src/math/DynamicVector.hpp

/*
 * Copyright (c) 2005 The University of Notre Dame. All Rights Reserved.
 *
 * The University of Notre Dame grants you ("Licensee") a
 * non-exclusive, royalty free, license to use, modify and
 * redistribute this software in source and binary code form, provided
 * that the following conditions are met:
 *
 * 1. Acknowledgement of the program authors must be made in any
 *    publication of scientific results based in part on use of the
 *    program.  An acceptable form of acknowledgement is citation of
 *    the article in which the program was described (Matthew
 *    A. Meineke, Charles F. Vardeman II, Teng Lin, Christopher
 *    J. Fennell and J. Daniel Gezelter, "OOPSE: An Object-Oriented
 *    Parallel Simulation Engine for Molecular Dynamics,"
 *    J. Comput. Chem. 26, pp. 252-271 (2005))
 *
 * 2. Redistributions of source code must retain the above copyright
 *    notice, this list of conditions and the following disclaimer.
 *
 * 3. Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in the
 *    documentation and/or other materials provided with the
 *    distribution.
 *
 * This software is provided "AS IS," without a warranty of any
 * kind. All express or implied conditions, representations and
 * warranties, including any implied warranty of merchantability,
 * fitness for a particular purpose or non-infringement, are hereby
 * excluded.  The University of Notre Dame and its licensors shall not
 * be liable for any damages suffered by licensee as a result of
 * using, modifying or distributing the software or its
 * derivatives. In no event will the University of Notre Dame or its
 * licensors be liable for any lost revenue, profit or data, or for
 * direct, indirect, special, consequential, incidental or punitive
 * damages, however caused and regardless of the theory of liability,
 * arising out of the use of or inability to use software, even if the
 * University of Notre Dame has been advised of the possibility of
 * such damages.
 */
 
/**
 * @file DynamicVector.hpp
 * @author Teng Lin
 * @date 09/14/2004
 * @version 1.0
 */
 
#ifndef MATH_DYNAMICVECTOR_HPP
#define MATH_DYNAMICVECTOR_HPP

#include <cassert>
#include <cmath>
#include <iostream>
#include <math.h>
#include <algorithm>
#include <vector>

namespace oopse {
    
  /**
   * @class DynamicVector DynamicVector.hpp "math/DynamicVector.hpp"
   * @brief Fix length vector class
   */
  template<typename Real, typename Alloc = std::allocator<Real> >
  class DynamicVector : public std::vector<Real, Alloc> {
  
  public:
      typedef Real value_type;
      typedef std::vector<Real, Alloc> VectorType;
      typedef typename VectorType::pointer pointer;
      typedef typename VectorType::const_pointer const_pointer;
      typedef typename VectorType::reference reference;
      typedef typename VectorType::const_reference const_reference;
      typedef typename VectorType::iterator iterator;
      typedef typename VectorType::const_iterator const_iterator;
      typedef typename VectorType::const_reverse_iterator  const_reverse_iterator;
      typedef typename VectorType::reverse_iterator reverse_iterator;
      typedef typename VectorType::size_type size_type;
      typedef typename VectorType::difference_type difference_type;
      typedef typename VectorType::allocator_type allocator_type;


      // [23.2.4.1] construct/copy/destroy
      // (assign() and get_allocator() are also listed in this section)
      /**
       *  @brief  Default constructor creates no elements.
       */      explicit
      DynamicVector(const allocator_type& alloc = allocator_type())
      : std::vector<Real, Alloc>(alloc) { }
  
      /**
       *  @brief  Create a %DynamicVector with copies of an exemplar element.
       *  @param  n  The number of elements to initially create.
       *  @param  value  An element to copy.
       *
       *  This constructor fills the %DynamicVector with @a n copies of @a value.
       */
      DynamicVector(size_type n, const value_type& value,
             const allocator_type& alloc = allocator_type())
      : std::vector<Real, Alloc>(n, value, alloc){ }

      /**
       *  @brief  Create a %DynamicVector with default elements.
       *  @param  n  The number of elements to initially create.
       *
       *  This constructor fills the %DynamicVector with @a n copies of a
       *  default-constructed element.
       */
      explicit
      DynamicVector(size_type n) : std::vector<Real, Alloc>(n) { }

