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V2.1.0 1. add thirdparty 2. delete src 3. add example_JointCtrl 4. add armModel 5. add comments
2022-11-15 16:05:20 +08:00
// $Id: Array.hh 249 2008-11-20 09:58:23Z schaerf $
// This file is part of EasyLocalpp: a C++ Object-Oriented framework
// aimed at easing the development of Local Search algorithms.
// Copyright (C) 2001--2008 Andrea Schaerf, Luca Di Gaspero.
//
// This software may be modified and distributed under the terms
// of the MIT license. See the LICENSE file for details.
#if !defined(_ARRAY_HH)
#define _ARRAY_HH
#include <set>
#include <stdexcept>
#include <iostream>
#include <iomanip>
#include <cmath>
#include <cstdlib>
namespace quadprogpp {
enum MType { DIAG };
template <typename T>
class Vector
{
public:
Vector();
Vector(const unsigned int n);
Vector(const T& a, const unsigned int n); //initialize to constant value
Vector(const T* a, const unsigned int n); // Initialize to array
Vector(const Vector &rhs); // copy constructor
~Vector(); // destructor
inline void set(const T* a, const unsigned int n);
Vector<T> extract(const std::set<unsigned int>& indexes) const;
inline T& operator[](const unsigned int& i); //i-th element
inline const T& operator[](const unsigned int& i) const;
inline unsigned int size() const;
inline void resize(const unsigned int n);
inline void resize(const T& a, const unsigned int n);
Vector<T>& operator=(const Vector<T>& rhs); //assignment
Vector<T>& operator=(const T& a); //assign a to every element
inline Vector<T>& operator+=(const Vector<T>& rhs);
inline Vector<T>& operator-=(const Vector<T>& rhs);
inline Vector<T>& operator*=(const Vector<T>& rhs);
inline Vector<T>& operator/=(const Vector<T>& rhs);
inline Vector<T>& operator^=(const Vector<T>& rhs);
inline Vector<T>& operator+=(const T& a);
inline Vector<T>& operator-=(const T& a);
inline Vector<T>& operator*=(const T& a);
inline Vector<T>& operator/=(const T& a);
inline Vector<T>& operator^=(const T& a);
private:
unsigned int n; // size of array. upper index is n-1
T* v; // storage for data
};
template <typename T>
Vector<T>::Vector()
: n(0), v(0)
{}
template <typename T>
Vector<T>::Vector(const unsigned int n)
: v(new T[n])
{
this->n = n;
}
template <typename T>
Vector<T>::Vector(const T& a, const unsigned int n)
: v(new T[n])
{
this->n = n;
for (unsigned int i = 0; i < n; i++)
v[i] = a;
}
template <typename T>
Vector<T>::Vector(const T* a, const unsigned int n)
: v(new T[n])
{
this->n = n;
for (unsigned int i = 0; i < n; i++)
v[i] = *a++;
}
template <typename T>
Vector<T>::Vector(const Vector<T>& rhs)
: v(new T[rhs.n])
{
this->n = rhs.n;
for (unsigned int i = 0; i < n; i++)
v[i] = rhs[i];
}
template <typename T>
Vector<T>::~Vector()
{
if (v != 0)
delete[] (v);
}
template <typename T>
void Vector<T>::resize(const unsigned int n)
{
if (n == this->n)
return;
if (v != 0)
delete[] (v);
v = new T[n];
this->n = n;
}
template <typename T>
void Vector<T>::resize(const T& a, const unsigned int n)
{
resize(n);
for (unsigned int i = 0; i < n; i++)
v[i] = a;
}
template <typename T>
inline Vector<T>& Vector<T>::operator=(const Vector<T>& rhs)
// postcondition: normal assignment via copying has been performed;
// if vector and rhs were different sizes, vector
// has been resized to match the size of rhs
{
if (this != &rhs)
{
resize(rhs.n);
for (unsigned int i = 0; i < n; i++)
v[i] = rhs[i];
}
return *this;
}
template <typename T>
inline Vector<T> & Vector<T>::operator=(const T& a) //assign a to every element
{
for (unsigned int i = 0; i < n; i++)
v[i] = a;
return *this;
}
template <typename T>
inline T & Vector<T>::operator[](const unsigned int& i) //subscripting
{
return v[i];
}
template <typename T>
inline const T& Vector<T>::operator[](const unsigned int& i) const //subscripting
{
return v[i];
}
template <typename T>
inline unsigned int Vector<T>::size() const
{
return n;
}
template <typename T>
inline void Vector<T>::set(const T* a, unsigned int n)
{
resize(n);
for (unsigned int i = 0; i < n; i++)
v[i] = a[i];
}
template <typename T>
inline Vector<T> Vector<T>::extract(const std::set<unsigned int>& indexes) const
{
Vector<T> tmp(indexes.size());
unsigned int i = 0;
for (std::set<unsigned int>::const_iterator el = indexes.begin(); el != indexes.end(); el++)
{
if (*el >= n)
throw std::logic_error("Error extracting subvector: the indexes are out of vector bounds");
tmp[i++] = v[*el];
}
return tmp;
}
template <typename T>
inline Vector<T>& Vector<T>::operator+=(const Vector<T>& rhs)
{
if (this->size() != rhs.size())
throw std::logic_error("Operator+=: vectors have different sizes");
for (unsigned int i = 0; i < n; i++)
v[i] += rhs[i];
return *this;
}
template <typename T>
inline Vector<T>& Vector<T>::operator+=(const T& a)
{
for (unsigned int i = 0; i < n; i++)
v[i] += a;
return *this;
}
template <typename T>
inline Vector<T> operator+(const Vector<T>& rhs)
{
return rhs;
}
template <typename T>
inline Vector<T> operator+(const Vector<T>& lhs, const Vector<T>& rhs)
{
if (lhs.size() != rhs.size())
throw std::logic_error("Operator+: vectors have different sizes");
Vector<T> tmp(lhs.size());
for (unsigned int i = 0; i < lhs.size(); i++)
tmp[i] = lhs[i] + rhs[i];
return tmp;
}
template <typename T>
inline Vector<T> operator+(const Vector<T>& lhs, const T& a)
{
Vector<T> tmp(lhs.size());
for (unsigned int i = 0; i < lhs.size(); i++)
tmp[i] = lhs[i] + a;
return tmp;
}
template <typename T>
inline Vector<T> operator+(const T& a, const Vector<T>& rhs)
{
Vector<T> tmp(rhs.size());
for (unsigned int i = 0; i < rhs.size(); i++)
tmp[i] = a + rhs[i];
return tmp;
}
template <typename T>
inline Vector<T>& Vector<T>::operator-=(const Vector<T>& rhs)
{
if (this->size() != rhs.size())
throw std::logic_error("Operator-=: vectors have different sizes");
for (unsigned int i = 0; i < n; i++)
v[i] -= rhs[i];
return *this;
}
template <typename T>
inline Vector<T>& Vector<T>::operator-=(const T& a)
{
for (unsigned int i = 0; i < n; i++)
v[i] -= a;
return *this;
}
template <typename T>
inline Vector<T> operator-(const Vector<T>& rhs)
{
return (T)(-1) * rhs;
}
template <typename T>
inline Vector<T> operator-(const Vector<T>& lhs, const Vector<T>& rhs)
{
if (lhs.size() != rhs.size())
throw std::logic_error("Operator-: vectors have different sizes");
Vector<T> tmp(lhs.size());
for (unsigned int i = 0; i < lhs.size(); i++)
tmp[i] = lhs[i] - rhs[i];
return tmp;
}
template <typename T>
inline Vector<T> operator-(const Vector<T>& lhs, const T& a)
{
Vector<T> tmp(lhs.size());
for (unsigned int i = 0; i < lhs.size(); i++)
tmp[i] = lhs[i] - a;
return tmp;
}
template <typename T>
inline Vector<T> operator-(const T& a, const Vector<T>& rhs)
{
Vector<T> tmp(rhs.size());
for (unsigned int i = 0; i < rhs.size(); i++)
