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LinalgBackendEigen.h
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LinalgBackendEigen.h
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/*
* Copyright (c) 2016, Shogun-Toolbox e.V. <shogun-team@shogun-toolbox.org>
* All rights reserved.
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions are met:
*
* 1. Redistributions of source code must retain the above copyright notice,
* this list of conditions and the following disclaimer.
*
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
*
* 3. Neither the name of the copyright holder nor the names of its
* contributors may be used to endorse or promote products derived from
* this software without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
* AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
* ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE
* LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
* CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
* SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
* INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
* CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
* POSSIBILITY OF SUCH DAMAGE.
*
* Authors: 2016 Pan Deng, Soumyajit De, Heiko Strathmann, Viktor Gal
*/
#ifndef LINALG_BACKEND_EIGEN_H__
#define LINALG_BACKEND_EIGEN_H__
#include <numeric>
#include <shogun/mathematics/Math.h>
#include <shogun/mathematics/eigen3.h>
#include <shogun/mathematics/linalg/LinalgBackendBase.h>
#include <shogun/mathematics/linalg/LinalgEnums.h>
#include <shogun/mathematics/linalg/LinalgMacros.h>
namespace shogun
{
/** @brief Linalg methods with Eigen3 backend */
class LinalgBackendEigen : public LinalgBackendBase
{
public:
/** Implementation of @see LinalgBackendBase::add */
#define BACKEND_GENERIC_IN_PLACE_ADD(Type, Container) \
virtual void add( \
const Container<Type>& a, const Container<Type>& b, Type alpha, \
Type beta, Container<Type>& result) const;
DEFINE_FOR_NUMERIC_PTYPE(BACKEND_GENERIC_IN_PLACE_ADD, SGVector)
DEFINE_FOR_NUMERIC_PTYPE(BACKEND_GENERIC_IN_PLACE_ADD, SGMatrix)
#undef BACKEND_GENERIC_IN_PLACE_ADD
/** Implementation of @see LinalgBackendBase::add_col_vec */
#define BACKEND_GENERIC_ADD_COL_VEC(Type, Container) \
virtual void add_col_vec( \
const SGMatrix<Type>& A, index_t i, const SGVector<Type>& b, \
Container<Type>& result, Type alpha, Type beta) const;
DEFINE_FOR_NUMERIC_PTYPE(BACKEND_GENERIC_ADD_COL_VEC, SGVector)
DEFINE_FOR_NUMERIC_PTYPE(BACKEND_GENERIC_ADD_COL_VEC, SGMatrix)
#undef BACKEND_GENERIC_ADD_COL_VEC
/** Implementation of @see LinalgBackendBase::add_diag */
#define BACKEND_GENERIC_ADD_DIAG(Type, Container) \
virtual void add_diag( \
SGMatrix<Type>& A, const SGVector<Type>& b, Type alpha, Type beta) \
const;
DEFINE_FOR_NUMERIC_PTYPE(BACKEND_GENERIC_ADD_DIAG, SGMatrix)
#undef BACKEND_GENERIC_ADD_DIAG
/** Implementation of @see LinalgBackendBase::add_vector */
#define BACKEND_GENERIC_ADD(Type, Container) \
virtual void add_vector( \
const SGMatrix<Type>& A, const SGVector<Type>& b, \
SGMatrix<Type>& result, Type alpha, Type beta) const;
DEFINE_FOR_NUMERIC_PTYPE(BACKEND_GENERIC_ADD, SGMatrix)
#undef BACKEND_GENERIC_ADD
/** Implementation of @see LinalgBackendBase::add_scalar */
#define BACKEND_GENERIC_ADD_SCALAR(Type, Container) \
