From 44861dcbfeee041223c4aac1ee075e92fa4daa01 Mon Sep 17 00:00:00 2001 From: Stanislaw Halik Date: Sun, 18 Sep 2016 12:42:15 +0200 Subject: update --- eigen/unsupported/Eigen/src/SVD/BDCSVD.h | 748 ++++++++++++++++++++++ eigen/unsupported/Eigen/src/SVD/CMakeLists.txt | 6 + eigen/unsupported/Eigen/src/SVD/JacobiSVD.h | 782 +++++++++++++++++++++++ eigen/unsupported/Eigen/src/SVD/SVDBase.h | 236 +++++++ eigen/unsupported/Eigen/src/SVD/TODOBdcsvd.txt | 29 + eigen/unsupported/Eigen/src/SVD/doneInBDCSVD.txt | 21 + 6 files changed, 1822 insertions(+) create mode 100644 eigen/unsupported/Eigen/src/SVD/BDCSVD.h create mode 100644 eigen/unsupported/Eigen/src/SVD/CMakeLists.txt create mode 100644 eigen/unsupported/Eigen/src/SVD/JacobiSVD.h create mode 100644 eigen/unsupported/Eigen/src/SVD/SVDBase.h create mode 100644 eigen/unsupported/Eigen/src/SVD/TODOBdcsvd.txt create mode 100644 eigen/unsupported/Eigen/src/SVD/doneInBDCSVD.txt (limited to 'eigen/unsupported/Eigen/src/SVD') diff --git a/eigen/unsupported/Eigen/src/SVD/BDCSVD.h b/eigen/unsupported/Eigen/src/SVD/BDCSVD.h new file mode 100644 index 0000000..11d4882 --- /dev/null +++ b/eigen/unsupported/Eigen/src/SVD/BDCSVD.h @@ -0,0 +1,748 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// We used the "A Divide-And-Conquer Algorithm for the Bidiagonal SVD" +// research report written by Ming Gu and Stanley C.Eisenstat +// The code variable names correspond to the names they used in their +// report +// +// Copyright (C) 2013 Gauthier Brun +// Copyright (C) 2013 Nicolas Carre +// Copyright (C) 2013 Jean Ceccato +// Copyright (C) 2013 Pierre Zoppitelli +// +// Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_BDCSVD_H +#define EIGEN_BDCSVD_H + +#define EPSILON 0.0000000000000001 + +#define ALGOSWAP 32 + +namespace Eigen { +/** \ingroup SVD_Module + * + * + * \class BDCSVD + * + * \brief class Bidiagonal Divide and Conquer SVD + * + * \param MatrixType the type of the matrix of which we are computing the SVD decomposition + * We plan to have a very similar interface to JacobiSVD on this class. + * It should be used to speed up the calcul of SVD for big matrices. + */ +template +class BDCSVD : public SVDBase<_MatrixType> +{ + typedef SVDBase<_MatrixType> Base; + +public: + using Base::rows; + using Base::cols; + + typedef _MatrixType MatrixType; + typedef typename MatrixType::Scalar Scalar; + typedef typename NumTraits::Real RealScalar; + typedef typename MatrixType::Index Index; + enum { + RowsAtCompileTime = MatrixType::RowsAtCompileTime, + ColsAtCompileTime = MatrixType::ColsAtCompileTime, + DiagSizeAtCompileTime = EIGEN_SIZE_MIN_PREFER_DYNAMIC(RowsAtCompileTime, ColsAtCompileTime), + MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime, + MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime, + MaxDiagSizeAtCompileTime = EIGEN_SIZE_MIN_PREFER_FIXED(MaxRowsAtCompileTime, MaxColsAtCompileTime), + MatrixOptions = MatrixType::Options + }; + + typedef Matrix + MatrixUType; + typedef Matrix + MatrixVType; + typedef typename internal::plain_diag_type::type SingularValuesType; + typedef typename internal::plain_row_type::type RowType; + typedef typename internal::plain_col_type::type ColType; + typedef Matrix MatrixX; + typedef Matrix MatrixXr; + typedef Matrix VectorType; + + /** \brief Default Constructor. + * + * The default constructor is useful in cases in which the user intends to + * perform decompositions via BDCSVD::compute(const MatrixType&). + */ + BDCSVD() + : SVDBase<_MatrixType>::SVDBase(), + algoswap(ALGOSWAP) + {} + + + /** \brief Default Constructor with memory preallocation + * + * Like the default constructor but with preallocation of the internal data + * according to the specified problem size. + * \sa BDCSVD() + */ + BDCSVD(Index rows, Index cols, unsigned int computationOptions = 0) + : SVDBase<_MatrixType>::SVDBase(), + algoswap(ALGOSWAP) + { + allocate(rows, cols, computationOptions); + } + + /** \brief Constructor performing the decomposition of given matrix. + * + * \param matrix the matrix to decompose + * \param computationOptions optional parameter allowing to specify if you want full or thin U or V unitaries to be computed. + * By default, none is computed. This is a bit - field, the possible bits are #ComputeFullU, #ComputeThinU, + * #ComputeFullV, #ComputeThinV. + * + * Thin unitaries are only available if your matrix type has a Dynamic number of columns (for example MatrixXf). They also are not + * available with the (non - default) FullPivHouseholderQR preconditioner. + */ + BDCSVD(const MatrixType& matrix, unsigned int computationOptions = 0) + : SVDBase<_MatrixType>::SVDBase(), + algoswap(ALGOSWAP) + { + compute(matrix, computationOptions); + } + + ~BDCSVD() + { + } + /** \brief Method performing the decomposition of given matrix using custom options. + * + * \param matrix the matrix to decompose + * \param computationOptions optional parameter allowing to specify if you want full or thin U or V unitaries to be computed. + * By default, none is computed. This is a bit - field, the possible bits are #ComputeFullU, #ComputeThinU, + * #ComputeFullV, #ComputeThinV. + * + * Thin unitaries are only available if your matrix type has a Dynamic number of columns (for example MatrixXf). They also are not + * available with the (non - default) FullPivHouseholderQR preconditioner. + */ + SVDBase& compute(const MatrixType& matrix, unsigned int computationOptions); + + /** \brief Method performing the decomposition of given matrix using current options. + * + * \param matrix the matrix to decompose + * + * This method uses the current \a computationOptions, as already passed to the constructor or to compute(const MatrixType&, unsigned int). + */ + SVDBase& compute(const MatrixType& matrix) + { + return compute(matrix, this->m_computationOptions); + } + + void setSwitchSize(int s) + { + eigen_assert(s>3 && "BDCSVD the size of the algo switch has to be greater than 4"); + algoswap = s; + } + + + /** \returns a (least squares) solution of \f$ A x = b \f$ using the current SVD decomposition of A. + * + * \param b the right - hand - side of the equation to solve. + * + * \note Solving requires both U and V to be computed. Thin U and V are enough, there is no need for full U or V. + * + * \note SVD solving is implicitly least - squares. Thus, this method serves both purposes of exact solving and least - squares solving. + * In other words, the returned solution is guaranteed to minimize the Euclidean norm \f$ \Vert A x - b \Vert \f$. + */ + template + inline const internal::solve_retval + solve(const MatrixBase& b) const + { + eigen_assert(this->m_isInitialized && "BDCSVD is not initialized."); + eigen_assert(SVDBase<_MatrixType>::computeU() && SVDBase<_MatrixType>::computeV() && + "BDCSVD::solve() requires both unitaries U and V to be computed (thin unitaries suffice)."); + return internal::solve_retval(*this, b.derived()); + } + + + const MatrixUType& matrixU() const + { + eigen_assert(this->m_isInitialized && "SVD is not initialized."); + if (isTranspose){ + eigen_assert(this->computeV() && "This SVD decomposition didn't compute U. Did you ask for it?"); + return this->m_matrixV; + } + else + { + eigen_assert(this->computeU() && "This SVD decomposition didn't compute U. Did you ask for it?"); + return this->m_matrixU; + } + + } + + + const MatrixVType& matrixV() const + { + eigen_assert(this->m_isInitialized && "SVD is not initialized."); + if (isTranspose){ + eigen_assert(this->computeU() && "This