tmp[i] = a - rhs[i];
return tmp;
}
template <typename T>
inline Vector<T>& Vector<T>::operator*=(const Vector<T>& rhs)
{
if (this->size() != rhs.size())
throw std::logic_error("Operator*=: vectors have different sizes");
for (unsigned int i = 0; i < n; i++)
v[i] *= rhs[i];
return *this;
}
template <typename T>
inline Vector<T>& Vector<T>::operator*=(const T& a)
{
for (unsigned int i = 0; i < n; i++)
v[i] *= a;
return *this;
}
template <typename T>
inline Vector<T> operator*(const Vector<T>& lhs, const Vector<T>& rhs)
{
if (lhs.size() != rhs.size())
throw std::logic_error("Operator*: vectors have different sizes");
Vector<T> tmp(lhs.size());
for (unsigned int i = 0; i < lhs.size(); i++)
tmp[i] = lhs[i] * rhs[i];
return tmp;
}
template <typename T>
inline Vector<T> operator*(const Vector<T>& lhs, const T& a)
{
Vector<T> tmp(lhs.size());
for (unsigned int i = 0; i < lhs.size(); i++)
tmp[i] = lhs[i] * a;
return tmp;
}
template <typename T>
inline Vector<T> operator*(const T& a, const Vector<T>& rhs)
{
Vector<T> tmp(rhs.size());
for (unsigned int i = 0; i < rhs.size(); i++)
tmp[i] = a * rhs[i];
return tmp;
}
template <typename T>
inline Vector<T>& Vector<T>::operator/=(const Vector<T>& rhs)
{
if (this->size() != rhs.size())
throw std::logic_error("Operator/=: vectors have different sizes");
for (unsigned int i = 0; i < n; i++)
v[i] /= rhs[i];
return *this;
}
template <typename T>
inline Vector<T>& Vector<T>::operator/=(const T& a)
{
for (unsigned int i = 0; i < n; i++)
v[i] /= a;
return *this;
}
template <typename T>
inline Vector<T> operator/(const Vector<T>& lhs, const Vector<T>& rhs)
{
if (lhs.size() != rhs.size())
throw std::logic_error("Operator/: vectors have different sizes");
Vector<T> tmp(lhs.size());
for (unsigned int i = 0; i < lhs.size(); i++)
tmp[i] = lhs[i] / rhs[i];
return tmp;
}
template <typename T>
inline Vector<T> operator/(const Vector<T>& lhs, const T& a)
{
Vector<T> tmp(lhs.size());
for (unsigned int i = 0; i < lhs.size(); i++)
tmp[i] = lhs[i] / a;
return tmp;
}
template <typename T>
inline Vector<T> operator/(const T& a, const Vector<T>& rhs)
{
Vector<T> tmp(rhs.size());
for (unsigned int i = 0; i < rhs.size(); i++)
tmp[i] = a / rhs[i];
return tmp;
}
template <typename T>
inline Vector<T> operator^(const Vector<T>& lhs, const Vector<T>& rhs)
{
if (lhs.size() != rhs.size())
throw std::logic_error("Operator^: vectors have different sizes");
Vector<T> tmp(lhs.size());
for (unsigned int i = 0; i < lhs.size(); i++)
tmp[i] = pow(lhs[i], rhs[i]);
return tmp;
}
template <typename T>
inline Vector<T> operator^(const Vector<T>& lhs, const T& a)
{
Vector<T> tmp(lhs.size());
for (unsigned int i = 0; i < lhs.size(); i++)
tmp[i] = pow(lhs[i], a);
return tmp;
}
template <typename T>
inline Vector<T> operator^(const T& a, const Vector<T>& rhs)
{
Vector<T> tmp(rhs.size());
for (unsigned int i = 0; i < rhs.size(); i++)
tmp[i] = pow(a, rhs[i]);
return tmp;
}
template <typename T>
inline Vector<T>& Vector<T>::operator^=(const Vector<T>& rhs)
{
if (this->size() != rhs.size())
throw std::logic_error("Operator^=: vectors have different sizes");
for (unsigned int i = 0; i < n; i++)
v[i] = pow(v[i], rhs[i]);
return *this;
}
template <typename T>
inline Vector<T>& Vector<T>::operator^=(const T& a)
{
for (unsigned int i = 0; i < n; i++)
v[i] = pow(v[i], a);
return *this;
}
template <typename T>
inline bool operator==(const Vector<T>& v, const Vector<T>& w)
{
if (v.size() != w.size())
throw std::logic_error("Vectors of different size are not confrontable");
for (unsigned i = 0; i < v.size(); i++)
if (v[i] != w[i])
return false;
return true;
}
template <typename T>
inline bool operator!=(const Vector<T>& v, const Vector<T>& w)
{
if (v.size() != w.size())
throw std::logic_error("Vectors of different size are not confrontable");
for (unsigned i = 0; i < v.size(); i++)
if (v[i] != w[i])
return true;
return false;
}
template <typename T>
inline bool operator<(const Vector<T>& v, const Vector<T>& w)
{
if (v.size() != w.size())
throw std::logic_error("Vectors of different size are not confrontable");
for (unsigned i = 0; i < v.size(); i++)
if (v[i] >= w[i])
return false;
return true;
}
template <typename T>
inline bool operator<=(const Vector<T>& v, const Vector<T>& w)
{
if (v.size() != w.size())
throw std::logic_error("Vectors of different size are not confrontable");
for (unsigned i = 0; i < v.size(); i++)
if (v[i] > w[i])
return false;
return true;
}
template <typename T>
inline bool operator>(const Vector<T>& v, const Vector<T>& w)
{
if (v.size() != w.size())
throw std::logic_error("Vectors of different size are not confrontable");
for (unsigned i = 0; i < v.size(); i++)
if (v[i] <= w[i])
return false;
return true;
}
template <typename T>
inline bool operator>=(const Vector<T>& v, const Vector<T>& w)
{
if (v.size() != w.size())
throw std::logic_error("Vectors of different size are not confrontable");
for (unsigned i = 0; i < v.size(); i++)
if (v[i] < w[i])
return false;
return true;
}
/**
Input/Output
*/
template <typename T>
inline std::ostream& operator<<(std::ostream& os, const Vector<T>& v)
{
os << std::endl << v.size() << std::endl;
for (unsigned int i = 0; i < v.size() - 1; i++)
os << std::setw(20) << std::setprecision(16) << v[i] << ", ";
os << std::setw(20) << std::setprecision(16) << v[v.size() - 1] << std::endl;
return os;
}
template <typename T>
std::istream& operator>>(std::istream& is, Vector<T>& v)
{
int elements;
char comma;
is >> elements;
v.resize(elements);
for (unsigned int i = 0; i < elements; i++)
is >> v[i] >> comma;
return is;
}
/**
Index utilities
*/
std::set<unsigned int> seq(unsigned int s, unsigned int e);
std::set<unsigned int> singleton(unsigned int i);
template <typename T>
class CanonicalBaseVector : public Vector<T>
{
public:
CanonicalBaseVector(unsigned int i, unsigned int n);
inline void reset(unsigned int i);
private:
unsigned int e;
};
template <typename T>
CanonicalBaseVector<T>::CanonicalBaseVector(unsigned int i, unsigned int n)
: Vector<T>((T)0, n), e(i)
{ (*this)[e] = (T)1; }
template <typename T>
inline void CanonicalBaseVector<T>::reset(unsigned int i)
{
(*this)[e] = (T)0;
e = i;
(*this)[e] = (T)1;
}
#include <stdexcept>
template <typename T>
inline T sum(const Vector<T>& v)
{
T tmp = (T)0;
for (unsigned int i = 0; i < v.size(); i++)
tmp += v[i];
return tmp;
}
template <typename T>
inline T prod(const Vector<T>& v)
{
T tmp = (T)1;
for (unsigned int i = 0; i < v.size(); i++)
tmp *= v[i];
return tmp;
}
template <typename T>
inline T mean(const Vector<T>& v)
{
T sum = (T)0;
for (unsigned int i = 0; i < v.size(); i++)
sum += v[i];
return sum / v.size();
}
template <typename T>
inline T median(const Vector<T>& v)
{
Vector<T> tmp = sort(v);
if (v.size() % 2 == 1) // it is an odd-sized vector