virtual void add_scalar(Container<Type>& a, Type b) const;
DEFINE_FOR_NUMERIC_PTYPE(BACKEND_GENERIC_ADD_SCALAR, SGVector)
DEFINE_FOR_NUMERIC_PTYPE(BACKEND_GENERIC_ADD_SCALAR, SGMatrix)
#undef BACKEND_GENERIC_ADD_SCALAR
/** Implementation of @see LinalgBackendBase::center_matrix */
#define BACKEND_GENERIC_CENTER_MATRIX(Type, Container) \
virtual void center_matrix(Container<Type>& A) const;
DEFINE_FOR_NON_INTEGER_PTYPE(BACKEND_GENERIC_CENTER_MATRIX, SGMatrix)
#undef BACKEND_GENERIC_CENTER_MATRIX
/** Implementation of @see LinalgBackendBase::cholesky_factor */
#define BACKEND_GENERIC_CHOLESKY_FACTOR(Type, Container) \
virtual Container<Type> cholesky_factor( \
const Container<Type>& A, const bool lower) const;
DEFINE_FOR_NON_INTEGER_PTYPE(BACKEND_GENERIC_CHOLESKY_FACTOR, SGMatrix)
#undef BACKEND_GENERIC_CHOLESKY_FACTOR
/** Implementation of @see LinalgBackendBase::cholesky_solver */
#define BACKEND_GENERIC_CHOLESKY_SOLVER(Type, Container) \
virtual SGVector<Type> cholesky_solver( \
const Container<Type>& L, const SGVector<Type>& b, const bool lower) \
const;
DEFINE_FOR_NON_INTEGER_PTYPE(BACKEND_GENERIC_CHOLESKY_SOLVER, SGMatrix)
#undef BACKEND_GENERIC_CHOLESKY_SOLVER
/** Implementation of @see LinalgBackendBase::ldlt_factor */
#define BACKEND_GENERIC_LDLT_FACTOR(Type, Container) \
virtual void ldlt_factor( \
const Container<Type>& A, Container<Type>& L, SGVector<Type>& d, \
SGVector<index_t>& p, const bool lower) const;
DEFINE_FOR_NON_INTEGER_PTYPE(BACKEND_GENERIC_LDLT_FACTOR, SGMatrix)
#undef BACKEND_GENERIC_LDLT_FACTOR
/** Implementation of @see LinalgBackendBase::ldlt_solver */
#define BACKEND_GENERIC_LDLT_SOLVER(Type, Container) \
virtual SGVector<Type> ldlt_solver( \
const Container<Type>& L, const SGVector<Type>& d, \
const SGVector<index_t>& p, const SGVector<Type>& b, const bool lower) \
const;
DEFINE_FOR_NON_INTEGER_PTYPE(BACKEND_GENERIC_LDLT_SOLVER, SGMatrix)
#undef BACKEND_GENERIC_LDLT_SOLVER
/** Implementation of @see linalg::cross_entropy */
#define BACKEND_GENERIC_CROSS_ENTROPY(Type, Container) \
virtual Type cross_entropy( \
const Container<Type>& P, const Container<Type>& Q) const;
DEFINE_FOR_NON_INTEGER_REAL_PTYPE(
BACKEND_GENERIC_CROSS_ENTROPY, SGMatrix)
#undef BACKEND_GENERIC_CROSS_ENTROPY
/** Implementation of @see LinalgBackendBase::dot */
#define BACKEND_GENERIC_DOT(Type, Container) \
virtual Type dot(const Container<Type>& a, const Container<Type>& b) const;
DEFINE_FOR_ALL_PTYPE(BACKEND_GENERIC_DOT, SGVector)
#undef BACKEND_GENERIC_DOT
/** Implementation of @see LinalgBackendBase::eigen_solver */
#define BACKEND_GENERIC_EIGEN_SOLVER(Type, Container) \
virtual void eigen_solver( \
const Container<Type>& A, SGVector<Type>& eigenvalues, \
SGMatrix<Type>& eigenvectors) const;
DEFINE_FOR_NON_INTEGER_PTYPE(BACKEND_GENERIC_EIGEN_SOLVER, SGMatrix)
#undef BACKEND_GENERIC_EIGEN_SOLVER
/** Implementation of @see LinalgBackendBase::eigen_solver_symmetric */
#define BACKEND_GENERIC_EIGEN_SOLVER_SYMMETRIC(Type, Container) \
virtual void eigen_solver_symmetric( \
const Container<Type>& A, SGVector<Type>& eigenvalues, \
SGMatrix<Type>& eigenvectors, index_t k) const;
DEFINE_FOR_NON_INTEGER_PTYPE(
BACKEND_GENERIC_EIGEN_SOLVER_SYMMETRIC, SGMatrix)
#undef BACKEND_GENERIC_EIGEN_SOLVER_SYMMETRIC