SVD decomposition didn't compute V. Did you ask for it?"); + return this->m_matrixU; + } + else + { + eigen_assert(this->computeV() && "This SVD decomposition didn't compute V. Did you ask for it?"); + return this->m_matrixV; + } + } + +private: + void allocate(Index rows, Index cols, unsigned int computationOptions); + void divide (Index firstCol, Index lastCol, Index firstRowW, + Index firstColW, Index shift); + void deflation43(Index firstCol, Index shift, Index i, Index size); + void deflation44(Index firstColu , Index firstColm, Index firstRowW, Index firstColW, Index i, Index j, Index size); + void deflation(Index firstCol, Index lastCol, Index k, Index firstRowW, Index firstColW, Index shift); + void copyUV(MatrixXr naiveU, MatrixXr naiveV, MatrixX householderU, MatrixX houseHolderV); + +protected: + MatrixXr m_naiveU, m_naiveV; + MatrixXr m_computed; + Index nRec; + int algoswap; + bool isTranspose, compU, compV; + +}; //end class BDCSVD + + +// Methode to allocate ans initialize matrix and attributs +template +void BDCSVD::allocate(Index rows, Index cols, unsigned int computationOptions) +{ + isTranspose = (cols > rows); + if (SVDBase::allocate(rows, cols, computationOptions)) return; + m_computed = MatrixXr::Zero(this->m_diagSize + 1, this->m_diagSize ); + if (isTranspose){ + compU = this->computeU(); + compV = this->computeV(); + } + else + { + compV = this->computeU(); + compU = this->computeV(); + } + if (compU) m_naiveU = MatrixXr::Zero(this->m_diagSize + 1, this->m_diagSize + 1 ); + else m_naiveU = MatrixXr::Zero(2, this->m_diagSize + 1 ); + + if (compV) m_naiveV = MatrixXr::Zero(this->m_diagSize, this->m_diagSize); + + + //should be changed for a cleaner implementation + if (isTranspose){ + bool aux; + if (this->computeU()||this->computeV()){ + aux = this->m_computeFullU; + this->m_computeFullU = this->m_computeFullV; + this->m_computeFullV = aux; + aux = this->m_computeThinU; + this->m_computeThinU = this->m_computeThinV; + this->m_computeThinV = aux; + } + } +}// end allocate + +// Methode which compute the BDCSVD for the int +template<> +SVDBase >& +BDCSVD >::compute(const MatrixType& matrix, unsigned int computationOptions) { + allocate(matrix.rows(), matrix.cols(), computationOptions); + this->m_nonzeroSingularValues = 0; + m_computed = Matrix::Zero(rows(), cols()); + for (int i=0; im_diagSize; i++) { + this->m_singularValues.coeffRef(i) = 0; + } + if (this->m_computeFullU) this->m_matrixU = Matrix::Zero(rows(), rows()); + if (this->m_computeFullV) this->m_matrixV = Matrix::Zero(cols(), cols()); + this->m_isInitialized = true; + return *this; +} + + +// Methode which compute the BDCSVD +template +SVDBase& +BDCSVD::compute(const MatrixType& matrix, unsigned int computationOptions) +{ + allocate(matrix.rows(), matrix.cols(), computationOptions); + using std::abs; + + //**** step 1 Bidiagonalization isTranspose = (matrix.cols()>matrix.rows()) ; + MatrixType copy; + if (isTranspose) copy = matrix.adjoint(); + else copy = matrix; + + internal::UpperBidiagonalization bid(copy); + + //**** step 2 Divide + // this is ugly and has to be redone (care of complex cast) + MatrixXr temp; + temp = bid.bidiagonal().toDenseMatrix().transpose(); + m_computed.setZero(); + for (int i=0; im_diagSize - 1; i++) { + m_computed(i, i) = temp(i, i); + m_computed(i + 1, i) = temp(i + 1, i); + } + m_computed(this->m_diagSize - 1, this->m_diagSize - 1) = temp(this->m_diagSize - 1, this->m_diagSize - 1); + divide(0, this->m_diagSize - 1, 0, 0, 0); + + //**** step 3 copy + for (int i=0; im_diagSize; i++) { + RealScalar a = abs(m_computed.coeff(i, i)); + this->m_singularValues.coeffRef(i) = a; + if (a == 0){ + this->m_nonzeroSingularValues = i; + break; + } + else if (i == this->m_diagSize - 1) + { + this->m_nonzeroSingularValues = i + 1; + break; + } + } + copyUV(m_naiveV, m_naiveU, bid.householderU(), bid.householderV()); + this->m_isInitialized = true; + return *this; +}// end compute + + +template +void BDCSVD::copyUV(MatrixXr naiveU, MatrixXr naiveV, MatrixX householderU, MatrixX householderV){ + if (this->computeU()){ + MatrixX temp = MatrixX::Zero(naiveU.rows(), naiveU.cols()); + temp.real() = naiveU; + if (this->m_computeThinU){ + this->m_matrixU = MatrixX::Identity(householderU.cols(), this->m_nonzeroSingularValues ); + this->m_matrixU.block(0, 0, this->m_diagSize, this->m_nonzeroSingularValues) = + temp.block(0, 0, this->m_diagSize, this->m_nonzeroSingularValues); + this->m_matrixU = householderU * this->m_matrixU ; + } + else + { + this->m_matrixU = MatrixX::Identity(householderU.cols(), householderU.cols()); + this->m_matrixU.block(0, 0, this->m_diagSize, this->m_diagSize) = temp.block(0, 0, this->m_diagSize, this->m_diagSize); + this->m_matrixU = householderU * this->m_matrixU ; + } + } + if (this->computeV()){ + MatrixX temp = MatrixX::Zero(naiveV.rows(), naiveV.cols()); + temp.real() = naiveV; + if (this->m_computeThinV){ + this->m_matrixV = MatrixX::Identity(householderV.cols(),this->m_nonzeroSingularValues ); + this->m_matrixV.block(0, 0, this->m_nonzeroSingularValues, this->m_nonzeroSingularValues) = + temp.block(0, 0, this->m_nonzeroSingularValues, this->m_nonzeroSingularValues); + this->m_matrixV = householderV * this->m_matrixV ; + } + else + { + this->m_matrixV = MatrixX::Identity(householderV.cols(), householderV.cols()); + this->m_matrixV.block(0, 0, this->m_diagSize, this->m_diagSize) = temp.block(0, 0, this->m_diagSize, this->m_diagSize); + this->m_matrixV = householderV * this->m_matrixV; + } + } +} + +// The divide algorithm is done "in place", we are always working on subsets of the same matrix. The divide methods takes as argument the +// place of the submatrix we are currently working on. + +//@param firstCol : The Index of the first column of the submatrix of m_computed and for m_naiveU; +//@param lastCol : The Index of the last column of the submatrix of m_computed and for m_naiveU; +// lastCol + 1 - firstCol is the size of the submatrix. +//@param firstRowW : The Index of the first row of the matrix W that we are to change. (see the reference paper section 1 for more information on W) +//@param firstRowW : Same as firstRowW with the column. +//@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 +// to become the first column (*coeff) and to shift all the other columns to the right. There are more details on the reference paper. +template +void BDCSVD::divide (Index firstCol, Index lastCol, Index firstRowW, + Index firstColW, Index shift) +{ + // requires nbRows = nbCols + 1; + using std::pow; + using std::sqrt; + using std::abs; + const Index n = lastCol - firstCol + 1; + const Index k = n/2; + RealScalar alphaK; + RealScalar betaK; + RealScalar r0; + RealScalar lambda, phi, c0, s0; + MatrixXr l, f; + // We use the other algorithm which is more efficient for small + // matrices. + if (n < algoswap){ + JacobiSVD b(m_computed.block(firstCol, firstCol, n + 1, n), + ComputeFullU | (ComputeFullV * compV)) ; + if (compU) m_naiveU.block(firstCol, firstCol, n + 1, n + 1).real() << b.matrixU(); + else + { + m_naiveU.row(0).segment(firstCol, n + 1).real() << b.matrixU().row(0); + m_naiveU.row(1).segment(firstCol, n + 1).real() << b.matrixU().row(n); + } + if (compV) m_naiveV.block(firstRowW, firstColW, n, n).real() << b.matrixV(); + m_computed.block(firstCol + shift, firstCol + shift, n + 1, n).setZero(); + for (int i=0; i= firstCol; i--) + { + m_naiveU.col(i + 1).segment(firstCol, k + 1) << m_naiveU.col(i).segment(firstCol, k + 1); + } + // we shift q1 at the left with a factor 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)); + // 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; + // q2 *= c0 + m_naiveU.col(lastCol + 1).segment(firstCol + k + 1, n - k) *= c0; + } + else + { + 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 + m_naiveU(0, lastCol + 1) = (q1 * ( - s0)); + // first column = q2 * s0 + m_naiveU(1, firstCol) = m_naiveU(1, lastCol + 1) *s0; + // q2 *= c0 + m_naiveU(1, lastCol + 1) *= c0; + m_naiveU.row(1).segment(firstCol + 1, k).setZero(); + 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(); + + + // the line below do the deflation of the matrix for the third part of the algorithm + // Here the deflation is commented because the third part of the algorithm is not implemented + // the third part of the algorithm is a fast SVD on the matrix m_computed which works thanks to the deflation + + deflation(firstCol, lastCol, k, firstRowW, firstColW, shift); + + // Third part of the algorithm, since the real third part of the algorithm is not implemeted we use a JacobiSVD + JacobiSVD res= JacobiSVD(m_computed.block(firstCol + shift, firstCol +shift, n + 1, n), + ComputeFullU | (ComputeFullV * compV)) ; + if (compU) m_naiveU.block(firstCol, firstCol, n + 1, n + 1) *= res.matrixU(); + else m_naiveU.block(0, firstCol, 2, n + 1) *= res.matrixU(); + + if (compV) m_naiveV.block(firstRowW, firstColW, n, n) *= res.matrixV(); + m_computed.block(firstCol + shift, firstCol + shift, n, n) << MatrixXr::Zero(n, n); + for (int i=0; i= 1, di almost null and zi non null. +// We use a rotation to zero out zi applied to the left of M +template +void BDCSVD::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; + return; + } + c/=r; + s/=r; + m_computed(firstCol + shift, firstCol + shift) = r; + m_computed(i, firstCol + shift) = 0; + m_computed(i, i) = 0; + if (compU){ + m_naiveU.col(firstCol).segment(firstCol,size) = + c * m_naiveU.col(firstCol).segment(firstCol, size) - + s * m_naiveU.col(i).segment(firstCol, size) ; + + m_naiveU.col(i).segment(firstCol, size) = + (c + s*s/c) * m_naiveU.col(i).segment(firstCol, size) + + (s/c) * m_naiveU.col(firstCol).segment(firstCol,size); + } +}// end deflation 43 + + +// page 13 +// i,j >= 1, i != j and |di - dj| < epsilon * norm2(M) +// We apply two rotations to have zj = 0; +template +void BDCSVD::deflation44(Index firstColu , Index firstColm, Index firstRowW, Index firstColW, Index i, Index j, Index size){ + using std::abs; + using std::sqrt; + using std::conj; + using std::pow; + 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){ + m_computed(firstColm + i, firstColm + i) = m_computed(firstColm + j, firstColm + j); + return; + } + c/=r; + s/=r; + 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){ + 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) ; + + m_naiveU.col(firstColu + j).segment(firstColu, size) = + (c + s*s/c) * m_naiveU.col(firstColu + j).segment(firstColu, size) + + (s/c) * m_naiveU.col(firstColu + i).segment(firstColu, size); + } + if (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) ; + + m_naiveV.col(firstColW + j).segment(firstRowW, size - 1) = + (c + s*s/c) * m_naiveV.col(firstColW + j).segment(firstRowW, size - 1) - + (s/c) * m_naiveV.col(firstColW + i).segment(firstRowW, size - 1); + } +}// end deflation 44 + + + +template +void BDCSVD::deflation(Index firstCol, Index lastCol, Index k, Index firstRowW, Index firstColW, Index shift){ + //condition 4.1 + RealScalar EPS = EPSILON * (std::max(m_computed(firstCol + shift + 1, firstCol + shift + 1), m_computed(firstCol + k, firstCol + k))); + const Index length = lastCol + 1 - firstCol; + if (m_computed(firstCol + shift, firstCol + shift) < EPS){ + m_computed(firstCol + shift, firstCol + shift) = EPS; + } + //condition 4.2 + for (Index i=firstCol + shift + 1;i<=lastCol + shift;i++){ + if (std::abs(m_computed(i, firstCol + shift)) < EPS){ + 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){ + 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]; + + 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++; + } + } + } + //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++){ + realCol[pos] = pos + firstCol + shift; + realInd[pos] = pos; + } + const Index Zero = firstCol + shift; + VectorType temp; + 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; + const Index J = realCol[j]; + + //diag displace + aux = m_computed(I, I); + m_computed(I, I) = m_computed(J, J); + m_computed(J, J) = aux; + + //firstrow displace + aux = m_computed(I, Zero); + m_computed(I, Zero) = m_computed(J, Zero); + m_computed(J, Zero) = aux; + + // change columns + if (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; + } + 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; + } + if (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; + } + + //update real pos + realCol[realI] = J; + realCol[j] = I; + realInd[J - Zero] = realI; + realInd[I - Zero] = j; + } + for (Index i = firstCol + shift + 1; i +struct solve_retval, Rhs> + : solve_retval_base, Rhs> +{ + typedef BDCSVD<_MatrixType> BDCSVDType; + EIGEN_MAKE_SOLVE_HELPERS(BDCSVDType, Rhs) + + template void evalTo(Dest& dst) const + { + eigen_assert(rhs().rows() == dec().rows()); + // A = U S V^* + // So A^{ - 1} = V S^{ - 1} U^* + Index diagSize = (std::min)(dec().rows(), dec().cols()); + typename BDCSVDType::SingularValuesType invertedSingVals(diagSize); + Index nonzeroSingVals = dec().nonzeroSingularValues(); + invertedSingVals.head(nonzeroSingVals) = dec().singularValues().head(nonzeroSingVals).array().inverse(); + invertedSingVals.tail(diagSize - nonzeroSingVals).setZero(); + + dst = dec().matrixV().leftCols(diagSize) + * invertedSingVals.asDiagonal() + * dec().matrixU().leftCols(diagSize).adjoint() + * rhs(); + return; + } +}; + +} //end namespace internal + + /** \svd_module + * + * \return the singular value decomposition of \c *this computed by + * BDC Algorithm + * + * \sa class BDCSVD + */ +/* +template +BDCSVD::PlainObject> +MatrixBase::bdcSvd(unsigned int computationOptions) const +{ + return BDCSVD(*this, computationOptions); +} +*/ + +} // end namespace Eigen + +#endif diff --git a/eigen/unsupported/Eigen/src/SVD/CMakeLists.txt b/eigen/unsupported/Eigen/src/SVD/CMakeLists.txt new file mode 100644 index 0000000..b40baf0 --- /dev/null +++ b/eigen/unsupported/Eigen/src/SVD/CMakeLists.txt @@ -0,0 +1,6 @@ +FILE(GLOB Eigen_SVD_SRCS "*.h") + +INSTALL(FILES + ${Eigen_SVD_SRCS} + DESTINATION ${INCLUDE_INSTALL_DIR}unsupported/Eigen/src/SVD COMPONENT Devel + ) diff --git a/eigen/unsupported/Eigen/src/SVD/JacobiSVD.h b/eigen/unsupported/Eigen/src/SVD/JacobiSVD.h new file mode 100644 index 0000000..02fac40 --- /dev/null +++ b/eigen/unsupported/Eigen/src/SVD/JacobiSVD.h @@ -0,0 +1,782 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2009-2010 Benoit Jacob +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_JACOBISVD_H +#define EIGEN_JACOBISVD_H + +namespace Eigen { + +namespace internal { +// forward declaration (needed by ICC) +// the empty body is required by MSVC +template::IsComplex> +struct svd_precondition_2x2_block_to_be_real {}; + +/*** QR preconditioners (R-SVD) + *** + *** Their role is to reduce the problem of computing the SVD to the case of a square matrix. + *** This approach, known as R-SVD, is an optimization for rectangular-enough matrices, and is a requirement for + *** JacobiSVD which by itself is only able to work on square matrices. + ***/ + +enum { PreconditionIfMoreColsThanRows, PreconditionIfMoreRowsThanCols }; + +template +struct qr_preconditioner_should_do_anything +{ + enum { a = MatrixType::RowsAtCompileTime != Dynamic && + MatrixType::ColsAtCompileTime != Dynamic && + MatrixType::ColsAtCompileTime <= MatrixType::RowsAtCompileTime, + b = MatrixType::RowsAtCompileTime != Dynamic && + MatrixType::ColsAtCompileTime != Dynamic && + MatrixType::RowsAtCompileTime <= MatrixType::ColsAtCompileTime, + ret = !