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/*
Copyright (C) 2000, 2001, 2002, 2003 RiskMap srl
Copyright (C) 2003, 2004, 2005, 2006 StatPro Italia srl
Copyright (C) 2003, 2004 Ferdinando Ametrano
This file is part of QuantLib, a free-software/open-source library
for financial quantitative analysts and developers - http://quantlib.org/
QuantLib is free software: you can redistribute it and/or modify it
under the terms of the QuantLib license. You should have received a
copy of the license along with this program; if not, please email
<quantlib-dev@lists.sf.net>. The license is also available online at
<http://quantlib.org/license.shtml>.
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 license for more details.
*/
/*! \file matrix.hpp
\brief matrix used in linear algebra.
*/
#ifndef quantlib_matrix_hpp
#define quantlib_matrix_hpp
#include <ql/math/array.hpp>
#include <ql/utilities/steppingiterator.hpp>
namespace QuantLib {
//! %Matrix used in linear algebra.
/*! This class implements the concept of Matrix as used in linear
algebra. As such, it is <b>not</b> meant to be used as a
container.
*/
class Matrix {
public:
//! \name Constructors, destructor, and assignment
//@{
//! creates a null matrix
Matrix();
//! creates a matrix with the given dimensions
Matrix(Size rows, Size columns);
//! creates the matrix and fills it with <tt>value</tt>
Matrix(Size rows, Size columns, Real value);
Matrix(const Matrix&);
Matrix(const Disposable<Matrix>&);
Matrix& operator=(const Matrix&);
Matrix& operator=(const Disposable<Matrix>&);
//@}
//! \name Algebraic operators
/*! \pre all matrices involved in an algebraic expression must have
the same size.
*/
//@{
const Matrix& operator+=(const Matrix&);
const Matrix& operator-=(const Matrix&);
const Matrix& operator*=(Real);
const Matrix& operator/=(Real);
//@}
typedef Real* iterator;
typedef const Real* const_iterator;
typedef boost::reverse_iterator<iterator> reverse_iterator;
typedef boost::reverse_iterator<const_iterator> const_reverse_iterator;
typedef Real* row_iterator;
typedef const Real* const_row_iterator;
typedef boost::reverse_iterator<row_iterator> reverse_row_iterator;
typedef boost::reverse_iterator<const_row_iterator>
const_reverse_row_iterator;
typedef step_iterator<iterator> column_iterator;
typedef step_iterator<const_iterator> const_column_iterator;
typedef boost::reverse_iterator<column_iterator>
reverse_column_iterator;
typedef boost::reverse_iterator<const_column_iterator>
const_reverse_column_iterator;
//! \name Iterator access
//@{
const_iterator begin() const;
iterator begin();
const_iterator end() const;
iterator end();
const_reverse_iterator rbegin() const;
reverse_iterator rbegin();
const_reverse_iterator rend() const;
reverse_iterator rend();
const_row_iterator row_begin(Size i) const;
row_iterator row_begin(Size i);
const_row_iterator row_end(Size i) const;
row_iterator row_end(Size i);
const_reverse_row_iterator row_rbegin(Size i) const;
reverse_row_iterator row_rbegin(Size i);
const_reverse_row_iterator row_rend(Size i) const;
reverse_row_iterator row_rend(Size i);
const_column_iterator column_begin(Size i) const;
column_iterator column_begin(Size i);
const_column_iterator column_end(Size i) const;
column_iterator column_end(Size i);