return tmp[v.size() / 2];
else
return 0.5 * (tmp[v.size() / 2 - 1] + tmp[v.size() / 2]);
}
template <typename T>
inline T stdev(const Vector<T>& v, bool sample_correction = false)
{
return sqrt(var(v, sample_correction));
}
template <typename T>
inline T var(const Vector<T>& v, bool sample_correction = false)
{
T sum = (T)0, ssum = (T)0;
unsigned int n = v.size();
for (unsigned int i = 0; i < n; i++)
{
sum += v[i];
ssum += (v[i] * v[i]);
}
if (!sample_correction)
return (ssum / n) - (sum / n) * (sum / n);
else
return n * ((ssum / n) - (sum / n) * (sum / n)) / (n - 1);
}
template <typename T>
inline T max(const Vector<T>& v)
{
T value = v[0];
for (unsigned int i = 1; i < v.size(); i++)
value = std::max(v[i], value);
return value;
}
template <typename T>
inline T min(const Vector<T>& v)
{
T value = v[0];
for (unsigned int i = 1; i < v.size(); i++)
value = std::min(v[i], value);
return value;
}
template <typename T>
inline unsigned int index_max(const Vector<T>& v)
{
unsigned int max = 0;
for (unsigned int i = 1; i < v.size(); i++)
if (v[i] > v[max])
max = i;
return max;
}
template <typename T>
inline unsigned int index_min(const Vector<T>& v)
{
unsigned int min = 0;
for (unsigned int i = 1; i < v.size(); i++)
if (v[i] < v[min])
min = i;
return min;
}
template <typename T>
inline T dot_prod(const Vector<T>& a, const Vector<T>& b)
{
T sum = (T)0;
if (a.size() != b.size())
throw std::logic_error("Dotprod error: the vectors are not the same size");
for (unsigned int i = 0; i < a.size(); i++)
sum += a[i] * b[i];
return sum;
}
/**
Single element mathematical functions
*/
template <typename T>
inline Vector<T> exp(const Vector<T>& v)
{
Vector<T> tmp(v.size());
for (unsigned int i = 0; i < v.size(); i++)
tmp[i] = exp(v[i]);
return tmp;
}
template <typename T>
inline Vector<T> log(const Vector<T>& v)
{
Vector<T> tmp(v.size());
for (unsigned int i = 0; i < v.size(); i++)
tmp[i] = log(v[i]);
return tmp;
}
template <typename T>
inline Vector<T> vec_sqrt(const Vector<T>& v)
{
Vector<T> tmp(v.size());
for (unsigned int i = 0; i < v.size(); i++)
tmp[i] = sqrt(v[i]);
return tmp;
}
template <typename T>
inline Vector<T> pow(const Vector<T>& v, double a)
{
Vector<T> tmp(v.size());
for (unsigned int i = 0; i < v.size(); i++)
tmp[i] = pow(v[i], a);
return tmp;
}
template <typename T>
inline Vector<T> abs(const Vector<T>& v)
{
Vector<T> tmp(v.size());
for (unsigned int i = 0; i < v.size(); i++)
tmp[i] = (T)fabs(v[i]);
return tmp;
}
template <typename T>
inline Vector<T> sign(const Vector<T>& v)
{
Vector<T> tmp(v.size());
for (unsigned int i = 0; i < v.size(); i++)
tmp[i] = v[i] > 0 ? +1 : v[i] == 0 ? 0 : -1;
return tmp;
}
template <typename T>
inline unsigned int partition(Vector<T>& v, unsigned int begin, unsigned int end)
{
unsigned int i = begin + 1, j = begin + 1;
T pivot = v[begin];
while (j <= end)
{
if (v[j] < pivot) {
std::swap(v[i], v[j]);
i++;
}
j++;
}
v[begin] = v[i - 1];
v[i - 1] = pivot;
return i - 2;
}
template <typename T>
inline void quicksort(Vector<T>& v, unsigned int begin, unsigned int end)
{
if (end > begin)
{
unsigned int index = partition(v, begin, end);
quicksort(v, begin, index);
quicksort(v, index + 2, end);
}
}
template <typename T>
inline Vector<T> sort(const Vector<T>& v)
{
Vector<T> tmp(v);
quicksort<T>(tmp, 0, tmp.size() - 1);
return tmp;
}
template <typename T>
inline Vector<double> rank(const Vector<T>& v)
{
Vector<T> tmp(v);
Vector<double> tmp_rank(0.0, v.size());
for (unsigned int i = 0; i < tmp.size(); i++)
{
unsigned int smaller = 0, equal = 0;
for (unsigned int j = 0; j < tmp.size(); j++)
if (i == j)
continue;
else
if (tmp[j] < tmp[i])
smaller++;
else if (tmp[j] == tmp[i])
equal++;
tmp_rank[i] = smaller + 1;
if (equal > 0)
{
for (unsigned int j = 1; j <= equal; j++)
tmp_rank[i] += smaller + 1 + j;
tmp_rank[i] /= (double)(equal + 1);
}
}
return tmp_rank;
}
//enum MType { DIAG };
template <typename T>
class Matrix
{
public:
Matrix(); // Default constructor
Matrix(const unsigned int n, const unsigned int m); // Construct a n x m matrix
Matrix(const T& a, const unsigned int n, const unsigned int m); // Initialize the content to constant a
Matrix(MType t, const T& a, const T& o, const unsigned int n, const unsigned int m);
Matrix(MType t, const Vector<T>& v, const T& o, const unsigned int n, const unsigned int m);
Matrix(const T* a, const unsigned int n, const unsigned int m); // Initialize to array
Matrix(const Matrix<T>& rhs); // Copy constructor
~Matrix(); // destructor
inline T* operator[](const unsigned int& i) { return v[i]; } // Subscripting: row i
inline const T* operator[](const unsigned int& i) const { return v[i]; }; // const subsctipting
inline void resize(const unsigned int n, const unsigned int m);
inline void resize(const T& a, const unsigned int n, const unsigned int m);
inline Vector<T> extractRow(const unsigned int i) const;
inline Vector<T> extractColumn(const unsigned int j) const;
inline Vector<T> extractDiag() const;
inline Matrix<T> extractRows(const std::set<unsigned int>& indexes) const;
inline Matrix<T> extractColumns(const std::set<unsigned int>& indexes) const;
inline Matrix<T> extract(const std::set<unsigned int>& r_indexes, const std::set<unsigned int>& c_indexes) const;
inline void set(const T* a, unsigned int n, unsigned int m);
inline void set(const std::set<unsigned int>& r_indexes, const std::set<unsigned int>& c_indexes, const Matrix<T>& m);
inline void setRow(const unsigned int index, const Vector<T>& v);
inline void setRow(const unsigned int index, const Matrix<T>& v);
inline void setRows(const std::set<unsigned int>& indexes, const Matrix<T>& m);
inline void setColumn(const unsigned int index, const Vector<T>& v);
inline void setColumn(const unsigned int index, const Matrix<T>& v);
inline void setColumns(const std::set<unsigned int>& indexes, const Matrix<T>& m);
inline unsigned int nrows() const { return n; } // number of rows
inline unsigned int ncols() const { return m; } // number of columns
inline Matrix<T>& operator=(const Matrix<T>& rhs); // Assignment operator
inline Matrix<T>& operator=(const T& a); // Assign to every element value a
inline Matrix<T>& operator+=(const Matrix<T>& rhs);
inline Matrix<T>& operator-=(const Matrix<T>& rhs);
inline Matrix<T>& operator*=(const Matrix<T>& rhs);
inline Matrix<T>& operator/=(const Matrix<T>& rhs);
inline Matrix<T>& operator^=(const Matrix<T>& rhs);
inline Matrix<T>& operator+=(const T& a);
inline Matrix<T>& operator-=(const T& a);
inline Matrix<T>& operator*=(const T& a);
inline Matrix<T>& operator/=(const T& a);
inline Matrix<T>& operator^=(const T& a);
inline operator Vector<T>();
private:
unsigned int n; // number of rows
unsigned int m; // number of columns
T **v; // storage for data
};
template <typename T>
Matrix<T>::Matrix()