( (QRPreconditioner == NoQRPreconditioner) || + (Case == PreconditionIfMoreColsThanRows && bool(a)) || + (Case == PreconditionIfMoreRowsThanCols && bool(b)) ) + }; +}; + +template::ret +> struct qr_preconditioner_impl {}; + +template +class qr_preconditioner_impl +{ +public: + typedef typename MatrixType::Index Index; + void allocate(const JacobiSVD&) {} + bool run(JacobiSVD&, const MatrixType&) + { + return false; + } +}; + +/*** preconditioner using FullPivHouseholderQR ***/ + +template +class qr_preconditioner_impl +{ +public: + typedef typename MatrixType::Index Index; + typedef typename MatrixType::Scalar Scalar; + enum + { + RowsAtCompileTime = MatrixType::RowsAtCompileTime, + MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime + }; + typedef Matrix WorkspaceType; + + void allocate(const JacobiSVD& svd) + { + if (svd.rows() != m_qr.rows() || svd.cols() != m_qr.cols()) + { + m_qr.~QRType(); + ::new (&m_qr) QRType(svd.rows(), svd.cols()); + } + if (svd.m_computeFullU) m_workspace.resize(svd.rows()); + } + + bool run(JacobiSVD& svd, const MatrixType& matrix) + { + if(matrix.rows() > matrix.cols()) + { + m_qr.compute(matrix); + svd.m_workMatrix = m_qr.matrixQR().block(0,0,matrix.cols(),matrix.cols()).template triangularView(); + if(svd.m_computeFullU) m_qr.matrixQ().evalTo(svd.m_matrixU, m_workspace); + if(svd.computeV()) svd.m_matrixV = m_qr.colsPermutation(); + return true; + } + return false; + } +private: + typedef FullPivHouseholderQR QRType; + QRType m_qr; + WorkspaceType m_workspace; +}; + +template +class qr_preconditioner_impl +{ +public: + typedef typename MatrixType::Index Index; + typedef typename MatrixType::Scalar Scalar; + enum + { + RowsAtCompileTime = MatrixType::RowsAtCompileTime, + ColsAtCompileTime = MatrixType::ColsAtCompileTime, + MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime, + MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime, + Options = MatrixType::Options + }; + typedef Matrix + TransposeTypeWithSameStorageOrder; + + void allocate(const JacobiSVD& svd) + { + if (svd.cols() != m_qr.rows() || svd.rows() != m_qr.cols()) + { + m_qr.~QRType(); + ::new (&m_qr) QRType(svd.cols(), svd.rows()); + } + m_adjoint.resize(svd.cols(), svd.rows()); + if (svd.m_computeFullV) m_workspace.resize(svd.cols()); + } + + bool run(JacobiSVD& svd, const MatrixType& matrix) + { + if(matrix.cols() > matrix.rows()) + { + m_adjoint = matrix.adjoint(); + m_qr.compute(m_adjoint); + svd.m_workMatrix = m_qr.matrixQR().block(0,0,matrix.rows(),matrix.rows()).template triangularView().adjoint(); + if(svd.m_computeFullV) m_qr.matrixQ().evalTo(svd.m_matrixV, m_workspace); + if(svd.computeU()) svd.m_matrixU = m_qr.colsPermutation(); + return true; + } + else return false; + } +private: + typedef FullPivHouseholderQR QRType; + QRType m_qr; + TransposeTypeWithSameStorageOrder m_adjoint; + typename internal::plain_row_type::type m_workspace; +}; + +/*** preconditioner using ColPivHouseholderQR ***/ + +template +class qr_preconditioner_impl +{ +public: + typedef typename MatrixType::Index Index; + + void allocate(const JacobiSVD& svd) + { + if (svd.rows() != m_qr.rows() || svd.cols() != m_qr.cols()) + { + m_qr.~QRType(); + ::new (&m_qr) QRType(svd.rows(), svd.cols()); + } + if (svd.m_computeFullU) m_workspace.resize(svd.rows()); + else if (svd.m_computeThinU) m_workspace.resize(svd.cols()); + } + + bool run(JacobiSVD& svd, const MatrixType& matrix) + { + if(matrix.rows() > matrix.cols()) + { + m_qr.compute(matrix); + svd.m_workMatrix = m_qr.matrixQR().block(0,0,matrix.cols(),matrix.cols()).template triangularView(); + if(svd.m_computeFullU) m_qr.householderQ().evalTo(svd.m_matrixU, m_workspace); + else if(svd.m_computeThinU) + { + svd.m_matrixU.setIdentity(matrix.rows(), matrix.cols()); + m_qr.householderQ().applyThisOnTheLeft(svd.m_matrixU, m_workspace); + } + if(svd.computeV()) svd.m_matrixV = m_qr.colsPermutation(); + return true; + } + return false; + } + +private: + typedef ColPivHouseholderQR QRType; + QRType m_qr; + typename internal::plain_col_type::type m_workspace; +}; + +template +class qr_preconditioner_impl +{ +public: + typedef typename MatrixType::Index Index; + typedef typename MatrixType::Scalar Scalar; + enum + { + RowsAtCompileTime = MatrixType::RowsAtCompileTime, + ColsAtCompileTime = MatrixType::ColsAtCompileTime, + MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime, + MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime, + Options = MatrixType::Options + }; + + typedef Matrix + TransposeTypeWithSameStorageOrder; + + void allocate(const JacobiSVD& svd) + { + if (svd.cols() != m_qr.rows() || svd.rows() != m_qr.cols()) + { + m_qr.~QRType(); + ::new (&m_qr) QRType(svd.cols(), svd.rows()); + } + if (svd.m_computeFullV) m_workspace.resize(svd.cols()); + else if (svd.m_computeThinV) m_workspace.resize(svd.rows()); + m_adjoint.resize(svd.cols(), svd.rows()); + } + + bool run(JacobiSVD& svd, const MatrixType& matrix) + { + if(matrix.cols() > matrix.rows()) + { + m_adjoint = matrix.adjoint(); + m_qr.compute(m_adjoint); + + svd.m_workMatrix = m_qr.matrixQR().block(0,0,matrix.rows(),matrix.rows()).template triangularView().adjoint(); + if(svd.m_computeFullV) m_qr.householderQ().evalTo(svd.m_matrixV, m_workspace); + else if(svd.m_computeThinV) + { + svd.m_matrixV.setIdentity(matrix.cols(), matrix.rows()); + m_qr.householderQ().applyThisOnTheLeft(svd.m_matrixV, m_workspace); + } + if(svd.computeU()) svd.m_matrixU = m_qr.colsPermutation(); + return true; + } + else return false; + } + +private: + typedef ColPivHouseholderQR QRType; + QRType m_qr; + TransposeTypeWithSameStorageOrder m_adjoint; + typename internal::plain_row_type::type m_workspace; +}; + +/*** preconditioner using HouseholderQR ***/ + +template +class qr_preconditioner_impl +{ +public: + typedef typename MatrixType::Index Index; + + void allocate(const JacobiSVD& svd) + { + if (svd.rows() != m_qr.rows() || svd.cols() != m_qr.cols()) + { + m_qr.~QRType(); + ::new (&m_qr) QRType(svd.rows(), svd.cols()); + } + if (svd.m_computeFullU) m_workspace.resize(svd.rows()); + else if (svd.m_computeThinU) m_workspace.resize(svd.cols()); + } + + bool run(JacobiSVD& svd, const MatrixType& matrix) + { + if(matrix.rows() > matrix.cols()) + { + m_qr.compute(matrix); + svd.m_workMatrix = m_qr.matrixQR().block(0,0,matrix.cols(),matrix.cols()).template triangularView(); + if(svd.m_computeFullU) m_qr.householderQ().evalTo(svd.m_matrixU, m_workspace); + else if(svd.m_computeThinU) + { + svd.m_matrixU.setIdentity(matrix.rows(), matrix.cols()); + m_qr.householderQ().applyThisOnTheLeft(svd.m_matrixU, m_workspace); + } + if(svd.computeV()) svd.m_matrixV.setIdentity(matrix.cols(), matrix.cols()); + return true; + } + return false; + } +private: + typedef HouseholderQR QRType; + QRType m_qr; + typename internal::plain_col_type::type m_workspace; +}; + +template +class qr_preconditioner_impl +{ +public: + typedef typename MatrixType::Index Index; + typedef typename MatrixType::Scalar Scalar; + enum + { + RowsAtCompileTime = MatrixType::RowsAtCompileTime, + ColsAtCompileTime = MatrixType::ColsAtCompileTime, + MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime, + MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime, + Options = MatrixType::Options + }; + + typedef Matrix + TransposeTypeWithSameStorageOrder; + + void allocate(const JacobiSVD& svd) + { + if (svd.cols() != m_qr.rows() || svd.rows() != m_qr.cols()) + { + m_qr.