src/math/Vector.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 Vector.hpp
 * @author Teng Lin
 * @date 09/14/2004
 * @version 1.0
 */
 
#ifndef MATH_VECTOR_HPP
#define MATH_VECTOR_HPP

#include <cassert>
#include <cmath>
#include <iostream>
#include <math.h>
namespace oopse {

  static const double epsilon = 0.000001;

  template<typename T>
  inline bool equal(T e1, T e2) {
    return e1 == e2;
  }

  template<>
  inline bool equal(float e1, float e2) {
    return fabs(e1 - e2) < epsilon;
  }

  template<>
  inline bool equal(double e1, double e2) {
    return fabs(e1 - e2) < epsilon;
  }

    
  /**
   * @class Vector Vector.hpp "math/Vector.hpp"
   * @brief Fix length vector class
   */
  template<typename Real, unsigned int Dim>
  class Vector{
  public:

    typedef Real ElemType;
    typedef Real* ElemPoinerType;

    /** default constructor */
    inline Vector(){
      for (unsigned int i = 0; i < Dim; i++)
        this->data_[i] = 0;
    }

    /** Constructs and initializes a Vector from a vector */
    inline Vector(const Vector<Real, Dim>& v) {
      *this  = v;
    }

    /** copy assignment operator */
    inline Vector<Real, Dim>& operator=(const Vector<Real, Dim>& v) {
      if (this == &v)
        return *this;
                
      for (unsigned int i = 0; i < Dim; i++)            
        this->data_[i] = v[i];
                
      return *this;
    }

    template<typename T>
    inline Vector(const T& s){
      for (unsigned int i = 0; i < Dim; i++)
        this->data_[i] = s;
    }
            
    /** Constructs and initializes a Vector from an array */            
    inline Vector( Real* v) {
      for (unsigned int i = 0; i < Dim; i++)
        this->data_[i] = v[i];
    }

    /** 
     * Returns reference of ith element.
     * @return reference of ith element
     * @param i index
     */
    inline Real& operator[](unsigned int  i) {
      assert( i < Dim);
      return this->data_[i];
    }

    /** 
     * Returns reference of ith element.
     * @return reference of ith element
     * @param i index
     */
    inline Real& operator()(unsigned int  i) {
      assert( i < Dim);
      return this->data_[i];
    }

    /** 
     * Returns constant reference of ith element.
     * @return reference of ith element
     * @param i index
     */
    inline  const Real& operator[](unsigned int i) const {
      assert( i < Dim);
      return this->data_[i];
    }

    /** 
     * Returns constant reference of ith element.
     * @return reference of ith element
     * @param i index
     */
    inline  const Real& operator()(unsigned int i) const {
      assert( i < Dim);
      return this->data_[i];
    }

    /** Copy the internal data to an array*/
    void getArray(Real* array) {
      for (unsigned int i = 0; i < Dim; i ++) {
        array[i] = this->data_[i];
      }                
    }

    /** Returns the pointer of internal array */
    Real* getArrayPointer() {
      return this->data_;
    }
            
    /**
     * 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 Vector<Real, Dim>& v) {

      for (unsigned int i = 0; i < Dim; i ++) {
        if (!equal(this->data_[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 Vector<Real, Dim>& v) {
      return !(*this == v);
    }
             
    /** Negates the value of this vector in place. */           
    inline void negate() {
      for (unsigned int i = 0; i < Dim; i++)
        this->data_[i] = -this->data_[i];
    }

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

    /**
     * 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 Vector<Real, Dim>& v1, const Vector<Real, Dim>& v2 ) {
      for (unsigned int i = 0; i < Dim; i++)
        this->data_[i] = v1.data_[i] + v2.data_[i];
    }

    /**
     * Sets the value of this vector to the difference  of itself and v1 (*this -= v1).
     * @param v1 the other vector
     */
    inline void sub( const Vector<Real, Dim>& v1 ) {
      for (unsigned int i = 0; i < Dim; i++)
        this->data_[i] -= v1.data_[i];
    }

    /**
     * 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 Vector<Real, Dim>& v1, const Vector  &v2 ){
      for (unsigned int i = 0; i < Dim; i++)
        this->data_[i] = v1.data_[i] - v2.data_[i];
    }