      /**
       *  @brief  %Vector copy constructor.
       *  @param  x  A %DynamicVector of identical element and allocator types.
       *
       *  The newly-created %DynamicVector uses a copy of the allocation
       *  object used by @a x.  All the elements of @a x are copied,
       *  but any extra memory in
       *  @a x (for fast expansion) will not be copied.
       */
      DynamicVector(const DynamicVector& x)
      : std::vector<Real, Alloc>(x) {}

      template<typename _InputIterator>
        DynamicVector(_InputIterator first, _InputIterator last,
               const allocator_type& alloc = allocator_type())
        : std::vector<Real, Alloc>(first, last, alloc) {}
            
    /**
     * Tests if this vetor is equal to other vector
     * @return true if equal, otherwise return false
     * @param v vector to be compared
     */
    inline bool operator ==(const DynamicVector<Real>& v) {

      for (unsigned int i = 0; i < this->size(); i ++) {
        if (!equal((*this)[i], v[i])) {
          return false;
        }
      }
                
      return true;
    }

    /**
     * Tests if this vetor is not equal to other vector
     * @return true if equal, otherwise return false
     * @param v vector to be compared
     */
    inline bool operator !=(const DynamicVector<Real>& v) {
      return !(*this == v);
    }
             
    /** Negates the value of this vector in place. */           
    inline void negate() {
      for (unsigned int i = 0; i < this->size(); i++)
        (*this)[i] = -(*this)[i];
    }

    /**
     * Sets the value of this vector to the negation of vector v1.
     * @param v1 the source vector
     */
    inline void negate(const DynamicVector<Real>& v1) {
      for (unsigned int i = 0; i < this->size(); i++)
        (*this)[i] = -v1[i];

    }
            
    /**
     * Sets the value of this vector to the sum of itself and v1 (*this += v1).
     * @param v1 the other vector
     */
    inline void add( const DynamicVector<Real>& v1 ) {
      std::transform(this->begin(), this->end(), v1.begin(),this->begin(),std::plus<Real>());
    }

    /**
     * Sets the value of this vector to the sum of v1 and v2 (*this = v1 + v2).
     * @param v1 the first vector
     * @param v2 the second vector
     */
    inline void add( const DynamicVector<Real>& v1, const DynamicVector<Real>& v2 ) {
      std::transform(v1.begin(), v1.end(), v2.begin(),this->begin(),std::plus<Real>());
    }

    /**
     * Sets the value of this vector to the difference  of itself and v1 (*this -= v1).
     * @param v1 the other vector
     */
    inline void sub( const DynamicVector<Real>& v1 ) {
        std::transform(this->begin(), this->end(), v1.begin(),this->begin(),std::minus<Real>());
    }

    /**
     * Sets the value of this vector to the difference of vector v1 and v2 (*this = v1 - v2).
     * @param v1 the first vector
     * @param v2 the second vector
     */
    inline void sub( const DynamicVector<Real>& v1, const DynamicVector  &v2 ){
      std::transform(v1.begin(), v1.end(), v2.begin(),this->begin(),std::minus<Real>());    
    }

    /**
     * Sets the value of this vector to the scalar multiplication of itself (*this *= s).
     * @param s the scalar value
     */
    inline void mul( Real s ) {
      for (unsigned int i = 0; i < this->size(); i++)
        (*this)[i] *= s;
    }

    /**
     * Sets the value of this vector to the scalar multiplication of vector v1  
     * (*this = s * v1).
     * @param v1 the vector            
     * @param s the scalar value
     */
    inline void mul( const DynamicVector<Real>& v1, Real s) {
      for (unsigned int i = 0; i < this->size(); i++)
        (*this)[i] = s * v1[i];
    }

    /**
     * Sets the value of this vector to the scalar division of itself  (*this /= s ).
     * @param s the scalar value
     */             
    inline void div( Real s) {
      for (unsigned int i = 0; i < this->size(); i++)            
        (*this)[i] /= s;
    }

