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/* Ergo, version 3.8, a program for linear scaling electronic structure
* calculations.
* Copyright (C) 2019 Elias Rudberg, Emanuel H. Rubensson, Pawel Salek,
* and Anastasia Kruchinina.
*
* This program is free software: you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program. If not, see <http://www.gnu.org/licenses/>.
*
* Primary academic reference:
* Ergo: An open-source program for linear-scaling electronic structure
* calculations,
* Elias Rudberg, Emanuel H. Rubensson, Pawel Salek, and Anastasia
* Kruchinina,
* SoftwareX 7, 107 (2018),
* <http://dx.doi.org/10.1016/j.softx.2018.03.005>
*
* For further information about Ergo, see <http://www.ergoscf.org>.
*/
/** @file MatrixGeneral.h General matrix class
*
* Copyright(c) Emanuel Rubensson 2006
*
* @author Emanuel Rubensson @a responsible @a author
* @date January 2006
*
*/
#ifndef MAT_MATRIXGENERAL
#define MAT_MATRIXGENERAL
#include "MatrixBase.h"
namespace mat {
/** Normal matrix
*
* This class belongs to the matrix API
*
*
* Treal: Type for real numbers
*
* Tmatrix: The matrix class
*
* Tperm: Permutation used in the matrix class
*
* @see MatrixBase
* @see MatrixSymmetric
* @see MatrixTriangular
*
*/
template<typename Treal, typename Tmatrix>
class MatrixGeneral : public MatrixBase<Treal, Tmatrix> {
public:
typedef VectorGeneral<Treal, typename Tmatrix::VectorType> VectorType;
MatrixGeneral()
:MatrixBase<Treal, Tmatrix>() {} /**< Default constructor */
explicit MatrixGeneral(const MatrixGeneral<Treal, Tmatrix>& matr)
:MatrixBase<Treal, Tmatrix>(matr) {} /**< Copy constructor */
explicit MatrixGeneral(const MatrixSymmetric<Treal, Tmatrix>& symm)
:MatrixBase<Treal, Tmatrix>(symm) {
this->matrixPtr->symToNosym();
}/**< Copy from symmetric matrix constructor */
explicit MatrixGeneral(const MatrixTriangular<Treal, Tmatrix>& triang)
:MatrixBase<Treal, Tmatrix>(triang) {}
/**< Copy from triangular matrix constructor */
#if 0
template<typename Tfull>
inline void assign_from_full
(Tfull const* const fullmatrix,
const int totnrows, const int totncols) {
this->matrixPtr->assign_from_full(fullmatrix, totnrows, totncols);
}
inline void assign_from_full
(Treal const* const fullmatrix,
const int totnrows, const int totncols) {
this->matrixPtr->assign_from_full(fullmatrix, totnrows, totncols);
}
#endif
inline void assignFromFull
(std::vector<Treal> const & fullMat) {
assert((int)fullMat.size() == this->get_nrows() * this->get_ncols());
this->matrixPtr->assignFromFull(fullMat);
}
inline void fullMatrix(std::vector<Treal> & fullMat) const {
this->matrixPtr->fullMatrix(fullMat);
}
inline void fullMatrix
(std::vector<Treal> & fullMat,
std::vector<int> const & rowInversePermutation,
std::vector<int> const & colInversePermutation) const {
std::vector<int> rowind;
std::vector<int> colind;
std::vector<Treal> values;
get_all_values(rowind, colind, values,
rowInversePermutation,
colInversePermutation);
fullMat.assign(this->get_nrows()*this->get_ncols(),0);
for (unsigned int ind = 0; ind < values.size(); ++ind)
fullMat[rowind[ind] + this->get_nrows() * colind[ind]] =
values[ind];
}
/**< Save matrix as full matrix.
* Whole matrix is written in columnwise order.
* Both lower and upper triangle.
* Permutation is used.
*/
inline void assign_from_sparse
(std::vector<int> const & rowind,
std::vector<int> const & colind,
std::vector<Treal> const & values,
SizesAndBlocks const & newRows,
SizesAndBlocks const & newCols) {
this->resetSizesAndBlocks(newRows, newCols);
this->matrixPtr->assignFromSparse(rowind, colind, values);
}
/**< Assign from sparse matrix given by three arrays.
* The arrays contain row indices, column indices and values.
* The indices start at zero.
* nval is the length of the three arrays.
* @warning All indexing start at zero.