: n(0), m(0), v(0)
{}
template <typename T>
Matrix<T>::Matrix(unsigned int n, unsigned int m)
: v(new T*[n])
{
this->n = n; this->m = m;
v[0] = new T[m * n];
for (unsigned int i = 1; i < n; i++)
v[i] = v[i - 1] + m;
}
template <typename T>
Matrix<T>::Matrix(const T& a, unsigned int n, unsigned int m)
: v(new T*[n])
{
this->n = n; this->m = m;
v[0] = new T[m * n];
for (unsigned int i = 1; i < n; i++)
v[i] = v[i - 1] + m;
for (unsigned int i = 0; i < n; i++)
for (unsigned int j = 0; j < m; j++)
v[i][j] = a;
}
template <class T>
Matrix<T>::Matrix(const T* a, unsigned int n, unsigned int m)
: v(new T*[n])
{
this->n = n; this->m = m;
v[0] = new T[m * n];
for (unsigned int i = 1; i < n; i++)
v[i] = v[i - 1] + m;
for (unsigned int i = 0; i < n; i++)
for (unsigned int j = 0; j < m; j++)
v[i][j] = *a++;
}
template <class T>
Matrix<T>::Matrix(MType t, const T& a, const T& o, unsigned int n, unsigned int m)
: v(new T*[n])
{
this->n = n; this->m = m;
v[0] = new T[m * n];
for (unsigned int i = 1; i < n; i++)
v[i] = v[i - 1] + m;
switch (t)
{
case DIAG:
for (unsigned int i = 0; i < n; i++)
for (unsigned int j = 0; j < m; j++)
if (i != j)
v[i][j] = o;
else
v[i][j] = a;
break;
default:
throw std::logic_error("Matrix type not supported");
}
}
template <class T>
Matrix<T>::Matrix(MType t, const Vector<T>& a, const T& o, unsigned int n, unsigned int m)
: v(new T*[n])
{
this->n = n; this->m = m;
v[0] = new T[m * n];
for (unsigned int i = 1; i < n; i++)
v[i] = v[i - 1] + m;
switch (t)
{
case DIAG:
for (unsigned int i = 0; i < n; i++)
for (unsigned int j = 0; j < m; j++)
if (i != j)
v[i][j] = o;
else
v[i][j] = a[i];
break;
default:
throw std::logic_error("Matrix type not supported");
}
}
template <typename T>
Matrix<T>::Matrix(const Matrix<T>& rhs)
: v(new T*[rhs.n])
{
n = rhs.n; m = rhs.m;
v[0] = new T[m * n];
for (unsigned int i = 1; i < n; i++)
v[i] = v[i - 1] + m;
for (unsigned int i = 0; i < n; i++)
for (unsigned int j = 0; j < m; j++)
v[i][j] = rhs[i][j];
}
template <typename T>
Matrix<T>::~Matrix()
{
if (v != 0) {
delete[] (v[0]);
delete[] (v);
}
}
template <typename T>
inline Matrix<T>& Matrix<T>::operator=(const Matrix<T> &rhs)
// postcondition: normal assignment via copying has been performed;
// if matrix and rhs were different sizes, matrix
// has been resized to match the size of rhs
{
if (this != &rhs)
{
resize(rhs.n, rhs.m);
for (unsigned int i = 0; i < n; i++)
for (unsigned int j = 0; j < m; j++)
v[i][j] = rhs[i][j];
}
return *this;
}
template <typename T>
inline Matrix<T>& Matrix<T>::operator=(const T& a) // assign a to every element
{
for (unsigned int i = 0; i < n; i++)
for (unsigned int j = 0; j < m; j++)
v[i][j] = a;
return *this;
}
template <typename T>
inline void Matrix<T>::resize(const unsigned int n, const unsigned int m)
{
if (n == this->n && m == this->m)
return;
if (v != 0)
{
delete[] (v[0]);
delete[] (v);
}
this->n = n; this->m = m;
v = new T*[n];
v[0] = new T[m * n];
for (unsigned int i = 1; i < n; i++)
v[i] = v[i - 1] + m;
}
template <typename T>
inline void Matrix<T>::resize(const T& a, const unsigned int n, const unsigned int m)
{
resize(n, m);
for (unsigned int i = 0; i < n; i++)
for (unsigned int j = 0; j < m; j++)
v[i][j] = a;
}
template <typename T>
inline Vector<T> Matrix<T>::extractRow(const unsigned int i) const
{
if (i >= n)
throw std::logic_error("Error in extractRow: trying to extract a row out of matrix bounds");
Vector<T> tmp(v[i], m);
return tmp;
}
template <typename T>
inline Vector<T> Matrix<T>::extractColumn(const unsigned int j) const
{
if (j >= m)
throw std::logic_error("Error in extractRow: trying to extract a row out of matrix bounds");
Vector<T> tmp(n);
for (unsigned int i = 0; i < n; i++)
tmp[i] = v[i][j];
return tmp;
}
template <typename T>
inline Vector<T> Matrix<T>::extractDiag() const
{
unsigned int d = std::min(n, m);
Vector<T> tmp(d);
for (unsigned int i = 0; i < d; i++)
tmp[i] = v[i][i];
return tmp;
}
template <typename T>
inline Matrix<T> Matrix<T>::extractRows(const std::set<unsigned int>& indexes) const
{
Matrix<T> tmp(indexes.size(), m);
unsigned int i = 0;
for (std::set<unsigned int>::const_iterator el = indexes.begin(); el != indexes.end(); el++)
{
for (unsigned int j = 0; j < m; j++)
{
if (*el >= n)
throw std::logic_error("Error extracting rows: the indexes are out of matrix bounds");
tmp[i][j] = v[*el][j];
}
i++;
}
return tmp;
}
template <typename T>
inline Matrix<T> Matrix<T>::extractColumns(const std::set<unsigned int>& indexes) const
{
Matrix<T> tmp(n, indexes.size());
unsigned int j = 0;
for (std::set<unsigned int>::const_iterator el = indexes.begin(); el != indexes.end(); el++)
{
for (unsigned int i = 0; i < n; i++)
{
if (*el >= m)
throw std::logic_error("Error extracting columns: the indexes are out of matrix bounds");
tmp[i][j] = v[i][*el];
}
j++;
}
return tmp;
}
template <typename T>
inline Matrix<T> Matrix<T>::extract(const std::set<unsigned int>& r_indexes, const std::set<unsigned int>& c_indexes) const
{
Matrix<T> tmp(r_indexes.size(), c_indexes.size());
unsigned int i = 0, j;
for (std::set<unsigned int>::const_iterator r_el = r_indexes.begin(); r_el != r_indexes.end(); r_el++)
{
if (*r_el >= n)
throw std::logic_error("Error extracting submatrix: the indexes are out of matrix bounds");
j = 0;
for (std::set<unsigned int>::const_iterator c_el = c_indexes.begin(); c_el != c_indexes.end(); c_el++)
{
if (*c_el >= m)
throw std::logic_error("Error extracting rows: the indexes are out of matrix bounds");
tmp[i][j] = v[*r_el][*c_el];
j++;
}
i++;
}
return tmp;
}
template <typename T>
inline void Matrix<T>::setRow(unsigned int i, const Vector<T>& a)
{
if (i >= n)
throw std::logic_error("Error in setRow: trying to set a row out of matrix bounds");
if (this->m != a.size())
throw std::logic_error("Error setting matrix row: ranges are not compatible");
for (unsigned int j = 0; j < ncols(); j++)
v[i][j] = a[j];
}
template <typename T>
inline void Matrix<T>::setRow(unsigned int i, const Matrix<T>& a)
{
if (i >= n)
throw std::logic_error("Error in setRow: trying to set a row out of matrix bounds");
if (this->m != a.ncols())
throw std::logic_error("Error setting matrix column: ranges are not compatible");
if (a.nrows() != 1)
throw std::logic_error("Error setting matrix column with a non-row matrix");
for (unsigned int j = 0; j < ncols(); j++)
v[i][j] = a[0][j];
}
template <typename T>
inline void Matrix<T>::setRows(const std::set<unsigned int>& indexes, const Matrix<T>& m)
{
unsigned int i = 0;
if (indexes.size() != m.nrows() || this->m != m.ncols())
throw std::logic_error("Error setting matrix rows: ranges are not compatible");
for (std::set<unsigned int>::const_iterator el = indexes.begin(); el != indexes.end(); el++)
{
for (unsigned int j = 0; j < ncols(); j++)
{