/** Implementation of @see LinalgBackendBase::element_prod */
#define BACKEND_GENERIC_IN_PLACE_VECTOR_ELEMENT_PROD(Type, Container) \
virtual void element_prod( \
const Container<Type>& a, const Container<Type>& b, \
Container<Type>& result) const;
DEFINE_FOR_ALL_PTYPE(
BACKEND_GENERIC_IN_PLACE_VECTOR_ELEMENT_PROD, SGVector)
#undef BACKEND_GENERIC_IN_PLACE_VECTOR_ELEMENT_PROD
/** Implementation of @see LinalgBackendBase::element_prod */
#define BACKEND_GENERIC_IN_PLACE_MATRIX_ELEMENT_PROD(Type, Container) \
virtual void element_prod( \
const Container<Type>& a, const Container<Type>& b, \
Container<Type>& result, bool transpose_A, bool transpose_B) const;
DEFINE_FOR_ALL_PTYPE(
BACKEND_GENERIC_IN_PLACE_MATRIX_ELEMENT_PROD, SGMatrix)
#undef BACKEND_GENERIC_IN_PLACE_MATRIX_ELEMENT_PROD
/** Implementation of @see LinalgBackendBase::element_prod */
#define BACKEND_GENERIC_IN_PLACE_BLOCK_ELEMENT_PROD(Type, Container) \
virtual void element_prod( \
const linalg::Block<Container<Type>>& a, \
const linalg::Block<Container<Type>>& b, Container<Type>& result, \
bool transpose_A, bool transpose_B) const;
DEFINE_FOR_ALL_PTYPE(
BACKEND_GENERIC_IN_PLACE_BLOCK_ELEMENT_PROD, SGMatrix)
#undef BACKEND_GENERIC_IN_PLACE_BLOCK_ELEMENT_PROD
/** Implementation of @see linalg::exponent */
#define BACKEND_GENERIC_EXPONENT(Type, Container) \
virtual void exponent(const Container<Type>& a, Container<Type>& result) \
const
DEFINE_FOR_ALL_PTYPE(BACKEND_GENERIC_EXPONENT, SGVector)
DEFINE_FOR_ALL_PTYPE(BACKEND_GENERIC_EXPONENT, SGMatrix)
#undef BACKEND_GENERIC_EXPONENT
/** Implementation of @see LinalgBackendBase::identity */
#define BACKEND_GENERIC_IDENTITY(Type, Container) \
virtual void identity(Container<Type>& identity_matrix) const;
DEFINE_FOR_ALL_PTYPE(BACKEND_GENERIC_IDENTITY, SGMatrix)
#undef BACKEND_GENERIC_IDENTITY
/** Implementation of @see LinalgBackendBase::logistic */
#define BACKEND_GENERIC_LOGISTIC(Type, Container) \
virtual void logistic(const Container<Type>& a, Container<Type>& result) \
const;
DEFINE_FOR_NUMERIC_PTYPE(BACKEND_GENERIC_LOGISTIC, SGMatrix)
#undef BACKEND_GENERIC_LOGISTIC
/** Implementation of @see LinalgBackendBase::matrix_prod */
#define BACKEND_GENERIC_IN_PLACE_MATRIX_PROD(Type, Container) \
virtual void matrix_prod( \
const SGMatrix<Type>& a, const Container<Type>& b, \
Container<Type>& result, bool transpose_A, bool transpose_B) const;
DEFINE_FOR_ALL_PTYPE(BACKEND_GENERIC_IN_PLACE_MATRIX_PROD, SGVector)
DEFINE_FOR_ALL_PTYPE(BACKEND_GENERIC_IN_PLACE_MATRIX_PROD, SGMatrix)
#undef BACKEND_GENERIC_IN_PLACE_MATRIX_PROD
/** Implementation of @see LinalgBackendBase::max */
#define BACKEND_GENERIC_MAX(Type, Container) \
virtual Type max(const Container<Type>& a) const;
DEFINE_FOR_REAL_PTYPE(BACKEND_GENERIC_MAX, SGVector)
DEFINE_FOR_REAL_PTYPE(BACKEND_GENERIC_MAX, SGMatrix)
#undef BACKEND_GENERIC_MAX
/** Implementation of @see LinalgBackendBase::mean */
#define BACKEND_GENERIC_REAL_MEAN(Type, Container) \
virtual float64_t mean(const Container<Type>& a) const;
DEFINE_FOR_REAL_PTYPE(BACKEND_GENERIC_REAL_MEAN, SGVector)
DEFINE_FOR_REAL_PTYPE(BACKEND_GENERIC_REAL_MEAN, SGMatrix)
#undef BACKEND_GENERIC_REAL_MEAN
/** Implementation of @see LinalgBackendBase::mean */
#define BACKEND_GENERIC_COMPLEX_MEAN(Container) \