*/
inline void assign_from_sparse
(std::vector<int> const & rowind,
std::vector<int> const & colind,
std::vector<Treal> const & values,
std::vector<int> const & rowPermutation,
std::vector<int> const & colPermutation) {
std::vector<int> newRowind;
std::vector<int> newColind;
MatrixBase<Treal, Tmatrix>::
getPermutedIndexes(rowind, rowPermutation, newRowind);
MatrixBase<Treal, Tmatrix>::
getPermutedIndexes(colind, colPermutation, newColind);
this->matrixPtr->assignFromSparse(newRowind, newColind, values);
}
/**< Same as above, except taking two additional arguments
* specifying the permutation of rows and columns.
* Also assuming that sizes and blocks are already known
*/
inline void assign_from_sparse
(std::vector<int> const & rowind,
std::vector<int> const & colind,
std::vector<Treal> const & values,
SizesAndBlocks const & newRows,
SizesAndBlocks const & newCols,
std::vector<int> const & rowPermutation,
std::vector<int> const & colPermutation) {
this->resetSizesAndBlocks(newRows, newCols);
assign_from_sparse(rowind, colind, values,
rowPermutation, colPermutation);
}
/**< Same as above, except not assuming that sizes and blocks are set.
*/
inline void get_values
(std::vector<int> const & rowind,
std::vector<int> const & colind,
std::vector<Treal> & values) const {
this->matrixPtr->getValues(rowind, colind, values);
}
/**< Get values given by row and column index lists.
* Input arrays contain row and column indices.
* The output array contains values for the given indices.
* nval is the length of the three arrays.
* @warning All indexing start at zero.
*/
inline void get_values
(std::vector<int> const & rowind,
std::vector<int> const & colind,
std::vector<Treal> & values,
std::vector<int> const & rowPermutation,
std::vector<int> const & colPermutation) const {
std::vector<int> newRowind;
std::vector<int> newColind;
MatrixBase<Treal, Tmatrix>::
getPermutedIndexes(rowind, rowPermutation, newRowind);
MatrixBase<Treal, Tmatrix>::
getPermutedIndexes(colind, colPermutation, newColind);
this->matrixPtr->getValues(newRowind, newColind, values);
}
/**< Same as above, except taking two additional arguments
* specifying the permutation of rows and columns.
*/
inline void get_all_values
(std::vector<int> & rowind,
std::vector<int> & colind,
std::vector<Treal> & values) const {
rowind.resize(0);
colind.resize(0);
values.resize(0);
this->matrixPtr->getAllValues(rowind, colind, values);
}
/**< Get all values and corresponding row and column index lists,
* in matrix.
* nval is the length of the three arrays and is preferably
* computed with nvalues() before hand.
* Returns the number of values.
* @see nvalues()
* @warning All indexing start at zero.
*/
inline void get_all_values
(std::vector<int> & rowind,
std::vector<int> & colind,
std::vector<Treal> & values,
std::vector<int> const & rowInversePermutation,
std::vector<int> const & colInversePermutation) const {
std::vector<int> tmpRowind;
std::vector<int> tmpColind;
tmpRowind.reserve(rowind.capacity());
tmpColind.reserve(colind.capacity());
values.resize(0);
this->matrixPtr->getAllValues(tmpRowind, tmpColind, values);
MatrixBase<Treal, Tmatrix>::
getPermutedIndexes(tmpRowind, rowInversePermutation, rowind);
MatrixBase<Treal, Tmatrix>::
getPermutedIndexes(tmpColind, colInversePermutation, colind);
}
/**< Same as above, except taking two additional arguments
* specifying the permutation of rows and columns.
