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>
#include "config.h"
namespace oopse {

  static const RealType 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(RealType e1, RealType 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(), (RealType)1);
    }           

    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:	2759
Committed:	Wed May 17 21:51:42 2006 UTC (18 years, 1 month ago) by tim
File size:	13812 byte(s)
Log Message:	Adding single precision capabilities to c++ side
#	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	#include "config.h"
57	namespace oopse {
58
59	static const RealType epsilon = 0.000001;
60
61	template<typename T>
62	inline bool equal(T e1, T e2) {
63	return e1 == e2;
64	}
65
66	//template<>
67	//inline bool equal(float e1, float e2) {
68	// return fabs(e1 - e2) < epsilon;
69	//}
70
71	template<>
72	inline bool equal(RealType e1, RealType e2) {
73	return fabs(e1 - e2) < epsilon;
74	}
75
76
77	/**
78	* @class Vector Vector.hpp "math/Vector.hpp"
79	* @brief Fix length vector class
80	*/
81	template<typename Real, unsigned int Dim>
82	class Vector{
83	public:
84
85	typedef Real ElemType;
86	typedef Real* ElemPoinerType;
87
88	/** default constructor */
89	inline Vector(){
90	for (unsigned int i = 0; i < Dim; i++)
91	this->data_[i] = 0;
92	}
93
94	/** Constructs and initializes a Vector from a vector */
95	inline Vector(const Vector<Real, Dim>& v) {
96	*this = v;
97	}
98
99	/** copy assignment operator */
100	inline Vector<Real, Dim>& operator=(const Vector<Real, Dim>& v) {
101	if (this == &v)
102	return *this;
103
104	for (unsigned int i = 0; i < Dim; i++)
105	this->data_[i] = v[i];
106
107	return *this;
108	}
109
110	template<typename T>
111	inline Vector(const T& s){
112	for (unsigned int i = 0; i < Dim; i++)
113	this->data_[i] = s;
114	}
115
116	/** Constructs and initializes a Vector from an array */
117	inline Vector( Real* v) {
118	for (unsigned int i = 0; i < Dim; i++)
119	this->data_[i] = v[i];
120	}
121
122	/**
123	* Returns reference of ith element.
124	* @return reference of ith element
125	* @param i index
126	*/
127	inline Real& operator[](unsigned int i) {
128	assert( i < Dim);
129	return this->data_[i];
130	}
131
132	/**
133	* Returns reference of ith element.
134	* @return reference of ith element
135	* @param i index
136	*/
137	inline Real& operator()(unsigned int i) {
138	assert( i < Dim);
139	return this->data_[i];
140	}
141
142	/**
143	* Returns constant reference of ith element.
144	* @return reference of ith element
145	* @param i index
146	*/
147	inline const Real& operator[](unsigned int i) const {
148	assert( i < Dim);
149	return this->data_[i];
150	}
151
152	/**
153	* Returns constant reference of ith element.
154	* @return reference of ith element
155	* @param i index
156	*/
157	inline const Real& operator()(unsigned int i) const {
158	assert( i < Dim);
159	return this->data_[i];
160	}
161
162	/** Copy the internal data to an array*/
163	void getArray(Real* array) {
164	for (unsigned int i = 0; i < Dim; i ++) {
165	array[i] = this->data_[i];
166	}
167	}
168
169	/** Returns the pointer of internal array */
170	Real* getArrayPointer() {
171	return this->data_;
172	}
173
174	/**
175	* Tests if this vetor is equal to other vector
176	* @return true if equal, otherwise return false
177	* @param v vector to be compared
178	*/
179	inline bool operator ==(const Vector<Real, Dim>& v) {
180
181	for (unsigned int i = 0; i < Dim; i ++) {
182	if (!equal(this->data_[i], v[i])) {
183	return false;
184	}
185	}
186
187	return true;
188	}
189
190	/**
191	* Tests if this vetor is not equal to other vector
192	* @return true if equal, otherwise return false
193	* @param v vector to be compared
194	*/
195	inline bool operator !=(const Vector<Real, Dim>& v) {
196	return !(*this == v);
197	}
198
199	/** Negates the value of this vector in place. */
200	inline void negate() {
201	for (unsigned int i = 0; i < Dim; i++)
202	this->data_[i] = -this->data_[i];
203	}
204
205	/**
206	* Sets the value of this vector to the negation of vector v1.
