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quadprog++ and Eigen library test
Dependencies: mbed Eigen FastPWM
Revision 2:e843c1b0b25c, committed 2019-09-24
- Comitter:
- jsoh91
- Date:
- Tue Sep 24 00:20:12 2019 +0000
- Parent:
- 1:27f1640d930d
- Commit message:
- QP and Eigen library test project;
Changed in this revision
diff -r 27f1640d930d -r e843c1b0b25c Array.cpp --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/Array.cpp Tue Sep 24 00:20:12 2019 +0000 @@ -0,0 +1,33 @@ +// $Id: Array.cc 201 2008-05-18 19:47:38Z digasper $ +// This file is part of QuadProg++: +// Copyright (C) 2006--2009 Luca Di Gaspero. +// +// This software may be modified and distributed under the terms +// of the MIT license. See the LICENSE file for details. + +#include "Array.h" + +/** + Index utilities + */ + +namespace quadprogpp { + +std::set<unsigned int> seq(unsigned int s, unsigned int e) +{ + std::set<unsigned int> tmp; + for (unsigned int i = s; i <= e; i++) + tmp.insert(i); + + return tmp; +} + +std::set<unsigned int> singleton(unsigned int i) +{ + std::set<unsigned int> tmp; + tmp.insert(i); + + return tmp; +} + +} // namespace quadprogpp
diff -r 27f1640d930d -r e843c1b0b25c Array.h --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/Array.h Tue Sep 24 00:20:12 2019 +0000 @@ -0,0 +1,2543 @@ +// $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]) +{ + register unsigned int i; + this->n = n; this->m = m; + v[0] = new T[m * n]; + for (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]) +{ + register unsigned int i, j; + this->n = n; this->m = m; + v[0] = new T[m * n]; + for (i = 1; i < n; i++) + v[i] = v[i - 1] + m; + for (i = 0; i < n; i++) + for (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]) +{ + register unsigned int i, j; + this->n = n; this->m = m; + v[0] = new T[m * n]; + for (i = 1; i < n; i++) + v[i] = v[i - 1] + m; + for (i = 0; i < n; i++) + for (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]) +{ + register unsigned int i, j; + this->n = n; this->m = m; + v[0] = new T[m * n]; + for (i = 1; i < n; i++) + v[i] = v[i - 1] + m; + switch (t) + { + case DIAG: + for (i = 0; i < n; i++) + for (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]) +{ + register unsigned int i, j; + this->n = n; this->m = m; + v[0] = new T[m * n]; + for (i = 1; i < n; i++) + v[i] = v[i - 1] + m; + switch (t) + { + case DIAG: + for (i = 0; i < n; i++) + for (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]) +{ + register unsigned int i, j; + n = rhs.n; m = rhs.m; + v[0] = new T[m * n]; + for (i = 1; i < n; i++) + v[i] = v[i - 1] + m; + for (i = 0; i < n; i++) + for (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 +{ + register unsigned int i, j; + if (this != &rhs) + { + resize(rhs.n, rhs.m); + for (i = 0; i < n; i++) + for (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 +{ + register unsigned int i, j; + for (i = 0; i < n; i++) + for (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) +{ + register unsigned int i; + 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 (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) +{ + register unsigned int i, j; + resize(n, m); + for (i = 0; i < n; i++) + for (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 +{ + register unsigned int i; + if (j >= m) + throw std::logic_error("Error in extractRow: trying to extract a row out of matrix bounds"); + Vector<T> tmp(n); + + for (i = 0; i < n; i++) + tmp[i] = v[i][j]; + + return tmp; +} + +template <typename T> +inline Vector<T> Matrix<T>::extractDiag() const +{ + register unsigned int d = std::min(n, m), i; + + Vector<T> tmp(d); + + for (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); + register unsigned int i = 0, j; + + for (std::set<unsigned int>::const_iterator el = indexes.begin(); el != indexes.end(); el++) + { + for (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()); + register unsigned int i, j = 0; + + for (std::set<unsigned int>::const_iterator el = indexes.begin(); el != indexes.end(); el++) + { + for (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()); + register 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--) // FIXME: in NR it was l >= 1 but there subscripts start from one + { // 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"); + register int i, j, k, n = A.ncols(); + register double sum; + LL = A; + + for (i = 0; i < n; i++) + { + for (j = i; j < n; j++) + { + sum = LL[i][j]; + for (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 (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"); + register int i, j, n = b.size(); + y.resize(n); + + y[0] = b[0] / L[0][0]; + for (i = 1; i < n; i++) + { + y[i] = b[i]; + for (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"); + register int i, j, n = y.size(); + x.resize(n); + + x[n - 1] = y[n - 1] / U[n - 1][n - 1]; + for (i = n - 2; i >= 0; i--) + { + x[i] = y[i]; + for (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.ncols()) + 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_