* Note, however, that this permutation is the inverse
* permutation compared to the permutations provided in the
* functions "assign_from_sparse", "add_values", and "get_values"
* @warning permutation is inverse compared to other functions
*/
#if 0
inline void fullmatrix(Treal* const full,
const int totnrows, const int totncols) const {
this->matrixPtr->fullmatrix(full, totnrows, totncols);
}
#endif
MatrixGeneral<Treal, Tmatrix>&
operator=(const MatrixGeneral<Treal, Tmatrix>& mat) {
MatrixBase<Treal, Tmatrix>::operator=(mat);
return *this;
}
inline MatrixGeneral<Treal, Tmatrix>&
operator=(const Xtrans<MatrixGeneral<Treal, Tmatrix> >& mt) {
if (mt.tA)
MatrixBase<Treal, Tmatrix>::operator=(transpose(mt.A));
else
MatrixBase<Treal, Tmatrix>::operator=(mt.A);
return *this;
}
MatrixGeneral<Treal, Tmatrix>&
operator=(const MatrixSymmetric<Treal, Tmatrix>& symm) {
MatrixBase<Treal, Tmatrix>::operator=(symm);
this->matrixPtr->symToNosym();
return *this;
}
MatrixGeneral<Treal, Tmatrix>&
operator=(const MatrixTriangular<Treal, Tmatrix>& triang) {
MatrixBase<Treal, Tmatrix>::operator=(triang);
return *this;
}
inline MatrixGeneral<Treal, Tmatrix>& operator=(int const k) {
*this->matrixPtr = k;
return *this;
}
inline Treal frob() const {
return this->matrixPtr->frob();
}
static inline Treal frob_diff
(const MatrixGeneral<Treal, Tmatrix>& A,
const MatrixGeneral<Treal, Tmatrix>& B) {
return Tmatrix::frobDiff(*A.matrixPtr, *B.matrixPtr);
}
Treal eucl(Treal const requestedAccuracy,
int maxIter = -1) const;
void thresh(Treal const threshold,
normType const norm);
inline void frob_thresh(Treal threshold) {
this->matrixPtr->frob_thresh(threshold);
}
Treal eucl_thresh(Treal const threshold);
inline void gershgorin(Treal& lmin, Treal& lmax) {
this->matrixPtr->gershgorin(lmin, lmax);
}
static inline Treal trace_ab
(const MatrixGeneral<Treal, Tmatrix>& A,
const MatrixGeneral<Treal, Tmatrix>& B) {
return Tmatrix::trace_ab(*A.matrixPtr, *B.matrixPtr);
}
static inline Treal trace_aTb
(const MatrixGeneral<Treal, Tmatrix>& A,
const MatrixGeneral<Treal, Tmatrix>& B) {
return Tmatrix::trace_aTb(*A.matrixPtr, *B.matrixPtr);
}
inline size_t nnz() const { /* Note: size_t instead of int here to avoid integer overflow. */
return this->matrixPtr->nnz();
}
inline size_t nvalues() const { /* Note: size_t instead of int here to avoid integer overflow. */
return this->matrixPtr->nvalues();
}
inline void write_to_buffer(void* buffer, const int n_bytes) const {
this->write_to_buffer_base(buffer, n_bytes, matrix_matr);
}
inline void read_from_buffer(void* buffer, const int n_bytes) {
this->read_from_buffer_base(buffer, n_bytes, matrix_matr);
}
/* OPERATIONS ONLY INVOLVING ORDINARY MATRICES */
/** C = alpha * op(A) * op(B) */
MatrixGeneral<Treal, Tmatrix>& operator=
(const XYZ<Treal,
MatrixGeneral<Treal, Tmatrix>,
MatrixGeneral<Treal, Tmatrix> >& smm);
/** C = op(A) * op(B) */
MatrixGeneral<Treal, Tmatrix>& operator=
(const XY<MatrixGeneral<Treal, Tmatrix>,
MatrixGeneral<Treal, Tmatrix> >& mm);
/** C += alpha * op(A) * op(B) */
MatrixGeneral<Treal, Tmatrix>& operator+=
(const XYZ<Treal,
MatrixGeneral<Treal, Tmatrix>,
MatrixGeneral<Treal, Tmatrix> >& smm);
/** C = alpha * op(A) * op(B) + beta * C */
MatrixGeneral<Treal, Tmatrix>& operator=
(const XYZpUV<Treal,