virtual complex128_t mean(const Container<complex128_t>& a) const;
BACKEND_GENERIC_COMPLEX_MEAN(SGVector)
BACKEND_GENERIC_COMPLEX_MEAN(SGMatrix)
#undef BACKEND_GENERIC_COMPLEX_MEAN
/** Implementation of @see linalg::multiply_by_logistic_derivative */
#define BACKEND_GENERIC_MULTIPLY_BY_LOGISTIC_DERIV(Type, Container) \
virtual void multiply_by_logistic_derivative( \
const Container<Type>& a, Container<Type>& result) const;
DEFINE_FOR_NUMERIC_PTYPE(
BACKEND_GENERIC_MULTIPLY_BY_LOGISTIC_DERIV, SGMatrix)
#undef BACKEND_GENERIC_MULTIPLY_BY_LOGISTIC_DERIV
/** Implementation of @see linalg::multiply_by_rectified_linear_derivative */
#define BACKEND_GENERIC_MULTIPLY_BY_RECTIFIED_LINEAR_DERIV(Type, Container) \
virtual void multiply_by_rectified_linear_derivative( \
const Container<Type>& a, Container<Type>& result) const;
DEFINE_FOR_NON_INTEGER_REAL_PTYPE(
BACKEND_GENERIC_MULTIPLY_BY_RECTIFIED_LINEAR_DERIV, SGMatrix)
#undef BACKEND_GENERIC_MULTIPLY_BY_RECTIFIED_LINEAR_DERIV
/** Implementation of @see LinalgBackendBase::qr_solver */
#define BACKEND_GENERIC_QR_SOLVER(Type, Container) \
virtual Container<Type> qr_solver( \
const SGMatrix<Type>& A, const Container<Type>& b) const;
DEFINE_FOR_NON_INTEGER_PTYPE(BACKEND_GENERIC_QR_SOLVER, SGVector)
DEFINE_FOR_NON_INTEGER_PTYPE(BACKEND_GENERIC_QR_SOLVER, SGMatrix)
#undef BACKEND_GENERIC_QR_SOLVER
/** Implementation of @see LinalgBackendBase::range_fill */
#define BACKEND_GENERIC_RANGE_FILL(Type, Container) \
virtual void range_fill(Container<Type>& a, const Type start) const;
DEFINE_FOR_ALL_PTYPE(BACKEND_GENERIC_RANGE_FILL, SGVector)
DEFINE_FOR_ALL_PTYPE(BACKEND_GENERIC_RANGE_FILL, SGMatrix)
#undef BACKEND_GENERIC_RANGE_FILL
/** Implementation of @see linalg::rectified_linear */
#define BACKEND_GENERIC_RECTIFIED_LINEAR(Type, Container) \
virtual void rectified_linear( \
const Container<Type>& a, Container<Type>& result) const;
DEFINE_FOR_REAL_PTYPE(BACKEND_GENERIC_RECTIFIED_LINEAR, SGMatrix)
#undef BACKEND_GENERIC_RECTIFIED_LINEAR
/** Implementation of @see linalg::scale */
#define BACKEND_GENERIC_IN_PLACE_SCALE(Type, Container) \
virtual void scale( \
const Container<Type>& a, Type alpha, Container<Type>& result) const;
DEFINE_FOR_ALL_PTYPE(BACKEND_GENERIC_IN_PLACE_SCALE, SGVector)
DEFINE_FOR_ALL_PTYPE(BACKEND_GENERIC_IN_PLACE_SCALE, SGMatrix)
#undef BACKEND_GENERIC_IN_PLACE_SCALE
/** Implementation of @see LinalgBackendBase::set_const */
#define BACKEND_GENERIC_SET_CONST(Type, Container) \
virtual void set_const(Container<Type>& a, const Type value) const;
DEFINE_FOR_ALL_PTYPE(BACKEND_GENERIC_SET_CONST, SGVector)
DEFINE_FOR_ALL_PTYPE(BACKEND_GENERIC_SET_CONST, SGMatrix)
#undef BACKEND_GENERIC_SET_CONST
/** Implementation of @see linalg::softmax */
#define BACKEND_GENERIC_SOFTMAX(Type, Container) \
virtual void softmax(Container<Type>& a) const;
DEFINE_FOR_NON_INTEGER_REAL_PTYPE(BACKEND_GENERIC_SOFTMAX, SGMatrix)
#undef BACKEND_GENERIC_SOFTMAX
/** Implementation of @see linalg::squared_error */
#define BACKEND_GENERIC_SQUARED_ERROR(Type, Container) \
virtual Type squared_error( \
const Container<Type>& P, const Container<Type>& Q) const;
DEFINE_FOR_NON_INTEGER_REAL_PTYPE(
BACKEND_GENERIC_SQUARED_ERROR, SGMatrix)
#undef BACKEND_GENERIC_SQUARED_ERROR
/** Implementation of @see LinalgBackendBase::sum */