if (*el >= n)
throw std::logic_error("Error in setRows: trying to set a row out of matrix bounds");
v[*el][j] = m[i][j];
}
i++;
}
}
template <typename T>
inline void Matrix<T>::setColumn(unsigned int j, const Vector<T>& a)
{
if (j >= m)
throw std::logic_error("Error in setColumn: trying to set a column out of matrix bounds");
if (this->n != a.size())
throw std::logic_error("Error setting matrix column: ranges are not compatible");
for (unsigned int i = 0; i < nrows(); i++)
v[i][j] = a[i];
}
template <typename T>
inline void Matrix<T>::setColumn(unsigned int j, const Matrix<T>& a)
{
if (j >= m)
throw std::logic_error("Error in setColumn: trying to set a column out of matrix bounds");
if (this->n != a.nrows())
throw std::logic_error("Error setting matrix column: ranges are not compatible");
if (a.ncols() != 1)
throw std::logic_error("Error setting matrix column with a non-column matrix");
for (unsigned int i = 0; i < nrows(); i++)
v[i][j] = a[i][0];
}
template <typename T>
inline void Matrix<T>::setColumns(const std::set<unsigned int>& indexes, const Matrix<T>& a)
{
unsigned int j = 0;
if (indexes.size() != a.ncols() || this->n != a.nrows())
throw std::logic_error("Error setting matrix columns: ranges are not compatible");
for (std::set<unsigned int>::const_iterator el = indexes.begin(); el != indexes.end(); el++)
{
for (unsigned int i = 0; i < nrows(); i++)
{
if (*el >= m)
throw std::logic_error("Error in setColumns: trying to set a column out of matrix bounds");
v[i][*el] = a[i][j];
}
j++;
}
}
template <typename T>
inline void Matrix<T>::set(const std::set<unsigned int>& r_indexes, const std::set<unsigned int>& c_indexes, const Matrix<T>& a)
{
unsigned int i = 0, j;
if (c_indexes.size() != a.ncols() || r_indexes.size() != a.nrows())
throw std::logic_error("Error setting matrix elements: ranges are not compatible");
for (std::set<unsigned int>::const_iterator r_el = r_indexes.begin(); r_el != r_indexes.end(); r_el++)
{
if (*r_el >= n)
throw std::logic_error("Error in set: trying to set a row out of matrix bounds");
j = 0;
for (std::set<unsigned int>::const_iterator c_el = c_indexes.begin(); c_el != c_indexes.end(); c_el++)
{
if (*c_el >= m)
throw std::logic_error("Error in set: trying to set a column out of matrix bounds");
v[*r_el][*c_el] = a[i][j];
j++;
}
i++;
}
}
template <typename T>
inline void Matrix<T>::set(const T* a, unsigned int n, unsigned int m)
{
if (this->n != n || this->m != m)
resize(n, m);
unsigned int k = 0;
for (unsigned int i = 0; i < n; i++)
for (unsigned int j = 0; j < m; j++)
v[i][j] = a[k++];
}
template <typename T>
Matrix<T> operator+(const Matrix<T>& rhs)
{
return rhs;
}
template <typename T>
Matrix<T> operator+(const Matrix<T>& lhs, const Matrix<T>& rhs)
{
if (lhs.ncols() != rhs.ncols() || lhs.nrows() != rhs.nrows())
throw std::logic_error("Operator+: matrices have different sizes");
Matrix<T> tmp(lhs.nrows(), lhs.ncols());
for (unsigned int i = 0; i < lhs.nrows(); i++)
for (unsigned int j = 0; j < lhs.ncols(); j++)
tmp[i][j] = lhs[i][j] + rhs[i][j];
return tmp;
}
template <typename T>
Matrix<T> operator+(const Matrix<T>& lhs, const T& a)
{
Matrix<T> tmp(lhs.nrows(), lhs.ncols());
for (unsigned int i = 0; i < lhs.nrows(); i++)
for (unsigned int j = 0; j < lhs.ncols(); j++)
tmp[i][j] = lhs[i][j] + a;
return tmp;
}
template <typename T>
Matrix<T> operator+(const T& a, const Matrix<T>& rhs)
{
Matrix<T> tmp(rhs.nrows(), rhs.ncols());
for (unsigned int i = 0; i < rhs.nrows(); i++)
for (unsigned int j = 0; j < rhs.ncols(); j++)
tmp[i][j] = a + rhs[i][j];
return tmp;
}
template <typename T>
inline Matrix<T>& Matrix<T>::operator+=(const Matrix<T>& rhs)
{
if (m != rhs.ncols() || n != rhs.nrows())
throw std::logic_error("Operator+=: matrices have different sizes");
for (unsigned int i = 0; i < n; i++)
for (unsigned int j = 0; j < m; j++)
v[i][j] += rhs[i][j];
return *this;
}
template <typename T>
inline Matrix<T>& Matrix<T>::operator+=(const T& a)
{
for (unsigned int i = 0; i < n; i++)
for (unsigned int j = 0; j < m; j++)
v[i][j] += a;
return *this;
}
template <typename T>
Matrix<T> operator-(const Matrix<T>& rhs)
{
return (T)(-1) * rhs;
}
template <typename T>
Matrix<T> operator-(const Matrix<T>& lhs, const Matrix<T>& rhs)
{
if (lhs.ncols() != rhs.ncols() || lhs.nrows() != rhs.nrows())
throw std::logic_error("Operator-: matrices have different sizes");
Matrix<T> tmp(lhs.nrows(), lhs.ncols());
for (unsigned int i = 0; i < lhs.nrows(); i++)
for (unsigned int j = 0; j < lhs.ncols(); j++)
tmp[i][j] = lhs[i][j] - rhs[i][j];
return tmp;
}
template <typename T>
Matrix<T> operator-(const Matrix<T>& lhs, const T& a)
{
Matrix<T> tmp(lhs.nrows(), lhs.ncols());
for (unsigned int i = 0; i < lhs.nrows(); i++)
for (unsigned int j = 0; j < lhs.ncols(); j++)
tmp[i][j] = lhs[i][j] - a;
return tmp;
}
template <typename T>
Matrix<T> operator-(const T& a, const Matrix<T>& rhs)
{
Matrix<T> tmp(rhs.nrows(), rhs.ncols());
for (unsigned int i = 0; i < rhs.nrows(); i++)
for (unsigned int j = 0; j < rhs.ncols(); j++)
tmp[i][j] = a - rhs[i][j];
return tmp;
}
template <typename T>
inline Matrix<T>& Matrix<T>::operator-=(const Matrix<T>& rhs)
{
if (m != rhs.ncols() || n != rhs.nrows())
throw std::logic_error("Operator-=: matrices have different sizes");
for (unsigned int i = 0; i < n; i++)
for (unsigned int j = 0; j < m; j++)
v[i][j] -= rhs[i][j];
return *this;
}
template <typename T>
inline Matrix<T>& Matrix<T>::operator-=(const T& a)
{
for (unsigned int i = 0; i < n; i++)
for (unsigned int j = 0; j < m; j++)
v[i][j] -= a;
return *this;
}
template <typename T>
Matrix<T> operator*(const Matrix<T>& lhs, const Matrix<T>& rhs)
{
if (lhs.ncols() != rhs.ncols() || lhs.nrows() != rhs.nrows())
throw std::logic_error("Operator*: matrices have different sizes");
Matrix<T> tmp(lhs.nrows(), lhs.ncols());
for (unsigned int i = 0; i < lhs.nrows(); i++)
for (unsigned int j = 0; j < lhs.ncols(); j++)
tmp[i][j] = lhs[i][j] * rhs[i][j];
return tmp;
}
template <typename T>
Matrix<T> operator*(const Matrix<T>& lhs, const T& a)
{
Matrix<T> tmp(lhs.nrows(), lhs.ncols());
for (unsigned int i = 0; i < lhs.nrows(); i++)
for (unsigned int j = 0; j < lhs.ncols(); j++)
tmp[i][j] = lhs[i][j] * a;
return tmp;
}
template <typename T>
Matrix<T> operator*(const T& a, const Matrix<T>& rhs)
{
Matrix<T> tmp(rhs.nrows(), rhs.ncols());
for (unsigned int i = 0; i < rhs.nrows(); i++)
for (unsigned int j = 0; j < rhs.ncols(); j++)
tmp[i][j] = a * rhs[i][j];
return tmp;
}
template <typename T>
inline Matrix<T>& Matrix<T>::operator*=(const Matrix<T>& rhs)
{
if (m != rhs.ncols() || n != rhs.nrows())
throw std::logic_error("Operator*=: matrices have different sizes");
for (unsigned int i = 0; i < n; i++)
for (unsigned int j = 0; j < m; j++)
v[i][j] *= rhs[i][j];
return *this;