~QRType(); + ::new (&m_qr) QRType(svd.cols(), svd.rows()); + } + if (svd.m_computeFullV) m_workspace.resize(svd.cols()); + else if (svd.m_computeThinV) m_workspace.resize(svd.rows()); + m_adjoint.resize(svd.cols(), svd.rows()); + } + + bool run(JacobiSVD& svd, const MatrixType& matrix) + { + if(matrix.cols() > matrix.rows()) + { + m_adjoint = matrix.adjoint(); + m_qr.compute(m_adjoint); + + svd.m_workMatrix = m_qr.matrixQR().block(0,0,matrix.rows(),matrix.rows()).template triangularView().adjoint(); + if(svd.m_computeFullV) m_qr.householderQ().evalTo(svd.m_matrixV, m_workspace); + else if(svd.m_computeThinV) + { + svd.m_matrixV.setIdentity(matrix.cols(), matrix.rows()); + m_qr.householderQ().applyThisOnTheLeft(svd.m_matrixV, m_workspace); + } + if(svd.computeU()) svd.m_matrixU.setIdentity(matrix.rows(), matrix.rows()); + return true; + } + else return false; + } + +private: + typedef HouseholderQR QRType; + QRType m_qr; + TransposeTypeWithSameStorageOrder m_adjoint; + typename internal::plain_row_type::type m_workspace; +}; + +/*** 2x2 SVD implementation + *** + *** JacobiSVD consists in performing a series of 2x2 SVD subproblems + ***/ + +template +struct svd_precondition_2x2_block_to_be_real +{ + typedef JacobiSVD SVD; + typedef typename SVD::Index Index; + static void run(typename SVD::WorkMatrixType&, SVD&, Index, Index) {} +}; + +template +struct svd_precondition_2x2_block_to_be_real +{ + typedef JacobiSVD SVD; + typedef typename MatrixType::Scalar Scalar; + typedef typename MatrixType::RealScalar RealScalar; + typedef typename SVD::Index Index; + static void run(typename SVD::WorkMatrixType& work_matrix, SVD& svd, Index p, Index q) + { + using std::sqrt; + Scalar z; + JacobiRotation rot; + RealScalar n = sqrt(numext::abs2(work_matrix.coeff(p,p)) + numext::abs2(work_matrix.coeff(q,p))); + if(n==0) + { + z = abs(work_matrix.coeff(p,q)) / work_matrix.coeff(p,q); + work_matrix.row(p) *= z; + if(svd.computeU()) svd.m_matrixU.col(p) *= conj(z); + z = abs(work_matrix.coeff(q,q)) / work_matrix.coeff(q,q); + work_matrix.row(q) *= z; + if(svd.computeU()) svd.m_matrixU.col(q) *= conj(z); + } + else + { + rot.c() = conj(work_matrix.coeff(p,p)) / n; + rot.s() = work_matrix.coeff(q,p) / n; + work_matrix.applyOnTheLeft(p,q,rot); + if(svd.computeU()) svd.m_matrixU.applyOnTheRight(p,q,rot.adjoint()); + if(work_matrix.coeff(p,q) != Scalar(0)) + { + Scalar z = abs(work_matrix.coeff(p,q)) / work_matrix.coeff(p,q); + work_matrix.col(q) *= z; + if(svd.computeV()) svd.m_matrixV.col(q) *= z; + } + if(work_matrix.coeff(q,q) != Scalar(0)) + { + z = abs(work_matrix.coeff(q,q)) / work_matrix.coeff(q,q); + work_matrix.row(q) *= z; + if(svd.computeU()) svd.m_matrixU.col(q) *= conj(z); + } + } + } +}; + +template +void real_2x2_jacobi_svd(const MatrixType& matrix, Index p, Index q, + JacobiRotation *j_left, + JacobiRotation *j_right) +{ + using std::sqrt; + Matrix m; + m << numext::real(matrix.coeff(p,p)), numext::real(matrix.coeff(p,q)), + numext::real(matrix.coeff(q,p)), numext::real(matrix.coeff(q,q)); + JacobiRotation rot1; + RealScalar t = m.coeff(0,0) + m.coeff(1,1); + RealScalar d = m.coeff(1,0) - m.coeff(0,1); + if(t == RealScalar(0)) + { + rot1.c() = RealScalar(0); + rot1.s() = d > RealScalar(0) ? RealScalar(1) : RealScalar(-1); + } + else + { + RealScalar u = d / t; + rot1.c() = RealScalar(1) / sqrt(RealScalar(1) + numext::abs2(u)); + rot1.s() = rot1.c() * u; + } + m.applyOnTheLeft(0,1,rot1); + j_right->makeJacobi(m,0,1); + *j_left = rot1 * j_right->transpose(); +} + +} // end namespace internal + +/** \ingroup SVD_Module + * + * + * \class JacobiSVD + * + * \brief Two-sided Jacobi SVD decomposition of a rectangular matrix + * + * \param MatrixType the type of the matrix of which we are computing the SVD decomposition + * \param QRPreconditioner this optional parameter allows to specify the type of QR decomposition that will be used internally + * for the R-SVD step for non-square matrices. See discussion of possible values below. + * + * SVD decomposition consists in decomposing any n-by-p matrix \a A as a product + * \f[ A = U S V^* \f] + * where \a U is a n-by-n unitary, \a V is a p-by-p unitary, and \a S is a n-by-p real positive matrix which is zero outside of its main diagonal; + * the diagonal entries of S are known as the \em singular \em values of \a A and the columns of \a U and \a V are known as the left + * and right \em singular \em vectors of \a A respectively. + * + * Singular values are always sorted in decreasing order. + * + * This JacobiSVD decomposition computes only the singular values by default. If you want \a U or \a V, you need to ask for them explicitly. + * + * You can ask for only \em thin \a U or \a V to be computed, meaning the following. In case of a rectangular n-by-p matrix, letting \a m be the + * smaller value among \a n and \a p, there are only \a m singular vectors; the remaining columns of \a U and \a V do not correspond to actual + * singular vectors. Asking for \em thin \a U or \a V means asking for only their \a m first columns to be formed. So \a U is then a n-by-m matrix, + * and \a V is then a p-by-m matrix. Notice that thin \a U and \a V are all you need for (least squares) solving. + * + * Here's an example demonstrating basic usage: + * \include JacobiSVD_basic.cpp + * Output: \verbinclude JacobiSVD_basic.out + * + * This JacobiSVD class is a two-sided Jacobi R-SVD decomposition, ensuring optimal reliability and accuracy. The downside is that it's slower than + * bidiagonalizing SVD algorithms for large square matrices; however its complexity is still \f$ O(n^2p) \f$ where \a n is the smaller dimension and + * \a p is the greater dimension, meaning that it is still of the same order of complexity as the faster bidiagonalizing R-SVD algorithms. + * In particular, like any R-SVD, it takes advantage of non-squareness in that its complexity is only linear in the greater dimension. + * + * If the input matrix has inf or nan coefficients, the result of the computation is undefined, but the computation is guaranteed to + * terminate in finite (and reasonable) time. + * + * The possible values for QRPreconditioner are: + * \li ColPivHouseholderQRPreconditioner is the default. In practice it's very safe. It uses column-pivoting QR. + * \li FullPivHouseholderQRPreconditioner, is the safest and slowest. It uses full-pivoting QR. + * Contrary to other QRs, it doesn't allow computing thin unitaries. + * \li HouseholderQRPreconditioner is the fastest, and less safe and accurate than the pivoting variants. It uses non-pivoting QR. + * This is very similar in safety and accuracy to the bidiagonalization process used by bidiagonalizing SVD algorithms (since bidiagonalization + * is inherently non-pivoting). However the resulting SVD is still more reliable than bidiagonalizing SVDs because the Jacobi-based iterarive + * process is more reliable than the optimized bidiagonal SVD iterations. + * \li NoQRPreconditioner allows not to use a QR preconditioner at all. This is useful if you know that you will only be computing + * JacobiSVD decompositions of square