    /**
     * Sets the value of this vector to the scalar division of vector v1  (*this = v1 / s ).
     * @param v1 the source vector
     * @param s the scalar value
     */                         
    inline void div( const DynamicVector<Real>& v1, Real s ) {
      for (unsigned int i = 0; i < this->size(); i++)
        (*this)[i] = v1[i] / s;
    }

    /** @see #add */
    inline DynamicVector<Real>& operator +=( const DynamicVector<Real>& v1 ) {
      add(v1);
      return *this;
    }

    /** @see #sub */
    inline DynamicVector<Real>& operator -=( const DynamicVector<Real>& v1 ) {
      sub(v1);
      return *this;
    }

    /** @see #mul */
    inline DynamicVector<Real>& operator *=( Real s) {
      mul(s);
      return *this;
    }

    /** @see #div */
    inline DynamicVector<Real>& operator /=( Real s ) {
      div(s);
      return *this;
    }

    /**
     * Returns the length of this vector.
     * @return the length of this vector
     */
    inline Real length() {
      return sqrt(lengthSquare());  
    }
            
    /**
     * Returns the squared length of this vector.
     * @return the squared length of this vector
     */
    inline Real lengthSquare() {
      return dot(*this, *this);
    }
            
    /** Normalizes this vector in place */
    inline void normalize() {
      Real len;

      len = length();
                
      //if (len < oopse:epsilon)
      //  throw();
                
      *this /= len;
    }

    /**
     * Tests if this vector is normalized
     * @return true if this vector is normalized, otherwise return false
     */
    inline bool isNormalized() {
      return equal(lengthSquare(), 1.0);
    }           
    
  };

  /** unary minus*/
  template<typename Real>    
  inline DynamicVector<Real> operator -(const DynamicVector<Real>& v1){
    DynamicVector<Real> tmp(v1);
    tmp.negate();
    return tmp;
  }

  /**
   * Return the sum of two vectors  (v1 - v2). 
   * @return the sum of two vectors
   * @param v1 the first vector
   * @param v2 the second vector
   */   
  template<typename Real>    
  inline DynamicVector<Real> operator +(const DynamicVector<Real>& v1, const DynamicVector<Real>& v2) {
    DynamicVector<Real> result;
        
    result.add(v1, v2);
    return result;        
  }

  /**
   * Return the difference of two vectors  (v1 - v2). 
   * @return the difference of two vectors
   * @param v1 the first vector
   * @param v2 the second vector
   */  
  template<typename Real>    
  DynamicVector<Real> operator -(const DynamicVector<Real>& v1, const DynamicVector<Real>& v2) {
    DynamicVector<Real> result;
    result.sub(v1, v2);
    return result;        
  }
    
  /**
   * Returns the vaule of scalar multiplication of this vector v1 (v1 * r). 
   * @return  the vaule of scalar multiplication of this vector
   * @param v1 the source vector
   * @param s the scalar value
   */ 
  template<typename Real>                 
  DynamicVector<Real> operator * ( const DynamicVector<Real>& v1, Real s) {       
    DynamicVector<Real> result;
    result.mul(v1,s);
    return result;           
  }
    
  /**
   * Returns the vaule of scalar multiplication of this vector v1 (v1 * r). 
   * @return  the vaule of scalar multiplication of this vector
   * @param s the scalar value
   * @param v1 the source vector
   */  
  template<typename Real>
  DynamicVector<Real> operator * ( Real s, const DynamicVector<Real>& v1 ) {
    DynamicVector<Real> result;
    result.mul(v1, s);
    return result;           
  }

  /**
   * Returns the  value of division of a vector by a scalar. 
   * @return  the vaule of scalar division of this vector
   * @param v1 the source vector
   * @param s the scalar value
   */
  template<typename Real>    
  DynamicVector<Real> operator / ( const DynamicVector<Real>& v1, Real s) {       
    DynamicVector<Real> result;
    result.div( v1,s);
    return result;           
  }
    
