diff options
author | Gauthier Brun <gauthier.brun@gmail.com> | 2013-06-19 00:03:27 +0200 |
---|---|---|
committer | Gauthier Brun <gauthier.brun@gmail.com> | 2013-06-19 00:03:27 +0200 |
commit | 8105b5ed3fd163f4b2574a2f0a6257cf119bab95 (patch) | |
tree | d1864b8c601e2a0af4ef9cd1cc0897b4fedaa020 | |
parent | ba79e39c5c641888f58bff01febe9b81c4a22cbc (diff) |
new unsupported and not finished SVD, using a divide and conquert algorithm, with tests and benchmark
-rw-r--r-- | unsupported/Eigen/SVD | 39 | ||||
-rw-r--r-- | unsupported/Eigen/src/SVD/BDCSVD.h | 744 | ||||
-rw-r--r-- | unsupported/Eigen/src/SVD/CMakeLists.txt | 6 | ||||
-rw-r--r-- | unsupported/Eigen/src/SVD/JacobiSVD.h | 782 | ||||
-rw-r--r-- | unsupported/Eigen/src/SVD/SVDBase.h | 236 | ||||
-rw-r--r-- | unsupported/Eigen/src/SVD/TODOBdcsvd.txt | 29 | ||||
-rw-r--r-- | unsupported/Eigen/src/SVD/doneInBDCSVD.txt | 21 | ||||
-rw-r--r-- | unsupported/bench/bench_svd.cpp | 123 | ||||
-rw-r--r-- | unsupported/test/bdcsvd.cpp | 213 | ||||
-rw-r--r-- | unsupported/test/jacobisvd.cpp | 198 | ||||
-rw-r--r-- | unsupported/test/svd_common.h | 261 |
11 files changed, 2652 insertions, 0 deletions
diff --git a/unsupported/Eigen/SVD b/unsupported/Eigen/SVD new file mode 100644 index 000000000..7cc059280 --- /dev/null +++ b/unsupported/Eigen/SVD @@ -0,0 +1,39 @@ +#ifndef EIGEN_SVD_MODULE_H +#define EIGEN_SVD_MODULE_H + +#include <Eigen/QR> +#include <Eigen/Householder> +#include <Eigen/Jacobi> + +#include "../../Eigen/src/Core/util/DisableStupidWarnings.h" + +/** \defgroup SVD_Module SVD module + * + * + * + * This module provides SVD decomposition for matrices (both real and complex). + * This decomposition is accessible via the following MatrixBase method: + * - MatrixBase::jacobiSvd() + * + * \code + * #include <Eigen/SVD> + * \endcode + */ + +#include "../../Eigen/src/misc/Solve.h" +#include "../../Eigen/src/SVD/UpperBidiagonalization.h" +#include "src/SVD/SVDBase.h" +#include "src/SVD/JacobiSVD.h" +#include "src/SVD/BDCSVD.h" +#if defined(EIGEN_USE_LAPACKE) && !defined(EIGEN_USE_LAPACKE_STRICT) +#include "../../Eigen/src/SVD/JacobiSVD_MKL.h" +#endif + +#ifdef EIGEN2_SUPPORT +#include "../../Eigen/src/Eigen2Support/SVD.h" +#endif + +#include "../../Eigen/src/Core/util/ReenableStupidWarnings.h" + +#endif // EIGEN_SVD_MODULE_H +/* vim: set filetype=cpp et sw=2 ts=2 ai: */ diff --git a/unsupported/Eigen/src/SVD/BDCSVD.h b/unsupported/Eigen/src/SVD/BDCSVD.h new file mode 100644 index 000000000..87ec33a05 --- /dev/null +++ b/unsupported/Eigen/src/SVD/BDCSVD.h @@ -0,0 +1,744 @@ +// 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 <brun.gauthier@gmail.com> +// Copyright (C) 2013 Nicolas Carre <nicolas.carre@ensimag.fr> +// Copyright (C) 2013 Jean Ceccato <jean.ceccato@ensimag.fr> +// Copyright (C) 2013 Pierre Zoppitelli <pierre.zoppitelli@ensimag.fr> +// +// 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<typename _MatrixType> +class BDCSVD : public SVDBase<_MatrixType> +{ + +public: + typedef _MatrixType MatrixType; + typedef typename SVDBase<_MatrixType>::MatrixType::Scalar Scalar; + typedef typename NumTraits<typename MatrixType::Scalar>::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<Scalar, RowsAtCompileTime, RowsAtCompileTime, + MatrixOptions, MaxRowsAtCompileTime, MaxRowsAtCompileTime> + MatrixUType; + typedef Matrix<Scalar, ColsAtCompileTime, ColsAtCompileTime, + MatrixOptions, MaxColsAtCompileTime, MaxColsAtCompileTime> + MatrixVType; + typedef typename internal::plain_diag_type<MatrixType, RealScalar>::type SingularValuesType; + typedef typename internal::plain_row_type<MatrixType>::type RowType; + typedef typename internal::plain_col_type<MatrixType>::type ColType; + typedef Matrix<Scalar, Dynamic, Dynamic> MatrixX; + typedef Matrix<RealScalar, Dynamic, Dynamic> MatrixXr; + typedef Matrix<RealScalar, Dynamic, 1> 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<MatrixType>& 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<MatrixType>& 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<typename Rhs> + inline const internal::solve_retval<BDCSVD, Rhs> + solve(const MatrixBase<Rhs>& 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<BDCSVD, Rhs>(*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<typename MatrixType> +void BDCSVD<MatrixType>::allocate(Index rows, Index cols, unsigned int computationOptions) +{ + isTranspose = (cols > rows); + if (SVDBase<MatrixType>::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<Matrix<int, Dynamic, Dynamic> >& +BDCSVD<Matrix<int, Dynamic, Dynamic> >::compute(const MatrixType& matrix, unsigned int computationOptions) { + allocate(matrix.rows(), matrix.cols(), computationOptions); + this->m_nonzeroSingularValues = 0; + m_computed = Matrix<int, Dynamic, Dynamic>::Zero(rows(), cols()); + for (int i=0; i<this->m_diagSize; i++) { + this->m_singularValues.coeffRef(i) = 0; + } + if (this->m_computeFullU) this->m_matrixU = Matrix<int, Dynamic, Dynamic>::Zero(rows(), rows()); + if (this->m_computeFullV) this->m_matrixV = Matrix<int, Dynamic, Dynamic>::Zero(cols(), cols()); + this->m_isInitialized = true; + return *this; +} + + +// Methode which compute the BDCSVD +template<typename MatrixType> +SVDBase<MatrixType>& +BDCSVD<MatrixType>::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<MatrixX > 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; i<this->m_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; i<this->m_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<typename MatrixType> +void BDCSVD<MatrixType>::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<typename MatrixType> +void BDCSVD<MatrixType>::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<MatrixXr> 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<n; i++) + { + m_computed(firstCol + shift + i, firstCol + shift +i) = b.singularValues().coeffRef(i); + } + return; + } + // We use the divide and conquer algorithm + alphaK = m_computed(firstCol + k, firstCol + k); + betaK = m_computed(firstCol + k + 1, firstCol + k); + // The divide must be done in that order in order to have good results. Divide change the data inside the