MatrixGeneral<Treal, Tmatrix>,
MatrixGeneral<Treal, Tmatrix>,
Treal,
MatrixGeneral<Treal, Tmatrix> >& smmpsm);
/** C = A + B */
MatrixGeneral<Treal, Tmatrix>& operator=
(XpY<MatrixGeneral<Treal, Tmatrix>,
MatrixGeneral<Treal, Tmatrix> > const & mpm);
/** B += A */
MatrixGeneral<Treal, Tmatrix>& operator+=
(MatrixGeneral<Treal, Tmatrix> const & A);
MatrixGeneral<Treal, Tmatrix>& operator-=
(MatrixGeneral<Treal, Tmatrix> const & A);
/** B += alpha * A */
MatrixGeneral<Treal, Tmatrix>& operator+=
(XY<Treal, MatrixGeneral<Treal, Tmatrix> > const & sm);
/* OPERATIONS INVOLVING SYMMETRIC MATRICES */
/** C = alpha * A * B : A is symmetric */
MatrixGeneral<Treal, Tmatrix>& operator=
(const XYZ<Treal,
MatrixSymmetric<Treal, Tmatrix>,
MatrixGeneral<Treal, Tmatrix> >& smm);
/** C = A * B : A is symmetric */
MatrixGeneral<Treal, Tmatrix>& operator=
(const XY<MatrixSymmetric<Treal, Tmatrix>,
MatrixGeneral<Treal, Tmatrix> >& mm);
/** C += alpha * A * B : A is symmetric */
MatrixGeneral<Treal, Tmatrix>& operator+=
(const XYZ<Treal,
MatrixSymmetric<Treal, Tmatrix>,
MatrixGeneral<Treal, Tmatrix> >& smm);
/** C = alpha * A * B + beta * C : A is symmetric */
MatrixGeneral<Treal, Tmatrix>& operator=
(const XYZpUV<Treal,
MatrixSymmetric<Treal, Tmatrix>,
MatrixGeneral<Treal, Tmatrix>,
Treal,
MatrixGeneral<Treal, Tmatrix> >& smmpsm);
/** C = alpha * B * A : A is symmetric */
MatrixGeneral<Treal, Tmatrix>& operator=
(const XYZ<Treal,
MatrixGeneral<Treal, Tmatrix>,
MatrixSymmetric<Treal, Tmatrix> >& smm);
/** C = B * A : A is symmetric */
MatrixGeneral<Treal, Tmatrix>& operator=
(const XY<MatrixGeneral<Treal, Tmatrix>,
MatrixSymmetric<Treal, Tmatrix> >& mm);
/** C += alpha * B * A : A is symmetric */
MatrixGeneral<Treal, Tmatrix>& operator+=
(const XYZ<Treal,
MatrixGeneral<Treal, Tmatrix>,
MatrixSymmetric<Treal, Tmatrix> >& smm);
/** C = alpha * B * A + beta * C : A is symmetric */
MatrixGeneral<Treal, Tmatrix>& operator=
(const XYZpUV<Treal,
MatrixGeneral<Treal, Tmatrix>,
MatrixSymmetric<Treal, Tmatrix>,
Treal,
MatrixGeneral<Treal, Tmatrix> >& smmpsm);
/** C = alpha * A * B : A and B are symmetric */
MatrixGeneral<Treal, Tmatrix>& operator=
(const XYZ<Treal,
MatrixSymmetric<Treal, Tmatrix>,
MatrixSymmetric<Treal, Tmatrix> >& smm);
/** C = A * B : A and B are symmetric */
MatrixGeneral<Treal, Tmatrix>& operator=
(const XY<MatrixSymmetric<Treal, Tmatrix>,
MatrixSymmetric<Treal, Tmatrix> >& mm);
/** C += alpha * A * B : A and B are symmetric */
MatrixGeneral<Treal, Tmatrix>& operator+=
(const XYZ<Treal,
MatrixSymmetric<Treal, Tmatrix>,
MatrixSymmetric<Treal, Tmatrix> >& smm);
/** C = alpha * A * B + beta * C : A and B are symmetric */
MatrixGeneral<Treal, Tmatrix>& operator=
(const XYZpUV<Treal,
MatrixSymmetric<Treal, Tmatrix>,
MatrixSymmetric<Treal, Tmatrix>,
Treal,
MatrixGeneral<Treal, Tmatrix> >& smmpsm);
/* OPERATIONS INVOLVING UPPER TRIANGULAR MATRICES */
/** B = alpha * op(A) * B : A is upper triangular */
MatrixGeneral<Treal, Tmatrix>& operator=
(const XYZ<Treal,
MatrixTriangular<Treal, Tmatrix>,
MatrixGeneral<Treal, Tmatrix> >& smm);
/** B = alpha * B * op(A) : A is upper triangular */
MatrixGeneral<Treal, Tmatrix>& operator=
(const XYZ<Treal,
MatrixGeneral<Treal, Tmatrix>,
MatrixTriangular<Treal, Tmatrix> >& smm);
void random() {
