynamic memory allocation
|
||||
for (int pos = 0; pos< length; pos++)
|
||||
{
|
||||
realCol[pos] = pos + firstCol + shift;
|
||||
realInd[pos] = pos;
|
||||
}
|
||||
const Index Zero = firstCol + shift;
|
||||
VectorType temp;
|
||||
for (int i = 1; i < length - 1; i++){
|
||||
for (int i = 1; i < length - 1; i++)
|
||||
{
|
||||
const Index I = i + Zero;
|
||||
const Index realI = realInd[i];
|
||||
const Index j = permutation[length - i] - Zero;
|
||||
@ -825,25 +795,25 @@ void BDCSVD<MatrixType>::deflation(Index firstCol, Index lastCol, Index k, Index
|
||||
m_computed(J, Zero) = aux;
|
||||
|
||||
// change columns
|
||||
if (compU) {
|
||||
if (m_compU)
|
||||
{
|
||||
temp = m_naiveU.col(I - shift).segment(firstCol, length + 1);
|
||||
m_naiveU.col(I - shift).segment(firstCol, length + 1) <<
|
||||
m_naiveU.col(J - shift).segment(firstCol, length + 1);
|
||||
m_naiveU.col(J - shift).segment(firstCol, length + 1) << temp;
|
||||
m_naiveU.col(I - shift).segment(firstCol, length + 1) = m_naiveU.col(J - shift).segment(firstCol, length + 1);
|
||||
m_naiveU.col(J - shift).segment(firstCol, length + 1) = temp;
|
||||
}
|
||||
else
|
||||
{
|
||||
temp = m_naiveU.col(I - shift).segment(0, 2);
|
||||
m_naiveU.col(I - shift).segment(0, 2) <<
|
||||
m_naiveU.col(J - shift).segment(0, 2);
|
||||
m_naiveU.col(J - shift).segment(0, 2) << temp;
|
||||
m_naiveU.col(I - shift).template head<2>() = m_naiveU.col(J - shift).segment(0, 2);
|
||||
m_naiveU.col(J - shift).template head<2>() = temp;
|
||||
}
|
||||
if (compV) {
|
||||
if (m_compV)
|
||||
{
|
||||
const Index CWI = I + firstColW - Zero;
|
||||
const Index CWJ = J + firstColW - Zero;
|
||||
temp = m_naiveV.col(CWI).segment(firstRowW, length);
|
||||
m_naiveV.col(CWI).segment(firstRowW, length) << m_naiveV.col(CWJ).segment(firstRowW, length);
|
||||
m_naiveV.col(CWJ).segment(firstRowW, length) << temp;
|
||||
m_naiveV.col(CWI).segment(firstRowW, length) = m_naiveV.col(CWJ).segment(firstRowW, length);
|
||||
m_naiveV.col(CWJ).segment(firstRowW, length) = temp;
|
||||
}
|
||||
|
||||
//update real pos
|
||||
@ -852,20 +822,13 @@ void BDCSVD<MatrixType>::deflation(Index firstCol, Index lastCol, Index k, Index
|
||||
realInd[J - Zero] = realI;
|
||||
realInd[I - Zero] = j;
|
||||
}
|
||||
for (Index i = firstCol + shift + 1; i<lastCol + shift;i++){
|
||||
if ((m_computed(i + 1, i + 1) - m_computed(i, i)) < EPS){
|
||||
deflation44(firstCol ,
|
||||
firstCol + shift,
|
||||
firstRowW,
|
||||
firstColW,
|
||||
i - Zero,
|
||||
i + 1 - Zero,
|
||||
length);
|
||||
}
|
||||
}
|
||||
delete [] permutation;
|
||||
delete [] realInd;
|
||||
delete [] realCol;
|
||||
for (Index i = firstCol + shift + 1; i<lastCol + shift;i++)
|
||||
if ((m_computed(i + 1, i + 1) - m_computed(i, i)) < epsilon)
|
||||
deflation44(firstCol, firstCol + shift, firstRowW, firstColW, i - Zero, i + 1 - Zero, length);
|
||||
|
||||
delete[] permutation;
|
||||
delete[] realInd;
|
||||
delete[] realCol;
|
||||
}//end deflation
|
||||
|
||||
|
||||
|
||||
Loading…
x
Reference in New Issue
Block a user