207	* @param v1 the source vector
208	*/
209	inline void negate(const Vector<Real, Dim>& v1) {
210	for (unsigned int i = 0; i < Dim; i++)
211	this->data_[i] = -v1.data_[i];
212
213	}
214
215	/**
216	* Sets the value of this vector to the sum of itself and v1 (*this += v1).
217	* @param v1 the other vector
218	*/
219	inline void add( const Vector<Real, Dim>& v1 ) {
220	for (unsigned int i = 0; i < Dim; i++)
221	this->data_[i] += v1.data_[i];
222	}
223
224	/**
225	* Sets the value of this vector to the sum of v1 and v2 (*this = v1 + v2).
226	* @param v1 the first vector
227	* @param v2 the second vector
228	*/
229	inline void add( const Vector<Real, Dim>& v1, const Vector<Real, Dim>& v2 ) {
230	for (unsigned int i = 0; i < Dim; i++)
231	this->data_[i] = v1.data_[i] + v2.data_[i];
232	}
233
234	/**
235	* Sets the value of this vector to the difference of itself and v1 (*this -= v1).
236	* @param v1 the other vector
237	*/
238	inline void sub( const Vector<Real, Dim>& v1 ) {
239	for (unsigned int i = 0; i < Dim; i++)
240	this->data_[i] -= v1.data_[i];
241	}
242
243	/**
244	* Sets the value of this vector to the difference of vector v1 and v2 (*this = v1 - v2).
245	* @param v1 the first vector
246	* @param v2 the second vector
247	*/
248	inline void sub( const Vector<Real, Dim>& v1, const Vector &v2 ){
249	for (unsigned int i = 0; i < Dim; i++)
250	this->data_[i] = v1.data_[i] - v2.data_[i];
251	}
252
253	/**
254	* Sets the value of this vector to the scalar multiplication of itself (this = s).
255	* @param s the scalar value
256	*/
257	inline void mul( Real s ) {
258	for (unsigned int i = 0; i < Dim; i++)
259	this->data_[i] *= s;
260	}
261
262	/**
263	* Sets the value of this vector to the scalar multiplication of vector v1
264	* (this = s v1).
265	* @param v1 the vector
266	* @param s the scalar value
267	*/
268	inline void mul( const Vector<Real, Dim>& v1, Real s) {
269	for (unsigned int i = 0; i < Dim; i++)
270	this->data_[i] = s * v1.data_[i];
271	}
272
273	/**
274	* Sets the value of this vector to the scalar division of itself (*this /= s ).
275	* @param s the scalar value
276	*/
277	inline void div( Real s) {
278	for (unsigned int i = 0; i < Dim; i++)
279	this->data_[i] /= s;
280	}
281
282	/**
283	* Sets the value of this vector to the scalar division of vector v1 (*this = v1 / s ).
284	* @param v1 the source vector
285	* @param s the scalar value
286	*/
287	inline void div( const Vector<Real, Dim>& v1, Real s ) {
288	for (unsigned int i = 0; i < Dim; i++)
289	this->data_[i] = v1.data_[i] / s;
290	}
291
292	/** @see #add */
293	inline Vector<Real, Dim>& operator +=( const Vector<Real, Dim>& v1 ) {
294	add(v1);
295	return *this;
296	}
297
298	/** @see #sub */
299	inline Vector<Real, Dim>& operator -=( const Vector<Real, Dim>& v1 ) {
300	sub(v1);
301	return *this;
302	}
303
304	/** @see #mul */
305	inline Vector<Real, Dim>& operator *=( Real s) {
306	mul(s);
307	return *this;
308	}
309
310	/** @see #div */
311	inline Vector<Real, Dim>& operator /=( Real s ) {
312	div(s);
313	return *this;
314	}
315
316	/**
317	* Returns the length of this vector.
318	* @return the length of this vector
319	*/
320	inline Real length() {
321	return sqrt(lengthSquare());
322	}
323
324	/**
325	* Returns the squared length of this vector.
326	* @return the squared length of this vector
327	*/
328	inline Real lengthSquare() {
329	return dot(this, this);
330	}
331
332	/** Normalizes this vector in place */
333	inline void normalize() {
334	Real len;
335
336	len = length();
337
338	//if (len < oopse:epsilon)
339	// throw();
340
341	*this /= len;
342	}
343
344	/**
345	* Tests if this vector is normalized
346	* @return true if this vector is normalized, otherwise return false
347	*/
348	inline bool isNormalized() {
349	return equal(lengthSquare(), (RealType)1);
350	}
351
352	unsigned int size() {return Dim;}
353	protected:
354	Real data_[Dim];
355
356	};
357
358	/** unary minus*/
359	template<typename Real, unsigned int Dim>
360	inline Vector<Real, Dim> operator -(const Vector<Real, Dim>& v1){
361	Vector<Real, Dim> tmp(v1);
362	tmp.negate();
363	return tmp;
364	}
365
366	/**
367	* Return the sum of two vectors (v1 - v2).