this->matrixPtr->random();
}
void randomZeroStructure(Treal probabilityBeingZero) {
this->matrixPtr->randomZeroStructure(probabilityBeingZero);
}
template<typename TRule>
void setElementsByRule(TRule & rule) {
this->matrixPtr->setElementsByRule(rule);
return;
}
std::string obj_type_id() const {return "MatrixGeneral";}
protected:
inline void writeToFileProt(std::ofstream & file) const {
this->writeToFileBase(file, matrix_matr);
}
inline void readFromFileProt(std::ifstream & file) {
this->readFromFileBase(file, matrix_matr);
}
private:
};
template<typename Treal, typename Tmatrix>
Treal MatrixGeneral<Treal, Tmatrix>::
eucl(Treal const requestedAccuracy,
int maxIter) const {
VectorType guess;
SizesAndBlocks cols;
this->getCols(cols);
guess.resetSizesAndBlocks(cols);
guess.rand();
mat::ATAMatrix<MatrixGeneral<Treal, Tmatrix>, Treal> ata(*this);
if (maxIter < 0)
maxIter = this->get_nrows() * 100;
arn::LanczosLargestMagnitudeEig
<Treal, ATAMatrix<MatrixGeneral<Treal, Tmatrix>, Treal>, VectorType>
lan(ata, guess, maxIter);
lan.setRelTol( 100 * mat::getMachineEpsilon<Treal>() );
lan.run();
Treal eVal = 0;
Treal acc = 0;
lan.getLargestMagnitudeEig(eVal, acc);
Interval<Treal> euclInt( sqrt(eVal-acc),
sqrt(eVal+acc) );
if ( euclInt.low() < 0 )
euclInt = Interval<Treal>( 0, sqrt(eVal+acc) );
if ( euclInt.length() / 2.0 > requestedAccuracy ) {
std::cout << "req: " << requestedAccuracy
<< " obt: " << euclInt.length() / 2.0 << std::endl;
throw std::runtime_error("Desired accuracy not obtained in Lanczos.");
}
return euclInt.midPoint();
}
template<typename Treal, typename Tmatrix>
void MatrixGeneral<Treal, Tmatrix>::
thresh(Treal const threshold,
normType const norm) {
switch (norm) {
case frobNorm:
this->frob_thresh(threshold);
break;
default:
throw Failure("MatrixGeneral<Treal, Tmatrix>::"
"thresh(Treal const, "
"normType const): "
"Thresholding not imlpemented for selected norm");
}
}
template<typename Treal, typename Tmatrix>
Treal MatrixGeneral<Treal, Tmatrix>::
eucl_thresh(Treal const threshold) {
EuclTruncationGeneral<MatrixGeneral<Treal, Tmatrix>, Treal> TruncObj( *this );
return TruncObj.run( threshold );
}
/* OPERATIONS ONLY INVOLVING ORDINARY MATRICES */
/* C = alpha * op(A) * op(B) */
template<typename Treal, typename Tmatrix>
MatrixGeneral<Treal, Tmatrix>&
MatrixGeneral<Treal, Tmatrix>::operator=
(const XYZ<Treal,
MatrixGeneral<Treal, Tmatrix>,
MatrixGeneral<Treal, Tmatrix> >& smm) {
assert(this != &smm.B && this != &smm.C);
this->matrixPtr.haveDataStructureSet(true);
Tmatrix::gemm(smm.tB, smm.tC, smm.A,
*smm.B.matrixPtr, *smm.C.matrixPtr,
0, *this->matrixPtr);
return *this;
}
/* C = op(A) * op(B) */
template<typename Treal, typename Tmatrix>
MatrixGeneral<Treal, Tmatrix>&
MatrixGeneral<Treal, Tmatrix>::operator=
(const XY<MatrixGeneral<Treal, Tmatrix>,
MatrixGeneral<Treal, Tmatrix> >& mm) {
assert(this != &mm.A && this != &mm.B);
Tmatrix::gemm(mm.tA, mm.tB, 1.0,
*mm.A.matrixPtr, *mm.B.matrixPtr,
0, *this->matrixPtr);
return *this;
}
/* C += alpha * op(A) * op(B) */
template<typename Treal, typename Tmatrix>
MatrixGeneral<Treal, Tmatrix>&
MatrixGeneral<Treal, Tmatrix>::operator+=
(const XYZ<Treal,
MatrixGeneral<Treal, Tmatrix>,
MatrixGeneral<Treal, Tmatrix> >& smm) {
assert(this != &smm.B && this != &smm.C);