diff -r 27f1640d930d -r e843c1b0b25c Eigen.lib --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/Eigen.lib Tue Sep 24 00:20:12 2019 +0000 @@ -0,0 +1,1 @@ +https://os.mbed.com/users/jsoh91/code/Eigen/#3b8049da21b8
diff -r 27f1640d930d -r e843c1b0b25c main.cpp --- a/main.cpp Wed Aug 21 05:18:06 2019 +0000 +++ b/main.cpp Tue Sep 24 00:20:12 2019 +0000 @@ -3,62 +3,345 @@ #define PIN_A PA_8 // channel 1 #define PIN_B PA_7 // complementary -#define PWM_ARR 0x8CA /// timer autoreload value 40k loop, 40k pwm +#define PWM_ARR 4500 /// timer autoreload value 40k loop, 40k pwm + +#include "quadprog.h" +#include <cstdlib> +#include "Eigen/Dense.h" + +using namespace std; +using namespace Eigen; + +MatrixXd AA = MatrixXd::Zero(6,1); + +class JS_QP +{ +private: + int NUMCOLS;//length of X + int NUMEQ; + int NUMINEQ; + + MatrixXd A_ineq,B_ineq; + MatrixXd A_eq,B_eq; + +public: + MatrixXd H,F; + MatrixXd X; + +public: + void setNums(int _xlength, int numEqConstraints, int numIneqConstraints) + { + NUMCOLS = _xlength;//should be 18+12+3*contact + NUMEQ = numEqConstraints;//NUMCOLS(dynamics) + NUMCOLS(contactconstraints + swingleg) + //contact to be weight? + NUMINEQ = numIneqConstraints;//friction cone approximation -ufz<fx<ufz, -ufz<fy<ufz ->4 + + //maybe matrix assignment here + X = MatrixXd::Zero(NUMCOLS,1); + A_eq = MatrixXd::Zero(NUMEQ, NUMCOLS); + B_eq = MatrixXd::Zero(NUMEQ, 1); + + A_ineq = MatrixXd::Zero(NUMINEQ, NUMCOLS); + B_ineq = MatrixXd::Zero(NUMINEQ, 1); + + + H = MatrixXd::Zero(NUMCOLS,NUMCOLS); + F = MatrixXd::Zero(NUMCOLS,1); + } + + void make_EQ(MatrixXd A, MatrixXd b) + { + //Aeq*X = Beq + A_eq = A; + B_eq = b; + } + + void make_IEQ(MatrixXd A, MatrixXd b) + { + // Aineq*X < Bineq + A_ineq = A; + B_ineq = b; + } + + void make_HF(MatrixXd A, MatrixXd b, int mode=-1) + { + //min (0.5* x H x + F x) + if(mode == -1) { + H = A.transpose() * A + MatrixXd::Identity(NUMCOLS,NUMCOLS)*1e-3; + F = -A.transpose() * b; -float dtc_a=0.1; -float dtc_b=0.2; -void Init_PWM(); -DigitalOut check(PC_9); -DigitalIn a1(PB_7); -DigitalIn a2(PB_6); + } else { + H = A; + F = b; + + } + + } + + MatrixXd solve_QP() + { + quadprogpp::Vector<double> outX; + quadprogpp::Matrix<double> G; + quadprogpp::Vector<double> g0; + quadprogpp::Matrix<double> CE; + quadprogpp::Vector<double> ce0; + quadprogpp::Matrix<double> CI; + quadprogpp::Vector<double> ci0; + //min 0.5 * x G x + g0 x + //CE^T x + ce0 = 0 + //CI^T x + ci0 >= 0 + + G.resize(NUMCOLS,NUMCOLS); + g0.resize(NUMCOLS); + for(int i=0; i<NUMCOLS; i++) { + for(int j=0; j<NUMCOLS; j++) { + G[i][j] = H(i,j); + } + g0[i] = F(i,0); + } + CE.resize(NUMCOLS,NUMEQ); + ce0.resize(NUMEQ); + for(int i=0; i<NUMCOLS; i++) { + for(int j=0; j<NUMEQ; j++) { + CE[i][j] = -A_eq(j,i); + } + } + for(int j=0; j<NUMEQ; j++) { + ce0[j] = B_eq(j,0); + } + CI.resize(NUMCOLS,NUMINEQ); + ci0.resize(NUMINEQ); + for(int i=0; i<NUMCOLS; i++) { + for(int j=0; j<NUMINEQ; j++) { + CI[i][j] = -A_ineq(j,i); + } + } + for(int j=0; j<NUMINEQ; j++) { + ci0[j] = B_ineq(j,0); + } + outX.resize(NUMCOLS); + + solve_quadprog(G, g0, CE, ce0, CI, ci0, outX); + for(int i=0; i<NUMCOLS; i++) { + X(i,0) = outX[i]; + } + + return X; + + } + +public: + +}; + +JS_QP js_qp; + +//MatrixXd AA; -extern "C" void TIM1_UP_TIM10_IRQHandler(void) { - if (TIM1->SR & TIM_SR_UIF ) { - check=1; - TIM1->CCR1 = (PWM_ARR)*(1.0f-dtc_a); // Write duty cycles - check=0; +float dtc_a=0; +void Init_PWM(); + +AnalogIn Vfb(PA_5); + +extern "C" void TIM1_UP_TIM10_IRQHandler(void) +{ + if (TIM1->SR & TIM_SR_UIF ) { + + float Vth = 0.51f; + + if(Vfb >= Vth) { //PA_8 이게 하이 + dtc_a -= 0.001f; + } + + else { + dtc_a += 0.001f; + } + + if(dtc_a>=0.9f) + dtc_a = 0.9f; + + if(dtc_a <= 0.0f) + dtc_a = 0.0f; + + dtc_a = 0.5f; + + TIM1->CCR1 = (PWM_ARR)*(1.0f-dtc_a); // Write duty cycles + } -TIM1->SR = 0x0; // reset the status register + TIM1->SR = 0x0; // reset the status register } +Timer t; -int main(){ - check=1; - Init_PWM(); - TIM1->CR1 ^= TIM_CR1_UDIS; - while(1); +double t_old=0; + +int main() +{ + + MatrixXd Aa = MatrixXd::Zero(20,2); + MatrixXd Ba = MatrixXd::Zero(20,10); + MatrixXd Ga = MatrixXd::Zero(20,20); + + Aa << + 1.000000,-1.000000 + ,0.000000,0.783386 + ,1.000000,-1.783386 + ,0.000000,0.613693 + ,1.000000,-2.397079 + ,0.000000,0.480759 + ,1.000000,-2.877838 + ,0.000000,0.376620 + ,1.000000,-3.254458 + ,0.000000,0.295039 + ,1.000000,-3.549496 + ,0.000000,0.231129 + ,1.000000,-3.780626 + ,0.000000,0.181063 + ,1.000000,-3.961689 + ,0.000000,0.141842 + ,1.000000,-4.103531 + ,0.000000,0.111117 + ,1.000000,-4.214648 + ,0.000000,0.087048; + + + Ba << + 0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000 + ,0.471698,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000 + ,-0.471698,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000 + ,0.369522,0.471698,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000 + ,-0.841220,-0.471698,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000 + ,0.289478,0.369522,0.471698,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000 + ,-1.130698,-0.841220,-0.471698,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000 + ,0.226773,0.289478,0.369522,0.471698,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000 + ,-1.357471,-1.130698,-0.841220,-0.471698,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000 + ,0.177651,0.226773,0.289478,0.369522,0.471698,0.000000,0.000000,0.000000,0.000000,0.000000 + ,-1.535122,-1.357471,-1.130698,-0.841220,-0.471698,0.000000,0.000000,0.000000,0.000000,0.000000 + ,0.139169,0.177651,0.226773,0.289478,0.369522,0.471698,0.000000,0.000000,0.000000,0.000000 + ,-1.674291,-1.535122,-1.357471,-1.130698,-0.841220,-0.471698,0.000000,0.000000,0.000000,0.000000 + ,0.109023,0.139169,0.177651,0.226773,0.289478,0.369522,0.471698,0.000000,0.000000,0.000000 + ,-1.783314,-1.674291,-1.535122,-1.357471,-1.130698,-0.841220,-0.471698,0.000000,0.000000,0.000000 + ,0.085407,0.109023,0.139169,0.177651,0.226773,0.289478,0.369522,0.471698,0.000000,0.000000 + ,-1.868721,-1.783314,-1.674291,-1.535122,-1.357471,-1.130698,-0.841220,-0.471698,0.000000,0.000000 + ,0.066907,0.085407,0.109023,0.139169,0.177651,0.226773,0.289478,0.369522,0.471698,0.000000 + ,-1.935628,-1.868721,-1.783314,-1.674291,-1.535122,-1.357471,-1.130698,-0.841220,-0.471698,0.000000 + ,0.052414,0.066907,0.085407,0.109023,0.139169,0.177651,0.226773,0.289478,0.369522,0.471698; + + + Ga << + 1.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000 + ,0.000000,-0.198113,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000 + ,1.000000,0.198113,1.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000 + ,0.000000,-0.155199,0.000000,-0.198113,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000 + ,1.000000,0.353312,1.000000,0.198113,1.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000 + ,0.000000,-0.121581,0.000000,-0.155199,0.000000,-0.198113,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000 + ,1.000000,0.474893,1.000000,0.353312,1.000000,0.198113,1.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000 + ,0.000000,-0.095245,0.000000,-0.121581,0.000000,-0.155199,0.000000,-0.198113,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000 + ,1.000000,0.570138,1.000000,0.474893,1.000000,0.353312,1.000000,0.198113,1.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000 + ,0.000000,-0.074613,0.000000,-0.095245,0.000000,-0.121581,0.000000,-0.155199,0.000000,-0.198113,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000 + ,1.000000,0.644751,1.000000,0.570138,1.000000,0.474893,1.000000,0.353312,1.000000,0.198113,1.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000 + ,0.000000,-0.058451,0.000000,-0.074613,0.000000,-0.095245,0.000000,-0.121581,0.000000,-0.155199,0.000000,-0.198113,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000 + ,1.000000,0.703202,1.000000,0.644751,1.000000,0.570138,1.000000,0.474893,1.000000,0.353312,1.000000,0.198113,1.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000 + ,0.000000,-0.045790,0.000000,-0.058451,0.000000,-0.074613,0.000000,-0.095245,0.000000,-0.121581,0.000000,-0.155199,0.000000,-0.198113,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000 + ,1.000000,0.748992,1.000000,0.703202,1.000000,0.644751,1.000000,0.570138,1.000000,0.474893,1.000000,0.353312,1.000000,0.198113,1.000000,0.000000,0.000000,0.000000,0.000000,0.000000 + ,0.000000,-0.035871,0.000000,-0.045790,0.000000,-0.058451,0.000000,-0.074613,0.000000,-0.095245,0.000000,-0.121581,0.000000,-0.155199,0.000000,-0.198113,0.000000,0.000000,0.000000,0.000000 + ,1.000000,0.784863,1.000000,0.748992,1.000000,0.703202,1.000000,0.644751,1.000000,0.570138,1.000000,0.474893,1.000000,0.353312,1.000000,0.198113,1.000000,0.000000,0.000000,0.000000 + ,0.000000,-0.028101,0.000000,-0.035871,0.000000,-0.045790,0.000000,-0.058451,0.000000,-0.074613,0.000000,-0.095245,0.000000,-0.121581,0.000000,-0.155199,0.000000,-0.198113,0.000000,0.000000 + ,1.000000,0.812964,1.000000,0.784863,1.000000,0.748992,1.000000,0.703202,1.000000,0.644751,1.000000,0.570138,1.000000,0.474893,1.000000,0.353312,1.000000,0.198113,1.000000,0.000000 + ,0.000000,-0.022014,0.000000,-0.028101,0.000000,-0.035871,0.000000,-0.045790,0.000000,-0.058451,0.000000,-0.074613,0.000000,-0.095245,0.000000,-0.121581,0.000000,-0.155199,0.000000,-0.198113; + + MatrixXd ref_a = MatrixXd::Zero(20,1); + MatrixXd w0_a = MatrixXd::Zero(20,1); + + MatrixXd At; + MatrixXd Bt; + + MatrixXd X_state = MatrixXd::Zero(2,1); + + Bt = ref_a - Aa*X_state - Ga*w0_a; + At = Ba; + + MatrixXd Q = MatrixXd::Identity(20,20); + MatrixXd R = MatrixXd::Identity(10,10); + + MatrixXd H; + MatrixXd F; + + H = At.transpose() * Q * At + R; + F = -At.transpose()*Bt; + + + MatrixXd out; + + MatrixXd Aieq = MatrixXd::Zero(20,10); + MatrixXd bieq = MatrixXd::Zero(20,1); + + Aieq.block(0,0,10,10) = MatrixXd::Identity(10,10); + Aieq.block(10,0,10,10) = -MatrixXd::Identity(10,10); + + for(int i=0; i<10; i++) { + bieq(i,0) = 10; + bieq(i+10,0) = 10; + } + + + while(1) { + + js_qp.setNums(10,0,20); + + js_qp.make_HF(H,F,1); + js_qp.make_IEQ(Aieq,bieq); + + t.reset(); + t.start(); + + out = js_qp.solve_QP(); + + t.stop(); + + + cout << "out : " << endl; + cout << out << endl; + cout << "time : " << endl; + cout << t.read() << endl; + + + wait(1); + + } } -void Init_PWM(){ +void Init_PWM() +{ RCC->APB2ENR |= RCC_APB2ENR_TIM1EN; // enable TIM1 clock - FastPWM pwm_a(PIN_A); // 단순히 핀 설정용 + FastPWM pwm_a(PIN_A); // 단순히 핀 설정용 FastPWM pwm_b(PIN_B); - - //ISR Setup - + + //ISR Setup + NVIC_EnableIRQ(TIM1_UP_TIM10_IRQn); //Enable TIM1 IRQ TIM1->DIER |= TIM_DIER_UIE; // enable update interrupt TIM1->CR1 = 0x40; // CMS = 10, interrupt only when counting up // Center-aligned mode TIM1->CR1 |= TIM_CR1_UDIS; - TIM1->CR1 |= TIM_CR1_ARPE; // autoreload on, - TIM1->RCR |= 0x001; // update event once per up/down count of tim1 + TIM1->CR1 |= TIM_CR1_ARPE; // autoreload on, + TIM1->RCR |= 0x001; // update event once per up/down count of tim1 TIM1->EGR |= TIM_EGR_UG; - + //PWM Setup - TIM1->PSC = 0x0; // no prescaler, timer counts up in sync with the peripheral clock + TIM1->PSC = 0; // no prescaler, timer counts up in sync with the peripheral clock TIM1->ARR = PWM_ARR; // set auto reload, 40 khz // TIM1->CCER |= ~(TIM_CCER_CC1NP); // Interupt when low side is on. TIM1->CR1 |= TIM_CR1_CEN; // enable TIM1 - - // for complementary + + // for complementary TIM1->CCER|=0b1111; - } \ No newline at end of file +} \ No newline at end of file
diff -r 27f1640d930d -r e843c1b0b25c quadprog.cpp --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/quadprog.cpp Tue Sep 24 00:20:12 2019 +0000 @@ -0,0 +1,738 @@ +/* +File $Id: QuadProg++.cc 232 2007-06-21 12:29:00Z digasper $ + + Author: Luca Di Gaspero + DIEGM - University of Udine, Italy + luca.digaspero@uniud.it + http://www.diegm.uniud.it/digaspero/ + + This software may be modified and distributed under the terms + of the MIT license. See the LICENSE file for details. + + */ + +#include <iostream> +#include <algorithm> +#include <cmath> +#include <limits> +#include <sstream> +#include <stdexcept> +#include "quadprog.h" +#include "math.h" + +//#define TRACE_SOLVER + +namespace quadprogpp +{ + +// Utility functions for updating some data needed by the solution method +void compute_d(Vector<double>& d, const Matrix<double>& J, const Vector<double>& np); +void update_z(Vector<double>& z, const Matrix<double>& J, const Vector<double>& d, int iq); +void update_r(const Matrix<double>& R, Vector<double>& r, const Vector<double>& d, int iq); +bool add_constraint(Matrix<double>& R, Matrix<double>& J, Vector<double>& d, int& iq, double& rnorm); +void delete_constraint(Matrix<double>& R, Matrix<double>& J, Vector<int>& A, Vector<double>& u, int n, int p, int& iq, int l); + +// Utility functions for computing the Cholesky decomposition and solving +// linear systems +void cholesky_decomposition(Matrix<double>& A); +void cholesky_solve(const Matrix<double>& L, Vector<double>& x, const Vector<double>& b); +void forward_elimination(const Matrix<double>& L, Vector<double>& y, const Vector<double>& b); +void backward_elimination(const Matrix<double>& U, Vector<double>& x, const Vector<double>& y); + +// Utility functions for computing the scalar product and the euclidean +// distance between two numbers +double scalar_product(const Vector<double>& x, const Vector<double>& y); +double distance(double a, double b); + +// Utility functions for printing vectors and matrices +void print_matrix(char* name, const Matrix<double>& A, int n = -1, int m = -1); + +template<typename T> +void print_vector(char* name, const Vector<T>& v, int n = -1); + +// The Solving function, implementing the Goldfarb-Idnani method + +double solve_quadprog(Matrix<double>& G, Vector<double>& g0, + const Matrix<double>& CE, const Vector<double>& ce0, + const Matrix<double>& CI, const Vector<double>& ci0, + Vector<double>& x) +{ + std::ostringstream msg; + int n = G.ncols(), p = CE.ncols(), m = CI.ncols(); + if (G.nrows() != n) { + msg << "The matrix G is not a squared matrix (" << G.nrows() << " x " << G.ncols() << ")"; +// throw std::logic_error(msg.str()); + } + if (CE.nrows() != n) { + msg << "The matrix CE is incompatible (incorrect number of rows " << CE.nrows() << " , expecting " << n << ")"; +// throw std::logic_error(msg.str()); + } + if (ce0.size() != p) { + msg << "The vector ce0 is incompatible (incorrect dimension " << ce0.size() << ", expecting " << p << ")"; +// throw std::logic_error(msg.str()); + } + if (CI.nrows() != n) { + msg << "The matrix CI is incompatible (incorrect number of rows " << CI.nrows() << " , expecting " << n << ")"; +// throw std::logic_error(msg.str()); + } + if (ci0.size() != m) { + msg << "The vector ci0 is incompatible (incorrect dimension " << ci0.size() << ", expecting " << m << ")"; +// throw std::logic_error(msg.str()); + } + x.resize(n); + register int i, j, k, l; /* indices */ + int ip; // this is the index of the constraint to be added to the active set + Matrix<double> R(n, n), J(n, n); + Vector<double> s(m + p), z(n), r(m + p), d(n), np(n), u(m + p), x_old(n), u_old(m + p); + double f_value, psi, c1, c2, sum, ss, R_norm; + double inf; + if (std::numeric_limits<double>::has_infinity) + inf = std::numeric_limits<double>::infinity(); + else + inf = 1.0E300; + double t, t1, t2; /* t is the step lenght, which is the minimum of the partial step length t1 + * and the full step length t2 */ + Vector<int> A(m + p), A_old(m + p), iai(m + p); + int q, iq, iter = 0; + Vector<bool> iaexcl(m + p); + + /* p is the number of equality constraints */ + /* m is the number of inequality constraints */ + q = 0; /* size of the active set A (containing the indices of the active constraints) */ +#ifdef TRACE_SOLVER + std::cout << std::endl << "Starting solve_quadprog" << std::endl; + print_matrix("G", G); + print_vector("g0", g0); + print_matrix("CE", CE); + print_vector("ce0", ce0); + print_matrix("CI", CI); + print_vector("ci0", ci0); +#endif + + /* + * Preprocessing phase + */ + + /* compute the trace of the original matrix G */ + c1 = 0.0; + for (i = 0; i < n; i++) { + c1 += G[i][i]; + } + /* decompose the matrix G in the form L^T L */ + cholesky_decomposition(G); +#ifdef TRACE_SOLVER + print_matrix("G", G); +#endif + /* initialize the matrix R */ + for (i = 0; i < n; i++) { + d[i] = 0.0; + for (j = 0; j < n; j++) + R[i][j] = 0.0; + } + R_norm = 1.0; /* this variable will hold the norm of the matrix R */ + + /* compute the inverse of the factorized matrix G^-1, this is the initial value for H */ + c2 = 0.0; + for (i = 0; i < n; i++) { + d[i] = 1.0; + forward_elimination(G, z, d); + for (j = 0; j < n; j++) + J[i][j] = z[j]; + c2 += z[i]; + d[i] = 0.0; + } +#ifdef TRACE_SOLVER + print_matrix("J", J); +#endif + + /* c1 * c2 is an estimate for cond(G) */ + + /* + * Find the unconstrained minimizer of the quadratic form 0.5 * x G x + g0 x + * this is a feasible point in the dual space + * x = G^-1 * g0 + */ + cholesky_solve(G, x, g0); + for (i = 0; i < n; i++) + x[i] = -x[i]; + /* and compute the current solution value */ + f_value = 0.5 * scalar_product(g0, x); +#ifdef TRACE_SOLVER + std::cout << "Unconstrained solution: " << f_value << std::endl; + print_vector("x", x); +#endif + + /* Add equality constraints to the working set A */ + iq = 0; + for (i = 0; i < p; i++) { + for (j = 0; j < n; j++) + np[j] = CE[j][i]; + compute_d(d, J, np); + update_z(z, J, d, iq); + update_r(R, r, d, iq); +#ifdef TRACE_SOLVER + print_matrix("R", R, n, iq); + print_vector("z", z); + print_vector("r", r, iq); + print_vector("d", d); +#endif + + /* compute full step length t2: i.e., the minimum step in primal space s.t. the contraint + becomes feasible */ + t2 = 0.0; + if (fabs(scalar_product(z, z)) > std::numeric_limits<double>::epsilon()) // i.e. z != 0 + t2 = (-scalar_product(np, x) - ce0[i]) / scalar_product(z, np); + + /* set x = x + t2 * z */ + for (k = 0; k < n; k++) + x[k] += t2 * z[k]; + + /* set u = u+ */ + u[iq] = t2; + for (k = 0; k < iq; k++) + u[k] -= t2 * r[k]; + + /* compute the new solution value */ + f_value += 0.5 * (t2 * t2) * scalar_product(z, np); + A[i] = -i - 1; + + if (!add_constraint(R, J, d, iq, R_norm)) { + // Equality constraints are linearly dependent +// throw std::runtime_error("Constraints are linearly dependent"); + return f_value; + } + } + + /* set iai = K \ A */ + for (i = 0; i < m; i++) + iai[i] = i; + +l1: + iter++; +#ifdef TRACE_SOLVER + print_vector("x", x); +#endif + /* step 1: choose a violated constraint */ + for (i = p; i < iq; i++) { + ip = A[i]; + iai[ip] = -1; + } + + /* compute s[x] = ci^T * x + ci0 for all elements of K \ A */ + ss = 0.0; + psi = 0.0; /* this value will contain the sum of all infeasibilities */ + ip = 0; /* ip will be the index of the chosen violated constraint */ + for (i = 0; i < m; i++) { + iaexcl[i] = true; + sum = 0.0; + for (j = 0; j < n; j++) + sum += CI[j][i] * x[j]; + sum += ci0[i]; + s[i] = sum; + psi += std::min(0.0, sum); + } +#ifdef TRACE_SOLVER + print_vector("s", s, m); +#endif + + + if (fabs(psi) <= m * std::numeric_limits<double>::epsilon() * c1 * c2* 100.0) { + /* numerically there are