submatrices + // and the divide of the right submatrice reads one column of the left submatrice. That's why we need to treat the + // right submatrix before the left one. + divide(k + 1 + firstCol, lastCol, k + 1 + firstRowW, k + 1 + firstColW, shift); + divide(firstCol, k - 1 + firstCol, firstRowW, firstColW + 1, shift + 1); + if (compU) + { + lambda = m_naiveU(firstCol + k, firstCol + k); + phi = m_naiveU(firstCol + k + 1, lastCol + 1); + } + else + { + lambda = m_naiveU(1, firstCol + k); + phi = m_naiveU(0, lastCol + 1); + } + r0 = sqrt((abs(alphaK * lambda) * abs(alphaK * lambda)) + + abs(betaK * phi) * abs(betaK * phi)); + if (compU) + { + l = m_naiveU.row(firstCol + k).segment(firstCol, k); + f = m_naiveU.row(firstCol + k + 1).segment(firstCol + k + 1, n - k - 1); + } + else + { + l = m_naiveU.row(1).segment(firstCol, k); + f = m_naiveU.row(0).segment(firstCol + k + 1, n - k - 1); + } + if (compV) m_naiveV(firstRowW+k, firstColW) = 1; + if (r0 == 0) + { + c0 = 1; + s0 = 0; + } + else + { + c0 = alphaK * lambda / r0; + s0 = betaK * phi / r0; + } + if (compU) + { + MatrixXr q1 (m_naiveU.col(firstCol + k).segment(firstCol, k + 1)); + // we shiftW Q1 to the right + for (Index i = firstCol + k - 1; 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<MatrixXr> res= JacobiSVD<MatrixXr>(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<n; i++) + m_computed(firstCol + shift + i, firstCol + shift +i) = res.singularValues().coeffRef(i); + // end of the third part + + +}// end divide + + +// page 12_13 +// 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){ + 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 <typename MatrixType> +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; + 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 <typename MatrixType> +void BDCSVD<MatrixType>::deflation(Index firstCol, Index lastCol, Index k, Index firstRowW, Index firstColW, Index shift){ + //condition 4.1 + RealScalar EPS = EPSILON * (std::max<RealScalar>(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<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; + +}//end deflation + + +namespace internal{ + +template<typename _MatrixType, typename Rhs> +struct solve_retval<BDCSVD<_MatrixType>, Rhs> + : solve_retval_base<BDCSVD<_MatrixType>, Rhs> +{ + typedef BDCSVD<_MatrixType> BDCSVDType; + EIGEN_MAKE_SOLVE_HELPERS(BDCSVDType, Rhs) + + template<typename Dest> 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<typename Derived> +BDCSVD<typename MatrixBase<Derived>::PlainObject> +MatrixBase<Derived>::bdcSvd(unsigned int computationOptions) const +{ + return BDCSVD<PlainObject>(*this, computationOptions); +} +*/ + +} // end namespace Eigen + +#endif diff --git a/unsupported/Eigen/src/SVD/CMakeLists.txt b/unsupported/Eigen/src/SVD/CMakeLists.txt new file mode 100644 index 000000000..b40baf092 --- /dev/null +++ b/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/unsupported/Eigen/src/SVD/JacobiSVD.h b/unsupported/Eigen/src/SVD/JacobiSVD.h new file mode 100644 index 000000000..02fac409e --- /dev/null +++ b/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 <jacob.benoit.1@gmail.com> +// +// 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<typename MatrixType, int QRPreconditioner, + bool IsComplex = NumTraits<typename MatrixType::Scalar>::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<typename MatrixType, int QRPreconditioner, int Case> +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<typename MatrixType, int QRPreconditioner, int Case, + bool DoAnything = qr_preconditioner_should_do_anything<MatrixType, QRPreconditioner, Case>::ret +> struct qr_preconditioner_impl {}; + +template<typename MatrixType, int QRPreconditioner, int Case> +class qr_preconditioner_impl<MatrixType, QRPreconditioner, Case, false> +{ +public: + typedef typename MatrixType::Index Index; + void allocate(const JacobiSVD<MatrixType, QRPreconditioner>&) {} + bool run(JacobiSVD<MatrixType, QRPreconditioner>&, const MatrixType&) + { + return false; + } +}; + +/*** preconditioner using FullPivHouseholderQR ***/ + +template<typename MatrixType> +class qr_preconditioner_impl<MatrixType, FullPivHouseholderQRPreconditioner, PreconditionIfMoreRowsThanCols, true> +{ +public: + typedef typename MatrixType::Index Index; + typedef typename MatrixType::Scalar Scalar; + enum + { + RowsAtCompileTime = MatrixType::RowsAtCompileTime, + MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime + }; + typedef Matrix<Scalar, 1, RowsAtCompileTime, RowMajor, 1, MaxRowsAtCompileTime> WorkspaceType; + + void allocate(const JacobiSVD<MatrixType, FullPivHouseholderQRPreconditioner>& 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<MatrixType, FullPivHouseholderQRPreconditioner>& 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<Upper>(); + 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<MatrixType> QRType; + QRType m_qr; + WorkspaceType m_workspace; +}; + +template<typename MatrixType> +class qr_preconditioner_impl<MatrixType, FullPivHouseholderQRPreconditioner, PreconditionIfMoreColsThanRows, true> +{ +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<Scalar, ColsAtCompileTime, RowsAtCompileTime, Options, MaxColsAtCompileTime, MaxRowsAtCompileTime> + TransposeTypeWithSameStorageOrder; + + void allocate(const JacobiSVD<MatrixType, FullPivHouseholderQRPreconditioner>& 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<MatrixType, FullPivHouseholderQRPreconditioner>& 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<Upper>().