Tmatrix::gemm(smm.tB, smm.tC, smm.A,
*smm.B.matrixPtr, *smm.C.matrixPtr,
1, *this->matrixPtr);
return *this;
}
/* C = alpha * op(A) * op(B) + beta * C */
template<typename Treal, typename Tmatrix>
MatrixGeneral<Treal, Tmatrix>&
MatrixGeneral<Treal, Tmatrix>::operator=
(const XYZpUV<Treal,
MatrixGeneral<Treal, Tmatrix>,
MatrixGeneral<Treal, Tmatrix>,
Treal,
MatrixGeneral<Treal, Tmatrix> >& smmpsm) {
assert(this != &smmpsm.B && this != &smmpsm.C);
assert(!smmpsm.tE);
if (this == &smmpsm.E)
Tmatrix::gemm(smmpsm.tB, smmpsm.tC, smmpsm.A,
*smmpsm.B.matrixPtr, *smmpsm.C.matrixPtr,
smmpsm.D, *this->matrixPtr);
else
throw Failure("MatrixGeneral<Treal, Tmatrix>::operator="
"(const XYZpUV<Treal, MatrixGeneral"
"<Treal, Tmatrix> >&) : D = alpha "
"* op(A) * op(B) + beta * C not supported for C != D");
return *this;
}
/* C = A + B */
template<typename Treal, typename Tmatrix>
inline MatrixGeneral<Treal, Tmatrix>&
MatrixGeneral<Treal, Tmatrix>::operator=
(const XpY<MatrixGeneral<Treal, Tmatrix>,
MatrixGeneral<Treal, Tmatrix> >& mpm) {
assert(this != &mpm.A);
(*this) = mpm.B;
Tmatrix::add(1.0, *mpm.A.matrixPtr, *this->matrixPtr);
return *this;
}
/* B += A */
template<typename Treal, typename Tmatrix>
inline MatrixGeneral<Treal, Tmatrix>&
MatrixGeneral<Treal, Tmatrix>::operator+=
(MatrixGeneral<Treal, Tmatrix> const & A) {
Tmatrix::add(1.0, *A.matrixPtr, *this->matrixPtr);
return *this;
}
/* B -= A */
template<typename Treal, typename Tmatrix>
inline MatrixGeneral<Treal, Tmatrix>&
MatrixGeneral<Treal, Tmatrix>::operator-=
(MatrixGeneral<Treal, Tmatrix> const & A) {
Tmatrix::add(-1.0, *A.matrixPtr, *this->matrixPtr);
return *this;
}
/* B += alpha * A */
template<typename Treal, typename Tmatrix>
inline MatrixGeneral<Treal, Tmatrix>&
MatrixGeneral<Treal, Tmatrix>::operator+=
(XY<Treal, MatrixGeneral<Treal, Tmatrix> > const & sm) {
assert(!sm.tB);
Tmatrix::add(sm.A, *sm.B.matrixPtr, *this->matrixPtr);
return *this;
}
/* OPERATIONS INVOLVING SYMMETRIC MATRICES */
/* C = alpha * A * B : A is symmetric */
template<typename Treal, typename Tmatrix>
MatrixGeneral<Treal, Tmatrix>&
MatrixGeneral<Treal, Tmatrix>::operator=
(const XYZ<Treal,
MatrixSymmetric<Treal, Tmatrix>,
MatrixGeneral<Treal, Tmatrix> >& smm) {
assert(this != &smm.C);
assert(!smm.tB && !smm.tC);
this->matrixPtr.haveDataStructureSet(true);
Tmatrix::symm('L', 'U', smm.A,
*smm.B.matrixPtr, *smm.C.matrixPtr,
0, *this->matrixPtr);
return *this;
}
/* C = A * B : A is symmetric */
template<typename Treal, typename Tmatrix>
MatrixGeneral<Treal, Tmatrix>&
MatrixGeneral<Treal, Tmatrix>::operator=
(const XY<MatrixSymmetric<Treal, Tmatrix>,
MatrixGeneral<Treal, Tmatrix> >& mm) {
assert(this != &mm.B);
assert(!mm.tB);
Tmatrix::symm('L', 'U', 1.0,
*mm.A.matrixPtr, *mm.B.matrixPtr,
0, *this->matrixPtr);
return *this;
}
/* C += alpha * A * B : A is symmetric */
template<typename Treal, typename Tmatrix>
MatrixGeneral<Treal, Tmatrix>&
MatrixGeneral<Treal, Tmatrix>::operator+=
(const XYZ<Treal,
MatrixSymmetric<Treal, Tmatrix>,
MatrixGeneral<Treal, Tmatrix> >& smm) {
assert(this != &smm.C);
assert(!smm.tB && !smm.tC);
Tmatrix::symm('L', 'U', smm.A,
*smm.B.matrixPtr, *smm.C.matrixPtr,
1, *this->matrixPtr);
return *this;
}
/* C = alpha * A * B + beta * C : A is symmetric */
template<typename Treal, typename Tmatrix>