#define BACKEND_GENERIC_SUM(Type, Container) \
virtual Type sum(const Container<Type>& a, bool no_diag) const;
DEFINE_FOR_ALL_PTYPE(BACKEND_GENERIC_SUM, SGVector)
DEFINE_FOR_ALL_PTYPE(BACKEND_GENERIC_SUM, SGMatrix)
#undef BACKEND_GENERIC_SUM
/** Implementation of @see LinalgBackendBase::sum */
#define BACKEND_GENERIC_BLOCK_SUM(Type, Container) \
virtual Type sum(const linalg::Block<Container<Type>>& a, bool no_diag) \
const;
DEFINE_FOR_ALL_PTYPE(BACKEND_GENERIC_BLOCK_SUM, SGMatrix)
#undef BACKEND_GENERIC_BLOCK_SUM
/** Implementation of @see LinalgBackendBase::sum_symmetric */
#define BACKEND_GENERIC_SYMMETRIC_SUM(Type, Container) \
virtual Type sum_symmetric(const Container<Type>& a, bool no_diag) const;
DEFINE_FOR_ALL_PTYPE(BACKEND_GENERIC_SYMMETRIC_SUM, SGMatrix)
#undef BACKEND_GENERIC_SYMMETRIC_SUM
/** Implementation of @see LinalgBackendBase::sum_symmetric */
#define BACKEND_GENERIC_SYMMETRIC_BLOCK_SUM(Type, Container) \
virtual Type sum_symmetric( \
const linalg::Block<Container<Type>>& a, bool no_diag) const;
DEFINE_FOR_ALL_PTYPE(BACKEND_GENERIC_SYMMETRIC_BLOCK_SUM, SGMatrix)
#undef BACKEND_GENERIC_SYMMETRIC_BLOCK_SUM
/** Implementation of @see LinalgBackendBase::colwise_sum */
#define BACKEND_GENERIC_COLWISE_SUM(Type, Container) \
virtual SGVector<Type> colwise_sum(const Container<Type>& a, bool no_diag) \
const;
DEFINE_FOR_ALL_PTYPE(BACKEND_GENERIC_COLWISE_SUM, SGMatrix)
#undef BACKEND_GENERIC_COLWISE_SUM
/** Implementation of @see LinalgBackendBase::colwise_sum */
#define BACKEND_GENERIC_BLOCK_COLWISE_SUM(Type, Container) \
virtual SGVector<Type> colwise_sum( \
const linalg::Block<Container<Type>>& a, bool no_diag) const;
DEFINE_FOR_ALL_PTYPE(BACKEND_GENERIC_BLOCK_COLWISE_SUM, SGMatrix)
#undef BACKEND_GENERIC_BLOCK_COLWISE_SUM
/** Implementation of @see LinalgBackendBase::rowwise_sum */
#define BACKEND_GENERIC_ROWWISE_SUM(Type, Container) \
virtual SGVector<Type> rowwise_sum(const Container<Type>& a, bool no_diag) \
const;
DEFINE_FOR_ALL_PTYPE(BACKEND_GENERIC_ROWWISE_SUM, SGMatrix)
#undef BACKEND_GENERIC_ROWWISE_SUM
/** Implementation of @see LinalgBackendBase::rowwise_sum */
#define BACKEND_GENERIC_BLOCK_ROWWISE_SUM(Type, Container) \
virtual SGVector<Type> rowwise_sum( \
const linalg::Block<Container<Type>>& a, bool no_diag) const;
DEFINE_FOR_ALL_PTYPE(BACKEND_GENERIC_BLOCK_ROWWISE_SUM, SGMatrix)
#undef BACKEND_GENERIC_BLOCK_ROWWISE_SUM
/** Implementation of @see LinalgBackendBase::svd */
#define BACKEND_GENERIC_SVD(Type, Container) \
virtual void svd( \
const Container<Type>& A, SGVector<Type> s, Container<Type> U, \
bool thin_U, linalg::SVDAlgorithm alg) const;
DEFINE_FOR_NON_INTEGER_PTYPE(BACKEND_GENERIC_SVD, SGMatrix)
#undef BACKEND_GENERIC_SVD
/** Implementation of @see LinalgBackendBase::trace */
#define BACKEND_GENERIC_TRACE(Type, Container) \
virtual Type trace(const Container<Type>& A) const;
DEFINE_FOR_ALL_PTYPE(BACKEND_GENERIC_TRACE, SGMatrix)
#undef BACKEND_GENERIC_TRACE
/** Implementation of @see LinalgBackendBase::transpose_matrix */
#define BACKEND_GENERIC_TRANSPOSE_MATRIX(Type, Container) \
virtual Container<Type> transpose_matrix(const Container<Type>& A) const;
DEFINE_FOR_ALL_PTYPE(BACKEND_GENERIC_TRANSPOSE_MATRIX, SGMatrix)
#undef BACKEND_GENERIC_TRANSPOSE_MATRIX
/** Implementation of @see LinalgBackendBase::triangular_solver */