not infeasibilities anymore */ + q = iq; + + return f_value; + } + + /* save old values for u and A */ + for (i = 0; i < iq; i++) { + u_old[i] = u[i]; + A_old[i] = A[i]; + } + /* and for x */ + for (i = 0; i < n; i++) + x_old[i] = x[i]; + +l2: /* Step 2: check for feasibility and determine a new S-pair */ + for (i = 0; i < m; i++) { + if (s[i] < ss && iai[i] != -1 && iaexcl[i]) { + ss = s[i]; + ip = i; + } + } + if (ss >= 0.0) { + q = iq; + + return f_value; + } + + /* set np = n[ip] */ + for (i = 0; i < n; i++) + np[i] = CI[i][ip]; + /* set u = [u 0]^T */ + u[iq] = 0.0; + /* add ip to the active set A */ + A[iq] = ip; + +#ifdef TRACE_SOLVER + std::cout << "Trying with constraint " << ip << std::endl; + print_vector("np", np); +#endif + +l2a:/* Step 2a: determine step direction */ + /* compute z = H np: the step direction in the primal space (through J, see the paper) */ + compute_d(d, J, np); + update_z(z, J, d, iq); + /* compute N* np (if q > 0): the negative of the step direction in the dual space */ + update_r(R, r, d, iq); +#ifdef TRACE_SOLVER + std::cout << "Step direction z" << std::endl; + print_vector("z", z); + print_vector("r", r, iq + 1); + print_vector("u", u, iq + 1); + print_vector("d", d); + print_vector("A", A, iq + 1); +#endif + + /* Step 2b: compute step length */ + l = 0; + /* Compute t1: partial step length (maximum step in dual space without violating dual feasibility */ + t1 = inf; /* +inf */ + /* find the index l s.t. it reaches the minimum of u+[x] / r */ + for (k = p; k < iq; k++) { + if (r[k] > 0.0) { + if (u[k] / r[k] < t1) { + t1 = u[k] / r[k]; + l = A[k]; + } + } + } + /* Compute t2: full step length (minimum step in primal space such that the constraint ip becomes feasible */ + if (fabs(scalar_product(z, z)) > std::numeric_limits<double>::epsilon()) { // i.e. z != 0 + t2 = -s[ip] / scalar_product(z, np); + if (t2 < 0) // patch suggested by Takano Akio for handling numerical inconsistencies + t2 = inf; + } else + t2 = inf; /* +inf */ + + /* the step is chosen as the minimum of t1 and t2 */ + t = std::min(t1, t2); +#ifdef TRACE_SOLVER + std::cout << "Step sizes: " << t << " (t1 = " << t1 << ", t2 = " << t2 << ") "; +#endif + + /* Step 2c: determine new S-pair and take step: */ + + /* case (i): no step in primal or dual space */ + if (t >= inf) { + /* QPP is infeasible */ + // FIXME: unbounded to raise + q = iq; + return inf; + } + /* case (ii): step in dual space */ + if (t2 >= inf) { + /* set u = u + t * [-r 1] and drop constraint l from the active set A */ + for (k = 0; k < iq; k++) + u[k] -= t * r[k]; + u[iq] += t; + iai[l] = l; + delete_constraint(R, J, A, u, n, p, iq, l); +#ifdef TRACE_SOLVER + std::cout << " in dual space: " + << f_value << std::endl; + print_vector("x", x); + print_vector("z", z); + print_vector("A", A, iq + 1); +#endif + goto l2a; + } + + /* case (iii): step in primal and dual space */ + + /* set x = x + t * z */ + for (k = 0; k < n; k++) + x[k] += t * z[k]; + /* update the solution value */ + f_value += t * scalar_product(z, np) * (0.5 * t + u[iq]); + /* u = u + t * [-r 1] */ + for (k = 0; k < iq; k++) + u[k] -= t * r[k]; + u[iq] += t; +#ifdef TRACE_SOLVER + std::cout << " in both spaces: " + << f_value << std::endl; + print_vector("x", x); + print_vector("u", u, iq + 1); + print_vector("r", r, iq + 1); + print_vector("A", A, iq + 1); +#endif + + if (fabs(t - t2) < std::numeric_limits<double>::epsilon()) { +#ifdef TRACE_SOLVER + std::cout << "Full step has taken " << t << std::endl; + print_vector("x", x); +#endif + /* full step has taken */ + /* add constraint ip to the active set*/ + if (!add_constraint(R, J, d, iq, R_norm)) { + iaexcl[ip] = false; + delete_constraint(R, J, A, u, n, p, iq, ip); +#ifdef TRACE_SOLVER + print_matrix("R", R); + print_vector("A", A, iq); + print_vector("iai", iai); +#endif + for (i = 0; i < m; i++) + iai[i] = i; + for (i = p; i < iq; i++) { + A[i] = A_old[i]; + u[i] = u_old[i]; + iai[A[i]] = -1; + } + for (i = 0; i < n; i++) + x[i] = x_old[i]; + goto l2; /* go to step 2 */ + } else + iai[ip] = -1; +#ifdef TRACE_SOLVER + print_matrix("R", R); + print_vector("A", A, iq); + print_vector("iai", iai); +#endif + goto l1; + } + + /* a patial step has taken */ +#ifdef TRACE_SOLVER + std::cout << "Partial step has taken " << t << std::endl; + print_vector("x", x); +#endif + /* drop constraint l */ + iai[l] = l; + delete_constraint(R, J, A, u, n, p, iq, l); +#ifdef TRACE_SOLVER + print_matrix("R", R); + print_vector("A", A, iq); +#endif + + /* update s[ip] = CI * x + ci0 */ + sum = 0.0; + for (k = 0; k < n; k++) + sum += CI[k][ip] * x[k]; + s[ip] = sum + ci0[ip]; + +#ifdef TRACE_SOLVER + print_vector("s", s, m); +#endif + goto l2a; +} + +inline void compute_d(Vector<double>& d, const Matrix<double>& J, const Vector<double>& np) +{ + register int i, j, n = d.size(); + register