MatrixGeneral<Treal, Tmatrix>&
MatrixGeneral<Treal, Tmatrix>::operator=
(const XYZpUV<Treal,
MatrixSymmetric<Treal, Tmatrix>,
MatrixGeneral<Treal, Tmatrix>,
Treal,
MatrixGeneral<Treal, Tmatrix> >& smmpsm) {
assert(this != &smmpsm.C);
assert(!smmpsm.tB && !smmpsm.tC && !smmpsm.tE);
if (this == &smmpsm.E)
Tmatrix::symm('L', 'U', smmpsm.A,
*smmpsm.B.matrixPtr, *smmpsm.C.matrixPtr,
smmpsm.D, *this->matrixPtr);
else
throw Failure("MatrixGeneral<Treal, Tmatrix>::operator="
"(const XYZpUV<Treal, MatrixGeneral"
"<Treal, Tmatrix>, MatrixSymmetric<Treal, "
"Tmatrix>, Treal, MatrixGeneral"
"<Treal, Tmatrix> >&) "
": D = alpha * A * B + beta * C (with A symmetric)"
" not supported for C != D");
return *this;
}
/* C = alpha * B * A : A is symmetric */
template<typename Treal, typename Tmatrix>
MatrixGeneral<Treal, Tmatrix>&
MatrixGeneral<Treal, Tmatrix>::operator=
(const XYZ<Treal,
MatrixGeneral<Treal, Tmatrix>,
MatrixSymmetric<Treal, Tmatrix> >& smm) {
assert(this != &smm.B);
assert(!smm.tB && !smm.tC);
this->matrixPtr.haveDataStructureSet(true);
Tmatrix::symm('R', 'U', smm.A,
*smm.C.matrixPtr, *smm.B.matrixPtr,
0, *this->matrixPtr);
return *this;
}
/* C = B * A : A is symmetric */
template<typename Treal, typename Tmatrix>
MatrixGeneral<Treal, Tmatrix>&
MatrixGeneral<Treal, Tmatrix>::operator=
(const XY<MatrixGeneral<Treal, Tmatrix>,
MatrixSymmetric<Treal, Tmatrix> >& mm) {
assert(this != &mm.A);
assert(!mm.tA && !mm.tB);
Tmatrix::symm('R', 'U', 1.0,
*mm.B.matrixPtr, *mm.A.matrixPtr,
0, *this->matrixPtr);
return *this;
}
/* C += alpha * B * A : A is symmetric */
template<typename Treal, typename Tmatrix>
MatrixGeneral<Treal, Tmatrix>&
MatrixGeneral<Treal, Tmatrix>::operator+=
(const XYZ<Treal,
MatrixGeneral<Treal, Tmatrix>,
MatrixSymmetric<Treal, Tmatrix> >& smm) {
assert(this != &smm.B);
assert(!smm.tB && !smm.tC);
Tmatrix::symm('R', 'U', smm.A,
*smm.C.matrixPtr, *smm.B.matrixPtr,
1, *this->matrixPtr);
return *this;
}
/* C = alpha * B * A + beta * C : A is symmetric */
template<typename Treal, typename Tmatrix>
MatrixGeneral<Treal, Tmatrix>&
MatrixGeneral<Treal, Tmatrix>::operator=
(const XYZpUV<Treal,
MatrixGeneral<Treal, Tmatrix>,
MatrixSymmetric<Treal, Tmatrix>,
Treal,
MatrixGeneral<Treal, Tmatrix> >& smmpsm) {
assert(this != &smmpsm.B);
assert(!smmpsm.tB && !smmpsm.tC && !smmpsm.tE);
if (this == &smmpsm.E)
Tmatrix::symm('R', 'U', smmpsm.A,
*smmpsm.C.matrixPtr, *smmpsm.B.matrixPtr,
smmpsm.D, *this->matrixPtr);
else
throw Failure("MatrixGeneral<Treal, Tmatrix>::operator="
"(const XYZpUV<Treal, MatrixSymmetric"
"<Treal, Tmatrix>, MatrixGeneral<Treal, "
"Tmatrix>, Treal, MatrixGeneral"
"<Treal, Tmatrix> >&) "
": D = alpha * B * A + beta * C (with A symmetric)"
" not supported for C != D");
return *this;
}
/** C = alpha * A * B : A and B are symmetric */
template<typename Treal, typename Tmatrix>
MatrixGeneral<Treal, Tmatrix>&
MatrixGeneral<Treal, Tmatrix>::operator=
(const XYZ<Treal,
MatrixSymmetric<Treal, Tmatrix>,
MatrixSymmetric<Treal, Tmatrix> >& smm) {
assert(!smm.tB && !smm.tC);
this->matrixPtr.haveDataStructureSet(true);
Tmatrix::ssmm(smm.A,
*smm.B.matrixPtr,
*smm.C.matrixPtr,
0,
*this->matrixPtr);
return *this;
}
/** C = A * B : A and B are symmetric */
template<typename Treal, typename Tmatrix>