  /**
   * Returns the dot product of two DynamicVectors
   * @param v1 first vector
   * @param v2 second vector
   * @return the dot product of v1 and v2
   */
  template<typename Real>    
  inline Real dot( const DynamicVector<Real>& v1, const DynamicVector<Real>& v2 ) {
    Real tmp;
    tmp = 0;
    assert(v1.size() == v2.size());
    for (unsigned int i = 0; i < v1.size(); i++)
      tmp += v1[i] * v2[i];

    return tmp;
  }

  /**
   * Returns the distance between  two DynamicVectors
   * @param v1 first vector
   * @param v2 second vector
   * @return the distance between v1 and v2
   */   
  template<typename Real>    
  inline Real distance( const DynamicVector<Real>& v1, const DynamicVector<Real>& v2 ) {
    DynamicVector<Real> tempDynamicVector = v1 - v2;
    return tempDynamicVector.length();
  }

  /**
   * Returns the squared distance between  two DynamicVectors
   * @param v1 first vector
   * @param v2 second vector
   * @return the squared distance between v1 and v2
   */
  template<typename Real>
  inline Real distanceSquare( const DynamicVector<Real>& v1, const DynamicVector<Real>& v2 ) {
    DynamicVector<Real> tempDynamicVector = v1 - v2;
    return tempDynamicVector.lengthSquare();
  }

  /**
   * Write to an output stream
   */
  template<typename Real>
  std::ostream &operator<< ( std::ostream& o, const DynamicVector<Real>& v) {

    o << "[ ";
        
    for (unsigned int i = 0 ; i< v.size(); i++) {
      o << v[i];