matrices. Non-square matrices require a QR preconditioner. Using this option will result in + * faster compilation and smaller executable code. It won't significantly speed up computation, since JacobiSVD is always checking + * if QR preconditioning is needed before applying it anyway. + * + * \sa MatrixBase::jacobiSvd() + */ +template +class JacobiSVD : public SVDBase<_MatrixType> +{ + public: + + typedef _MatrixType MatrixType; + typedef typename MatrixType::Scalar Scalar; + typedef typename NumTraits::Real RealScalar; + typedef typename MatrixType::Index Index; + enum { + RowsAtCompileTime = MatrixType::RowsAtCompileTime, + ColsAtCompileTime = MatrixType::ColsAtCompileTime, + DiagSizeAtCompileTime = EIGEN_SIZE_MIN_PREFER_DYNAMIC(RowsAtCompileTime,ColsAtCompileTime), + MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime, + MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime, + MaxDiagSizeAtCompileTime = EIGEN_SIZE_MIN_PREFER_FIXED(MaxRowsAtCompileTime,MaxColsAtCompileTime), + MatrixOptions = MatrixType::Options + }; + + typedef Matrix + MatrixUType; + typedef Matrix + MatrixVType; + typedef typename internal::plain_diag_type::type SingularValuesType; + typedef typename internal::plain_row_type::type RowType; + typedef typename internal::plain_col_type::type ColType; + typedef Matrix + WorkMatrixType; + + /** \brief Default Constructor. + * + * The default constructor is useful in cases in which the user intends to + * perform decompositions via JacobiSVD::compute(const MatrixType&). + */ + JacobiSVD() + : SVDBase<_MatrixType>::SVDBase() + {} + + + /** \brief Default Constructor with memory preallocation + * + * Like the default constructor but with preallocation of the internal data + * according to the specified problem size. + * \sa JacobiSVD() + */ + JacobiSVD(Index rows, Index cols, unsigned int computationOptions = 0) + : SVDBase<_MatrixType>::SVDBase() + { + allocate(rows, cols, computationOptions); + } + + /** \brief Constructor performing the decomposition of given matrix. + * + * \param matrix the matrix to decompose + * \param computationOptions optional parameter allowing to specify if you want full or thin U or V unitaries to be computed. + * By default, none is computed. This is a bit-field, the possible bits are #ComputeFullU, #ComputeThinU, + * #ComputeFullV, #ComputeThinV. + * + * Thin unitaries are only available if your matrix type has a Dynamic number of columns (for example MatrixXf). They also are not + * available with the (non-default) FullPivHouseholderQR preconditioner. + */ + JacobiSVD(const MatrixType& matrix, unsigned int computationOptions = 0) + : SVDBase<_MatrixType>::SVDBase() + { + compute(matrix, computationOptions); + } + + /** \brief Method performing the decomposition of given matrix using custom options. + * + * \param matrix the matrix to decompose + * \param computationOptions optional parameter allowing to specify if you want full or thin U or V unitaries to be computed. + * By default, none is computed. This is a bit-field, the possible bits are #ComputeFullU, #ComputeThinU, + * #ComputeFullV, #ComputeThinV. + * + * Thin unitaries are only available if your matrix type has a Dynamic number of columns (for example MatrixXf). They also are not + * available with the (non-default) FullPivHouseholderQR preconditioner. + */ + SVDBase& compute(const MatrixType& matrix, unsigned int computationOptions); + + /** \brief Method performing the decomposition of given matrix using current options. + * + * \param matrix the matrix to decompose + * + * This method uses the current \a computationOptions, as already passed to the constructor or to compute(const MatrixType&, unsigned int). + */ + SVDBase& compute(const MatrixType& matrix) + { + return compute(matrix, this->m_computationOptions); + } + + /** \returns a (least squares) solution of \f$ A x = b \f$ using the current SVD decomposition of A. + * + * \param b the right-hand-side of the equation to solve. + * + * \note Solving requires both U and V to be computed. Thin U and V are enough, there is no need for full U or V. + * + * \note SVD solving is implicitly least-squares. Thus, this method serves both purposes of exact solving and least-squares solving. + * In other words, the returned solution is guaranteed to minimize the Euclidean norm \f$ \Vert A x - b \Vert \f$. + */ + template + inline const internal::solve_retval + solve(const MatrixBase& b) const + { + eigen_assert(this->m_isInitialized && "JacobiSVD is not initialized."); + eigen_assert(SVDBase::computeU() && SVDBase::computeV() && "JacobiSVD::solve() requires both unitaries U and V to be computed (thin unitaries suffice)."); + return internal::solve_retval(*this, b.derived()); + } + + + + private: + void allocate(Index rows, Index cols, unsigned int computationOptions); + + protected: + WorkMatrixType m_workMatrix; + + template + friend struct internal::svd_precondition_2x2_block_to_be_real; + template + friend struct internal::qr_preconditioner_impl; + + internal::qr_preconditioner_impl m_qr_precond_morecols; + internal::qr_preconditioner_impl m_qr_precond_morerows; +}; + +template +void JacobiSVD::allocate(Index rows, Index cols, unsigned int computationOptions) +{ + if (SVDBase::allocate(rows, cols, computationOptions)) return; + + if (QRPreconditioner == FullPivHouseholderQRPreconditioner) + { + eigen_assert(!(this->m_computeThinU || this->m_computeThinV) && + "JacobiSVD: can't compute thin U or thin V with the FullPivHouseholderQR preconditioner. " + "Use the ColPivHouseholderQR preconditioner instead."); + } + + m_workMatrix.resize(this->m_diagSize, this->m_diagSize); + + if(this->m_cols>this->m_rows) m_qr_precond_morecols.allocate(*this); + if(this->m_rows>this->m_cols) m_qr_precond_morerows.allocate(*this); +} + +template +SVDBase& +JacobiSVD::compute(const MatrixType& matrix, unsigned int computationOptions) +{ + using std::abs; + allocate(matrix.rows(), matrix.cols(), computationOptions); + + // currently we stop when we reach precision 2*epsilon as the last bit of precision can require an unreasonable number of iterations, + // only worsening the precision of U and V as we accumulate more rotations + const RealScalar precision = RealScalar(2) * NumTraits::epsilon(); + + // limit for very small denormal numbers to be considered zero in order to avoid infinite loops (see bug 286) + const RealScalar considerAsZero = RealScalar(2) * std::numeric_limits::denorm_min(); + + /*** step 1. The R-SVD step: we use a QR decomposition to reduce to the case of a square matrix */ + + if(!m_qr_precond_morecols.run(*this, matrix) && !m_qr_precond_morerows.run(*this, matrix)) + { + m_workMatrix = matrix.block(0,0,this->m_diagSize,this->m_diagSize); + if(this->m_computeFullU) this->m_matrixU.setIdentity(this->m_rows,this->m_rows); + if(this->m_computeThinU) this->m_matrixU.setIdentity(this->m_rows,this->m_diagSize); + if(this->m_computeFullV) this->m_matrixV.setIdentity(this->m_cols,this->m_cols); + if(this->m_computeThinV) this->m_matrixV.setIdentity(this->m_cols, this->m_diagSize); + } + + /*** step 2. The main Jacobi SVD iteration. ***/ + + bool finished = false; + while(!finished) + { + finished = true; + + // do a sweep: for all index pairs (p,q), perform SVD of the corresponding 2x2 sub-matrix + + for(Index p = 1; p < this->m_diagSize; ++p) + { + for(Index q = 0; q < p; ++q) + { + // if this 2x2 sub-matrix is not diagonal already... + // notice that this comparison will evaluate to false if any NaN