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<TransposeTypeWithSameStorageOrder> QRType; + QRType m_qr; + TransposeTypeWithSameStorageOrder m_adjoint; + typename internal::plain_row_type<MatrixType>::type m_workspace; +}; + +/*** preconditioner using ColPivHouseholderQR ***/ + +template<typename MatrixType> +class qr_preconditioner_impl<MatrixType, ColPivHouseholderQRPreconditioner, PreconditionIfMoreRowsThanCols, true> +{ +public: + typedef typename MatrixType::Index Index; + + void allocate(const JacobiSVD<MatrixType, ColPivHouseholderQRPreconditioner>& 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<MatrixType, ColPivHouseholderQRPreconditioner>& 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<Upper>(); + 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<MatrixType> QRType; + QRType m_qr; + typename internal::plain_col_type<MatrixType>::type m_workspace; +}; + +template<typename MatrixType> +class qr_preconditioner_impl<MatrixType, ColPivHouseholderQRPreconditioner, PreconditionIfMoreColsThanRows, true> +{ +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<Scalar, ColsAtCompileTime, RowsAtCompileTime, Options, MaxColsAtCompileTime, MaxRowsAtCompileTime> + TransposeTypeWithSameStorageOrder; + + void allocate(const JacobiSVD<MatrixType, ColPivHouseholderQRPreconditioner>& 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<MatrixType, ColPivHouseholderQRPreconditioner>& 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<Upper>().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<TransposeTypeWithSameStorageOrder> QRType; + QRType m_qr; + TransposeTypeWithSameStorageOrder m_adjoint; + typename internal::plain_row_type<MatrixType>::type m_workspace; +}; + +/*** preconditioner using HouseholderQR ***/ + +template<typename MatrixType> +class qr_preconditioner_impl<MatrixType, HouseholderQRPreconditioner, PreconditionIfMoreRowsThanCols, true> +{ +public: + typedef typename MatrixType::Index Index; + + void allocate(const JacobiSVD<MatrixType, HouseholderQRPreconditioner>& 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<MatrixType, HouseholderQRPreconditioner>& 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<Upper>(); + 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<MatrixType> QRType; + QRType m_qr; + typename internal::plain_col_type<MatrixType>::type m_workspace; +}; + +template<typename MatrixType> +class qr_preconditioner_impl<MatrixType, HouseholderQRPreconditioner, PreconditionIfMoreColsThanRows, true> +{ +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<Scalar, ColsAtCompileTime, RowsAtCompileTime, Options, MaxColsAtCompileTime, MaxRowsAtCompileTime> + TransposeTypeWithSameStorageOrder; + + void allocate(const JacobiSVD<MatrixType, HouseholderQRPreconditioner>& 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<MatrixType, HouseholderQRPreconditioner>& 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<Upper>().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<TransposeTypeWithSameStorageOrder> QRType; + QRType m_qr; + TransposeTypeWithSameStorageOrder m_adjoint; + typename internal::plain_row_type<MatrixType>::type m_workspace; +}; + +/*** 2x2 SVD implementation + *** + *** JacobiSVD consists in performing a series of 2x2 SVD subproblems + ***/ + +template<typename MatrixType, int QRPreconditioner> +struct svd_precondition_2x2_block_to_be_real<MatrixType, QRPreconditioner, false> +{ + typedef JacobiSVD<MatrixType, QRPreconditioner> SVD; + typedef typename SVD::Index Index; + static void run(typename SVD::WorkMatrixType&, SVD&, Index, Index) {} +}; + +template<typename MatrixType, int QRPreconditioner> +struct svd_precondition_2x2_block_to_be_real<MatrixType, QRPreconditioner, true> +{ + typedef JacobiSVD<MatrixType, QRPreconditioner> 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<Scalar> 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<typename MatrixType, typename RealScalar, typename Index> +void real_2x2_jacobi_svd(const MatrixType& matrix, Index p, Index q, + JacobiRotation<RealScalar> *j_left, + JacobiRotation<RealScalar> *j_right) +{ + using std::sqrt; + Matrix<RealScalar,2,2> 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<RealScalar> 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<typename _MatrixType, int QRPreconditioner> +class JacobiSVD : public SVDBase<_MatrixType> +{ + public: + + typedef _MatrixType MatrixType; + typedef typename MatrixType::Scalar Scalar; + typedef typename NumTraits<typename MatrixType::Scalar>::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<Scalar, RowsAtCompileTime, RowsAtCompileTime, + MatrixOptions, MaxRowsAtCompileTime, MaxRowsAtCompileTime> + MatrixUType; + typedef Matrix<Scalar, ColsAtCompileTime, ColsAtCompileTime, + MatrixOptions, MaxColsAtCompileTime, MaxColsAtCompileTime> + MatrixVType; + typedef typename internal::plain_diag_type<MatrixType, RealScalar>::type SingularValuesType; + typedef typename internal::plain_row_type<MatrixType>::type RowType; + typedef typename internal::plain_col_type<MatrixType>::type ColType; + typedef Matrix<Scalar, DiagSizeAtCompileTime, DiagSizeAtCompileTime, + MatrixOptions, MaxDiagSizeAtCompileTime, MaxDiagSizeAtCompileTime> + 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<MatrixType>& 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<MatrixType>& 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<typename Rhs> + inline const internal::solve_retval<JacobiSVD, Rhs> + solve(const MatrixBase<Rhs>& b) const + { + eigen_assert(this->m_isInitialized && "JacobiSVD is not initialized."); + eigen_assert(SVDBase<MatrixType>::computeU() && SVDBase<MatrixType>::computeV() && "JacobiSVD::solve() requires both unitaries U and V to be computed (thin unitaries suffice)."); + return internal::solve_retval<JacobiSVD, Rhs>(*this, b.derived()); + } + + + + private: + void allocate(Index rows, Index cols, unsigned int computationOptions); + + protected: + WorkMatrixType m_workMatrix; + + template<typename __MatrixType, int _QRPreconditioner, bool _IsComplex> + friend struct internal::svd_precondition_2x2_block_to_be_real; + template<typename __MatrixType, int _QRPreconditioner, int _Case, bool _DoAnything> + friend struct internal::qr_preconditioner_impl; + + internal::qr_preconditioner_impl<MatrixType, QRPreconditioner, internal::PreconditionIfMoreColsThanRows> m_qr_precond_morecols; + internal::qr_preconditioner_impl<MatrixType, QRPreconditioner, internal::PreconditionIfMoreRowsThanCols> m_qr_precond_morerows; +}; + +template<typename MatrixType, int QRPreconditioner> +void JacobiSVD<MatrixType, QRPreconditioner>::allocate(Index rows, Index cols, unsigned int computationOptions) +{ + if (SVDBase<MatrixType>::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<typename