}
template <typename T>
inline Matrix<T>& Matrix<T>::operator*=(const T& a)
{
for (unsigned int i = 0; i < n; i++)
for (unsigned int j = 0; j < m; j++)
v[i][j] *= a;
return *this;
}
template <typename T>
Matrix<T> operator/(const Matrix<T>& lhs, const Matrix<T>& rhs)
{
if (lhs.ncols() != rhs.ncols() || lhs.nrows() != rhs.nrows())
throw std::logic_error("Operator+: matrices have different sizes");
Matrix<T> tmp(lhs.nrows(), lhs.ncols());
for (unsigned int i = 0; i < lhs.nrows(); i++)
for (unsigned int j = 0; j < lhs.ncols(); j++)
tmp[i][j] = lhs[i][j] / rhs[i][j];
return tmp;
}
template <typename T>
Matrix<T> operator/(const Matrix<T>& lhs, const T& a)
{
Matrix<T> tmp(lhs.nrows(), lhs.ncols());
for (unsigned int i = 0; i < lhs.nrows(); i++)
for (unsigned int j = 0; j < lhs.ncols(); j++)
tmp[i][j] = lhs[i][j] / a;
return tmp;
}
template <typename T>
Matrix<T> operator/(const T& a, const Matrix<T>& rhs)
{
Matrix<T> tmp(rhs.nrows(), rhs.ncols());
for (unsigned int i = 0; i < rhs.nrows(); i++)
for (unsigned int j = 0; j < rhs.ncols(); j++)
tmp[i][j] = a / rhs[i][j];
return tmp;
}
template <typename T>
inline Matrix<T>& Matrix<T>::operator/=(const Matrix<T>& rhs)
{
if (m != rhs.ncols() || n != rhs.nrows())
throw std::logic_error("Operator+=: matrices have different sizes");
for (unsigned int i = 0; i < n; i++)
for (unsigned int j = 0; j < m; j++)
v[i][j] /= rhs[i][j];
return *this;
}
template <typename T>
inline Matrix<T>& Matrix<T>::operator/=(const T& a)
{
for (unsigned int i = 0; i < n; i++)
for (unsigned int j = 0; j < m; j++)
v[i][j] /= a;
return *this;
}
template <typename T>
Matrix<T> operator^(const Matrix<T>& lhs, const T& a)
{
Matrix<T> tmp(lhs.nrows(), lhs.ncols());
for (unsigned int i = 0; i < lhs.nrows(); i++)
for (unsigned int j = 0; j < lhs.ncols(); j++)
tmp[i][j] = pow(lhs[i][j], a);
return tmp;
}
template <typename T>
inline Matrix<T>& Matrix<T>::operator^=(const Matrix<T>& rhs)
{
if (m != rhs.ncols() || n != rhs.nrows())
throw std::logic_error("Operator^=: matrices have different sizes");
for (unsigned int i = 0; i < n; i++)
for (unsigned int j = 0; j < m; j++)
v[i][j] = pow(v[i][j], rhs[i][j]);
return *this;
}
template <typename T>
inline Matrix<T>& Matrix<T>::operator^=(const T& a)
{
for (unsigned int i = 0; i < n; i++)
for (unsigned int j = 0; j < m; j++)
v[i][j] = pow(v[i][j], a);
return *this;
}
template <typename T>
inline Matrix<T>::operator Vector<T>()
{
if (n > 1 && m > 1)
throw std::logic_error("Error matrix cast to vector: trying to cast a multi-dimensional matrix");
if (n == 1)
return extractRow(0);
else
return extractColumn(0);
}
template <typename T>
inline bool operator==(const Matrix<T>& a, const Matrix<T>& b)
{
if (a.nrows() != b.nrows() || a.ncols() != b.ncols())
throw std::logic_error("Matrices of different size are not confrontable");
for (unsigned i = 0; i < a.nrows(); i++)
for (unsigned j = 0; j < a.ncols(); j++)
if (a[i][j] != b[i][j])
return false;
return true;
}
template <typename T>
inline bool operator!=(const Matrix<T>& a, const Matrix<T>& b)
{
if (a.nrows() != b.nrows() || a.ncols() != b.ncols())
throw std::logic_error("Matrices of different size are not confrontable");
for (unsigned i = 0; i < a.nrows(); i++)
for (unsigned j = 0; j < a.ncols(); j++)
if (a[i][j] != b[i][j])
return true;
return false;
}
/**
Input/Output
*/
template <typename T>
std::ostream& operator<<(std::ostream& os, const Matrix<T>& m)
{
os << std::endl << m.nrows() << " " << m.ncols() << std::endl;
for (unsigned int i = 0; i < m.nrows(); i++)
{
for (unsigned int j = 0; j < m.ncols() - 1; j++)
os << std::setw(20) << std::setprecision(16) << m[i][j] << ", ";
os << std::setw(20) << std::setprecision(16) << m[i][m.ncols() - 1] << std::endl;
}
return os;
}
template <typename T>
std::istream& operator>>(std::istream& is, Matrix<T>& m)
{
int rows, cols;
char comma;
is >> rows >> cols;
m.resize(rows, cols);
for (unsigned int i = 0; i < rows; i++)
for (unsigned int j = 0; j < cols; j++)
is >> m[i][j] >> comma;
return is;
}
template <typename T>
T sign(const T& v)
{
if (v >= (T)0.0)
return (T)1.0;
else
return (T)-1.0;
}
template <typename T>
T dist(const T& a, const T& b)
{
T abs_a = (T)fabs(a), abs_b = (T)fabs(b);
if (abs_a > abs_b)
return abs_a * sqrt((T)1.0 + (abs_b / abs_a) * (abs_b / abs_a));
else
return (abs_b == (T)0.0 ? (T)0.0 : abs_b * sqrt((T)1.0 + (abs_a / abs_b) * (abs_a / abs_b)));
}
template <typename T>
void svd(const Matrix<T>& A, Matrix<T>& U, Vector<T>& W, Matrix<T>& V)
{
int m = A.nrows(), n = A.ncols(), i, j, k, l, jj, nm;
const unsigned int max_its = 30;
bool flag;
Vector<T> rv1(n);
U = A;
W.resize(n);
V.resize(n, n);
T anorm, c, f, g, h, s, scale, x, y, z;
g = scale = anorm = (T)0.0;
// Householder reduction to bidiagonal form
for (i = 0; i < n; i++)
{
l = i + 1;
rv1[i] = scale * g;
g = s = scale = (T)0.0;
if (i < m)
{
for (k = i; k < m; k++)
scale += fabs(U[k][i]);
if (scale != (T)0.0)
{
for (k = i; k < m; k++)
{
U[k][i] /= scale;
s += U[k][i] * U[k][i];
}
f = U[i][i];
g = -sign(f) * sqrt(s);
h = f * g - s;
U[i][i] = f - g;
for (j = l; j < n; j++)
{
s = (T)0.0;
for (k = i; k < m; k++)
s += U[k][i] * U[k][j];
f = s / h;
for (k = i; k < m; k++)
U[k][j] += f * U[k][i];
}
for (k = i; k < m; k++)
U[k][i] *= scale;
}
}
W[i] = scale * g;
g = s = scale = (T)0.0;
if (i < m && i != n - 1)
{
for (k = l; k < n; k++)
scale += fabs(U[i][k]);
if (scale != (T)0.0)
{
for (k = l; k < n; k++)
{
U[i][k] /= scale;
s += U[i][k] * U[i][k];
}
f = U[i][l];
g = -sign(f) * sqrt(s);
h = f * g - s;
U[i][l] = f - g;
for (k = l; k <n; k++)
rv1[k] = U[i][k] / h;
for (j = l; j < m; j++)
{
s = (T)0.0;
for (k = l; k < n; k++)
s += U[j][k] * U[i][k];
for (k = l; k < n; k++)
U[j][k] += s * rv1[k];
}
for (k = l; k < n; k++)
U[i][k] *= scale;
}
}
anorm = std::max(anorm, fabs(W[i]) + fabs(rv1[i]));
}
// Accumulation of right-hand transformations
for (i = n - 1; i >= 0; i--)
{
if (i < n - 1)
{
if (g != (T)0.0)
{
for (j = l; j < n; j++)
V[j][i] = (U[i][j] / U[i][l]) / g;
for (j = l; j < n; j++)
{
s = (T)0.0;
for (k = l; k < n; k++)
s += U[i][k] * V[k][j];
for (k = l; k < n; k++)
V[k][j] += s * V[k][i];
}
}
for (j = l; j < n; j++)
V[i][j] = V[j][i] = (T)0.0;
}
V[i][i] = (T)1.0;
g = rv1[i];
l = i;
}
// Accumulation of left-hand transformations
for (i = std::min(m, n) - 1; i >= 0; i--)
{
l = i + 1;
g = W[i];
for (j = l; j < n; j++)
U[i][j] = (T)0.0;
if (g != (T)0.0)
{
g = (T)1.0 / g;
for (j = l; j < n; j++)
{
s = (T)0.0;
for (k = l; k < m; k++)
s += U[k][i] * U[k][j];
f = (s / U[i][i]) * g;
for (k = i; k < m; k++)
U[k][j] += f * U[k][i];
}
for (j = i; j < m; j++)
U[j][i] *= g;
}
else
for (j = i; j < m; j++)
U[j][i] = (T)0.0;
U[i][i]++;
}
// Diagonalization of the bidiagonal form: loop over singular values, and over allowed iterations.
