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author | Stanislaw Halik <sthalik@misaki.pl> | 2017-03-25 14:17:07 +0100 |
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committer | Stanislaw Halik <sthalik@misaki.pl> | 2017-03-25 14:17:07 +0100 |
commit | 35f7829af10c61e33dd2e2a7a015058e11a11ea0 (patch) | |
tree | 7135010dcf8fd0a49f3020d52112709bcb883bd6 /eigen/Eigen/src/Eigen2Support/SVD.h | |
parent | 6e8724193e40a932faf9064b664b529e7301c578 (diff) |
update
Diffstat (limited to 'eigen/Eigen/src/Eigen2Support/SVD.h')
-rw-r--r-- | eigen/Eigen/src/Eigen2Support/SVD.h | 637 |
1 files changed, 0 insertions, 637 deletions
diff --git a/eigen/Eigen/src/Eigen2Support/SVD.h b/eigen/Eigen/src/Eigen2Support/SVD.h deleted file mode 100644 index 3d03d22..0000000 --- a/eigen/Eigen/src/Eigen2Support/SVD.h +++ /dev/null @@ -1,637 +0,0 @@ -// This file is part of Eigen, a lightweight C++ template library -// for linear algebra. -// -// Copyright (C) 2008 Gael Guennebaud <g.gael@free.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 EIGEN2_SVD_H -#define EIGEN2_SVD_H - -namespace Eigen { - -/** \ingroup SVD_Module - * \nonstableyet - * - * \class SVD - * - * \brief Standard SVD decomposition of a matrix and associated features - * - * \param MatrixType the type of the matrix of which we are computing the SVD decomposition - * - * This class performs a standard SVD decomposition of a real matrix A of size \c M x \c N - * with \c M \>= \c N. - * - * - * \sa MatrixBase::SVD() - */ -template<typename MatrixType> class SVD -{ - private: - typedef typename MatrixType::Scalar Scalar; - typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar; - - enum { - PacketSize = internal::packet_traits<Scalar>::size, - AlignmentMask = int(PacketSize)-1, - MinSize = EIGEN_SIZE_MIN_PREFER_DYNAMIC(MatrixType::RowsAtCompileTime, MatrixType::ColsAtCompileTime) - }; - - typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> ColVector; - typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, 1> RowVector; - - typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MinSize> MatrixUType; - typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, MatrixType::ColsAtCompileTime> MatrixVType; - typedef Matrix<Scalar, MinSize, 1> SingularValuesType; - - public: - - SVD() {} // a user who relied on compiler-generated default compiler reported problems with MSVC in 2.0.7 - - SVD(const MatrixType& matrix) - : m_matU(matrix.rows(), (std::min)(matrix.rows(), matrix.cols())), - m_matV(matrix.cols(),matrix.cols()), - m_sigma((std::min)(matrix.rows(),matrix.cols())) - { - compute(matrix); - } - - template<typename OtherDerived, typename ResultType> - bool solve(const MatrixBase<OtherDerived> &b, ResultType* result) const; - - const MatrixUType& matrixU() const { return m_matU; } - const SingularValuesType& singularValues() const { return m_sigma; } - const MatrixVType& matrixV() const { return m_matV; } - - void compute(const MatrixType& matrix); - SVD& sort(); - - template<typename UnitaryType, typename PositiveType> - void computeUnitaryPositive(UnitaryType *unitary, PositiveType *positive) const; - template<typename PositiveType, typename UnitaryType> - void computePositiveUnitary(PositiveType *positive, UnitaryType *unitary) const; - template<typename RotationType, typename ScalingType> - void computeRotationScaling(RotationType *unitary, ScalingType *positive) const; - template<typename