MatrixType, int QRPreconditioner> +SVDBase<MatrixType>& +JacobiSVD<MatrixType, QRPreconditioner>::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<Scalar>::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<RealScalar>::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<MatrixType, QRPreconditioner>::run(m_workMatrix, *this, p, q); + JacobiRotation<RealScalar> 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<MatrixType>::computeU()) this->m_matrixU.applyOnTheRight(p,q,j_left.transpose()); + + m_workMatrix.applyOnTheRight(p,q,j_right); + if(SVDBase<MatrixType>::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<MatrixType>::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<MatrixType>::computeU()) this->m_matrixU.col(pos).swap(this->m_matrixU.col(i)); + if(SVDBase<MatrixType>::computeV()) this->m_matrixV.col(pos).swap(this->m_matrixV.col(i)); + } + } + + this->m_isInitialized = true; + return *this; +} + +namespace internal { +template<typename _MatrixType, int QRPreconditioner, typename Rhs> +struct solve_retval<JacobiSVD<_MatrixType, QRPreconditioner>, Rhs> + : solve_retval_base<JacobiSVD<_MatrixType, QRPreconditioner>, Rhs> +{ + typedef JacobiSVD<_MatrixType, QRPreconditioner> JacobiSVDType; + EIGEN_MAKE_SOLVE_HELPERS(JacobiSVDType,Rhs) + + template<typename Dest> 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<typename Derived> +JacobiSVD<typename MatrixBase<Derived>::PlainObject> +MatrixBase<Derived>::jacobiSvd(unsigned int computationOptions) const +{ + return JacobiSVD<PlainObject>(*this, computationOptions); +} + +} // end namespace Eigen + +#endif // EIGEN_JACOBISVD_H diff --git a/unsupported/Eigen/src/SVD/SVDBase.h b/unsupported/Eigen/src/SVD/SVDBase.h new file mode 100644 index 000000000..fd8af3b8c --- /dev/null +++ b/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 <jacob.benoit.1@gmail.com> +// +// Copyright (C) 2013 Gauthier Brun <brun.gauthier@gmail.com> +// Copyright (C) 2013 Nicolas Carre <nicolas.carre@ensimag.fr> +// Copyright (C) 2013 Jean Ceccato <jean.ceccato@ensimag.fr> +// Copyright (C) 2013 Pierre Zoppitelli <pierre.zoppitelli@ensimag.fr> +// +// 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<typename _MatrixType> +class SVDBase +{ + +public: + typedef _MatrixType MatrixType; + typedef typename MatrixType::Scalar Scalar; + typedef typename NumTraits<typename MatrixType::Scalar>::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<Scalar, RowsAtCompileTime, RowsAtCompileTime, + MatrixOptions, MaxRowsAtCompileTime, MaxRowsAtCompileTime> + MatrixUType; + typedef Matrix<Scalar, ColsAtCompileTime, ColsAtCompileTime, + MatrixOptions, MaxColsAtCompileTime, MaxColsAtCompileTime> + MatrixVType; + typedef typename internal::plain_diag_type<MatrixType, RealScalar>::type SingularValuesType; + typedef typename internal::plain_row_type<MatrixType>::type RowType; + typedef typename internal::plain_col_type<MatrixType>::type ColType; + typedef Matrix<Scalar, DiagSizeAtCompileTime, DiagSizeAtCompileTime, + MatrixOptions, MaxDiagSizeAtCompileTime, MaxDiagSizeAtCompileTime> + 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<typename MatrixType> +bool SVDBase<MatrixType>::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/unsupported/Eigen/src/SVD/TODOBdcsvd.txt b/unsupported/Eigen/src/SVD/TODOBdcsvd.txt new file mode 100644 index 000000000..0bc9a46e6 --- /dev/null +++ b/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<int>, ...) + +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/unsupported/Eigen/src/SVD/doneInBDCSVD.txt b/unsupported/Eigen/src/SVD/doneInBDCSVD.txt new file mode 100644 index 000000000..6fb6b84a6 --- /dev/null +++ b/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 : +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 + diff --git a/unsupported/bench/bench_svd.cpp b/unsupported/bench/bench_svd.cpp new file mode 100644 index 000000000..01d8231ae --- /dev/null +++ b/unsupported/bench/bench_svd.cpp @@ -0,0 +1,123 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2013 Gauthier Brun <brun.gauthier@gmail.com> +// Copyright (C) 2013 Nicolas Carre <nicolas.carre@ensimag.fr> +// Copyright (C) 2013 Jean Ceccato <jean.ceccato@ensimag.fr> +// Copyright (C) 2013 Pierre Zoppitelli <pierre.zoppitelli@ensimag.fr> +// +// 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/ + +// Bench to compare the efficiency of SVD algorithms + +#include <iostream> +#include <bench/BenchTimer.h> +#include <unsupported/Eigen/SVD> + + +using namespace Eigen; +using namespace std; + +// number of computations of each algorithm before the print of the time +#ifndef REPEAT +#define REPEAT 10 +#endif + +// number of tests of the same type +#ifndef NUMBER_SAMPLE +#define NUMBER_SAMPLE 2 +#endif + +template<typename MatrixType> +void bench_svd(const MatrixType& a = MatrixType()) +{ + MatrixType m = MatrixType::Random(a.rows(), a.cols()); + BenchTimer timerJacobi; + BenchTimer timerBDC; + timerJacobi.reset(); + timerBDC.reset(); + + cout << " Only compute Singular Values" <<endl; + for (int k=1; k<=NUMBER_SAMPLE; ++k) + { + timerBDC.start(); + for (int i=0; i<REPEAT; ++i) + { + BDCSVD<MatrixType> bdc_matrix(m); + } + timerBDC.stop(); + + timerJacobi.start(); + for (int i=0; i<REPEAT; ++i) + { + JacobiSVD<MatrixType> jacobi_matrix(m); + } + timerJacobi.stop(); + + + cout << "Sample " << k << " : " << REPEAT << " computations : Jacobi : " << fixed << timerJacobi.value() << "s "; + cout << " || " << " BDC : " << timerBDC.value() << "s " <<endl <<endl; + + if (timerBDC.value() >= timerJacobi.value()) + cout << "KO : BDC is " << timerJacobi.value() / timerBDC.value() << " times faster than Jacobi" <<endl; + else + cout << "OK : BDC is " << timerJacobi.value() / timerBDC.value() << " times faster than Jacobi" <<endl; + + } + cout << " =================" <<endl; + std::cout<< std::endl; + timerJacobi.reset(); + timerBDC.reset(); + cout << " Computes rotaion matrix" <<endl; + for (int k=1; k<=NUMBER_SAMPLE; ++k) + { + timerBDC.start(); + for (int i=0; i<REPEAT; ++i) + { + BDCSVD<MatrixType> bdc_matrix(m, ComputeFullU|ComputeFullV); + } + timerBDC.stop(); + + timerJacobi.start(); + for (int i=0; i<REPEAT; ++i) + { + JacobiSVD<MatrixType> jacobi_matrix(m, ComputeFullU|ComputeFullV); + } + timerJacobi.stop(); + + + cout << "Sample " << k << " : " << REPEAT << " computations : Jacobi : " << fixed << timerJacobi.value() << "s "; + cout << " || " << " BDC : " << timerBDC.value() << "s " <<endl <<endl; + + if (timerBDC.value() >= timerJacobi.value()) + cout << "KO : BDC is " << timerJacobi.value() / timerBDC.value() << " times faster than Jacobi" <<endl; + else + cout << "OK : BDC is " << timerJacobi.value() / timerBDC.value() << " times faster than Jacobi" <<endl; + + } + std::cout<< std::endl; +} + + + +int main(int argc, char* argv[]) +{ + std::cout<< std::endl; + + std::cout<<"On a (Dynamic, Dynamic) (6, 6) Matrix" <<std::endl; + bench_svd<Matrix<double,Dynamic,Dynamic> >(Matrix<double,Dynamic,Dynamic>(6, 6)); + + std::cout<<"On a (Dynamic, Dynamic) (32, 32) Matrix" <<std::endl; + bench_svd<Matrix<double,Dynamic,Dynamic> >(Matrix<double,Dynamic,Dynamic>(32, 32)); + + //std::cout<<"On a (Dynamic, Dynamic) (128, 128) Matrix" <<std::endl; + //bench_svd<Matrix<double,Dynamic,Dynamic> >(Matrix<double,Dynamic,Dynamic>(128, 128)); + + std::cout<<"On a (Dynamic, Dynamic) (160, 160) Matrix" <<std::endl; + bench_svd<Matrix<double,Dynamic,Dynamic> >(Matrix<double,Dynamic,Dynamic>(160, 160)); + + std::cout<< "--------------------------------------------------------------------"<< std::endl; + +} diff --git a/unsupported/test/bdcsvd.cpp b/unsupported/test/bdcsvd.cpp new file mode 100644 index 000000000..115a649b0 --- /dev/null +++ b/unsupported/test/bdcsvd.cpp @@ -0,0 +1,213 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2013 Gauthier Brun <brun.gauthier@gmail.com> +// Copyright (C) 2013 Nicolas Carre <nicolas.carre@ensimag.fr> +// Copyright (C) 2013 Jean Ceccato <jean.ceccato@ensimag.fr> +// Copyright (C) 2013 Pierre Zoppitelli <pierre.zoppitelli@ensimag.fr> +// +// 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/ + +#include "svd_common.h" +#include <iostream> +#include <Eigen/LU> + +// check if "svd" is the good image of "m" +template<typename MatrixType> +void bdcsvd_check_full(const MatrixType& m, const BDCSVD<MatrixType>& svd) +{ + svd_check_full< MatrixType, BDCSVD< MatrixType > >(m, svd); +} + +// Compare to a reference value +template<typename MatrixType> +void bdcsvd_compare_to_full(const MatrixType& m, + unsigned int computationOptions, + const BDCSVD<MatrixType>& referenceSvd) +{ + svd_compare_to_full< MatrixType, BDCSVD< MatrixType > >(m, computationOptions, referenceSvd); +} // end bdcsvd_compare_to_full + + +template<typename MatrixType> +void bdcsvd_solve(const MatrixType& m, unsigned int computationOptions) +{ + svd_solve< MatrixType, BDCSVD< MatrixType > >(m, computationOptions); +} // end template bdcsvd_solve + + +// test the computations options +template<typename MatrixType> +void bdcsvd_test_all_computation_options(const MatrixType& m) +{ + BDCSVD<MatrixType> fullSvd(m, ComputeFullU|ComputeFullV); + svd_test_computation_options_1< MatrixType, BDCSVD< MatrixType > >(m, fullSvd); + svd_test_computation_options_2< MatrixType, BDCSVD< MatrixType > >(m, fullSvd); +} // end bdcsvd_test_all_computation_options + + +// Call a test with all the computations options +template<typename MatrixType> +void bdcsvd(const MatrixType& a = MatrixType(), bool pickrandom = true) +{ + MatrixType m = pickrandom ? MatrixType::Random(a.rows(), a.cols()) : a; + bdcsvd_test_all_computation_options<MatrixType>(m); +} // end template bdcsvd + + +// verify assert +template<typename MatrixType> +void bdcsvd_verify_assert(const MatrixType& m) +{ + svd_verify_assert< MatrixType, BDCSVD< MatrixType > >(m); +}// end template bdcsvd_verify_assert + + +// test weird values +template<typename MatrixType> +void bdcsvd_inf_nan() +{ + svd_inf_nan< MatrixType, BDCSVD< MatrixType > >(); +}// end template bdcsvd_inf_nan + + + +void bdcsvd_preallocate() +{ + svd_preallocate< BDCSVD< MatrixXf > >(); +} // end bdcsvd_preallocate + + +// compare the Singular values returned with Jacobi and Bdc +template<typename MatrixType> +void compare_bdc_jacobi(const MatrixType& a = MatrixType(), unsigned int computationOptions = 0) +{ + std::cout << "debut compare" << std::endl; + MatrixType m = MatrixType::Random(a.rows(), a.cols()); + BDCSVD<MatrixType> bdc_svd(m); + JacobiSVD<MatrixType> jacobi_svd(m); + VERIFY_IS_APPROX(bdc_svd.singularValues(), jacobi_svd.singularValues()); + if(computationOptions & ComputeFullU) + VERIFY_IS_APPROX(bdc_svd.matrixU(), jacobi_svd.matrixU()); + if(computationOptions & ComputeThinU) + VERIFY_IS_APPROX(bdc_svd.matrixU(), jacobi_svd.matrixU()); + if(computationOptions & ComputeFullV) + VERIFY_IS_APPROX(bdc_svd.matrixV(), jacobi_svd.matrixV()); + if(computationOptions & ComputeThinV) + VERIFY_IS_APPROX(bdc_svd.matrixV(), jacobi_svd.matrixV()); + std::cout << "fin compare" << std::endl; +} // end template compare_bdc_jacobi + + +// call the tests +void test_bdcsvd() +{ + // test of Dynamic defined Matrix (42, 42) of float + CALL_SUBTEST_11(( bdcsvd_verify_assert<Matrix<float,Dynamic,Dynamic> > + (Matrix<float,Dynamic,Dynamic>(42,42)) )); + CALL_SUBTEST_11(( compare_bdc_jacobi<Matrix<float,Dynamic,Dynamic> > + (Matrix<float,Dynamic,Dynamic>(42,42), 0) )); + CALL_SUBTEST_11(( bdcsvd<Matrix<float,Dynamic,Dynamic> > + (Matrix<float,Dynamic,Dynamic>(42,42)) )); + + // test of Dynamic defined Matrix (50, 50) of double + CALL_SUBTEST_13(( bdcsvd_verify_assert<Matrix<double,Dynamic,Dynamic> > + (Matrix<double,Dynamic,Dynamic>(50,50)) )); + CALL_SUBTEST_13(( compare_bdc_jacobi<Matrix<double,Dynamic,Dynamic> > + (Matrix<double,Dynamic,Dynamic>(50,50), 0) )); + CALL_SUBTEST_13(( bdcsvd<Matrix<double,Dynamic,Dynamic> > + (Matrix<double,Dynamic,Dynamic>(50, 50)) )); + + // test of Dynamic defined Matrix (22, 22) of complex double + CALL_SUBTEST_14(( bdcsvd_verify_assert<Matrix<std::complex<double>,Dynamic,Dynamic> > + (Matrix<std::complex<double>,Dynamic,Dynamic>(22,22)) )); + CALL_SUBTEST_14(( compare_bdc_jacobi<Matrix<std::complex<double>,Dynamic,Dynamic> > + (Matrix<std::complex<double>, Dynamic, Dynamic> (22,22), 