MatrixGeneral<Treal, Tmatrix>&
MatrixGeneral<Treal, Tmatrix>::operator=
(const XY<MatrixSymmetric<Treal, Tmatrix>,
MatrixSymmetric<Treal, Tmatrix> >& mm) {
assert(!mm.tB);
Tmatrix::ssmm(1.0,
*mm.A.matrixPtr,
*mm.B.matrixPtr,
0,
*this->matrixPtr);
return *this;
}
/** C += alpha * A * B : A and B are symmetric */
template<typename Treal, typename Tmatrix>
MatrixGeneral<Treal, Tmatrix>&
MatrixGeneral<Treal, Tmatrix>::operator+=
(const XYZ<Treal,
MatrixSymmetric<Treal, Tmatrix>,
MatrixSymmetric<Treal, Tmatrix> >& smm) {
assert(!smm.tB && !smm.tC);
Tmatrix::ssmm(smm.A,
*smm.B.matrixPtr,
*smm.C.matrixPtr,
1,
*this->matrixPtr);
return *this;
}
/** C = alpha * A * B + beta * C : A and B are symmetric */
template<typename Treal, typename Tmatrix>
MatrixGeneral<Treal, Tmatrix>&
MatrixGeneral<Treal, Tmatrix>::operator=
(const XYZpUV<Treal,
MatrixSymmetric<Treal, Tmatrix>,
MatrixSymmetric<Treal, Tmatrix>,
Treal,
MatrixGeneral<Treal, Tmatrix> >& smmpsm) {
assert(!smmpsm.tB && !smmpsm.tC && !smmpsm.tE);
if (this == &smmpsm.E)
Tmatrix::ssmm(smmpsm.A,
*smmpsm.B.matrixPtr,
*smmpsm.C.matrixPtr,
smmpsm.D,
*this->matrixPtr);
else
throw Failure("MatrixGeneral<Treal, Tmatrix>::"
"operator=(const XYZpUV<"
"Treal, MatrixSymmetric<Treal, Tmatrix>, "
"MatrixSymmetric<Treal, Tmatrix>, Treal, "
"MatrixGeneral<Treal, Tmatrix> >&) "
": D = alpha * A * B + beta * C (with A and B symmetric)"
" not supported for C != D");
return *this;
}
/* OPERATIONS INVOLVING UPPER TRIANGULAR MATRICES */
/* B = alpha * op(A) * B : A is upper triangular */
template<typename Treal, typename Tmatrix>
MatrixGeneral<Treal, Tmatrix>&
MatrixGeneral<Treal, Tmatrix>::operator=
(const XYZ<Treal,
MatrixTriangular<Treal, Tmatrix>,
MatrixGeneral<Treal, Tmatrix> >& smm) {
assert(!smm.tC);
if (this == &smm.C)
Tmatrix::trmm('L', 'U', smm.tB, smm.A,
*smm.B.matrixPtr, *this->matrixPtr);
else
throw Failure("MatrixGeneral<Treal, Tmatrix>::operator="
"(const XYZ<Treal, MatrixTriangular"
"<Treal, Tmatrix>, MatrixGeneral<Treal,"
" Tmatrix> >& : D = alpha * op(A) * B (with"
" A upper triangular) not supported for B != D");
return *this;
}
/* A = alpha * A * op(B) : B is upper triangular */
template<typename Treal, typename Tmatrix>
MatrixGeneral<Treal, Tmatrix>&
MatrixGeneral<Treal, Tmatrix>::operator=
(const XYZ<Treal,
MatrixGeneral<Treal, Tmatrix>,
MatrixTriangular<Treal, Tmatrix> >& smm) {
assert(!smm.tB);
if (this == &smm.B)
Tmatrix::trmm('R', 'U', smm.tC, smm.A,
*smm.C.matrixPtr, *this->matrixPtr);
else
throw Failure("MatrixGeneral<Treal, Tmatrix>::operator="
"(const XYZ<Treal, MatrixGeneral"
"<Treal, Tmatrix>, MatrixTriangular<Treal,"
" Tmatrix> >& : D = alpha * A * op(B) (with"
" B upper triangular) not supported for A != D");
return *this;
}
/******* FUNCTIONS DECLARED OUTSIDE CLASS */
template<typename Treal, typename Tmatrix>
Treal trace(const XYZ<Treal,
MatrixGeneral<Treal, Tmatrix>,
MatrixGeneral<Treal, Tmatrix> >& smm) {
if ((!smm.tB && !smm.tC) || (smm.tB && smm.tC))
return smm.A * MatrixGeneral<Treal, Tmatrix>::
trace_ab(smm.B, smm.C);
else if (smm.tB)
return smm.A * MatrixGeneral<Treal, Tmatrix>::
trace_aTb(smm.B, smm.C);
else
return smm.A * MatrixGeneral<Treal, Tmatrix>::
trace_aTb(smm.C, smm.B);
}
} /* end namespace mat */
#endif
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