      if (i  != v.size() -1) {
        o<< ", ";
      }
    }

    o << " ]";
    return o;        
  }
    
}
#endif

Revision:	891
Committed:	Wed Feb 22 20:35:16 2006 UTC (19 years, 2 months ago) by tim
Original Path:	*trunk/src/math/DynamicVector.hpp*
File size:	14049 byte(s)
Log Message:	Adding Hydrodynamics Module
#	User	Rev	Content
1	tim	891	/*
2			* Copyright (c) 2005 The University of Notre Dame. All Rights Reserved.
3			*
4			* The University of Notre Dame grants you ("Licensee") a
5			* non-exclusive, royalty free, license to use, modify and
6			* redistribute this software in source and binary code form, provided
7			* that the following conditions are met:
8			*
9			* 1. Acknowledgement of the program authors must be made in any
10			* publication of scientific results based in part on use of the
11			* program. An acceptable form of acknowledgement is citation of
12			* the article in which the program was described (Matthew
13			* A. Meineke, Charles F. Vardeman II, Teng Lin, Christopher
14			* J. Fennell and J. Daniel Gezelter, "OOPSE: An Object-Oriented
15			* Parallel Simulation Engine for Molecular Dynamics,"
16			* J. Comput. Chem. 26, pp. 252-271 (2005))
17			*
18			* 2. Redistributions of source code must retain the above copyright
19			* notice, this list of conditions and the following disclaimer.
20			*
21			* 3. Redistributions in binary form must reproduce the above copyright
22			* notice, this list of conditions and the following disclaimer in the
23			* documentation and/or other materials provided with the
24			* distribution.
25			*
26			* This software is provided "AS IS," without a warranty of any
27			* kind. All express or implied conditions, representations and
28			* warranties, including any implied warranty of merchantability,
29			* fitness for a particular purpose or non-infringement, are hereby
30			* excluded. The University of Notre Dame and its licensors shall not
31			* be liable for any damages suffered by licensee as a result of
32			* using, modifying or distributing the software or its
33			* derivatives. In no event will the University of Notre Dame or its
34			* licensors be liable for any lost revenue, profit or data, or for
35			* direct, indirect, special, consequential, incidental or punitive
36			* damages, however caused and regardless of the theory of liability,
37			* arising out of the use of or inability to use software, even if the
38			* University of Notre Dame has been advised of the possibility of
39			* such damages.
40			*/
41
42			/**
43			* @file DynamicVector.hpp
44			* @author Teng Lin
45			* @date 09/14/2004
46			* @version 1.0
47			*/
48
49			#ifndef MATH_DYNAMICVECTOR_HPP
50			#define MATH_DYNAMICVECTOR_HPP
51
52			#include <cassert>
53			#include <cmath>
54			#include <iostream>
55			#include <math.h>
56			#include <algorithm>
57			#include <vector>
58
59			namespace oopse {
60
61			/**
62			* @class DynamicVector DynamicVector.hpp "math/DynamicVector.hpp"
63			* @brief Fix length vector class
64			*/
65			template<typename Real, typename Alloc = std::allocator<Real> >
66			class DynamicVector : public std::vector<Real, Alloc> {
67
68			public:
69			typedef Real value_type;
70			typedef std::vector<Real, Alloc> VectorType;
71			typedef typename VectorType::pointer pointer;
72			typedef typename VectorType::const_pointer const_pointer;
73			typedef typename VectorType::reference reference;
74			typedef typename VectorType::const_reference const_reference;
75			typedef typename VectorType::iterator iterator;
76			typedef typename VectorType::const_iterator const_iterator;
77			typedef typename VectorType::const_reverse_iterator const_reverse_iterator;
78			typedef typename VectorType::reverse_iterator reverse_iterator;
79			typedef typename VectorType::size_type size_type;
80			typedef typename VectorType::difference_type difference_type;
81			typedef typename VectorType::allocator_type allocator_type;
82
83
84			// [23.2.4.1] construct/copy/destroy
85			// (assign() and get_allocator() are also listed in this section)
86			/**
87			* @brief Default constructor creates no elements.
88			*/ explicit
89			DynamicVector(const allocator_type& alloc = allocator_type())
90			: std::vector<Real, Alloc>(alloc) { }
91
92			/**
93			* @brief Create a %DynamicVector with copies of an exemplar element.
94			* @param n The number of elements to initially create.
95			* @param value An element to copy.
96			*
97			* This constructor fills the %DynamicVector with @a n copies of @a value.
98			*/
99			DynamicVector(size_type n, const value_type& value,
100			const allocator_type& alloc = allocator_type())
101			: std::vector<Real, Alloc>(n, value, alloc){ }
102
103			/**
104			* @brief Create a %DynamicVector with default elements.
105			* @param n The number of elements to initially create.
106			*
107			* This constructor fills the %DynamicVector with @a n copies of a
108			* default-constructed element.
