eigen/Eigen/SVD

// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// 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_MODULE_H
#define EIGEN_SVD_MODULE_H

#include "QR"
#include "Householder"
#include "Jacobi"

#include "src/Core/util/DisableStupidWarnings.h"

/** \defgroup SVD_Module SVD module
  *
  *
  *
  * This module provides SVD decomposition for matrices (both real and complex).
  * Two decomposition algorithms are provided:
  *  - JacobiSVD implementing two-sided Jacobi iterations is numerically very accurate, fast for small matrices, but very slow for larger ones.
  *  - BDCSVD implementing a recursive divide & conquer strategy on top of an upper-bidiagonalization which remains fast for large problems.
  * These decompositions are accessible via the respective classes and following MatrixBase methods:
  *  - MatrixBase::jacobiSvd()
  *  - MatrixBase::bdcSvd()
  *
  * \code
  * #include <Eigen/SVD>
  * \endcode
  */

#include "src/misc/RealSvd2x2.h"
#include "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 "src/SVD/JacobiSVD_LAPACKE.h"
#endif

#include "src/Core/util/ReenableStupidWarnings.h"

#endif // EIGEN_SVD_MODULE_H
/* vim: set filetype=cpp et sw=2 ts=2 ai: */
Add missing licence header to some top header files 2015-10-26 18:46:05 +08:00			`// This file is part of Eigen, a lightweight C++ template library`
			`// for linear algebra.`
			`//`
			`// 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/.`

missing SVD header file 2008-08-20 04:18:46 +08:00			`#ifndef EIGEN_SVD_MODULE_H`
			`#define EIGEN_SVD_MODULE_H`

JacobiSVD: implement general R-SVD using full-pivoting QR, so we now support any rectangular matrix size by reducing to the smaller of the two dimensions (which is also an optimization) 2009-09-02 18:36:55 +08:00			`#include "QR"`
* add Jacobi transformations * add Jacobi (Hestenes) SVD decomposition for square matrices * add function for trivial Householder 2009-08-09 22:58:13 +08:00			`#include "Householder"`
			`#include "Jacobi"`
missing SVD header file 2008-08-20 04:18:46 +08:00
shut up stupid ICC warnings 2011-02-22 22:31:22 +08:00			`#include "src/Core/util/DisableStupidWarnings.h"`
Patch by Kenneth Riddile: disable MSVC warnings, reenable them outside of Eigen, and add a MSVC-friendly path in StaticAssert. 2008-12-19 04:48:02 +08:00
missing SVD header file 2008-08-20 04:18:46 +08:00			`/** \defgroup SVD_Module SVD module`
* mark Geometry as experimental * install QtAlignedMalloc * finish the renaming Regression->LeastSquares * install LeastSquares directory (!!!) * misc dox fixes 2009-01-26 21:53:43 +08:00			`*`
Remove \nonstable yet. The stability rules for Eigen3 are much simpler: - all what's not in unsupported/ is considered stable API (except internal stuff e.g. expression templates). 2010-06-29 22:10:47 +08:00			`*`
* mark Geometry as experimental * install QtAlignedMalloc * finish the renaming Regression->LeastSquares * install LeastSquares directory (!!!) * misc dox fixes 2009-01-26 21:53:43 +08:00			`*`
Document that JacobiSVD also handles complex matrices. Thanks to 'Jazzdude' for noting this on IRC. 2012-01-26 21:16:50 +08:00			`* This module provides SVD decomposition for matrices (both real and complex).`
Move D&C SVD to official SVD module. 2014-10-29 18:29:33 +08:00			`* Two decomposition algorithms are provided:`
			`* - JacobiSVD implementing two-sided Jacobi iterations is numerically very accurate, fast for small matrices, but very slow for larger ones.`
			`* - BDCSVD implementing a recursive divide & conquer strategy on top of an upper-bidiagonalization which remains fast for large problems.`
			`* These decompositions are accessible via the respective classes and following MatrixBase methods:`
Document that JacobiSVD also handles complex matrices. Thanks to 'Jazzdude' for noting this on IRC. 2012-01-26 21:16:50 +08:00			`* - MatrixBase::jacobiSvd()`
Move D&C SVD to official SVD module. 2014-10-29 18:29:33 +08:00			`* - MatrixBase::bdcSvd()`
missing SVD header file 2008-08-20 04:18:46 +08:00			`*`
			`* \code`
			`* #include <Eigen/SVD>`
			`* \endcode`
			`*/`

Update RealQZ to reduce 2x2 diagonal block of T corresponding to non reduced diagonal block of S to positive diagonal form. This step involve a real 2x2 SVD problem. The respective routine is thus in src/misc/ to be shared by both EVD and AVD modules. 2016-06-09 23:11:03 +08:00			`#include "src/misc/RealSvd2x2.h"`
Move D&C SVD to official SVD module. 2014-10-29 18:29:33 +08:00			`#include "src/SVD/UpperBidiagonalization.h"`
Reafctoring in D&C SVD unsupported module: clean and merge the SVDBase class to Eigen/SVD, rm copy/pasted JacobiSVD.h file 2014-09-02 00:16:20 +08:00			`#include "src/SVD/SVDBase.h"`
* JacobiSVD: - support complex numbers - big rewrite of the 2x2 kernel, much more robust * Jacobi: - fix weirdness in initial design, e.g. applyJacobiOnTheRight actually did the inverse transformation - fully support complex numbers - fix logic to decide whether to vectorize - remove several clumsy methods fix for complex numbers 2009-09-01 10:26:15 +08:00			`#include "src/SVD/JacobiSVD.h"`
Move D&C SVD to official SVD module. 2014-10-29 18:29:33 +08:00			`#include "src/SVD/BDCSVD.h"`
add a "using MKL" documentation page, add a minimal documentation of PARDISO wrapper classes, refine a bit the EIGEN_USE_* logic 2011-12-09 23:52:37 +08:00			`#if defined(EIGEN_USE_LAPACKE) && !defined(EIGEN_USE_LAPACKE_STRICT)`
Rename MKL files 2016-07-26 00:00:47 +08:00			`#include "src/SVD/JacobiSVD_LAPACKE.h"`
Intel(R) MKL support added. * * * License disclaimer changed to BSD license for MKL_support.h * * * Pardiso support fixed, test added. blas/lapack tests fixed: Scalar parameter was added in Cholesky, product_matrix_vector_triangular remaned to triangular_matrix_vector_product. * * * PARDISO test was added physically. 2011-12-05 15:52:21 +08:00			`#endif`
missing SVD header file 2008-08-20 04:18:46 +08:00
shut up stupid ICC warnings 2011-02-22 22:31:22 +08:00			`#include "src/Core/util/ReenableStupidWarnings.h"`
Patch by Kenneth Riddile: disable MSVC warnings, reenable them outside of Eigen, and add a MSVC-friendly path in StaticAssert. 2008-12-19 04:48:02 +08:00
missing SVD header file 2008-08-20 04:18:46 +08:00			`#endif // EIGEN_SVD_MODULE_H`
added comments to help vim understand the header files are c++. 2009-12-02 07:00:29 +08:00			`/* vim: set filetype=cpp et sw=2 ts=2 ai: */`