ScalingType, typename RotationType> - void computeScalingRotation(ScalingType *positive, RotationType *unitary) const; - - protected: - /** \internal */ - MatrixUType m_matU; - /** \internal */ - MatrixVType m_matV; - /** \internal */ - SingularValuesType m_sigma; -}; - -/** Computes / recomputes the SVD decomposition A = U S V^* of \a matrix - * - * \note this code has been adapted from JAMA (public domain) - */ -template<typename MatrixType> -void SVD<MatrixType>::compute(const MatrixType& matrix) -{ - const int m = matrix.rows(); - const int n = matrix.cols(); - const int nu = (std::min)(m,n); - ei_assert(m>=n && "In Eigen 2.0, SVD only works for MxN matrices with M>=N. Sorry!"); - ei_assert(m>1 && "In Eigen 2.0, SVD doesn't work on 1x1 matrices"); - - m_matU.resize(m, nu); - m_matU.setZero(); - m_sigma.resize((std::min)(m,n)); - m_matV.resize(n,n); - - RowVector e(n); - ColVector work(m); - MatrixType matA(matrix); - const bool wantu = true; - const bool wantv = true; - int i=0, j=0, k=0; - - // Reduce A to bidiagonal form, storing the diagonal elements - // in s and the super-diagonal elements in e. - int nct = (std::min)(m-1,n); - int nrt = (std::max)(0,(std::min)(n-2,m)); - for (k = 0; k < (std::max)(nct,nrt); ++k) - { - if (k < nct) - { - // Compute the transformation for the k-th column and - // place the k-th diagonal in m_sigma[k]. - m_sigma[k] = matA.col(k).end(m-k).norm(); - if (m_sigma[k] != 0.0) // FIXME - { - if (matA(k,k) < 0.0) - m_sigma[k] = -m_sigma[k]; - matA.col(k).end(m-k) /= m_sigma[k]; - matA(k,k) += 1.0; - } - m_sigma[k] = -m_sigma[k]; - } - - for (j = k+1; j < n; ++j) - { - if ((k < nct) && (m_sigma[k] != 0.0)) - { - // Apply the transformation. - Scalar t = matA.col(k).end(m-k).eigen2_dot(matA.col(j).end(m-k)); // FIXME dot product or cwise prod + .sum() ?? - t = -t/matA(k,k); - matA.col(j).end(m-k) += t * matA.col(k).end(m-k); - } - - // Place the k-th row of A into e for the - // subsequent calculation of the row transformation. - e[j] = matA(k,j); - } - - // Place the transformation in U for subsequent back multiplication. - if (wantu & (k < nct)) - m_matU.col(k).end(m-k) = matA.col(k).end(m-k); - - if (k < nrt) - { - // Compute the k-th row transformation and place the - // k-th super-diagonal in e[k]. - e[k] = e.end(n-k-1).norm(); - if (e[k] != 0.0) - { - if (e[k+1] < 0.0) - e[k] = -e[k]; - e.end(n-k-1) /= e[k]; - e[k+1] += 1.0; - } - e[k] = -e[k]; - if ((k+1 < m) & (e[k] != 0.0)) - { - // Apply the transformation. - work.end(m-k-1) = matA.corner(BottomRight,m-k-1,n-k-1) * e.end(n-k-1); - for (j = k+1; j < n; ++j) - matA.col(j).end(m-k-1) += (-e[j]/e[k+1]) * work.end(m-k-1); - } - - // Place the transformation in V for subsequent back multiplication. - if (wantv) - m_matV.col(k).end(n-k-1) = e.end(n-k-1); - } - } - - - // Set up the final bidiagonal matrix or order p. - int p = (std::min)(n,m+1); - if (nct < n) - m_sigma[nct] = matA(nct,nct); - if (m < p) - m_sigma[p-1] = 0.0; - if (nrt+1 < p) - e[nrt] = matA(nrt,p-1); - e[p-1] = 0.0; - - // If required, generate U. - if (wantu) - { - for (j = nct; j < nu; ++j) - { - m_matU.col(j).setZero(); - m_matU(j,j) = 1.0; - } - for (k = nct-1; k >= 0; k--) - { - if (m_sigma[k] != 0.0) - { - for (j = k+1; j < nu; ++j) - { - Scalar t = m_matU.col(k).end(m-k).eigen2_dot(m_matU.col(j).end(m-k)); // FIXME is it really a dot product we want ? - t = -t/m_matU(k,k); - m_matU.col(j).end(m-k) += t * m_matU.col(k).end(m-k); - } - m_matU.col(k).end(m-k) = - m_matU.col(k).end(m-k); - m_matU(k,k) = Scalar(1) + m_matU(k,k); - if (k-1>0) - m_matU.col(k).start(k-1).setZero(); - } - else - { - m_matU.col(k).setZero(); - m_matU(k,k) = 1.0; - } - } - } - - // If required, generate V. - if (wantv) - { - for (k = n-1; k >= 0; k--) - { - if ((k < nrt) & (e[k] != 0.0)) - { - for (j = k+1; j < nu; ++j) - { - Scalar t = m_matV.col(k).end(n-k-1).eigen2_dot(m_matV.col(j).end(n-k-1)); // FIXME is it really a dot product we want ? - t = -t/m_matV(k+1,k); - m_matV.col(j).end(n-k-1) += t * m_matV.col(k).end(n-k-1); - } - } - m_matV.col(k).setZero(); - m_matV(k,k) = 1.0; - } - } - - // Main iteration loop for the singular values. - int pp = p-1; - int iter = 0; - Scalar eps = ei_pow(Scalar(2),ei_is_same_type<Scalar,float>::ret ? Scalar(-23) : Scalar(-52)); - while (p > 0) - { - int k=0; - int kase=0; - - // Here is where a test for too many iterations would go. - - // This section of the program inspects for - // negligible elements in the s and e arrays. On - // completion the variables kase and k are set as follows. - - // kase = 1 if s(p) and e[k-1] are negligible and k<p - // kase = 2 if s(k) is negligible and k<p - // kase = 3 if e[k-1] is negligible, k<p, and - // s(k), ..., s(p) are not negligible (qr step). - // kase = 4 if e(p-1) is negligible (convergence). - - for (k = p-2; k >= -1; --k) - { - if (k == -1) - break; - if (ei_abs(e[k]) <= eps*(ei_abs(m_sigma[k]) + ei_abs(m_sigma[k+1]))) - { - e[k] = 0.0; - break; - } - } - if (k == p-2) - { - kase = 4; - } - else - { - int ks; - for (ks = p-1; ks >= k; --ks) - { - if (ks == k) - break; - Scalar t = (ks != p ? ei_abs(e[ks]) : Scalar(0)) + (ks != k+1 ? ei_abs(e[ks-1]) : Scalar(0)); - if (ei_abs(m_sigma[ks]) <= eps*t) - { - m_sigma[ks] = 0.0; - break; - } - } - if (ks == k) - { - kase = 3; - } - else if (ks == p-1) - { - kase = 1; - } - else - { - kase = 2; - k = ks; - } - } - ++k; - - // Perform the task indicated by kase. - switch (kase) - { - - // Deflate negligible s(p). - case 1: - { - Scalar f(e[p-2]); - e[p-2] = 0.0; - for (j = p-2; j >= k; --j) - { - Scalar t(numext::hypot(m_sigma[j],f)); - Scalar cs(m_sigma[j]/t); - Scalar sn(f/t); - m_sigma[j] = t; - if (j != k) - { - f = -sn*e[j-1]; - e[j-1] = cs*e[j-1]; - } - if (wantv) - { - for (i = 0; i < n; ++i) - { - t = cs*m_matV(i,j) + sn*m_matV(i,p-1); - m_matV(i,p-1) = -sn*m_matV(i,j) + cs*m_matV(i,p-1); - m_matV(i,j) = t; - } - } - } - } - break; - - // Split at negligible s(k). - case 2: - { - Scalar f(e[k-1]); - e[k-1] = 0.0; - for (j = k; j < p; ++j) - { - Scalar t(numext::hypot(m_sigma[j],f)); - Scalar cs( m_sigma[j]/t); - Scalar sn(f/t); - m_sigma[j] = t; - f = -sn*e[j]; - e[j] = cs*e[j]; - if (wantu) - { - for (i = 0; i < m; ++i) - { - t = cs*m_matU(i,j) + sn*m_matU(i,k-1); - m_matU(i,k-1) = -sn*m_matU(i,j) + cs*m_matU(i,k-1); - m_matU(i,j) = t; - } - } - } - } - break; - - // Perform one qr step. - case 3: - { - // Calculate the shift. - Scalar scale = (std::max)((std::max)((std::max)((std::max)( - ei_abs(m_sigma[p-1]),ei_abs(m_sigma[p-2])),ei_abs(e[p-2])), - ei_abs(m_sigma[k])),ei_abs(e[k])); - Scalar sp = m_sigma[p-1]/scale; - Scalar spm1 = m_sigma[p-2]/scale; - Scalar epm1 = e[p-2]/scale; - Scalar sk = m_sigma[k]/scale; - Scalar ek = e[k]/scale; - Scalar b = ((spm1 + sp)*(spm1 - sp) + epm1*epm1)/Scalar(2); - Scalar c = (sp*epm1)*(sp*epm1); - Scalar