for (k = n - 1; k >= 0; k--)
{
for (unsigned int its = 0; its < max_its; its++)
{
flag = true;
for (l = k; l >= 0; l--)
{ // Test for splitting
nm = l - 1; // Note that rV[0] is always zero
if ((T)(fabs(rv1[l]) + anorm) == anorm)
{
flag = false;
break;
}
if ((T)(fabs(W[nm]) + anorm) == anorm)
break;
}
if (flag)
{
// Cancellation of rv1[l], if l > 0 FIXME: it was l > 1 in NR
c = (T)0.0;
s = (T)1.0;
for (i = l; i <= k; i++)
{
f = s * rv1[i];
rv1[i] *= c;
if ((T)(fabs(f) + anorm) == anorm)
break;
g = W[i];
h = dist(f, g);
W[i] = h;
h = (T)1.0 / h;
c = g * h;
s = -f * h;
for (j = 0; j < m; j++)
{
y = U[j][nm];
z = U[j][i];
U[j][nm] = y * c + z * s;
U[j][i] = z * c - y * s;
}
}
}
z = W[k];
if (l == k)
{ // Convergence
if (z < (T)0.0)
{ // Singular value is made nonnegative
W[k] = -z;
for (j = 0; j < n; j++)
V[j][k] = -V[j][k];
}
break;
}
if (its == max_its)
throw std::logic_error("Error svd: no convergence in the maximum number of iterations");
x = W[l];
nm = k - 1;
y = W[nm];
g = rv1[nm];
h = rv1[k];
f = ((y - z) * (y + z) + (g - h) * (g + h)) / (2.0 * h * y);
g = dist(f, (T)1.0);
f = ((x - z) * (x + z) + h * ((y / (f + sign(f)*fabs(g))) - h)) / x;
c = s = (T)1.0; // Next QR transformation
for (j = l; j <= nm; j++)
{
i = j + 1;
g = rv1[i];
y = W[i];
h = s * g;
g *= c;
z = dist(f, h);
rv1[j] = z;
c = f / z;
s = h / z;
f = x * c + g * s;
g = g * c - x * s;
h = y * s;
y *= c;
for (jj = 0; jj < n; jj++)
{
x = V[jj][j];
z = V[jj][i];
V[jj][j] = x * c + z * s;
V[jj][i] = z * c - x * s;
}
z = dist(f, h);
W[j] = z;
if (z != 0) // Rotation can be arbitrary if z = 0
{
z = (T)1.0 / z;
c = f * z;
s = h * z;
}
f = c * g + s * y;
x = c * y - s * g;
for (jj = 0; jj < m; jj++)
{
y = U[jj][j];
z = U[jj][i];
U[jj][j] = y * c + z * s;
U[jj][i] = z * c - y * s;
}
}
rv1[l] = (T)0.0;
rv1[k] = f;
W[k] = x;
}
}
}
template <typename T>
Matrix<T> pinv(const Matrix<T>& A)
{
Matrix<T> U, V, x, tmp(A.ncols(), A.nrows());
Vector<T> W;
CanonicalBaseVector<T> e(0, A.nrows());
svd(A, U, W, V);
for (unsigned int i = 0; i < A.nrows(); i++)
{
e.reset(i);
tmp.setColumn(i, dot_prod(dot_prod(dot_prod(V, Matrix<double>(DIAG, 1.0 / W, 0.0, W.size(), W.size())), t(U)), e));
}
return tmp;
}
template <typename T>
int lu(const Matrix<T>& A, Matrix<T>& LU, Vector<unsigned int>& index)
{
if (A.ncols() != A.nrows())
throw std::logic_error("Error in LU decomposition: matrix must be squared");
int i, p, j, k, n = A.ncols(), ex;
T val, tmp;
Vector<T> d(n);
LU = A;
index.resize(n);
ex = 1;
for (i = 0; i < n; i++)
{
index[i] = i;
val = (T)0.0;
for (j = 0; j < n; j++)
val = std::max(val, (T)fabs(LU[i][j]));
if (val == (T)0.0)
std::logic_error("Error in LU decomposition: matrix was singular");
d[i] = val;
}
for (k = 0; k < n - 1; k++)
{
p = k;
val = fabs(LU[k][k]) / d[k];
for (i = k + 1; i < n; i++)
{
tmp = fabs(LU[i][k]) / d[i];
if (tmp > val)
{
val = tmp;
p = i;
}
}
if (val == (T)0.0)
std::logic_error("Error in LU decomposition: matrix was singular");
if (p > k)
{
ex = -ex;
std::swap(index[k], index[p]);
std::swap(d[k], d[p]);
for (j = 0; j < n; j++)
std::swap(LU[k][j], LU[p][j]);
}
for (i = k + 1; i < n; i++)
{
LU[i][k] /= LU[k][k];
for (j = k + 1; j < n; j++)
LU[i][j] -= LU[i][k] * LU[k][j];
}
}
if (LU[n - 1][n - 1] == (T)0.0)
std::logic_error("Error in LU decomposition: matrix was singular");
return ex;
}
template <typename T>
Vector<T> lu_solve(const Matrix<T>& LU, const Vector<T>& b, Vector<unsigned int>& index)
{
if (LU.ncols() != LU.nrows())
throw std::logic_error("Error in LU solve: LU matrix should be squared");
unsigned int n = LU.ncols();
if (b.size() != n)
throw std::logic_error("Error in LU solve: b vector must be of the same dimensions of LU matrix");
Vector<T> x((T)0.0, n);
int i, j, p;
T sum;
p = index[0];
x[0] = b[p];
for (i = 1; i < n; i++)
{
sum = (T)0.0;
for (j = 0; j < i; j++)
sum += LU[i][j] * x[j];
p = index[i];
x[i] = b[p] - sum;
}
x[n - 1] /= LU[n - 1][n - 1];
for (i = n - 2; i >= 0; i--)
{
sum = (T)0.0;
for (j = i + 1; j < n; j++)
sum += LU[i][j] * x[j];
x[i] = (x[i] - sum) / LU[i][i];
}
return x;
}
template <typename T>
void lu_solve(const Matrix<T>& LU, Vector<T>& x, const Vector<T>& b, Vector<unsigned int>& index)
{
x = lu_solve(LU, b, index);
}
template <typename T>
Matrix<T> lu_inverse(const Matrix<T>& A)
{
if (A.ncols() != A.nrows())
throw std::logic_error("Error in LU invert: matrix must be squared");
unsigned int n = A.ncols();
Matrix<T> A1(n, n), LU;
Vector<unsigned int> index;
lu(A, LU, index);
CanonicalBaseVector<T> e(0, n);
for (unsigned i = 0; i < n; i++)
{
e.reset(i);
A1.setColumn(i, lu_solve(LU, e, index));
}
return A1;
}
template <typename T>
T lu_det(const Matrix<T>& A)
{
if (A.ncols() != A.nrows())
throw std::logic_error("Error in LU determinant: matrix must be squared");
unsigned int d;
Matrix<T> LU;
Vector<unsigned int> index;
d = lu(A, LU, index);
return d * prod(LU.extractDiag());
}
template <typename T>
void cholesky(const Matrix<T> A, Matrix<T>& LL)
{
if (A.ncols() != A.nrows())
throw std::logic_error("Error in Cholesky decomposition: matrix must be squared");
int n = A.ncols();
double sum;
LL = A;
for (unsigned int i = 0; i < n; i++)
{
for (unsigned int j = i; j < n; j++)
{
sum = LL[i][j];
for (int k = i - 1; k >= 0; k--)
sum -= LL[i][k] * LL[j][k];
if (i == j)
{
if (sum <= 0.0)
throw std::logic_error("Error in Cholesky decomposition: matrix is not postive definite");
LL[i][i] = sqrt(sum);
}
else
LL[j][i] = sum / LL[i][i];
}
for (unsigned int k = i + 1; k < n; k++)
LL[i][k] = LL[k][i];
}
}
template <typename T>
Matrix<T> cholesky(const Matrix<T> A)
{
Matrix<T> LL;
cholesky(A, LL);
return LL;
}
template <typename T>
Vector<T> cholesky_solve(const Matrix<T>& LL, const Vector<T>& b)
{
if (LL.ncols() != LL.nrows())
throw std::logic_error("Error in Cholesky solve: matrix must be squared");
unsigned int n = LL.ncols();
if (b.size() != n)
throw std::logic_error("Error in Cholesky decomposition: b vector must be of the same dimensions of LU matrix");
Vector<T> x, y;
/* Solve L * y = b */
forward_elimination(LL, y, b);
/* Solve L^T * x = y */
backward_elimination(LL, x, y);
return x;
}
template <typename T>
void cholesky_solve(const Matrix<T>& LL, Vector<T>& x, const Vector<T>& b)
{
x = cholesky_solve(LL, b);
}
template <typename T>
void forward_elimination(const Matrix<T>& L, Vector<T>& y, const Vector<T> b)
{
if (L.ncols() != L.nrows())
throw std::logic_error("Error in Forward elimination: matrix must be squared (lower triangular)");
if (b.size() != L.nrows())
throw std::logic_error("Error in Forward elimination: b vector must be of the same dimensions of L matrix");
unsigned int n = b.size();
y.resize(n);
y[0] = b[0] / L[0][0];
for (unsigned int i = 1; i < n; i++)
{
y[i] = b[i];
for (unsigned int j = 0; j < i; j++)
y[i] -= L[i][j] * y[j];
y[i] = y[i] / L[i][i];
}
}
template <typename T>
Vector<T> forward_elimination(const Matrix<T>& L, const Vector<T> b)
{
Vector<T> y;
forward_elimination(L, y, b);
return y;
}
template <typename T>
void backward_elimination(const Matrix<T>& U, Vector<T>& x, const Vector<T>& y)
{
if (U.ncols() != U.nrows())
throw std::logic_error("Error in Backward elimination: matrix must be squared (upper triangular)");
if (y.size() != U.nrows())
throw std::logic_error("Error in Backward elimination: b vector must be of the same dimensions of U matrix");
int n = y.size();
x.resize(n);
x[n - 1] = y[n - 1] / U[n - 1][n - 1];
for (int i = n - 2; i >= 0; i--)
{
x[i] = y[i];
for (int j = i + 1; j < n; j++)
x[i] -= U[i][j] * x[j];
x[i] = x[i] / U[i][i];
}
}