368	* @return the sum of two vectors
369	* @param v1 the first vector
370	* @param v2 the second vector
371	*/
372	template<typename Real, unsigned int Dim>
373	inline Vector<Real, Dim> operator +(const Vector<Real, Dim>& v1, const Vector<Real, Dim>& v2) {
374	Vector<Real, Dim> result;
375
376	result.add(v1, v2);
377	return result;
378	}
379
380	/**
381	* Return the difference of two vectors (v1 - v2).
382	* @return the difference of two vectors
383	* @param v1 the first vector
384	* @param v2 the second vector
385	*/
386	template<typename Real, unsigned int Dim>
387	Vector<Real, Dim> operator -(const Vector<Real, Dim>& v1, const Vector<Real, Dim>& v2) {
388	Vector<Real, Dim> result;
389	result.sub(v1, v2);
390	return result;
391	}
392
393	/**
394	* Returns the vaule of scalar multiplication of this vector v1 (v1 * r).
395	* @return the vaule of scalar multiplication of this vector
396	* @param v1 the source vector
397	* @param s the scalar value
398	*/
399	template<typename Real, unsigned int Dim>
400	Vector<Real, Dim> operator * ( const Vector<Real, Dim>& v1, Real s) {
401	Vector<Real, Dim> result;
402	result.mul(v1,s);
403	return result;
404	}
405
406	/**
407	* Returns the vaule of scalar multiplication of this vector v1 (v1 * r).
408	* @return the vaule of scalar multiplication of this vector
409	* @param s the scalar value
410	* @param v1 the source vector
411	*/
412	template<typename Real, unsigned int Dim>
413	Vector<Real, Dim> operator * ( Real s, const Vector<Real, Dim>& v1 ) {
414	Vector<Real, Dim> result;
415	result.mul(v1, s);
416	return result;
417	}
418
419	/**
420	* Returns the value of division of a vector by a scalar.
421	* @return the vaule of scalar division of this vector
422	* @param v1 the source vector
423	* @param s the scalar value
424	*/
425	template<typename Real, unsigned int Dim>
426	Vector<Real, Dim> operator / ( const Vector<Real, Dim>& v1, Real s) {
427	Vector<Real, Dim> result;
428	result.div( v1,s);
429	return result;
430	}
431
432	/**
433	* Returns the dot product of two Vectors
434	* @param v1 first vector
435	* @param v2 second vector
436	* @return the dot product of v1 and v2
437	*/
438	template<typename Real, unsigned int Dim>
439	inline Real dot( const Vector<Real, Dim>& v1, const Vector<Real, Dim>& v2 ) {
440	Real tmp;
441	tmp = 0;
442
443	for (unsigned int i = 0; i < Dim; i++)
444	tmp += v1[i] * v2[i];
445
446	return tmp;
447	}
448
449	/**
450	* Returns the distance between two Vectors
451	* @param v1 first vector
452	* @param v2 second vector
453	* @return the distance between v1 and v2
454	*/
455	template<typename Real, unsigned int Dim>
456	inline Real distance( const Vector<Real, Dim>& v1, const Vector<Real, Dim>& v2 ) {
457	Vector<Real, Dim> tempVector = v1 - v2;
458	return tempVector.length();
459	}
460
461	/**
462	* Returns the squared distance between two Vectors
463	* @param v1 first vector
464	* @param v2 second vector
465	* @return the squared distance between v1 and v2
466	*/
467	template<typename Real, unsigned int Dim>
468	inline Real distanceSquare( const Vector<Real, Dim>& v1, const Vector<Real, Dim>& v2 ) {
469	Vector<Real, Dim> tempVector = v1 - v2;
470	return tempVector.lengthSquare();
471	}
472
473	/**
474	* Write to an output stream
475	*/
476	template<typename Real, unsigned int Dim>
477	std::ostream &operator<< ( std::ostream& o, const Vector<Real, Dim>& v) {
478
479	o << "[ ";
480
481	for (unsigned int i = 0 ; i< Dim; i++) {
482	o << v[i];
483
484	if (i != Dim -1) {
485	o<< ", ";
486	}
487	}
488
489	o << " ]";
490	return o;
491	}
492
493	}
494	#endif