shift(0); - if ((b != 0.0) || (c != 0.0)) - { - shift = ei_sqrt(b*b + c); - if (b < 0.0) - shift = -shift; - shift = c/(b + shift); - } - Scalar f = (sk + sp)*(sk - sp) + shift; - Scalar g = sk*ek; - - // Chase zeros. - - for (j = k; j < p-1; ++j) - { - Scalar t = numext::hypot(f,g); - Scalar cs = f/t; - Scalar sn = g/t; - if (j != k) - e[j-1] = t; - f = cs*m_sigma[j] + sn*e[j]; - e[j] = cs*e[j] - sn*m_sigma[j]; - g = sn*m_sigma[j+1]; - m_sigma[j+1] = cs*m_sigma[j+1]; - if (wantv) - { - for (i = 0; i < n; ++i) - { - t = cs*m_matV(i,j) + sn*m_matV(i,j+1); - m_matV(i,j+1) = -sn*m_matV(i,j) + cs*m_matV(i,j+1); - m_matV(i,j) = t; - } - } - t = numext::hypot(f,g); - cs = f/t; - sn = g/t; - m_sigma[j] = t; - f = cs*e[j] + sn*m_sigma[j+1]; - m_sigma[j+1] = -sn*e[j] + cs*m_sigma[j+1]; - g = sn*e[j+1]; - e[j+1] = cs*e[j+1]; - if (wantu && (j < m-1)) - { - for (i = 0; i < m; ++i) - { - t = cs*m_matU(i,j) + sn*m_matU(i,j+1); - m_matU(i,j+1) = -sn*m_matU(i,j) + cs*m_matU(i,j+1); - m_matU(i,j) = t; - } - } - } - e[p-2] = f; - iter = iter + 1; - } - break; - - // Convergence. - case 4: - { - // Make the singular values positive. - if (m_sigma[k] <= 0.0) - { - m_sigma[k] = m_sigma[k] < Scalar(0) ? -m_sigma[k] : Scalar(0); - if (wantv) - m_matV.col(k).start(pp+1) = -m_matV.col(k).start(pp+1); - } - - // Order the singular values. - while (k < pp) - { - if (m_sigma[k] >= m_sigma[k+1]) - break; - Scalar t = m_sigma[k]; - m_sigma[k] = m_sigma[k+1]; - m_sigma[k+1] = t; - if (wantv && (k < n-1)) - m_matV.col(k).swap(m_matV.col(k+1)); - if (wantu && (k < m-1)) - m_matU.col(k).swap(m_matU.col(k+1)); - ++k; - } - iter = 0; - p--; - } - break; - } // end big switch - } // end iterations -} - -template<typename MatrixType> -SVD<MatrixType>& SVD<MatrixType>::sort() -{ - int mu = m_matU.rows(); - int mv = m_matV.rows(); - int n = m_matU.cols(); - - for (int i=0; i<n; ++i) - { - int k = i; - Scalar p = m_sigma.coeff(i); - - for (int j=i+1; j<n; ++j) - { - if (m_sigma.coeff(j) > p) - { - k = j; - p = m_sigma.coeff(j); - } - } - if (k != i) - { - m_sigma.coeffRef(k) = m_sigma.coeff(i); // i.e. - m_sigma.coeffRef(i) = p; // swaps the i-th and the k-th elements - - int j = mu; - for(int s=0; j!=0; ++s, --j) - std::swap(m_matU.coeffRef(s,i), m_matU.coeffRef(s,k)); - - j = mv; - for (int s=0; j!=0; ++s, --j) - std::swap(m_matV.coeffRef(s,i), m_matV.coeffRef(s,k)); - } - } - return *this; -} - -/** \returns the solution of \f$ A x = b \f$ using the current SVD decomposition of A. - * The parts of the solution corresponding to zero singular values are ignored. - * - * \sa MatrixBase::svd(), LU::solve(), LLT::solve() - */ -template<typename MatrixType> -template<typename OtherDerived, typename ResultType> -bool SVD<MatrixType>::solve(const MatrixBase<OtherDerived> &b, ResultType* result) const -{ - ei_assert(b.rows() == m_matU.rows()); - - Scalar maxVal = m_sigma.cwise().abs().maxCoeff(); - for (int j=0; j<b.cols(); ++j) - { - Matrix<Scalar,MatrixUType::RowsAtCompileTime,1> aux = m_matU.transpose() * b.col(j); - - for (int i = 0; i <m_matU.cols(); ++i) - { - Scalar si = m_sigma.coeff(i); - if (ei_isMuchSmallerThan(ei_abs(si),maxVal)) - aux.coeffRef(i) = 0; - else - aux.coeffRef(i) /= si; - } - - result->col(j) = m_matV * aux; - } - return true; -} - -/** Computes the polar decomposition of the matrix, as a product unitary x positive. - * - * If either pointer is zero, the corresponding computation is