const_reverse_column_iterator column_rbegin(Size i) const;
reverse_column_iterator column_rbegin(Size i);
const_reverse_column_iterator column_rend(Size i) const;
reverse_column_iterator column_rend(Size i);
//@}
//! \name Element access
//@{
const_row_iterator operator[](Size) const;
const_row_iterator at(Size) const;
row_iterator operator[](Size);
row_iterator at(Size);
Disposable<Array> diagonal(void) const;
//@}
//! \name Inspectors
//@{
Size rows() const;
Size columns() const;
bool empty() const;
//@}
//! \name Utilities
//@{
void swap(Matrix&);
//@}
private:
boost::scoped_array<Real> data_;
Size rows_, columns_;
};
// algebraic operators
/*! \relates Matrix */
const Disposable<Matrix> operator+(const Matrix&, const Matrix&);
/*! \relates Matrix */
const Disposable<Matrix> operator-(const Matrix&, const Matrix&);
/*! \relates Matrix */
const Disposable<Matrix> operator*(const Matrix&, Real);
/*! \relates Matrix */
const Disposable<Matrix> operator*(Real, const Matrix&);
/*! \relates Matrix */
const Disposable<Matrix> operator/(const Matrix&, Real);
// vectorial products
/*! \relates Matrix */
const Disposable<Array> operator*(const Array&, const Matrix&);
/*! \relates Matrix */
const Disposable<Array> operator*(const Matrix&, const Array&);
/*! \relates Matrix */
const Disposable<Matrix> operator*(const Matrix&, const Matrix&);
// misc. operations
/*! \relates Matrix */
const Disposable<Matrix> transpose(const Matrix&);
/*! \relates Matrix */
const Disposable<Matrix> outerProduct(const Array& v1, const Array& v2);
/*! \relates Matrix */
template<class Iterator1, class Iterator2>
const Disposable<Matrix> outerProduct(Iterator1 v1begin, Iterator1 v1end,
Iterator2 v2begin, Iterator2 v2end);
/*! \relates Matrix */
void swap(Matrix&, Matrix&);
/*! \relates Matrix */
std::ostream& operator<<(std::ostream&, const Matrix&);
/*! \relates Matrix */
Disposable<Matrix> inverse(const Matrix& m);
/*! \relates Matrix */
Real determinant(const Matrix& m);
// inline definitions
inline Matrix::Matrix()
: data_((Real*)(0)), rows_(0), columns_(0) {}
inline Matrix::Matrix(Size rows, Size columns)
: data_(rows*columns > 0 ? new Real[rows*columns] : (Real*)(0)),
rows_(rows), columns_(columns) {}
inline Matrix::Matrix(Size rows, Size columns, Real value)
: data_(rows*columns > 0 ? new Real[rows*columns] : (Real*)(0)),
rows_(rows), columns_(columns) {
std::fill(begin(),end(),value);
}
inline Matrix::Matrix(const Matrix& from)
: data_(!from.empty() ? new Real[from.rows_*from.columns_] : (Real*)(0)),
rows_(from.rows_), columns_(from.columns_) {
#if defined(QL_PATCH_MSVC) && defined(QL_DEBUG)
if (!from.empty())
#endif
std::copy(from.begin(),from.end(),begin());
}
inline Matrix::Matrix(const Disposable<Matrix>& from)
: data_((Real*)(0)), rows_(0), columns_(0) {
swap(const_cast<Disposable<Matrix>&>(from));
}
inline Matrix& Matrix::operator=(const Matrix& from) {
// strong guarantee
Matrix temp(from);
swap(temp);
return *this;
}
inline Matrix& Matrix::operator=(const Disposable<Matrix>& from) {
swap(const_cast<Disposable<Matrix>&>(from));
return *this;
}
inline void Matrix::swap(Matrix& from) {
using std::swap;
data_.swap(from.data_);
swap(rows_,from.rows_);
swap(columns_,from.columns_);
}