#define BACKEND_GENERIC_TRIANGULAR_SOLVER(Type, Container) \
virtual Container<Type> triangular_solver( \
const SGMatrix<Type>& L, const Container<Type>& b, const bool lower) \
const;
DEFINE_FOR_NON_INTEGER_PTYPE(
BACKEND_GENERIC_TRIANGULAR_SOLVER, SGVector)
DEFINE_FOR_NON_INTEGER_PTYPE(
BACKEND_GENERIC_TRIANGULAR_SOLVER, SGMatrix)
#undef BACKEND_GENERIC_TRIANGULAR_SOLVER
/** Implementation of @see LinalgBackendBase::zero */
#define BACKEND_GENERIC_ZERO(Type, Container) \
virtual void zero(Container<Type>& a) const;
DEFINE_FOR_ALL_PTYPE(BACKEND_GENERIC_ZERO, SGVector)
DEFINE_FOR_ALL_PTYPE(BACKEND_GENERIC_ZERO, SGMatrix)
#undef BACKEND_GENERIC_ZERO
#undef DEFINE_FOR_ALL_PTYPE
#undef DEFINE_FOR_REAL_PTYPE
#undef DEFINE_FOR_NON_INTEGER_PTYPE
#undef DEFINE_FOR_NUMERIC_PTYPE
private:
/** Eigen3 vector result = alpha*A + beta*B method */
template <typename T>
void add_impl(
const SGVector<T>& a, const SGVector<T>& b, T alpha, T beta,
SGVector<T>& result) const;
/** Eigen3 matrix result = alpha*A + beta*B method */
template <typename T>
void add_impl(
const SGMatrix<T>& a, const SGMatrix<T>& b, T alpha, T beta,
SGMatrix<T>& result) const;
/** Eigen3 add column vector method */
template <typename T>
void add_col_vec_impl(
const SGMatrix<T>& A, index_t i, const SGVector<T>& b,
SGMatrix<T>& result, T alpha, T beta) const;
/** Eigen3 add column vector method */
template <typename T>
void add_col_vec_impl(
const SGMatrix<T>& A, index_t i, const SGVector<T>& b,
SGVector<T>& result, T alpha, T beta) const;
/** Eigen3 add diagonal vector method */
template <typename T>
void add_diag_impl(
SGMatrix<T>& A, const SGVector<T>& b, T alpha, T beta) const;
/** Eigen3 add vector to each column of matrix method */
template <typename T>
void add_vector_impl(
const SGMatrix<T>& A, const SGVector<T>& b, SGMatrix<T>& result,
T alpha, T beta) const;
/** Eigen3 vector add scalar method */
template <typename T>
void add_scalar_impl(SGVector<T>& a, T b) const;
/** Eigen3 matrix add scalar method */
template <typename T>
void add_scalar_impl(SGMatrix<T>& a, T b) const;
/** Eigen3 center matrix method */
template <typename T>
void center_matrix_impl(SGMatrix<T>& A) const;
/** Eigen3 Cholesky decomposition */
template <typename T>
SGMatrix<T>
cholesky_factor_impl(const SGMatrix<T>& A, const bool lower) const;
/** Eigen3 Cholesky solver */
template <typename T>
SGVector<T> cholesky_solver_impl(
const SGMatrix<T>& L, const SGVector<T>& b, const bool lower) const;
/** Eigen3 LDLT Cholesky decomposition */
template <typename T>
void ldlt_factor_impl(
const SGMatrix<T>& A, SGMatrix<T>& L, SGVector<T>& d,
SGVector<index_t>& p, const bool lower) const;
/** Eigen3 LDLT Cholesky solver */
template <typename T>
SGVector<T> ldlt_solver_impl(
const SGMatrix<T>& L, const SGVector<T>& d,
const SGVector<index_t>& p, const SGVector<T>& b,
const bool lower) const;
/** Eigen3 cross_entropy method
* The cross entropy is defined as \f$ H(P,Q) = - \sum_{ij}
* P[i,j]log(Q[i,j]) \f$
*/
template <typename T>
T cross_entropy_impl(const SGMatrix<T>& p, const SGMatrix<T>& q) const;
/** Eigen3 vector dot-product method */
template <typename T>
T dot_impl(const SGVector<T>& a, const SGVector<T>& b) const;
/** Eigen3 eigenvalues and eigenvectors computation for real matrices.