109			*/
110			explicit
111			DynamicVector(size_type n) : std::vector<Real, Alloc>(n) { }
112
113			/**
114			* @brief %Vector copy constructor.
115			* @param x A %DynamicVector of identical element and allocator types.
116			*
117			* The newly-created %DynamicVector uses a copy of the allocation
118			* object used by @a x. All the elements of @a x are copied,
119			* but any extra memory in
120			* @a x (for fast expansion) will not be copied.
121			*/
122			DynamicVector(const DynamicVector& x)
123			: std::vector<Real, Alloc>(x) {}
124
125			template<typename _InputIterator>
126			DynamicVector(_InputIterator first, _InputIterator last,
127			const allocator_type& alloc = allocator_type())
128			: std::vector<Real, Alloc>(first, last, alloc) {}
129
130			/**
131			* Tests if this vetor is equal to other vector
132			* @return true if equal, otherwise return false
133			* @param v vector to be compared
134			*/
135			inline bool operator ==(const DynamicVector<Real>& v) {
136
137			for (unsigned int i = 0; i < this->size(); i ++) {
138			if (!equal((*this)[i], v[i])) {
139			return false;
140			}
141			}
142
143			return true;
144			}
145
146			/**
147			* Tests if this vetor is not equal to other vector
148			* @return true if equal, otherwise return false
149			* @param v vector to be compared
150			*/
151			inline bool operator !=(const DynamicVector<Real>& v) {
152			return !(*this == v);
153			}
154
155			/** Negates the value of this vector in place. */
156			inline void negate() {
157			for (unsigned int i = 0; i < this->size(); i++)
158			(this)[i] = -(this)[i];
159			}
160
161			/**
162			* Sets the value of this vector to the negation of vector v1.
163			* @param v1 the source vector
164			*/
165			inline void negate(const DynamicVector<Real>& v1) {
166			for (unsigned int i = 0; i < this->size(); i++)
167			(*this)[i] = -v1[i];
168
169			}
170
171			/**
172			* Sets the value of this vector to the sum of itself and v1 (*this += v1).
173			* @param v1 the other vector
174			*/
175			inline void add( const DynamicVector<Real>& v1 ) {
176			std::transform(this->begin(), this->end(), v1.begin(),this->begin(),std::plus<Real>());
177			}
178
179			/**
180			* Sets the value of this vector to the sum of v1 and v2 (*this = v1 + v2).
181			* @param v1 the first vector
182			* @param v2 the second vector
183			*/
184			inline void add( const DynamicVector<Real>& v1, const DynamicVector<Real>& v2 ) {
185			std::transform(v1.begin(), v1.end(), v2.begin(),this->begin(),std::plus<Real>());
186			}
187
188			/**
189			* Sets the value of this vector to the difference of itself and v1 (*this -= v1).
190			* @param v1 the other vector
191			*/
192			inline void sub( const DynamicVector<Real>& v1 ) {
193			std::transform(this->begin(), this->end(), v1.begin(),this->begin(),std::minus<Real>());
194			}
195
196			/**
197			* Sets the value of this vector to the difference of vector v1 and v2 (*this = v1 - v2).
198			* @param v1 the first vector
199			* @param v2 the second vector
200			*/
201			inline void sub( const DynamicVector<Real>& v1, const DynamicVector &v2 ){
202			std::transform(v1.begin(), v1.end(), v2.begin(),this->begin(),std::minus<Real>());
203			}
204
205			/**
206			* Sets the value of this vector to the scalar multiplication of itself (this = s).
207			* @param s the scalar value
208			*/
209			inline void mul( Real s ) {
210			for (unsigned int i = 0; i < this->size(); i++)
211			(this)[i] = s;
212			}
213
214			/**
215			* Sets the value of this vector to the scalar multiplication of vector v1
216			* (this = s v1).
217			* @param v1 the vector
218			* @param s the scalar value
219			*/
220			inline void mul( const DynamicVector<Real>& v1, Real s) {
221			for (unsigned int i = 0; i < this->size(); i++)
222			(this)[i] = s v1[i];
223			}
224
225			/**
226			* Sets the value of this vector to the scalar division of itself (*this /= s ).
227			* @param s the scalar value
228			*/
229			inline void div( Real s) {
230			for (unsigned int i = 0; i < this->size(); i++)
231			(*this)[i] /= s;
232			}
233
234			/**
235			* Sets the value of this vector to the scalar division of vector v1 (*this = v1 / s ).
236			* @param v1 the source vector
237			* @param s the scalar value
238			*/
239			inline void div( const DynamicVector<Real>& v1, Real s ) {
240			for (unsigned int i = 0; i < this->size(); i++)
241			(*this)[i] = v1[i] / s;
242			}
243
244			/** @see #add */
245			inline DynamicVector<Real>& operator +=( const DynamicVector<Real>& v1 ) {
246			add(v1);
247			return *this;
248			}
249
250			/** @see #sub */
251			inline DynamicVector<Real>& operator -=( const DynamicVector<Real>& v1 ) {
252			sub(v1);
253			return *this;
254			}
255
256			/** @see #mul */
257			inline DynamicVector<Real>& operator *=( Real s) {
258			mul(s);
259			return *this;
260			}
261
262			/** @see #div */
263			inline DynamicVector<Real>& operator /=( Real s ) {