inline const Matrix& Matrix::operator+=(const Matrix& m) {
QL_REQUIRE(rows_ == m.rows_ && columns_ == m.columns_,
"matrices with different sizes (" <<
m.rows_ << "x" << m.columns_ << ", " <<
rows_ << "x" << columns_ << ") cannot be "
"added");
std::transform(begin(),end(),m.begin(),
begin(),std::plus<Real>());
return *this;
}
inline const Matrix& Matrix::operator-=(const Matrix& m) {
QL_REQUIRE(rows_ == m.rows_ && columns_ == m.columns_,
"matrices with different sizes (" <<
m.rows_ << "x" << m.columns_ << ", " <<
rows_ << "x" << columns_ << ") cannot be "
"subtracted");
std::transform(begin(),end(),m.begin(),begin(),
std::minus<Real>());
return *this;
}
inline const Matrix& Matrix::operator*=(Real x) {
std::transform(begin(),end(),begin(),
std::bind2nd(std::multiplies<Real>(),x));
return *this;
}
inline const Matrix& Matrix::operator/=(Real x) {
std::transform(begin(),end(),begin(),
std::bind2nd(std::divides<Real>(),x));
return *this;
}
inline Matrix::const_iterator Matrix::begin() const {
return data_.get();
}
inline Matrix::iterator Matrix::begin() {
return data_.get();
}
inline Matrix::const_iterator Matrix::end() const {
return data_.get()+rows_*columns_;
}
inline Matrix::iterator Matrix::end() {
return data_.get()+rows_*columns_;
}
inline Matrix::const_reverse_iterator Matrix::rbegin() const {
return const_reverse_iterator(end());
}
inline Matrix::reverse_iterator Matrix::rbegin() {
return reverse_iterator(end());
}
inline Matrix::const_reverse_iterator Matrix::rend() const {
return const_reverse_iterator(begin());
}
inline Matrix::reverse_iterator Matrix::rend() {
return reverse_iterator(begin());
}
inline Matrix::const_row_iterator
Matrix::row_begin(Size i) const {
#if defined(QL_EXTRA_SAFETY_CHECKS)
QL_REQUIRE(i<rows_,
"row index (" << i << ") must be less than " << rows_ <<
": matrix cannot be accessed out of range");
#endif
return data_.get()+columns_*i;
}
inline Matrix::row_iterator Matrix::row_begin(Size i) {
#if defined(QL_EXTRA_SAFETY_CHECKS)
QL_REQUIRE(i<rows_,
"row index (" << i << ") must be less than " << rows_ <<
": matrix cannot be accessed out of range");
#endif
return data_.get()+columns_*i;
}
inline Matrix::const_row_iterator Matrix::row_end(Size i) const{
#if defined(QL_EXTRA_SAFETY_CHECKS)
QL_REQUIRE(i<rows_,
"row index (" << i << ") must be less than " << rows_ <<
": matrix cannot be accessed out of range");
#endif
return data_.get()+columns_*(i+1);
}
inline Matrix::row_iterator Matrix::row_end(Size i) {
#if defined(QL_EXTRA_SAFETY_CHECKS)
QL_REQUIRE(i<rows_,
"row index (" << i << ") must be less than " << rows_ <<
": matrix cannot be accessed out of range");
#endif
return data_.get()+columns_*(i+1);
}
inline Matrix::const_reverse_row_iterator
Matrix::row_rbegin(Size i) const {
return const_reverse_row_iterator(row_end(i));
}
inline Matrix::reverse_row_iterator Matrix::row_rbegin(Size i) {
return reverse_row_iterator(row_end(i));
}
inline Matrix::const_reverse_row_iterator
Matrix::row_rend(Size i) const {
return const_reverse_row_iterator(row_begin(i));
}
inline Matrix::reverse_row_iterator Matrix::row_rend(Size i) {
return reverse_row_iterator(row_begin(i));
}
inline Matrix::const_column_iterator
Matrix::column_begin(Size i) const {
#if defined(QL_EXTRA_SAFETY_CHECKS)
QL_REQUIRE(i<columns_,
