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:	2596
Committed:	Wed Feb 22 20:35:16 2006 UTC (18 years, 4 months ago) by tim
File size:	14049 byte(s)
Log Message:	Adding Hydrodynamics Module
#	Content
1	/*
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