double sum; + + /* compute d = H^T * np */ + for (i = 0; i < n; i++) { + sum = 0.0; + for (j = 0; j < n; j++) + sum += J[j][i] * np[j]; + d[i] = sum; + } +} + +inline void update_z(Vector<double>& z, const Matrix<double>& J, const Vector<double>& d, int iq) +{ + register int i, j, n = z.size(); + + /* setting of z = H * d */ + for (i = 0; i < n; i++) { + z[i] = 0.0; + for (j = iq; j < n; j++) + z[i] += J[i][j] * d[j]; + } +} + +inline void update_r(const Matrix<double>& R, Vector<double>& r, const Vector<double>& d, int iq) +{ + register int i, j, n = d.size(); + register double sum; + + /* setting of r = R^-1 d */ + for (i = iq - 1; i >= 0; i--) { + sum = 0.0; + for (j = i + 1; j < iq; j++) + sum += R[i][j] * r[j]; + r[i] = (d[i] - sum) / R[i][i]; + } +} + +bool add_constraint(Matrix<double>& R, Matrix<double>& J, Vector<double>& d, int& iq, double& R_norm) +{ + int n = d.size(); +#ifdef TRACE_SOLVER + std::cout << "Add constraint " << iq << '/'; +#endif + register int i, j, k; + double cc, ss, h, t1, t2, xny; + + /* we have to find the Givens rotation which will reduce the element + d[j] to zero. + if it is already zero we don't have to do anything, except of + decreasing j */ + for (j = n - 1; j >= iq + 1; j--) { + /* The Givens rotation is done with the matrix (cc cs, cs -cc). + If cc is one, then element (j) of d is zero compared with element + (j - 1). Hence we don't have to do anything. + If cc is zero, then we just have to switch column (j) and column (j - 1) + of J. Since we only switch columns in J, we have to be careful how we + update d depending on the sign of gs. + Otherwise we have to apply the Givens rotation to these columns. + The i - 1 element of d has to be updated to h. */ + cc = d[j - 1]; + ss = d[j]; + h = distance(cc, ss); + if (fabs(h) < std::numeric_limits<double>::epsilon()) // h == 0 + continue; + d[j] = 0.0; + ss = ss / h; + cc = cc / h; + if (cc < 0.0) { + cc = -cc; + ss = -ss; + d[j - 1] = -h; + } else + d[j - 1] = h; + xny = ss / (1.0 + cc); + for (k = 0; k < n; k++) { + t1 = J[k][j - 1]; + t2 = J[k][j]; + J[k][j - 1] = t1 * cc + t2 * ss; + J[k][j] = xny * (t1 + J[k][j - 1]) - t2; + } + } + /* update the number of constraints added*/ + iq++; + /* To update R we have to put the iq components of the d vector + into column iq - 1 of R + */ + for (i = 0; i < iq; i++) + R[i][iq - 1] = d[i]; +#ifdef TRACE_SOLVER + std::cout << iq << std::endl; + print_matrix("R", R, iq, iq); + print_matrix("J", J); + print_vector("d", d, iq); +#endif + + if (fabs(d[iq - 1]) <= std::numeric_limits<double>::epsilon() * R_norm) { + // problem degenerate + return false; + } + R_norm = std::max<double>(R_norm, fabs(d[iq - 1])); + return true; +} + +void delete_constraint(Matrix<double>& R, Matrix<double>& J, Vector<int>& A, Vector<double>& u, int n, int p, int& iq, int l) +{ +#ifdef TRACE_SOLVER + std::cout << "Delete constraint " << l << ' ' << iq; +#endif + register int i, j, k, qq = -1; // just to prevent warnings from smart compilers + double cc, ss, h, xny, t1, t2; + + /* Find the index qq for active constraint l to be removed */ + for (i = p; i < iq; i++) + if (A[i] == l) { + qq = i; + break; + } + + /* remove the constraint from the active set and the duals */ + for (i = qq; i < iq - 1; i++) { + A[i] = A[i + 1]; + u[i] = u[i + 1]; + for (j = 0; j < n; j++) + R[j][i] = R[j][i + 1]; + } + + A[iq - 1] = A[iq]; + u[iq - 1] = u[iq]; + A[iq] = 0; + u[iq] = 0.0; + for (j = 0; j < iq; j++) + R[j][iq - 1] = 0.0; + /* constraint has been fully removed */ + iq--; +#ifdef TRACE_SOLVER + std::cout << '/' << iq << std::endl; +#endif + + if (iq == 0) + return; + + for (j = qq; j < iq; j++) { + cc = R[j][j]; + ss = R[j + 1][j]; + h = distance(cc, ss); + if (fabs(h) < std::numeric_limits<double>::epsilon()) // h == 0 + continue; + cc = cc / h; + ss = ss / h; + R[j + 1][j] = 0.0; + if (cc < 0.0) { + R[j][j] = -h; + cc = -cc; + ss = -ss; + } else + R[j][j] = h; + + xny = ss / (1.0 + cc); + for (k = j + 1; k < iq; k++) { + t1 = R[j][k]; + t2 = R[j + 1][k]; + R[j][k] = t1 * cc + t2 * ss; + R[j + 1][k] = xny * (t1 + R[j][k]) - t2; + } + for (k = 0; k < n; k++) { + t1 = J[k][j]; + t2 = J[k][j + 1]; + J[k][j] = t1 * cc + t2 * ss; + J[k][j + 1] = xny * (J[k][j] + t1) - t2; + } + } +} + +inline double distance(double a, double b) +{ + register double a1, b1, t; + a1 = fabs(a); + b1 = fabs(b); + if (a1 > b1) { + t = (b1 / a1); + return a1 * sqrt(1.0 + t * t); + } else if (b1 > a1) { + t = (a1 / b1); + return b1 * sqrt(1.0 + t * t); + } + return a1 * sqrt(2.0); +} + + +inline double scalar_product(const Vector<double>& x, const Vector<double>& y) +{ + register int i, n = x.size(); + register double sum; + + sum = 0.0; + for (i = 0; i < n; i++) + sum += x[i] * y[i]; + return sum; +} + +void cholesky_decomposition(Matrix<double>& A) +{ + register