"column index (" << i << ") must be less than " << columns_ <<
": matrix cannot be accessed out of range");
#endif
return const_column_iterator(data_.get()+i,columns_);
}
inline Matrix::column_iterator Matrix::column_begin(Size i) {
#if defined(QL_EXTRA_SAFETY_CHECKS)
QL_REQUIRE(i<columns_,
"column index (" << i << ") must be less than " << columns_ <<
": matrix cannot be accessed out of range");
#endif
return column_iterator(data_.get()+i,columns_);
}
inline Matrix::const_column_iterator
Matrix::column_end(Size i) const {
#if defined(QL_EXTRA_SAFETY_CHECKS)
QL_REQUIRE(i<columns_,
"column index (" << i << ") must be less than " << columns_ <<
": matrix cannot be accessed out of range");
#endif
return const_column_iterator(data_.get()+i+rows_*columns_,columns_);
}
inline Matrix::column_iterator Matrix::column_end(Size i) {
#if defined(QL_EXTRA_SAFETY_CHECKS)
QL_REQUIRE(i<columns_,
"column index (" << i << ") must be less than " << columns_ <<
": matrix cannot be accessed out of range");
#endif
return column_iterator(data_.get()+i+rows_*columns_,columns_);
}
inline Matrix::const_reverse_column_iterator
Matrix::column_rbegin(Size i) const {
return const_reverse_column_iterator(column_end(i));
}
inline Matrix::reverse_column_iterator
Matrix::column_rbegin(Size i) {
return reverse_column_iterator(column_end(i));
}
inline Matrix::const_reverse_column_iterator
Matrix::column_rend(Size i) const {
return const_reverse_column_iterator(column_begin(i));
}
inline Matrix::reverse_column_iterator
Matrix::column_rend(Size i) {
return reverse_column_iterator(column_begin(i));
}
inline Matrix::const_row_iterator
Matrix::operator[](Size i) const {
return row_begin(i);
}
inline Matrix::const_row_iterator
Matrix::at(Size i) const {
QL_REQUIRE(i < rows_, "matrix access out of range");
return row_begin(i);
}
inline Matrix::row_iterator Matrix::operator[](Size i) {
return row_begin(i);
}
inline Matrix::row_iterator Matrix::at(Size i) {
QL_REQUIRE(i < rows_, "matrix access out of range");
return row_begin(i);
}
inline Disposable<Array> Matrix::diagonal(void) const{
Size arraySize = std::min<Size>(rows(), columns());
Array tmp(arraySize);
for(Size i = 0; i < arraySize; i++)
tmp[i] = (*this)[i][i];
return tmp;
}
inline Size Matrix::rows() const {
return rows_;
}
inline Size Matrix::columns() const {
return columns_;
}
inline bool Matrix::empty() const {
return rows_ == 0 || columns_ == 0;
}
inline const Disposable<Matrix> operator+(const Matrix& m1,
const Matrix& m2) {
QL_REQUIRE(m1.rows() == m2.rows() &&
m1.columns() == m2.columns(),
"matrices with different sizes (" <<
m1.rows() << "x" << m1.columns() << ", " <<
m2.rows() << "x" << m2.columns() << ") cannot be "
"added");
Matrix temp(m1.rows(),m1.columns());
std::transform(m1.begin(),m1.end(),m2.begin(),temp.begin(),
std::plus<Real>());
return temp;
}
inline const Disposable<Matrix> operator-(const Matrix& m1,
const Matrix& m2) {
QL_REQUIRE(m1.rows() == m2.rows() &&
m1.columns() == m2.columns(),
"matrices with different sizes (" <<
m1.rows() << "x" << m1.columns() << ", " <<
m2.rows() << "x" << m2.columns() << ") cannot be "
"subtracted");
Matrix temp(m1.rows(),m1.columns());
std::transform(m1.begin(),m1.end(),m2.begin(),temp.begin(),
std::minus<Real>());