    /**
     * 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 < Dim; i++)
        this->data_[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 Vector<Real, Dim>& v1, Real s) {
      for (unsigned int i = 0; i < Dim; i++)
        this->data_[i] = s * v1.data_[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 < Dim; i++)            
        this->data_[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 Vector<Real, Dim>& v1, Real s ) {
      for (unsigned int i = 0; i < Dim; i++)
        this->data_[i] = v1.data_[i] / s;
    }

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

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

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

    /** @see #div */
    inline Vector<Real, Dim>& 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);
    }           

    unsigned int size() {return Dim;}
  protected:
    Real data_[Dim];
        
  };

  /** unary minus*/
  template<typename Real, unsigned int Dim>    
  inline Vector<Real, Dim> operator -(const Vector<Real, Dim>& v1){
    Vector<Real, Dim> 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, unsigned int Dim>    
  inline Vector<Real, Dim> operator +(const Vector<Real, Dim>& v1, const Vector<Real, Dim>& v2) {
    Vector<Real, Dim> 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, unsigned int Dim>    
  Vector<Real, Dim> operator -(const Vector<Real, Dim>& v1, const Vector<Real, Dim>& v2) {
    Vector<Real, Dim> 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, unsigned int Dim>                 
  Vector<Real, Dim> operator * ( const Vector<Real, Dim>& v1, Real s) {       
    Vector<Real, Dim> 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, unsigned int Dim>
  Vector<Real, Dim> operator * ( Real s, const Vector<Real, Dim>& v1 ) {
    Vector<Real, Dim> 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, unsigned int Dim>    
  Vector<Real, Dim> operator / ( const Vector<Real, Dim>& v1, Real s) {       
    Vector<Real, Dim> result;
    result.div( v1,s);
    return result;           
  }
    
  /**
   * Returns the dot product of two Vectors
   * @param v1 first vector
   * @param v2 second vector
   * @return the dot product of v1 and v2
   */
  template<typename Real, unsigned int Dim>    
  inline Real dot( const Vector<Real, Dim>& v1, const Vector<Real, Dim>& v2 ) {
    Real tmp;
    tmp = 0;

    for (unsigned int i = 0; i < Dim; i++)
      tmp += v1[i] * v2[i];

    return tmp;
  }

  /**
   * Returns the distance between  two Vectors
   * @param v1 first vector
   * @param v2 second vector
   * @return the distance between v1 and v2
   */   
  template<typename Real, unsigned int Dim>    
  inline Real distance( const Vector<Real, Dim>& v1, const Vector<Real, Dim>& v2 ) {
    Vector<Real, Dim> tempVector = v1 - v2;
    return tempVector.length();
  }