int i, j, k, n = A.nrows(); + register double sum; + + for (i = 0; i < n; i++) { + for (j = i; j < n; j++) { + sum = A[i][j]; + for (k = i - 1; k >= 0; k--) + sum -= A[i][k]*A[j][k]; + if (i == j) { + if (sum <= 0.0) { + std::ostringstream os; + // raise error + print_matrix("A", A); + os << "Error in cholesky decomposition, sum: " << sum; +// throw std::logic_error(os.str()); +// exit(-1); + } + A[i][i] = sqrt(sum); + } else + A[j][i] = sum / A[i][i]; + } + for (k = i + 1; k < n; k++) + A[i][k] = A[k][i]; + } +} + +void cholesky_solve(const Matrix<double>& L, Vector<double>& x, const Vector<double>& b) +{ + int n = L.nrows(); + Vector<double> y(n); + + /* Solve L * y = b */ + forward_elimination(L, y, b); + /* Solve L^T * x = y */ + backward_elimination(L, x, y); +} + +inline void forward_elimination(const Matrix<double>& L, Vector<double>& y, const Vector<double>& b) +{ + register int i, j, n = L.nrows(); + + y[0] = b[0] / L[0][0]; + for (i = 1; i < n; i++) { + y[i] = b[i]; + for (j = 0; j < i; j++) + y[i] -= L[i][j] * y[j]; + y[i] = y[i] / L[i][i]; + } +} + +inline void backward_elimination(const Matrix<double>& U, Vector<double>& x, const Vector<double>& y) +{ + register int i, j, n = U.nrows(); + + x[n - 1] = y[n - 1] / U[n - 1][n - 1]; + for (i = n - 2; i >= 0; i--) { + x[i] = y[i]; + for (j = i + 1; j < n; j++) + x[i] -= U[i][j] * x[j]; + x[i] = x[i] / U[i][i]; + } +} + +void print_matrix(char* name, const Matrix<double>& A, int n, int m) +{ + std::ostringstream s; + std::string t; + if (n == -1) + n = A.nrows(); + if (m == -1) + m = A.ncols(); + + s << name << ": " << std::endl; + for (int i = 0; i < n; i++) { + s << " "; + for (int j = 0; j < m; j++) + s << A[i][j] << ", "; + s << std::endl; + } + t = s.str(); + t = t.substr(0, t.size() - 3); // To remove the trailing space, comma and newline + + std::cout << t << std::endl; +} + +template<typename T> +void print_vector(char* name, const Vector<T>& v, int n) +{ + std::ostringstream s; + std::string t; + if (n == -1) + n = v.size(); + + s << name << ": " << std::endl << " "; + for (int i = 0; i < n; i++) { + s << v[i] << ", "; + } + t = s.str(); + t = t.substr(0, t.size() - 2); // To remove the trailing space and comma + + std::cout << t << std::endl; +} + +} // namespace quadprogpp
diff -r 27f1640d930d -r e843c1b0b25c quadprog.h --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/quadprog.h Tue Sep 24 00:20:12 2019 +0000 @@ -0,0 +1,76 @@ +/* + File $Id: QuadProg++.hh 232 2007-06-21 12:29:00Z digasper $ + + The quadprog_solve() function implements the algorithm of Goldfarb and Idnani + for the solution of a (convex) Quadratic Programming problem + by means of an active-set dual method. + +The problem is in the form: + +min 0.5 * x G x + g0 x +s.t. + CE^T x + ce0 = 0 + CI^T x + ci0 >= 0 + + The matrix and vectors dimensions are as follows: + G: n * n + g0: n + + CE: n * p + ce0: p + + CI: n * m + ci0: m + + x: n + + The function will return the cost of the solution written in the x vector or + std::numeric_limits::infinity() if the problem is infeasible. In the latter case + the value of the x vector is not correct. + + References: D. Goldfarb, A. Idnani. A numerically stable dual method for solving + strictly convex quadratic programs. Mathematical Programming 27 (1983) pp. 1-33. + + Notes: + 1. pay attention in setting up the vectors ce0 and ci0. + If the constraints of your problem are specified in the form + A^T x = b and C^T x >= d, then you should set ce0 = -b and ci0 = -d. + 2. The matrices have column dimension equal to MATRIX_DIM, + a constant set to 20 in this file (by means of a #define macro). + If the matrices are bigger than 20 x 20 the limit could be + increased by means of a -DMATRIX_DIM=n on the compiler command line. + 3. The matrix G is modified within the function since it is used to compute + the G = L^T L cholesky factorization for further computations inside the function. + If you need the original matrix G you should make a copy of it and pass the copy + to the function. + + Author: Luca Di Gaspero + DIEGM - University of Udine, Italy + luca.digaspero@uniud.it + http://www.diegm.uniud.it/digaspero/ + + The author will be grateful if the researchers using this software will + acknowledge the contribution of this function in their research papers. + + Copyright (c) 2007-2016 Luca Di Gaspero + + This software may be modified and distributed under the terms + of the MIT license. See the LICENSE file for details. +*/ + + +#ifndef _QUADPROGPP +#define _QUADPROGPP + +#include "Array.h" + +namespace quadprogpp { + +double solve_quadprog(Matrix<double>& G, Vector<double>& g0, + const Matrix<double>& CE, const Vector<double>& ce0, + const Matrix<double>& CI, const Vector<double>& ci0, + Vector<double>& x); + +} // namespace quadprogpp + +#endif // #define _QUADPROGPP