skipped. - * - * Only for square matrices. - * - * \sa computePositiveUnitary(), computeRotationScaling() - */ -template<typename MatrixType> -template<typename UnitaryType, typename PositiveType> -void SVD<MatrixType>::computeUnitaryPositive(UnitaryType *unitary, - PositiveType *positive) const -{ - ei_assert(m_matU.cols() == m_matV.cols() && "Polar decomposition is only for square matrices"); - if(unitary) *unitary = m_matU * m_matV.adjoint(); - if(positive) *positive = m_matV * m_sigma.asDiagonal() * m_matV.adjoint(); -} - -/** Computes the polar decomposition of the matrix, as a product positive x unitary. - * - * If either pointer is zero, the corresponding computation is skipped. - * - * Only for square matrices. - * - * \sa computeUnitaryPositive(), computeRotationScaling() - */ -template<typename MatrixType> -template<typename UnitaryType, typename PositiveType> -void SVD<MatrixType>::computePositiveUnitary(UnitaryType *positive, - PositiveType *unitary) const -{ - ei_assert(m_matU.rows() == m_matV.rows() && "Polar decomposition is only for square matrices"); - if(unitary) *unitary = m_matU * m_matV.adjoint(); - if(positive) *positive = m_matU * m_sigma.asDiagonal() * m_matU.adjoint(); -} - -/** decomposes the matrix as a product rotation x scaling, the scaling being - * not necessarily positive. - * - * If either pointer is zero, the corresponding computation is skipped. - * - * This method requires the Geometry module. - * - * \sa computeScalingRotation(), computeUnitaryPositive() - */ -template<typename MatrixType> -template<typename RotationType, typename ScalingType> -void SVD<MatrixType>::computeRotationScaling(RotationType *rotation, ScalingType *scaling) const -{ - ei_assert(m_matU.rows() == m_matV.rows() && "Polar decomposition is only for square matrices"); - Scalar x = (m_matU * m_matV.adjoint()).determinant(); // so x has absolute value 1 - Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> sv(m_sigma); - sv.coeffRef(0) *= x; - if(scaling) scaling->lazyAssign(m_matV * sv.asDiagonal() * m_matV.adjoint()); - if(rotation) - { - MatrixType m(m_matU); - m.col(0) /= x; - rotation->lazyAssign(m * m_matV.adjoint()); - } -} - -/** decomposes the matrix as a product scaling x rotation, the scaling being - * not necessarily positive. - * - * If either pointer is zero, the corresponding computation is skipped. - * - * This method requires the Geometry module. - * - * \sa computeRotationScaling(), computeUnitaryPositive() - */ -template<typename MatrixType> -template<typename ScalingType, typename RotationType> -void SVD<MatrixType>::computeScalingRotation(ScalingType *scaling, RotationType *rotation) const -{ - ei_assert(m_matU.rows() == m_matV.rows() && "Polar decomposition is only for square matrices"); - Scalar x = (m_matU * m_matV.adjoint()).determinant(); // so x has absolute value 1 - Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> sv(m_sigma); - sv.coeffRef(0) *= x; - if(scaling) scaling->lazyAssign(m_matU * sv.asDiagonal() * m_matU.adjoint()); - if(rotation) - { - MatrixType m(m_matU); - m.col(0) /= x; - rotation->lazyAssign(m * m_matV.adjoint()); - } -} - - -/** \svd_module - * \returns the SVD decomposition of \c *this - */ -template<typename Derived> -inline SVD<typename MatrixBase<Derived>::PlainObject> -MatrixBase<Derived>::svd() const -{ - return SVD<PlainObject>(derived()); -} - -} // end namespace Eigen - -#endif // EIGEN2_SVD_H |