0) )); + CALL_SUBTEST_14(( bdcsvd<Matrix<std::complex<double>,Dynamic,Dynamic> > + (Matrix<std::complex<double>,Dynamic,Dynamic>(22, 22)) )); + + // test of Dynamic defined Matrix (10, 10) of int + //CALL_SUBTEST_15(( bdcsvd_verify_assert<Matrix<int,Dynamic,Dynamic> > + // (Matrix<int,Dynamic,Dynamic>(10,10)) )); + //CALL_SUBTEST_15(( compare_bdc_jacobi<Matrix<int,Dynamic,Dynamic> > + // (Matrix<int,Dynamic,Dynamic>(10,10), 0) )); + //CALL_SUBTEST_15(( bdcsvd<Matrix<int,Dynamic,Dynamic> > + // (Matrix<int,Dynamic,Dynamic>(10, 10)) )); + + + // test of Dynamic defined Matrix (8, 6) of double + + CALL_SUBTEST_16(( bdcsvd_verify_assert<Matrix<double,Dynamic,Dynamic> > + (Matrix<double,Dynamic,Dynamic>(8,6)) )); + CALL_SUBTEST_16(( compare_bdc_jacobi<Matrix<double,Dynamic,Dynamic> > + (Matrix<double,Dynamic,Dynamic>(8, 6), 0) )); + CALL_SUBTEST_16(( bdcsvd<Matrix<double,Dynamic,Dynamic> > + (Matrix<double,Dynamic,Dynamic>(8, 6)) )); + + + + // test of Dynamic defined Matrix (36, 12) of float + CALL_SUBTEST_17(( compare_bdc_jacobi<Matrix<float,Dynamic,Dynamic> > + (Matrix<float,Dynamic,Dynamic>(36, 12), 0) )); + CALL_SUBTEST_17(( bdcsvd<Matrix<float,Dynamic,Dynamic> > + (Matrix<float,Dynamic,Dynamic>(36, 12)) )); + + // test of Dynamic defined Matrix (5, 8) of double + CALL_SUBTEST_18(( compare_bdc_jacobi<Matrix<double,Dynamic,Dynamic> > + (Matrix<double,Dynamic,Dynamic>(5, 8), 0) )); + CALL_SUBTEST_18(( bdcsvd<Matrix<double,Dynamic,Dynamic> > + (Matrix<double,Dynamic,Dynamic>(5, 8)) )); + + + // non regression tests + CALL_SUBTEST_3(( bdcsvd_verify_assert(Matrix3f()) )); + CALL_SUBTEST_4(( bdcsvd_verify_assert(Matrix4d()) )); + CALL_SUBTEST_7(( bdcsvd_verify_assert(MatrixXf(10,12)) )); + CALL_SUBTEST_8(( bdcsvd_verify_assert(MatrixXcd(7,5)) )); + + // SUBTESTS 1 and 2 on specifics matrix + for(int i = 0; i < g_repeat; i++) { + Matrix2cd m; + m << 0, 1, + 0, 1; + CALL_SUBTEST_1(( bdcsvd(m, false) )); + m << 1, 0, + 1, 0; + CALL_SUBTEST_1(( bdcsvd(m, false) )); + + Matrix2d n; + n << 0, 0, + 0, 0; + CALL_SUBTEST_2(( bdcsvd(n, false) )); + n << 0, 0, + 0, 1; + CALL_SUBTEST_2(( bdcsvd(n, false) )); + + // Statics matrix don't work with BDSVD yet + // bdc algo on a random 3x3 float matrix + // CALL_SUBTEST_3(( bdcsvd<Matrix3f>() )); + // bdc algo on a random 4x4 double matrix + // CALL_SUBTEST_4(( bdcsvd<Matrix4d>() )); + // bdc algo on a random 3x5 float matrix + // CALL_SUBTEST_5(( bdcsvd<Matrix<float,3,5> >() )); + + int r = internal::random<int>(1, 30), + c = internal::random<int>(1, 30); + CALL_SUBTEST_7(( bdcsvd<MatrixXf>(MatrixXf(r,c)) )); + CALL_SUBTEST_8(( bdcsvd<MatrixXcd>(MatrixXcd(r,c)) )); + (void) r; + (void) c; + + // Test on inf/nan matrix + CALL_SUBTEST_7( bdcsvd_inf_nan<MatrixXf>() ); + } + + CALL_SUBTEST_7(( bdcsvd<MatrixXf>(MatrixXf(internal::random<int>(EIGEN_TEST_MAX_SIZE/4, EIGEN_TEST_MAX_SIZE/2), internal::random<int>(EIGEN_TEST_MAX_SIZE/4, EIGEN_TEST_MAX_SIZE/2))) )); + CALL_SUBTEST_8(( bdcsvd<MatrixXcd>(MatrixXcd(internal::random<int>(EIGEN_TEST_MAX_SIZE/4, EIGEN_TEST_MAX_SIZE/3), internal::random<int>(EIGEN_TEST_MAX_SIZE/4, EIGEN_TEST_MAX_SIZE/3))) )); + + // Test problem size constructors + CALL_SUBTEST_7( BDCSVD<MatrixXf>(10,10) ); + +} // end test_bdcsvd diff --git a/unsupported/test/jacobisvd.cpp b/unsupported/test/jacobisvd.cpp new file mode 100644 index 000000000..b4e884eee --- /dev/null +++ b/unsupported/test/jacobisvd.cpp @@ -0,0 +1,198 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr> +// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com> +// +// 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/. + +#include "svd_common.h" + +template<typename MatrixType, int QRPreconditioner> +void jacobisvd_check_full(const MatrixType& m, const JacobiSVD<MatrixType, QRPreconditioner>& svd) +{ + svd_check_full<MatrixType, JacobiSVD<MatrixType, QRPreconditioner > >(m, svd); +} + +template<typename MatrixType, int QRPreconditioner> +void jacobisvd_compare_to_full(const MatrixType& m, + unsigned int computationOptions, + const JacobiSVD<MatrixType, QRPreconditioner>& referenceSvd) +{ + svd_compare_to_full<MatrixType, JacobiSVD<MatrixType, QRPreconditioner> >(m, computationOptions, referenceSvd); +} + + +template<typename MatrixType, int QRPreconditioner> +void jacobisvd_solve(const MatrixType& m, unsigned int computationOptions) +{ + svd_solve< MatrixType, JacobiSVD< MatrixType, QRPreconditioner > >(m, computationOptions); +} + + + +template<typename MatrixType, int QRPreconditioner> +void jacobisvd_test_all_computation_options(const MatrixType& m) +{ + + if (QRPreconditioner == NoQRPreconditioner && m.rows() != m.cols()) + return; + + JacobiSVD< MatrixType, QRPreconditioner > fullSvd(m, ComputeFullU|ComputeFullV); + svd_test_computation_options_1< MatrixType, JacobiSVD< MatrixType, QRPreconditioner > >(m, fullSvd); + + if(QRPreconditioner == FullPivHouseholderQRPreconditioner) + return; + svd_test_computation_options_2< MatrixType, JacobiSVD< MatrixType, QRPreconditioner > >(m, fullSvd); + +} + +template<typename MatrixType> +void jacobisvd(const MatrixType& a = MatrixType(), bool pickrandom = true) +{ + MatrixType m = pickrandom ? MatrixType::Random(a.rows(), a.cols()) : a; + + jacobisvd_test_all_computation_options<MatrixType, FullPivHouseholderQRPreconditioner>(m); + jacobisvd_test_all_computation_options<MatrixType, ColPivHouseholderQRPreconditioner>(m); + jacobisvd_test_all_computation_options<MatrixType, HouseholderQRPreconditioner>(m); + jacobisvd_test_all_computation_options<MatrixType, NoQRPreconditioner>(m); +} + + +template<typename MatrixType> +void jacobisvd_verify_assert(const MatrixType& m) +{ + + svd_verify_assert<MatrixType, JacobiSVD< MatrixType > >(m); + + typedef typename MatrixType::Index Index; + Index rows = m.rows(); + Index cols = m.cols(); + + enum { + RowsAtCompileTime = MatrixType::RowsAtCompileTime, + ColsAtCompileTime = MatrixType::ColsAtCompileTime + }; + + MatrixType a = MatrixType::Zero(rows, cols); + a.setZero(); + + if (ColsAtCompileTime == Dynamic) + { + JacobiSVD<MatrixType, FullPivHouseholderQRPreconditioner> svd_fullqr; + VERIFY_RAISES_ASSERT(svd_fullqr.compute(a, ComputeFullU|ComputeThinV)) + VERIFY_RAISES_ASSERT(svd_fullqr.compute(a, ComputeThinU|ComputeThinV)) + VERIFY_RAISES_ASSERT(svd_fullqr.compute(a, ComputeThinU|ComputeFullV)) + } +} + +template<typename MatrixType> +void jacobisvd_method() +{ + enum { Size = MatrixType::RowsAtCompileTime }; + typedef typename MatrixType::RealScalar RealScalar; + typedef Matrix<RealScalar, Size, 1> RealVecType; + MatrixType m = MatrixType::Identity(); + VERIFY_IS_APPROX(m.jacobiSvd().singularValues(), RealVecType::Ones()); + VERIFY_RAISES_ASSERT(m.jacobiSvd().matrixU()); + VERIFY_RAISES_ASSERT(m.jacobiSvd().matrixV()); + VERIFY_IS_APPROX(m.jacobiSvd(ComputeFullU|ComputeFullV).solve(m), m); +} + + + +template<typename MatrixType> +void jacobisvd_inf_nan() +{ + svd_inf_nan<MatrixType, JacobiSVD< MatrixType > >(); +} + + +// Regression test for bug 286: JacobiSVD loops indefinitely with some +// matrices containing denormal numbers. +void jacobisvd_bug286() +{ +#if defined __INTEL_COMPILER +// shut up warning #239: floating point underflow +#pragma warning push +#pragma warning disable 239 +#endif + Matrix2d M; + M << -7.90884e-313, -4.94e-324, + 0, 5.60844e-313; +#if defined __INTEL_COMPILER +#pragma warning pop +#endif + JacobiSVD<Matrix2d> svd; + svd.compute(M); // just check we don't loop indefinitely +} + + +void jacobisvd_preallocate() +{ + svd_preallocate< JacobiSVD <MatrixXf> >(); +} + +void test_jacobisvd() +{ + CALL_SUBTEST_11(( jacobisvd<Matrix<double,Dynamic,Dynamic> > + (Matrix<double,Dynamic,Dynamic>(16, 6)) )); + + CALL_SUBTEST_3(( jacobisvd_verify_assert(Matrix3f()) )); + CALL_SUBTEST_4(( jacobisvd_verify_assert(Matrix4d()) )); + CALL_SUBTEST_7(( jacobisvd_verify_assert(MatrixXf(10,12)) )); + CALL_SUBTEST_8(( jacobisvd_verify_assert(MatrixXcd(7,5)) )); + + for(int i = 0; i < g_repeat; i++) { + Matrix2cd m; + m << 0, 1, + 0, 1; + CALL_SUBTEST_1(( jacobisvd(m, false) )); + m << 1, 0, + 1, 0; + CALL_SUBTEST_1(( jacobisvd(m, false) )); + + Matrix2d n; + n << 0, 0, + 0, 0; + CALL_SUBTEST_2(( jacobisvd(n, false) )); + n << 0, 0, + 0, 1; + CALL_SUBTEST_2(( jacobisvd(n, false) )); + + CALL_SUBTEST_3(( jacobisvd<Matrix3f>() )); + CALL_SUBTEST_4(( jacobisvd<Matrix4d>() )); + CALL_SUBTEST_5(( jacobisvd<Matrix<float,3,5> >() )); + CALL_SUBTEST_6(( jacobisvd<Matrix<double,Dynamic,2> >(Matrix<double,Dynamic,2>(10,2)) )); + + int r = internal::random<int>(1, 30), + c = internal::random<int>(1, 30); + CALL_SUBTEST_7(( jacobisvd<MatrixXf>(MatrixXf(r,c)) )); + CALL_SUBTEST_8(( jacobisvd<MatrixXcd>(MatrixXcd(r,c)) )); + (void) r; + (void) c; + + // Test on inf/nan matrix + CALL_SUBTEST_7( jacobisvd_inf_nan<MatrixXf>() ); + } + + CALL_SUBTEST_7(( jacobisvd<MatrixXf>(MatrixXf(internal::random<int>(EIGEN_TEST_MAX_SIZE/4, EIGEN_TEST_MAX_SIZE/2), internal::random<int>(EIGEN_TEST_MAX_SIZE/4, EIGEN_TEST_MAX_SIZE/2))) )); + CALL_SUBTEST_8(( jacobisvd<MatrixXcd>(MatrixXcd(internal::random<int>(EIGEN_TEST_MAX_SIZE/4, EIGEN_TEST_MAX_SIZE/3), internal::random<int>(EIGEN_TEST_MAX_SIZE/4, EIGEN_TEST_MAX_SIZE/3))) )); + + + // test matrixbase method + CALL_SUBTEST_1(( jacobisvd_method<Matrix2cd>() )); + CALL_SUBTEST_3(( jacobisvd_method<Matrix3f>() )); + + + // Test problem size constructors + CALL_SUBTEST_7( JacobiSVD<MatrixXf>(10,10) ); + + // Check that preallocation avoids subsequent mallocs + CALL_SUBTEST_9( jacobisvd_preallocate() ); + + // Regression check for bug 286 + CALL_SUBTEST_2( jacobisvd_bug286() ); +} diff --git a/unsupported/test/svd_common.h b/unsupported/test/svd_common.h new file mode 100644 index 000000000..b40c23a2b --- /dev/null +++ b/unsupported/test/svd_common.h @@ -0,0 +1,261 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr> +// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com> +// +// Copyright (C) 2013 Gauthier Brun <brun.gauthier@gmail.com> +// Copyright (C) 2013 Nicolas Carre <nicolas.carre@ensimag.fr> +// Copyright (C) 2013 Jean Ceccato <jean.ceccato@ensimag.fr> +// Copyright (C) 2013 Pierre Zoppitelli <pierre.zoppitelli@ensimag.fr> +// +// 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/. + +// discard stack allocation as that too bypasses malloc +#define EIGEN_STACK_ALLOCATION_LIMIT 0 +#define EIGEN_RUNTIME_NO_MALLOC + +#include "main.h" +#include <unsupported/Eigen/SVD> +#include <Eigen/LU> + + +// check if "svd" is the good image of "m" +template<typename MatrixType, typename SVD> +void svd_check_full(const MatrixType& m, const SVD& svd) +{ + typedef typename MatrixType::Index Index; + Index rows = m.rows(); + Index cols = m.cols(); + enum { + RowsAtCompileTime = MatrixType::RowsAtCompileTime, + ColsAtCompileTime = MatrixType::ColsAtCompileTime + }; + + typedef typename MatrixType::Scalar Scalar; + typedef Matrix<Scalar, RowsAtCompileTime, RowsAtCompileTime> MatrixUType; + typedef Matrix<Scalar, ColsAtCompileTime, ColsAtCompileTime> MatrixVType; + + + MatrixType sigma = MatrixType::Zero(rows, cols); + sigma.diagonal() = svd.singularValues().template cast<Scalar>(); + MatrixUType u = svd.matrixU(); + MatrixVType v = svd.matrixV(); + VERIFY_IS_APPROX(m, u * sigma * v.adjoint()); + VERIFY_IS_UNITARY(u); + VERIFY_IS_UNITARY(v); +} // end svd_check_full + + + +// Compare to a reference value +template<typename MatrixType, typename SVD> +void svd_compare_to_full(const MatrixType& m, + unsigned int computationOptions, + const SVD& referenceSvd) +{ + typedef typename MatrixType::Index Index; + Index rows = m.rows(); + Index cols = m.cols(); + Index diagSize = (std::min)(rows, cols); + + SVD svd(m, computationOptions); + + VERIFY_IS_APPROX(svd.singularValues(), referenceSvd.singularValues()); + if(computationOptions & ComputeFullU) + VERIFY_IS_APPROX(svd.matrixU(), referenceSvd.matrixU()); + if(computationOptions & ComputeThinU) + VERIFY_IS_APPROX(svd.matrixU(), referenceSvd.matrixU().leftCols(diagSize)); + if(computationOptions & ComputeFullV) + VERIFY_IS_APPROX(svd.matrixV(), referenceSvd.matrixV()); + if(computationOptions & ComputeThinV) + VERIFY_IS_APPROX(svd.matrixV(), referenceSvd.matrixV().leftCols(diagSize)); +} // end svd_compare_to_full + + + +template<typename MatrixType, typename SVD> +void svd_solve(const MatrixType& m, unsigned