template <typename T>
Vector<T> backward_elimination(const Matrix<T>& U, const Vector<T> y)
{
Vector<T> x;
forward_elimination(U, x, y);
return x;
}
/* Setting default linear systems machinery */
// #define det lu_det
// #define inverse lu_inverse
// #define solve lu_solve
/* Random */
template <typename T>
void random(Matrix<T>& m)
{
for (unsigned int i = 0; i < m.nrows(); i++)
for (unsigned int j = 0; j < m.ncols(); j++)
m[i][j] = (T)(rand() / double(RAND_MAX));
}
/**
Aggregate functions
*/
template <typename T>
Vector<T> sum(const Matrix<T>& m)
{
Vector<T> tmp((T)0, m.ncols());
for (unsigned int j = 0; j < m.ncols(); j++)
for (unsigned int i = 0; i < m.nrows(); i++)
tmp[j] += m[i][j];
return tmp;
}
template <typename T>
Vector<T> r_sum(const Matrix<T>& m)
{
Vector<T> tmp((T)0, m.nrows());
for (unsigned int i = 0; i < m.nrows(); i++)
for (unsigned int j = 0; j < m.ncols(); j++)
tmp[i] += m[i][j];
return tmp;
}
template <typename T>
T all_sum(const Matrix<T>& m)
{
T tmp = (T)0;
for (unsigned int i = 0; i < m.nrows(); i++)
for (unsigned int j = 0; j < m.ncols(); j++)
tmp += m[i][j];
return tmp;
}
template <typename T>
Vector<T> prod(const Matrix<T>& m)
{
Vector<T> tmp((T)1, m.ncols());
for (unsigned int j = 0; j < m.ncols(); j++)
for (unsigned int i = 0; i < m.nrows(); i++)
tmp[j] *= m[i][j];
return tmp;
}
template <typename T>
Vector<T> r_prod(const Matrix<T>& m)
{
Vector<T> tmp((T)1, m.nrows());
for (unsigned int i = 0; i < m.nrows(); i++)
for (unsigned int j = 0; j < m.ncols(); j++)
tmp[i] *= m[i][j];
return tmp;
}
template <typename T>
T all_prod(const Matrix<T>& m)
{
T tmp = (T)1;
for (unsigned int i = 0; i < m.nrows(); i++)
for (unsigned int j = 0; j < m.ncols(); j++)
tmp *= m[i][j];
return tmp;
}
template <typename T>
Vector<T> mean(const Matrix<T>& m)
{
Vector<T> res((T)0, m.ncols());
for (unsigned int j = 0; j < m.ncols(); j++)
{
for (unsigned int i = 0; i < m.nrows(); i++)
res[j] += m[i][j];
res[j] /= m.nrows();
}
return res;
}
template <typename T>
Vector<T> r_mean(const Matrix<T>& m)
{
Vector<T> res((T)0, m.rows());
for (unsigned int i = 0; i < m.nrows(); i++)
{
for (unsigned int j = 0; j < m.ncols(); j++)
res[i] += m[i][j];
res[i] /= m.nrows();
}
return res;
}
template <typename T>
T all_mean(const Matrix<T>& m)
{
T tmp = (T)0;
for (unsigned int i = 0; i < m.nrows(); i++)
for (unsigned int j = 0; j < m.ncols(); j++)
tmp += m[i][j];
return tmp / (m.nrows() * m.ncols());
}
template <typename T>
Vector<T> var(const Matrix<T>& m, bool sample_correction = false)
{
Vector<T> res((T)0, m.ncols());
unsigned int n = m.nrows();
double sum, ssum;
for (unsigned int j = 0; j < m.ncols(); j++)
{
sum = (T)0.0; ssum = (T)0.0;
for (unsigned int i = 0; i < m.nrows(); i++)
{
sum += m[i][j];
ssum += (m[i][j] * m[i][j]);
}
if (!sample_correction)
res[j] = (ssum / n) - (sum / n) * (sum / n);
else
res[j] = n * ((ssum / n) - (sum / n) * (sum / n)) / (n - 1);
}
return res;
}
template <typename T>
Vector<T> stdev(const Matrix<T>& m, bool sample_correction = false)
{
return vec_sqrt(var(m, sample_correction));
}
template <typename T>
Vector<T> r_var(const Matrix<T>& m, bool sample_correction = false)
{
Vector<T> res((T)0, m.nrows());
double sum, ssum;
unsigned int n = m.ncols();
for (unsigned int i = 0; i < m.nrows(); i++)
{
sum = 0.0; ssum = 0.0;
for (unsigned int j = 0; j < m.ncols(); j++)
{
sum += m[i][j];
ssum += (m[i][j] * m[i][j]);
}
if (!sample_correction)
res[i] = (ssum / n) - (sum / n) * (sum / n);
else
res[i] = n * ((ssum / n) - (sum / n) * (sum / n)) / (n - 1);
}
return res;
}
template <typename T>
Vector<T> r_stdev(const Matrix<T>& m, bool sample_correction = false)
{
return vec_sqrt(r_var(m, sample_correction));
}
template <typename T>
Vector<T> max(const Matrix<T>& m)
{
Vector<T> res(m.ncols());
double value;
for (unsigned int j = 0; j < m.ncols(); j++)
{
value = m[0][j];
for (unsigned int i = 1; i < m.nrows(); i++)
value = std::max(m[i][j], value);
res[j] = value;
}
return res;
}
template <typename T>
Vector<T> r_max(const Matrix<T>& m)
{
Vector<T> res(m.nrows());
double value;
for (unsigned int i = 0; i < m.nrows(); i++)
{
value = m[i][0];
for (unsigned int j = 1; j < m.ncols(); j++)
value = std::max(m[i][j], value);
res[i] = value;
}
return res;
}
template <typename T>
Vector<T> min(const Matrix<T>& m)
{
Vector<T> res(m.ncols());
double value;
for (unsigned int j = 0; j < m.ncols(); j++)
{
value = m[0][j];
for (unsigned int i = 1; i < m.nrows(); i++)
value = std::min(m[i][j], value);
res[j] = value;
}
return res;
}
template <typename T>
Vector<T> r_min(const Matrix<T>& m)
{
Vector<T> res(m.nrows());
double value;
for (unsigned int i = 0; i < m.nrows(); i++)
{
value = m[i][0];
for (unsigned int j = 1; j < m.ncols(); j++)
value = std::min(m[i][j], value);
res[i] = value;
}
return res;
}
/**
Single element mathematical functions
*/
template <typename T>
Matrix<T> exp(const Matrix<T>&m)
{
Matrix<T> tmp(m.nrows(), m.ncols());
for (unsigned int i = 0; i < m.nrows(); i++)
for (unsigned int j = 0; j < m.ncols(); j++)
tmp[i][j] = exp(m[i][j]);
return tmp;
}
template <typename T>
Matrix<T> mat_sqrt(const Matrix<T>&m)
{
Matrix<T> tmp(m.nrows(), m.ncols());
for (unsigned int i = 0; i < m.nrows(); i++)
for (unsigned int j = 0; j < m.ncols(); j++)
tmp[i][j] = sqrt(m[i][j]);
return tmp;
}
/**
Matrix operators
*/
template <typename T>
Matrix<T> kron(const Vector<T>& b, const Vector<T>& a)
{
Matrix<T> tmp(b.size(), a.size());
for (unsigned int i = 0; i < b.size(); i++)
for (unsigned int j = 0; j < a.size(); j++)
tmp[i][j] = a[j] * b[i];
return tmp;
}
template <typename T>
Matrix<T> t(const Matrix<T>& a)
{
Matrix<T> tmp(a.ncols(), a.nrows());
for (unsigned int i = 0; i < a.nrows(); i++)
for (unsigned int j = 0; j < a.ncols(); j++)
tmp[j][i] = a[i][j];
return tmp;
}
template <typename T>
Matrix<T> dot_prod(const Matrix<T>& a, const Matrix<T>& b)
{
if (a.ncols() != b.nrows())
throw std::logic_error("Error matrix dot product: dimensions of the matrices are not compatible");
Matrix<T> tmp(a.nrows(), b.ncols());
for (unsigned int i = 0; i < tmp.nrows(); i++)
for (unsigned int j = 0; j < tmp.ncols(); j++)
{
tmp[i][j] = (T)0;
for (unsigned int k = 0; k < a.ncols(); k++)
tmp[i][j] += a[i][k] * b[k][j];
}
return tmp;
}
template <typename T>
Matrix<T> dot_prod(const Matrix<T>& a, const Vector<T>& b)
{
if (a.ncols() != b.size())
throw std::logic_error("Error matrix dot product: dimensions of the matrix and the vector are not compatible");
Matrix<T> tmp(a.nrows(), 1);
for (unsigned int i = 0; i < tmp.nrows(); i++)
{
tmp[i][0] = (T)0;
for (unsigned int k = 0; k < a.ncols(); k++)
tmp[i][0] += a[i][k] * b[k];
}
return tmp;
}
template <typename T>
Matrix<T> dot_prod(const Vector<T>& a, const Matrix<T>& b)
{
if (a.size() != b.nrows())
throw std::logic_error("Error matrix dot product: dimensions of the vector and matrix are not compatible");
Matrix<T> tmp(1, b.ncols());
for (unsigned int j = 0; j < tmp.ncols(); j++)
{
tmp[0][j] = (T)0;
for (unsigned int k = 0; k < a.size(); k++)
tmp[0][j] += a[k] * b[k][j];
}
return tmp;
}
template <typename T>
inline Matrix<double> rank(const Matrix<T> m)
{
Matrix<double> tmp(m.nrows(), m.ncols());
for (unsigned int j = 0; j < m.ncols(); j++)
tmp.setColumn(j, rank<T>(m.extractColumn(j)));
return tmp;
}
template <typename T>
inline Matrix<double> r_rank(const Matrix<T> m)
{
Matrix<double> tmp(m.nrows(), m.ncols());
for (unsigned int i = 0; i < m.nrows(); i++)
tmp.setRow(i, rank<T>(m.extractRow(i)));
return tmp;
}
} // namespace quadprogpp
#endif // define _ARRAY_HH_