*/
template <typename T>
void eigen_solver_impl(
const SGMatrix<T>& A, SGVector<T>& eigenvalues,
SGMatrix<T>& eigenvectors) const;
/** Eigen3 eigenvalues and eigenvectors computation for complex
* matrices. */
void eigen_solver_impl(
const SGMatrix<complex128_t>& A,
SGVector<complex128_t>& eigenvalues,
SGMatrix<complex128_t>& eigenvectors) const;
/** Eigen3 eigenvalues and eigenvectors computation of symmetric
* matrices */
template <typename T>
void eigen_solver_symmetric_impl(
const SGMatrix<T>& A, SGVector<T>& eigenvalues,
SGMatrix<T>& eigenvectors, index_t k) const;
/** Eigen3 matrix in-place elementwise product method */
template <typename T>
void element_prod_impl(
const SGMatrix<T>& a, const SGMatrix<T>& b, SGMatrix<T>& result,
bool transpose_A, bool transpose_B) const;
/** Eigen3 matrix block in-place elementwise product method */
template <typename T>
void element_prod_impl(
const linalg::Block<SGMatrix<T>>& a,
const linalg::Block<SGMatrix<T>>& b, SGMatrix<T>& result,
bool transpose_A, bool transpose_B) const;
/** Eigen3 vector in-place elementwise product method */
template <typename T>
void element_prod_impl(
const SGVector<T>& a, const SGVector<T>& b,
SGVector<T>& result) const;
/** Eigen3 vector exponent method */
template <typename T>
void exponent_impl(const SGVector<T>& a, SGVector<T>& result) const;
/** Eigen3 matrix exponent method */
template <typename T>
void exponent_impl(const SGMatrix<T>& a, SGMatrix<T>& result) const;
/** Eigen3 set matrix to identity method */
template <typename T>
void identity_impl(SGMatrix<T>& identity_matrix) const;
/** Eigen3 logistic method. Calculates f(x) = 1/(1+exp(-x)) */
template <typename T>
void logistic_impl(const SGMatrix<T>& a, SGMatrix<T>& result) const;
/** Eigen3 matrix * vector in-place product method */
template <typename T>
void matrix_prod_impl(
const SGMatrix<T>& a, const SGVector<T>& b, SGVector<T>& result,
bool transpose, bool transpose_B = false) const;
/** Eigen3 matrix in-place product method */
template <typename T>
void matrix_prod_impl(
const SGMatrix<T>& a, const SGMatrix<T>& b, SGMatrix<T>& result,
bool transpose_A, bool transpose_B) const;
/** Return the largest element in the vector with Eigen3 library */
template <typename T>
T max_impl(const SGVector<T>& vec) const;
/** Return the largest element in the matrix with Eigen3 library */
template <typename T>
T max_impl(const SGMatrix<T>& mat) const;
/** Real eigen3 vector and matrix mean method */
template <typename T, template <typename> class Container>
typename std::enable_if<!std::is_same<T, complex128_t>::value,
float64_t>::type
mean_impl(const Container<T>& a) const;
/** Complex eigen3 vector and matrix mean method */
template <template <typename> class Container>
complex128_t mean_impl(const Container<complex128_t>& a) const;
/** Eigen3 multiply_by_logistic_derivative method
* Performs the operation C(i,j) = C(i,j) * A(i,j) * (1.0-A(i,j)) for
* all i
* and j
*/
template <typename T>
void multiply_by_logistic_derivative_impl(
const SGMatrix<T>& a, SGMatrix<T>& result) const;
/** Eigen3 multiply_by_rectified_linear_derivative method
* Performs the operation C(i,j) = C(i,j) * (A(i,j)!=0) for all i and j
*/
template <typename T>
void multiply_by_rectified_linear_derivative_impl(
const SGMatrix<T>& a, SGMatrix<T>& result) const;
/** Eigen3 vector QR solver. */
template <typename T>
SGVector<T>
qr_solver_impl(const SGMatrix<T>& A, const SGVector<T>& b) const;
/** Eigen3 matrix QR solver. */
template <typename T>
SGMatrix<T>
qr_solver_impl(const SGMatrix<T>& A, const SGMatrix<T> b) const;
/** Range fill a vector or matrix with start...start+len-1. */
template <typename T, template <typename> class Container>
void range_fill_impl(Container<T>& a, const T start) const;