264			div(s);
265			return *this;
266			}
267
268			/**
269			* Returns the length of this vector.
270			* @return the length of this vector
271			*/
272			inline Real length() {
273			return sqrt(lengthSquare());
274			}
275
276			/**
277			* Returns the squared length of this vector.
278			* @return the squared length of this vector
279			*/
280			inline Real lengthSquare() {
281			return dot(this, this);
282			}
283
284			/** Normalizes this vector in place */
285			inline void normalize() {
286			Real len;
287
288			len = length();
289
290			//if (len < oopse:epsilon)
291			// throw();
292
293			*this /= len;
294			}
295
296			/**
297			* Tests if this vector is normalized
298			* @return true if this vector is normalized, otherwise return false
299			*/
300			inline bool isNormalized() {
301			return equal(lengthSquare(), 1.0);
302			}
303
304			};
305
306			/** unary minus*/
307			template<typename Real>
308			inline DynamicVector<Real> operator -(const DynamicVector<Real>& v1){
309			DynamicVector<Real> tmp(v1);
310			tmp.negate();
311			return tmp;
312			}
313
314			/**
315			* Return the sum of two vectors (v1 - v2).
316			* @return the sum of two vectors
317			* @param v1 the first vector
318			* @param v2 the second vector
319			*/
320			template<typename Real>
321			inline DynamicVector<Real> operator +(const DynamicVector<Real>& v1, const DynamicVector<Real>& v2) {
322			DynamicVector<Real> result;
323
324			result.add(v1, v2);
325			return result;
326			}
327
328			/**
329			* Return the difference of two vectors (v1 - v2).
330			* @return the difference of two vectors
331			* @param v1 the first vector
332			* @param v2 the second vector
333			*/
334			template<typename Real>
335			DynamicVector<Real> operator -(const DynamicVector<Real>& v1, const DynamicVector<Real>& v2) {
336			DynamicVector<Real> result;
337			result.sub(v1, v2);
338			return result;
339			}
340
341			/**
342			* Returns the vaule of scalar multiplication of this vector v1 (v1 * r).
343			* @return the vaule of scalar multiplication of this vector
344			* @param v1 the source vector
345			* @param s the scalar value
346			*/
347			template<typename Real>
348			DynamicVector<Real> operator * ( const DynamicVector<Real>& v1, Real s) {
349			DynamicVector<Real> result;
350			result.mul(v1,s);
351			return result;
352			}
353
354			/**
355			* Returns the vaule of scalar multiplication of this vector v1 (v1 * r).
356			* @return the vaule of scalar multiplication of this vector
357			* @param s the scalar value
358			* @param v1 the source vector
359			*/
360			template<typename Real>
361			DynamicVector<Real> operator * ( Real s, const DynamicVector<Real>& v1 ) {
362			DynamicVector<Real> result;
363			result.mul(v1, s);
364			return result;
365			}
366
367			/**
368			* Returns the value of division of a vector by a scalar.
369			* @return the vaule of scalar division of this vector
370			* @param v1 the source vector
371			* @param s the scalar value
372			*/
373			template<typename Real>
374			DynamicVector<Real> operator / ( const DynamicVector<Real>& v1, Real s) {
375			DynamicVector<Real> result;
376			result.div( v1,s);
377			return result;
378			}
379
380			/**
381			* Returns the dot product of two DynamicVectors
382			* @param v1 first vector
383			* @param v2 second vector
384			* @return the dot product of v1 and v2
385			*/
386			template<typename Real>
387			inline Real dot( const DynamicVector<Real>& v1, const DynamicVector<Real>& v2 ) {
388			Real tmp;
389			tmp = 0;
390			assert(v1.size() == v2.size());
391			for (unsigned int i = 0; i < v1.size(); i++)
392			tmp += v1[i] * v2[i];
393
394			return tmp;
395			}
396
397			/**
398			* Returns the distance between two DynamicVectors
399			* @param v1 first vector
400			* @param v2 second vector
401			* @return the distance between v1 and v2
402			*/
403			template<typename Real>
404			inline Real distance( const DynamicVector<Real>& v1, const DynamicVector<Real>& v2 ) {
405			DynamicVector<Real> tempDynamicVector = v1 - v2;
406			return tempDynamicVector.length();
407			}
408
409			/**
410			* Returns the squared distance between two DynamicVectors
411			* @param v1 first vector
412			* @param v2 second vector
413			* @return the squared distance between v1 and v2
414			*/
415			template<typename Real>
416			inline Real distanceSquare( const DynamicVector<Real>& v1, const DynamicVector<Real>& v2 ) {
417			DynamicVector<Real> tempDynamicVector = v1 - v2;
418			return tempDynamicVector.lengthSquare();
419			}
420
421			/**
422			* Write to an output stream
423			*/
424			template<typename Real>
425			std::ostream &operator<< ( std::ostream& o, const DynamicVector<Real>& v) {
426
427			o << "[ ";
428
429			for (unsigned int i = 0 ; i< v.size(); i++) {
430			o << v[i];
431
432			if (i != v.size() -1) {
433			o<< ", ";
434			}
435			}
436
437			o << " ]";
438			return o;
439			}
440
441			}
442			#endif
443