int computationOptions) +{ + typedef typename MatrixType::Scalar Scalar; + typedef typename MatrixType::Index Index; + Index rows = m.rows(); + Index cols = m.cols(); + + enum { + RowsAtCompileTime = MatrixType::RowsAtCompileTime, + ColsAtCompileTime = MatrixType::ColsAtCompileTime + }; + + typedef Matrix<Scalar, RowsAtCompileTime, Dynamic> RhsType; + typedef Matrix<Scalar, ColsAtCompileTime, Dynamic> SolutionType; + + RhsType rhs = RhsType::Random(rows, internal::random<Index>(1, cols)); + SVD svd(m, computationOptions); + SolutionType x = svd.solve(rhs); + // evaluate normal equation which works also for least-squares solutions + VERIFY_IS_APPROX(m.adjoint()*m*x,m.adjoint()*rhs); +} // end svd_solve + + +// test computations options +// 2 functions because Jacobisvd can return before the second function +template<typename MatrixType, typename SVD> +void svd_test_computation_options_1(const MatrixType& m, const SVD& fullSvd) +{ + svd_check_full< MatrixType, SVD >(m, fullSvd); + svd_solve< MatrixType, SVD >(m, ComputeFullU | ComputeFullV); +} + + +template<typename MatrixType, typename SVD> +void svd_test_computation_options_2(const MatrixType& m, const SVD& fullSvd) +{ + svd_compare_to_full< MatrixType, SVD >(m, ComputeFullU, fullSvd); + svd_compare_to_full< MatrixType, SVD >(m, ComputeFullV, fullSvd); + svd_compare_to_full< MatrixType, SVD >(m, 0, fullSvd); + + if (MatrixType::ColsAtCompileTime == Dynamic) { + // thin U/V are only available with dynamic number of columns + + svd_compare_to_full< MatrixType, SVD >(m, ComputeFullU|ComputeThinV, fullSvd); + svd_compare_to_full< MatrixType, SVD >(m, ComputeThinV, fullSvd); + svd_compare_to_full< MatrixType, SVD >(m, ComputeThinU|ComputeFullV, fullSvd); + svd_compare_to_full< MatrixType, SVD >(m, ComputeThinU , fullSvd); + svd_compare_to_full< MatrixType, SVD >(m, ComputeThinU|ComputeThinV, fullSvd); + svd_solve<MatrixType, SVD>(m, ComputeFullU | ComputeThinV); + svd_solve<MatrixType, SVD>(m, ComputeThinU | ComputeFullV); + svd_solve<MatrixType, SVD>(m, ComputeThinU | ComputeThinV); + + typedef typename MatrixType::Index Index; + Index diagSize = (std::min)(m.rows(), m.cols()); + SVD svd(m, ComputeThinU | ComputeThinV); + VERIFY_IS_APPROX(m, svd.matrixU().leftCols(diagSize) * svd.singularValues().asDiagonal() * svd.matrixV().leftCols(diagSize).adjoint()); + } +} + +template<typename MatrixType, typename SVD> +void svd_verify_assert(const MatrixType& m) +{ + typedef typename MatrixType::Scalar Scalar; + typedef typename MatrixType::Index Index; + Index rows = m.rows(); + Index cols = m.cols(); + + enum { + RowsAtCompileTime = MatrixType::RowsAtCompileTime, + ColsAtCompileTime = MatrixType::ColsAtCompileTime + }; + + typedef Matrix<Scalar, RowsAtCompileTime, 1> RhsType; + RhsType rhs(rows); + SVD svd; + VERIFY_RAISES_ASSERT(svd.matrixU()) + VERIFY_RAISES_ASSERT(svd.singularValues()) + VERIFY_RAISES_ASSERT(svd.matrixV()) + VERIFY_RAISES_ASSERT(svd.solve(rhs)) + MatrixType a = MatrixType::Zero(rows, cols); + a.setZero(); + svd.compute(a, 0); + VERIFY_RAISES_ASSERT(svd.matrixU()) + VERIFY_RAISES_ASSERT(svd.matrixV()) + svd.singularValues(); + VERIFY_RAISES_ASSERT(svd.solve(rhs)) + + if (ColsAtCompileTime == Dynamic) + { + svd.compute(a, ComputeThinU); + svd.matrixU(); + VERIFY_RAISES_ASSERT(svd.matrixV()) + VERIFY_RAISES_ASSERT(svd.solve(rhs)) + svd.compute(a, ComputeThinV); + svd.matrixV(); + VERIFY_RAISES_ASSERT(svd.matrixU()) + VERIFY_RAISES_ASSERT(svd.solve(rhs)) + } + else + { + VERIFY_RAISES_ASSERT(svd.compute(a, ComputeThinU)) + VERIFY_RAISES_ASSERT(svd.compute(a, ComputeThinV)) + } +} + +// work around stupid msvc error when constructing at compile time an expression that involves +// a division by zero, even if the numeric type has floating point +template<typename Scalar> +EIGEN_DONT_INLINE Scalar zero() { return Scalar(0); } + +// workaround aggressive optimization in ICC +template<typename T> EIGEN_DONT_INLINE T sub(T a, T b) { return a - b; } + + +template<typename MatrixType, typename SVD> +void svd_inf_nan() +{ + // all this function does is verify we don't iterate infinitely on nan/inf values + + SVD svd; + typedef typename MatrixType::Scalar Scalar; + Scalar some_inf = Scalar(1) / zero<Scalar>(); + VERIFY(sub(some_inf, some_inf) != sub(some_inf, some_inf)); + svd.compute(MatrixType::Constant(10,10,some_inf), ComputeFullU | ComputeFullV); + + Scalar some_nan = zero<Scalar> () / zero<Scalar> (); + VERIFY(some_nan != some_nan); + svd.compute(MatrixType::Constant(10,10,some_nan), ComputeFullU | ComputeFullV); + + MatrixType m = MatrixType::Zero(10,10); + m(internal::random<int>(0,9), internal::random<int>(0,9)) = some_inf; + svd.compute(m, ComputeFullU | ComputeFullV); + + m = MatrixType::Zero(10,10); + m(internal::random<int>(0,9), internal::random<int>(0,9)) = some_nan; + svd.compute(m, ComputeFullU | ComputeFullV); +} + + +template<typename SVD> +void svd_preallocate() +{ + Vector3f v(3.f, 2.f, 1.f); + MatrixXf m = v.asDiagonal(); + + internal::set_is_malloc_allowed(false); + VERIFY_RAISES_ASSERT(VectorXf v(10);) + SVD svd; + internal::set_is_malloc_allowed(true); + svd.compute(m); + VERIFY_IS_APPROX(svd.singularValues(), v); + + SVD svd2(3,3); + internal::set_is_malloc_allowed(false); + svd2.compute(m); + internal::set_is_malloc_allowed(true); + VERIFY_IS_APPROX(svd2.singularValues(), v); + VERIFY_RAISES_ASSERT(svd2.matrixU()); + VERIFY_RAISES_ASSERT(svd2.matrixV()); + svd2.compute(m, ComputeFullU | ComputeFullV); + VERIFY_IS_APPROX(svd2.matrixU(), Matrix3f::Identity()); + VERIFY_IS_APPROX(svd2.matrixV(), Matrix3f::Identity()); + internal::set_is_malloc_allowed(false); + svd2.compute(m); + internal::set_is_malloc_allowed(true); + + SVD svd3(3,3,ComputeFullU|ComputeFullV); + internal::set_is_malloc_allowed(false); + svd2.compute(m); + internal::set_is_malloc_allowed(true); + VERIFY_IS_APPROX(svd2.singularValues(), v); + VERIFY_IS_APPROX(svd2.matrixU(), Matrix3f::Identity()); + VERIFY_IS_APPROX(svd2.matrixV(), Matrix3f::Identity()); + internal::set_is_malloc_allowed(false); + svd2.compute(m, ComputeFullU|ComputeFullV); + internal::set_is_malloc_allowed(true); +} + + + + + |