is involved, ensuring that NaN's don't + // keep us iterating forever. Similarly, small denormal numbers are considered zero. + using std::max; + RealScalar threshold = (max)(considerAsZero, precision * (max)(abs(m_workMatrix.coeff(p,p)), + abs(m_workMatrix.coeff(q,q)))); + if((max)(abs(m_workMatrix.coeff(p,q)),abs(m_workMatrix.coeff(q,p))) > threshold) + { + finished = false; + + // perform SVD decomposition of 2x2 sub-matrix corresponding to indices p,q to make it diagonal + internal::svd_precondition_2x2_block_to_be_real::run(m_workMatrix, *this, p, q); + JacobiRotation j_left, j_right; + internal::real_2x2_jacobi_svd(m_workMatrix, p, q, &j_left, &j_right); + + // accumulate resulting Jacobi rotations + m_workMatrix.applyOnTheLeft(p,q,j_left); + if(SVDBase::computeU()) this->m_matrixU.applyOnTheRight(p,q,j_left.transpose()); + + m_workMatrix.applyOnTheRight(p,q,j_right); + if(SVDBase::computeV()) this->m_matrixV.applyOnTheRight(p,q,j_right); + } + } + } + } + + /*** step 3. The work matrix is now diagonal, so ensure it's positive so its diagonal entries are the singular values ***/ + + for(Index i = 0; i < this->m_diagSize; ++i) + { + RealScalar a = abs(m_workMatrix.coeff(i,i)); + this->m_singularValues.coeffRef(i) = a; + if(SVDBase::computeU() && (a!=RealScalar(0))) this->m_matrixU.col(i) *= this->m_workMatrix.coeff(i,i)/a; + } + + /*** step 4. Sort singular values in descending order and compute the number of nonzero singular values ***/ + + this->m_nonzeroSingularValues = this->m_diagSize; + for(Index i = 0; i < this->m_diagSize; i++) + { + Index pos; + RealScalar maxRemainingSingularValue = this->m_singularValues.tail(this->m_diagSize-i).maxCoeff(&pos); + if(maxRemainingSingularValue == RealScalar(0)) + { + this->m_nonzeroSingularValues = i; + break; + } + if(pos) + { + pos += i; + std::swap(this->m_singularValues.coeffRef(i), this->m_singularValues.coeffRef(pos)); + if(SVDBase::computeU()) this->m_matrixU.col(pos).swap(this->m_matrixU.col(i)); + if(SVDBase::computeV()) this->m_matrixV.col(pos).swap(this->m_matrixV.col(i)); + } + } + + this->m_isInitialized = true; + return *this; +} + +namespace internal { +template +struct solve_retval, Rhs> + : solve_retval_base, Rhs> +{ + typedef JacobiSVD<_MatrixType, QRPreconditioner> JacobiSVDType; + EIGEN_MAKE_SOLVE_HELPERS(JacobiSVDType,Rhs) + + template void evalTo(Dest& dst) const + { + eigen_assert(rhs().rows() == dec().rows()); + + // A = U S V^* + // So A^{-1} = V S^{-1} U^* + + Index diagSize = (std::min)(dec().rows(), dec().cols()); + typename JacobiSVDType::SingularValuesType invertedSingVals(diagSize); + + Index nonzeroSingVals = dec().nonzeroSingularValues(); + invertedSingVals.head(nonzeroSingVals) = dec().singularValues().head(nonzeroSingVals).array().inverse(); + invertedSingVals.tail(diagSize - nonzeroSingVals).setZero(); + + dst = dec().matrixV().leftCols(diagSize) + * invertedSingVals.asDiagonal() + * dec().matrixU().leftCols(diagSize).adjoint() + * rhs(); + } +}; +} // end namespace internal + +/** \svd_module + * + * \return the singular value decomposition of \c *this computed by two-sided + * Jacobi transformations. + * + * \sa class JacobiSVD + */ +template +JacobiSVD::PlainObject> +MatrixBase::jacobiSvd(unsigned int computationOptions) const +{ + return JacobiSVD(*this, computationOptions); +} + +} // end namespace Eigen + +#endif // EIGEN_JACOBISVD_H diff --git a/eigen/unsupported/Eigen/src/SVD/SVDBase.h b/eigen/unsupported/Eigen/src/SVD/SVDBase.h new file mode 100644 index 0000000..fd8af3b --- /dev/null +++ b/eigen/unsupported/Eigen/src/SVD/SVDBase.h @@ -0,0 +1,236 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2009-2010 Benoit Jacob +// +// Copyright (C) 2013 Gauthier Brun +// Copyright (C) 2013 Nicolas Carre +// Copyright (C) 2013 Jean Ceccato +// Copyright (C) 2013 Pierre Zoppitelli +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_SVD_H +#define EIGEN_SVD_H + +namespace Eigen { +/** \ingroup SVD_Module + * + * + * \class SVDBase + * + * \brief Mother class of SVD classes algorithms + * + * \param MatrixType the type of the matrix of which we are computing the SVD decomposition + * SVD decomposition consists in decomposing any n-by-p matrix \a A as a product + * \f[ A = U S V^* \f] + * where \a U is a n-by-n unitary, \a V is a p-by-p unitary, and \a S is a n-by-p real positive matrix which is zero outside of its main diagonal; + * the diagonal entries of S are known as the \em singular \em values of \a A and the columns of \a U and \a V are known as the left + * and right \em singular \em vectors of \a A respectively. + * + * Singular values are always sorted in decreasing order. + * + * + * You can ask for only \em thin \a U or \a V to be computed, meaning the following. In case of a rectangular n-by-p matrix, letting \a m be the + * smaller value among \a n and \a p, there are only \a m singular vectors; the remaining columns of \a U and \a V do not correspond to actual + * singular vectors. Asking for \em thin \a U or \a V means asking for only their \a m first columns to be formed. So \a U is then a n-by-m matrix, + * and \a V is then a p-by-m matrix. Notice that thin \a U and \a V are all you need for (least squares) solving. + * + * If the input matrix has inf or nan coefficients, the result of the computation is undefined, but the computation is guaranteed to + * terminate in finite (and reasonable) time. + * \sa MatrixBase::genericSvd() + */ +template +class SVDBase +{ + +public: + typedef _MatrixType MatrixType; + typedef typename MatrixType::Scalar Scalar; + typedef typename NumTraits::Real RealScalar; + typedef typename MatrixType::Index Index; + enum { + RowsAtCompileTime = MatrixType::RowsAtCompileTime, + ColsAtCompileTime = MatrixType::ColsAtCompileTime, + DiagSizeAtCompileTime = EIGEN_SIZE_MIN_PREFER_DYNAMIC(RowsAtCompileTime,ColsAtCompileTime), + MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime, + MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime, + MaxDiagSizeAtCompileTime = EIGEN_SIZE_MIN_PREFER_FIXED(MaxRowsAtCompileTime,MaxColsAtCompileTime), + MatrixOptions = MatrixType::Options + }; + + typedef Matrix + MatrixUType; + typedef Matrix + MatrixVType; + typedef typename internal::plain_diag_type::type SingularValuesType; + typedef typename internal::plain_row_type::type RowType; + typedef typename internal::plain_col_type::type ColType; + typedef Matrix + WorkMatrixType; + + + + + /** \brief Method performing the decomposition of given matrix using custom options. + * + * \param matrix the matrix to decompose + * \param computationOptions optional parameter allowing to specify if you want full or thin U or V unitaries to be computed. + * By default, none is computed. This is a bit-field, the possible bits are #ComputeFullU, #ComputeThinU, + * #ComputeFullV, #ComputeThinV. + * + * Thin unitaries are only available if your matrix type has a Dynamic number of columns (for example MatrixXf). They also are not + * available with the (non-default) FullPivHouseholderQR preconditioner. + */ + SVDBase& compute(const MatrixType& matrix, unsigned int computationOptions); + + /** \brief Method performing the decomposition of given matrix using current options. + * + * \param matrix the matrix to decompose + * + * This method uses the current \a computationOptions, as already passed to the constructor or to compute(const MatrixType&, unsigned int). + */ + //virtual SVDBase& compute(const MatrixType& matrix) = 0; + SVDBase& compute(const