return temp;
}
inline const Disposable<Matrix> operator*(const Matrix& m, Real x) {
Matrix temp(m.rows(),m.columns());
std::transform(m.begin(),m.end(),temp.begin(),
std::bind2nd(std::multiplies<Real>(),x));
return temp;
}
inline const Disposable<Matrix> operator*(Real x, const Matrix& m) {
Matrix temp(m.rows(),m.columns());
std::transform(m.begin(),m.end(),temp.begin(),
std::bind2nd(std::multiplies<Real>(),x));
return temp;
}
inline const Disposable<Matrix> operator/(const Matrix& m, Real x) {
Matrix temp(m.rows(),m.columns());
std::transform(m.begin(),m.end(),temp.begin(),
std::bind2nd(std::divides<Real>(),x));
return temp;
}
inline const Disposable<Array> operator*(const Array& v, const Matrix& m) {
QL_REQUIRE(v.size() == m.rows(),
"vectors and matrices with different sizes ("
<< v.size() << ", " << m.rows() << "x" << m.columns() <<
") cannot be multiplied");
Array result(m.columns());
for (Size i=0; i<result.size(); i++)
result[i] =
std::inner_product(v.begin(),v.end(),
m.column_begin(i),0.0);
return result;
}
inline const Disposable<Array> operator*(const Matrix& m, const Array& v) {
QL_REQUIRE(v.size() == m.columns(),
"vectors and matrices with different sizes ("
<< v.size() << ", " << m.rows() << "x" << m.columns() <<
") cannot be multiplied");
Array result(m.rows());
for (Size i=0; i<result.size(); i++)
result[i] =
std::inner_product(v.begin(),v.end(),m.row_begin(i),0.0);
return result;
}
inline const Disposable<Matrix> operator*(const Matrix& m1,
const Matrix& m2) {
QL_REQUIRE(m1.columns() == m2.rows(),
"matrices with different sizes (" <<
m1.rows() << "x" << m1.columns() << ", " <<
m2.rows() << "x" << m2.columns() << ") cannot be "
"multiplied");
Matrix result(m1.rows(),m2.columns());
for (Size i=0; i<result.rows(); i++)
for (Size j=0; j<result.columns(); j++)
result[i][j] =
std::inner_product(m1.row_begin(i), m1.row_end(i),
m2.column_begin(j), 0.0);
return result;
}
inline const Disposable<Matrix> transpose(const Matrix& m) {
Matrix result(m.columns(),m.rows());
#if defined(QL_PATCH_MSVC) && defined(QL_DEBUG)
if (!m.empty())
#endif
for (Size i=0; i<m.rows(); i++)
std::copy(m.row_begin(i),m.row_end(i),result.column_begin(i));
return result;
}
inline const Disposable<Matrix> outerProduct(const Array& v1,
const Array& v2) {
return outerProduct(v1.begin(), v1.end(), v2.begin(), v2.end());
}
template<class Iterator1, class Iterator2>
inline const Disposable<Matrix> outerProduct(Iterator1 v1begin,
Iterator1 v1end,
Iterator2 v2begin,
Iterator2 v2end) {
Size size1 = std::distance(v1begin, v1end);
QL_REQUIRE(size1>0, "null first vector");
Size size2 = std::distance(v2begin, v2end);
QL_REQUIRE(size2>0, "null second vector");
Matrix result(size1, size2);
for (Size i=0; v1begin!=v1end; i++, v1begin++)
std::transform(v2begin, v2end, result.row_begin(i),
std::bind1st(std::multiplies<Real>(), *v1begin));
return result;
}
inline void swap(Matrix& m1, Matrix& m2) {
m1.swap(m2);
}
inline std::ostream& operator<<(std::ostream& out, const Matrix& m) {
std::streamsize width = out.width();
for (Size i=0; i<m.rows(); i++) {
out << "| ";
for (Size j=0; j<m.columns(); j++)
out << std::setw(int(width)) << m[i][j] << " ";
out << "|\n";
}
return out;
}
}
#endif
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