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

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

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

      if (i  != Dim -1) {
        o<< ", ";
      }
    }

    o << " ]";
    return o;        
  }
    
}
#endif
Revision:	2588
Committed:	Fri Feb 10 15:12:14 2006 UTC (18 years, 4 months ago) by tim
File size:	13770 byte(s)
Log Message:	fix a bug in converting integer to double
#	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 Vector.hpp
44	* @author Teng Lin
45	* @date 09/14/2004
46	* @version 1.0
47	*/
48
49	#ifndef MATH_VECTOR_HPP
50	#define MATH_VECTOR_HPP
51
52	#include <cassert>
53	#include <cmath>
54	#include <iostream>
55	#include <math.h>
56	namespace oopse {
57
58	static const double epsilon = 0.000001;
59
60	template<typename T>
61	inline bool equal(T e1, T e2) {
62	return e1 == e2;
63	}
64
65	template<>
66	inline bool equal(float e1, float e2) {
67	return fabs(e1 - e2) < epsilon;
68	}
69
70	template<>
71	inline bool equal(double e1, double e2) {
72	return fabs(e1 - e2) < epsilon;
73	}
74
75
76	/**
77	* @class Vector Vector.hpp "math/Vector.hpp"
78	* @brief Fix length vector class
79	*/
80	template<typename Real, unsigned int Dim>
81	class Vector{
82	public:
83
84	typedef Real ElemType;
85	typedef Real* ElemPoinerType;
86
87	/** default constructor */
88	inline Vector(){
89	for (unsigned int i = 0; i < Dim; i++)
90	this->data_[i] = 0;
91	}
92
93	/** Constructs and initializes a Vector from a vector */
94	inline Vector(const Vector<Real, Dim>& v) {
95	*this = v;
96	}
97
98	/** copy assignment operator */
99	inline Vector<Real, Dim>& operator=(const Vector<Real, Dim>& v) {
100	if (this == &v)
101	return *this;
102
103	for (unsigned int i = 0; i < Dim; i++)
104	this->data_[i] = v[i];
105
106	return *this;
107	}
108
109	template<typename T>
110	inline Vector(const T& s){
111	for (unsigned int i = 0; i < Dim; i++)
112	this->data_[i] = s;
113	}
114
115	/** Constructs and initializes a Vector from an array */
116	inline Vector( Real* v) {
117	for (unsigned int i = 0; i < Dim; i++)
118	this->data_[i] = v[i];
119	}
120
121	/**
122	* Returns reference of ith element.
123	* @return reference of ith element
124	* @param i index
125	*/
126	inline Real& operator[](unsigned int i) {
127	assert( i < Dim);
128	return this->data_[i];
129	}
130
131	/**
132	* Returns reference of ith element.
133	* @return reference of ith element
134	* @param i index
135	*/
136	inline Real& operator()(unsigned int i) {
137	assert( i < Dim);
138	return this->data_[i];
139	}
140
141	/**
142	* Returns constant reference of ith element.
143	* @return reference of ith element
144	* @param i index
145	*/
146	inline const Real& operator[](unsigned int i) const {
147	assert( i < Dim);
148	return this->data_[i];
149	}
150
151	/**
152	* Returns constant reference of ith element.
153	* @return reference of ith element
154	* @param i index
155	*/
156	inline const Real& operator()(unsigned int i) const {
157	assert( i < Dim);
158	return this->data_[i];
159	}
160
161	/** Copy the internal data to an array*/
162	void getArray(Real* array) {
163	for (unsigned int i = 0; i < Dim; i ++) {
164	array[i] = this->data_[i];
165	}
166	}
167
168	/** Returns the pointer of internal array */
169	Real* getArrayPointer() {
170	return this->data_;
171	}
172
173	/**
174	* Tests if this vetor is equal to other vector
175	* @return true if equal, otherwise return false
176	* @param v vector to be compared
177	*/
178	inline bool operator ==(const Vector<Real, Dim>& v) {
179
180	for (unsigned int i = 0; i < Dim; i ++) {
181	if (!equal(this->data_[i], v[i])) {
182	return false;
183	}
184	}
185
186	return true;
187	}
188
189	/**
190	* Tests if this vetor is not equal to other vector
191	* @return true if equal, otherwise return false
192	* @param v vector to be compared
193	*/
194	inline bool operator !=(const Vector<Real, Dim>& v) {
195	return !(*this == v);
196	}
197
198	/** Negates the value of this vector in place. */