MatrixType& matrix); + + /** \returns the \a U matrix. + * + * For the SVDBase decomposition of a n-by-p matrix, letting \a m be the minimum of \a n and \a p, + * the U matrix is n-by-n if you asked for #ComputeFullU, and is n-by-m if you asked for #ComputeThinU. + * + * The \a m first columns of \a U are the left singular vectors of the matrix being decomposed. + * + * This method asserts that you asked for \a U to be computed. + */ + const MatrixUType& matrixU() const + { + eigen_assert(m_isInitialized && "SVD is not initialized."); + eigen_assert(computeU() && "This SVD decomposition didn't compute U. Did you ask for it?"); + return m_matrixU; + } + + /** \returns the \a V matrix. + * + * For the SVD decomposition of a n-by-p matrix, letting \a m be the minimum of \a n and \a p, + * the V matrix is p-by-p if you asked for #ComputeFullV, and is p-by-m if you asked for ComputeThinV. + * + * The \a m first columns of \a V are the right singular vectors of the matrix being decomposed. + * + * This method asserts that you asked for \a V to be computed. + */ + const MatrixVType& matrixV() const + { + eigen_assert(m_isInitialized && "SVD is not initialized."); + eigen_assert(computeV() && "This SVD decomposition didn't compute V. Did you ask for it?"); + return m_matrixV; + } + + /** \returns the vector of singular values. + * + * For the SVD decomposition of a n-by-p matrix, letting \a m be the minimum of \a n and \a p, the + * returned vector has size \a m. Singular values are always sorted in decreasing order. + */ + const SingularValuesType& singularValues() const + { + eigen_assert(m_isInitialized && "SVD is not initialized."); + return m_singularValues; + } + + + + /** \returns the number of singular values that are not exactly 0 */ + Index nonzeroSingularValues() const + { + eigen_assert(m_isInitialized && "SVD is not initialized."); + return m_nonzeroSingularValues; + } + + + /** \returns true if \a U (full or thin) is asked for in this SVD decomposition */ + inline bool computeU() const { return m_computeFullU || m_computeThinU; } + /** \returns true if \a V (full or thin) is asked for in this SVD decomposition */ + inline bool computeV() const { return m_computeFullV || m_computeThinV; } + + + inline Index rows() const { return m_rows; } + inline Index cols() const { return m_cols; } + + +protected: + // return true if already allocated + bool allocate(Index rows, Index cols, unsigned int computationOptions) ; + + MatrixUType m_matrixU; + MatrixVType m_matrixV; + SingularValuesType m_singularValues; + bool m_isInitialized, m_isAllocated; + bool m_computeFullU, m_computeThinU; + bool m_computeFullV, m_computeThinV; + unsigned int m_computationOptions; + Index m_nonzeroSingularValues, m_rows, m_cols, m_diagSize; + + + /** \brief Default Constructor. + * + * Default constructor of SVDBase + */ + SVDBase() + : m_isInitialized(false), + m_isAllocated(false), + m_computationOptions(0), + m_rows(-1), m_cols(-1) + {} + + +}; + + +template +bool SVDBase::allocate(Index rows, Index cols, unsigned int computationOptions) +{ + eigen_assert(rows >= 0 && cols >= 0); + + if (m_isAllocated && + rows == m_rows && + cols == m_cols && + computationOptions == m_computationOptions) + { + return true; + } + + m_rows = rows; + m_cols = cols; + m_isInitialized = false; + m_isAllocated = true; + m_computationOptions = computationOptions; + m_computeFullU = (computationOptions & ComputeFullU) != 0; + m_computeThinU = (computationOptions & ComputeThinU) != 0; + m_computeFullV = (computationOptions & ComputeFullV) != 0; + m_computeThinV = (computationOptions & ComputeThinV) != 0; + eigen_assert(!(m_computeFullU && m_computeThinU) && "SVDBase: you can't ask for both full and thin U"); + eigen_assert(!(m_computeFullV && m_computeThinV) && "SVDBase: you can't ask for both full and thin V"); + eigen_assert(EIGEN_IMPLIES(m_computeThinU || m_computeThinV, MatrixType::ColsAtCompileTime==Dynamic) && + "SVDBase: thin U and V are only available when your matrix has a dynamic number of columns."); + + m_diagSize = (std::min)(m_rows, m_cols); + m_singularValues.resize(m_diagSize); + if(RowsAtCompileTime==Dynamic) + m_matrixU.resize(m_rows, m_computeFullU ? m_rows + : m_computeThinU ? m_diagSize + : 0); + if(ColsAtCompileTime==Dynamic) + m_matrixV.resize(m_cols, m_computeFullV ? m_cols + : m_computeThinV ? m_diagSize + : 0); + + return false; +} + +}// end namespace + +#endif // EIGEN_SVD_H diff --git a/eigen/unsupported/Eigen/src/SVD/TODOBdcsvd.txt b/eigen/unsupported/Eigen/src/SVD/TODOBdcsvd.txt new file mode 100644 index 0000000..0bc9a46 --- /dev/null +++ b/eigen/unsupported/Eigen/src/SVD/TODOBdcsvd.txt @@ -0,0 +1,29 @@ +TO DO LIST + + + +(optional optimization) - do all the allocations in the allocate part + - support static matrices + - return a error at compilation time when using integer matrices (int, long, std::complex, ...) + +to finish the algorithm : + -implement the last part of the algorithm as described on the reference paper. + You may find more information on that part on this paper + + -to replace the call to JacobiSVD at the end of the divide algorithm, just after the call to + deflation. + +(suggested step by step resolution) + 0) comment the call to Jacobi in the last part of the divide method and everything right after + until the end of the method. What is commented can be a guideline to steps 3) 4) and 6) + 1) solve the secular equation (Characteristic equation) on the values that are not null (zi!=0 and di!=0), after the deflation + wich should be uncommented in the divide method + 2) remember the values of the singular values that are already computed (zi=0) + 3) assign the singular values found in m_computed at the right places (with the ones found in step 2) ) + in decreasing order + 4) set the firstcol to zero (except the first element) in m_computed + 5) compute all the singular vectors when CompV is set to true and only the left vectors when + CompV is set to false + 6) multiply naiveU and naiveV to the right by the matrices found, only naiveU when CompV is set to + false, /!\ if CompU is false NaiveU has only 2 rows + 7) delete everything commented in step 0) diff --git a/eigen/unsupported/Eigen/src/SVD/doneInBDCSVD.txt b/eigen/unsupported/Eigen/src/SVD/doneInBDCSVD.txt new file mode 100644 index 0000000..8563dda --- /dev/null +++ b/eigen/unsupported/Eigen/src/SVD/doneInBDCSVD.txt @@ -0,0 +1,21 @@ +This unsupported package is about a divide and conquer algorithm to compute SVD. + +The implementation follows as closely as possible the following reference paper : +http://www.cs.yale.edu/publications/techreports/tr933.pdf + +The code documentation uses the same names for variables as the reference paper. The code, deflation included, is +working but there are a few things that could be optimised as explained in the TODOBdsvd. + +In the code comments were put at the line where would be the third step of the algorithm so one could simply add the call +of a function doing the last part of the algorithm and that would not require any knowledge of the part we implemented. + +In the TODOBdcsvd we explain what is the main difficulty of the last part and suggest a reference paper to help solve it. + +The implemented has trouble with fixed size matrices. + +In the actual implementation, it returns matrices of zero when ask to do a svd on an int matrix. + + +Paper for the third part: +http://www.stat.uchicago.edu/~lekheng/courses/302/classics/greengard-rokhlin.pdf + -- cgit v1.2.3