/** Applies the elementwise rectified linear function f(x) = max(0,x) */
template <typename T>
void
rectified_linear_impl(const SGMatrix<T>& a, SGMatrix<T>& result) const;
/** Eigen3 vector inplace scale method: result = alpha * A */
template <typename T>
void
scale_impl(const SGVector<T>& a, T alpha, SGVector<T>& result) const;
/** Eigen3 matrix inplace scale method: result = alpha * A */
template <typename T>
void
scale_impl(const SGMatrix<T>& a, T alpha, SGMatrix<T>& result) const;
/** Eigen3 set const method */
template <typename T>
void set_const_impl(SGVector<T>& a, T value) const;
/** Eigen3 set matrix to const */
template <typename T>
void set_const_impl(SGMatrix<T>& a, T value) const;
/** Eigen3 softmax method */
template <typename T, template <typename> class Container>
void softmax_impl(Container<T>& a) const;
/** Eigen3 squared error method
* The squared error is defined as \f$ E(P,Q) = \frac{1}{2} \sum_{ij}
* (P[i,j]-Q[i,j])^2 \f$
*/
template <typename T>
T squared_error_impl(const SGMatrix<T>& p, const SGMatrix<T>& q) const;
/** Eigen3 vector sum method */
template <typename T>
T sum_impl(const SGVector<T>& vec, bool no_diag = false) const;
/** Eigen3 matrix sum method */
template <typename T>
T sum_impl(const SGMatrix<T>& mat, bool no_diag = false) const;
/** Eigen3 matrix block sum method */
template <typename T>
T sum_impl(
const linalg::Block<SGMatrix<T>>& mat, bool no_diag = false) const;
/** Eigen3 symmetric matrix sum method */
template <typename T>
T
sum_symmetric_impl(const SGMatrix<T>& mat, bool no_diag = false) const;
/** Eigen3 symmetric matrix block sum method */
template <typename T>
T sum_symmetric_impl(
const linalg::Block<SGMatrix<T>>& mat, bool no_diag = false) const;
/** Eigen3 matrix colwise sum method */
template <typename T>
SGVector<T>
colwise_sum_impl(const SGMatrix<T>& mat, bool no_diag) const;
/** Eigen3 matrix block colwise sum method */
template <typename T>
SGVector<T> colwise_sum_impl(
const linalg::Block<SGMatrix<T>>& mat, bool no_diag) const;
/** Eigen3 matrix rowwise sum method */
template <typename T>
SGVector<T>
rowwise_sum_impl(const SGMatrix<T>& mat, bool no_diag) const;
/** Eigen3 matrix block rowwise sum method */
template <typename T>
SGVector<T> rowwise_sum_impl(
const linalg::Block<SGMatrix<T>>& mat, bool no_diag) const;
/** Eigen3 compute svd method */
template <typename T>
void svd_impl(
const SGMatrix<T>& A, SGVector<T>& s, SGMatrix<T>& U, bool thin_U,
linalg::SVDAlgorithm alg) const;
/** Eigen3 compute trace method */
template <typename T>
T trace_impl(const SGMatrix<T>& A) const;
/** Eigen3 transpose matrix method */
template <typename T>
SGMatrix<T> transpose_matrix_impl(const SGMatrix<T>& A) const;
/** Eigen3 triangular solver method */
template <typename T>
SGMatrix<T> triangular_solver_impl(
const SGMatrix<T>& L, const SGMatrix<T>& b, const bool lower) const;
/** Eigen3 triangular solver method */
template <typename T>
SGVector<T> triangular_solver_impl(
const SGMatrix<T>& L, const SGVector<T>& b, const bool lower) const;
/** Eigen3 set vector to zero method */
template <typename T>
void zero_impl(SGVector<T>& a) const;
/** Eigen3 set matrix to zero method */
template <typename T>
void zero_impl(SGMatrix<T>& a) const;
};
/*
* Eigen's symmetric eigensolver uses a slower algorithm in comparison
* to LAPACK's dsyevr, so if LAPACK is available we use it for float64 type.
* This should be removed if eventually Eigen will provide a faster
* symmetric eigensolver (@see
* http://eigen.tuxfamily.org/bz/show_bug.cgi?id=522).
*/
#ifdef HAVE_LAPACK
template <>
void LinalgBackendEigen::eigen_solver_symmetric_impl<float64_t>(
const SGMatrix<float64_t>& A, SGVector<float64_t>& eigenvalues,
SGMatrix<float64_t>& eigenvectors, index_t k) const;
#endif
}
#endif // LINALG_BACKEND_EIGEN_H__