199	inline void negate() {
200	for (unsigned int i = 0; i < Dim; i++)
201	this->data_[i] = -this->data_[i];
202	}
203
204	/**
205	* Sets the value of this vector to the negation of vector v1.
206	* @param v1 the source vector
207	*/
208	inline void negate(const Vector<Real, Dim>& v1) {
209	for (unsigned int i = 0; i < Dim; i++)
210	this->data_[i] = -v1.data_[i];
211
212	}
213
214	/**
215	* Sets the value of this vector to the sum of itself and v1 (*this += v1).
216	* @param v1 the other vector
217	*/
218	inline void add( const Vector<Real, Dim>& v1 ) {
219	for (unsigned int i = 0; i < Dim; i++)
220	this->data_[i] += v1.data_[i];
221	}
222
223	/**
224	* Sets the value of this vector to the sum of v1 and v2 (*this = v1 + v2).
225	* @param v1 the first vector
226	* @param v2 the second vector
227	*/
228	inline void add( const Vector<Real, Dim>& v1, const Vector<Real, Dim>& v2 ) {
229	for (unsigned int i = 0; i < Dim; i++)
230	this->data_[i] = v1.data_[i] + v2.data_[i];
231	}
232
233	/**
234	* Sets the value of this vector to the difference of itself and v1 (*this -= v1).
235	* @param v1 the other vector
236	*/
237	inline void sub( const Vector<Real, Dim>& v1 ) {
238	for (unsigned int i = 0; i < Dim; i++)
239	this->data_[i] -= v1.data_[i];
240	}
241
242	/**
243	* Sets the value of this vector to the difference of vector v1 and v2 (*this = v1 - v2).
244	* @param v1 the first vector
245	* @param v2 the second vector
246	*/
247	inline void sub( const Vector<Real, Dim>& v1, const Vector &v2 ){
248	for (unsigned int i = 0; i < Dim; i++)
249	this->data_[i] = v1.data_[i] - v2.data_[i];
250	}
251
252	/**
253	* Sets the value of this vector to the scalar multiplication of itself (this = s).
254	* @param s the scalar value
255	*/
256	inline void mul( Real s ) {
257	for (unsigned int i = 0; i < Dim; i++)
258	this->data_[i] *= s;
259	}
260
261	/**
262	* Sets the value of this vector to the scalar multiplication of vector v1
263	* (this = s v1).
264	* @param v1 the vector
265	* @param s the scalar value
266	*/
267	inline void mul( const Vector<Real, Dim>& v1, Real s) {
268	for (unsigned int i = 0; i < Dim; i++)
269	this->data_[i] = s * v1.data_[i];
270	}
271
272	/**
273	* Sets the value of this vector to the scalar division of itself (*this /= s ).
274	* @param s the scalar value
275	*/
276	inline void div( Real s) {
277	for (unsigned int i = 0; i < Dim; i++)
278	this->data_[i] /= s;
279	}
280
281	/**
282	* Sets the value of this vector to the scalar division of vector v1 (*this = v1 / s ).
283	* @param v1 the source vector
284	* @param s the scalar value
285	*/
286	inline void div( const Vector<Real, Dim>& v1, Real s ) {
287	for (unsigned int i = 0; i < Dim; i++)
288	this->data_[i] = v1.data_[i] / s;
289	}
290
291	/** @see #add */
292	inline Vector<Real, Dim>& operator +=( const Vector<Real, Dim>& v1 ) {
293	add(v1);
294	return *this;
295	}
296
297	/** @see #sub */
298	inline Vector<Real, Dim>& operator -=( const Vector<Real, Dim>& v1 ) {
299	sub(v1);
300	return *this;
301	}
302
303	/** @see #mul */
304	inline Vector<Real, Dim>& operator *=( Real s) {
305	mul(s);
306	return *this;
307	}
308
309	/** @see #div */
310	inline Vector<Real, Dim>& operator /=( Real s ) {
311	div(s);
312	return *this;
313	}
314
315	/**
316	* Returns the length of this vector.
317	* @return the length of this vector
318	*/
319	inline Real length() {
320	return sqrt(lengthSquare());
321	}
322
323	/**
324	* Returns the squared length of this vector.
325	* @return the squared length of this vector
326	*/
327	inline Real lengthSquare() {
328	return dot(this, this);
329	}
330
331	/** Normalizes this vector in place */
332	inline void normalize() {
333	Real len;
334
335	len = length();
336
337	//if (len < oopse:epsilon)
338	// throw();
339
340	*this /= len;
341	}
342
343	/**
344	* Tests if this vector is normalized
345	* @return true if this vector is normalized, otherwise return false
346	*/
347	inline bool isNormalized() {
348	return equal(lengthSquare(), 1.0);
349	}
350
351	unsigned int size() {return Dim;}
352	protected:
353	Real data_[Dim];
354
355	};
356
357	/** unary minus*/
358	template<typename Real, unsigned int Dim>
359	inline Vector<Real, Dim> operator -(const Vector<Real, Dim>& v1){
360	Vector<Real, Dim> tmp(v1);
361	tmp.negate();
362	return tmp;
363	}
364
365	/**
366	* Return the sum of two vectors (v1 - v2).
367	* @return the sum of two vectors
368	* @param v1 the first vector
369	* @param v2 the second vector
370	*/
371	template<typename Real, unsigned int Dim>
372	inline Vector<Real, Dim> operator +(const Vector<Real, Dim>& v1, const Vector<Real, Dim>& v2) {
373	Vector<Real, Dim> result;
374
375	result.add(v1, v2);
376	return result;
377	}
378
379	/**
380	* Return the difference of two vectors (v1 - v2).
381	* @return the difference of two vectors
382	* @param v1 the first vector
383	* @param v2 the second vector
384	*/
385	template<typename Real, unsigned int Dim>
386	Vector<Real, Dim> operator -(const Vector<Real, Dim>& v1, const Vector<Real, Dim>& v2) {
387	Vector<Real, Dim> result;
388	result.sub(v1, v2);
389	return result;
390	}
391
392	/**
393	* Returns the vaule of scalar multiplication of this vector v1 (v1 * r).
394	* @return the vaule of scalar multiplication of this vector
395	* @param v1 the source vector
396	* @param s the scalar value
397	*/
398	template<typename Real, unsigned int Dim>
399	Vector<Real, Dim> operator * ( const Vector<Real, Dim>& v1, Real s) {
400	Vector<Real, Dim> result;
401	result.mul(v1,s);
402	return result;
403	}
404
405	/**
406	* Returns the vaule of scalar multiplication of this vector v1 (v1 * r).
407	* @return the vaule of scalar multiplication of this vector
408	* @param s the scalar value
409	* @param v1 the source vector
410	*/
411	template<typename Real, unsigned int Dim>
412	Vector<Real, Dim> operator * ( Real s, const Vector<Real, Dim>& v1 ) {
413	Vector<Real, Dim> result;
414	result.mul(v1, s);
415	return result;
416	}
417
418	/**
419	* Returns the value of division of a vector by a scalar.
420	* @return the vaule of scalar division of this vector
421	* @param v1 the source vector
422	* @param s the scalar value
423	*/
424	template<typename Real, unsigned int Dim>
425	Vector<Real, Dim> operator / ( const Vector<Real, Dim>& v1, Real s) {
426	Vector<Real, Dim> result;
427	result.div( v1,s);
428	return result;
429	}
430
431	/**
432	* Returns the dot product of two Vectors
433	* @param v1 first vector
434	* @param v2 second vector
435	* @return the dot product of v1 and v2
436	*/
437	template<typename Real, unsigned int Dim>
438	inline Real dot( const Vector<Real, Dim>& v1, const Vector<Real, Dim>& v2 ) {
439	Real tmp;
440	tmp = 0;
441
442	for (unsigned int i = 0; i < Dim; i++)
443	tmp += v1[i] * v2[i];
444
445	return tmp;
446	}
447
448	/**
449	* Returns the distance between two Vectors
450	* @param v1 first vector
451	* @param v2 second vector
452	* @return the distance between v1 and v2
453	*/
454	template<typename Real, unsigned int Dim>
455	inline Real distance( const Vector<Real, Dim>& v1, const Vector<Real, Dim>& v2 ) {
456	Vector<Real, Dim> tempVector = v1 - v2;
457	return tempVector.length();
458	}
459
460	/**
461	* Returns the squared distance between two Vectors
462	* @param v1 first vector
463	* @param v2 second vector
464	* @return the squared distance between v1 and v2
465	*/
466	template<typename Real, unsigned int Dim>
467	inline Real distanceSquare( const Vector<Real, Dim>& v1, const Vector<Real, Dim>& v2 ) {
468	Vector<Real, Dim> tempVector = v1 - v2;
469	return tempVector.lengthSquare();
470	}
471
472	/**
473	* Write to an output stream
474	*/
475	template<typename Real, unsigned int Dim>
476	std::ostream &operator<< ( std::ostream& o, const Vector<Real, Dim>& v) {
477
478	o << "[ ";
479
480	for (unsigned int i = 0 ; i< Dim; i++) {
481	o << v[i];
482
483	if (i != Dim -1) {
484	o<< ", ";
485	}
486	}
487
488	o << " ]";
489	return o;
490	}
491
492	}
493	#endif