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);
            }           
            
        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:	385
Committed:	Tue Mar 1 20:10:14 2005 UTC (20 years, 2 months ago) by tim
Original Path:	*trunk/src/math/Vector.hpp*
File size:	16225 byte(s)
Log Message:	fix compilation problem for g++ 3.4
#	User	Rev	Content
1	gezelter	246	/*
2			* Copyright (c) 2005 The University of Notre Dame. All Rights Reserved.
3	tim	70	*
4	gezelter	246	* 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	tim	70	*/
41	gezelter	246
42	tim	70	/**
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	tim	71	#include <iostream>
55	tim	253	#include <math.h>
56	tim	70	namespace oopse {
57
58	gezelter	246	static const double epsilon = 0.000001;
59	tim	76
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	tim	110
75	tim	76
76	tim	70	/**
77			* @class Vector Vector.hpp "math/Vector.hpp"
78			* @brief Fix length vector class
79			*/
80	tim	71	template<typename Real, unsigned int Dim>
81	tim	70	class Vector{
82			public:
83
84	tim	137	typedef Real ElemType;
85			typedef Real* ElemPoinerType;
86
87	tim	70	/** default constructor */
88			inline Vector(){
89			for (unsigned int i = 0; i < Dim; i++)
90	tim	385	this->data_[i] = 0;
91	tim	70	}
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	tim	385	this->data_[i] = v[i];
105	tim	70
106			return *this;
107			}
108	tim	101
109			template<typename T>
110			inline Vector(const T& s){
111			for (unsigned int i = 0; i < Dim; i++)
112	tim	385	this->data_[i] = s;
113	tim	101	}
114	tim	70
115			/** Constructs and initializes a Vector from an array */
116	tim	110	inline Vector( Real* v) {
117	tim	93	for (unsigned int i = 0; i < Dim; i++)
118	tim	385	this->data_[i] = v[i];
119	tim	70	}
120
121			/**
122			* Returns reference of ith element.
123			* @return reference of ith element
124			* @param i index
125			*/
126	tim	110	inline Real& operator[](unsigned int i) {
127	tim	70	assert( i < Dim);
128	tim	385	return this->data_[i];
129	tim	70	}
130
131			/**
132			* Returns reference of ith element.
133			* @return reference of ith element
134			* @param i index
135			*/
136	tim	110	inline Real& operator()(unsigned int i) {
137	tim	70	assert( i < Dim);
138	tim	385	return this->data_[i];
139	tim	70	}
140
141			/**
142			* Returns constant reference of ith element.
143			* @return reference of ith element
144			* @param i index
145			*/
146	tim	110	inline const Real& operator[](unsigned int i) const {
147	tim	70	assert( i < Dim);
148	tim	385	return this->data_[i];
149	tim	70	}
150
151			/**
152			* Returns constant reference of ith element.
153			* @return reference of ith element
154			* @param i index
155			*/
156	tim	110	inline const Real& operator()(unsigned int i) const {
157	tim	70	assert( i < Dim);
158	tim	385	return this->data_[i];
159	tim	70	}
160
161	tim	151	/** Copy the internal data to an array*/
162			void getArray(Real* array) {
163			for (unsigned int i = 0; i < Dim; i ++) {
164	tim	385	array[i] = this->data_[i];
165	tim	151	}
166			}
167
168	tim	137	/** Returns the pointer of internal array */
169			Real* getArrayPointer() {
170	tim	385	return this->data_;
171	tim	137	}
172
173	tim	76	/**
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	tim	385	if (!equal(this->data_[i], v[i])) {
182	tim	76	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	tim	70	/** Negates the value of this vector in place. */
199			inline void negate() {
200	tim	101	for (unsigned int i = 0; i < Dim; i++)
201	tim	385	this->data_[i] = -this->data_[i];
202	tim	70	}
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	tim	385	this->data_[i] = -v1.data_[i];
211	tim	70
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	tim	110	for (unsigned int i = 0; i < Dim; i++)
220	tim	385	this->data_[i] += v1.data_[i];
221	tim	110	}
222	tim	70
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	tim	93	for (unsigned int i = 0; i < Dim; i++)
230	tim	385	this->data_[i] = v1.data_[i] + v2.data_[i];
231	tim	70	}
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	tim	385	this->data_[i] -= v1.data_[i];
240	tim	70	}
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	tim	385	this->data_[i] = v1.data_[i] - v2.data_[i];
250	tim	70	}
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	tim	110	inline void mul( Real s ) {
257	tim	93	for (unsigned int i = 0; i < Dim; i++)
258	tim	385	this->data_[i] *= s;
259	tim	70	}
260
261			/**
262			* Sets the value of this vector to the scalar multiplication of vector v1
263			* (this = s v1).
264	tim	101	* @param v1 the vector
265	tim	70	* @param s the scalar value
266			*/
267	tim	110	inline void mul( const Vector<Real, Dim>& v1, Real s) {
268	tim	93	for (unsigned int i = 0; i < Dim; i++)
269	tim	385	this->data_[i] = s * v1.data_[i];
270	tim	70	}
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	tim	110	inline void div( Real s) {
277	tim	93	for (unsigned int i = 0; i < Dim; i++)
278	tim	385	this->data_[i] /= s;
279	tim	70	}
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	tim	110	inline void div( const Vector<Real, Dim>& v1, Real s ) {
287	tim	93	for (unsigned int i = 0; i < Dim; i++)
288	tim	385	this->data_[i] = v1.data_[i] / s;
289	tim	70	}
290
291			/** @see #add */
292	tim	71	inline Vector<Real, Dim>& operator +=( const Vector<Real, Dim>& v1 ) {
293	tim	70	add(v1);
294			return *this;
295			}
296
297			/** @see #sub */
298	tim	71	inline Vector<Real, Dim>& operator -=( const Vector<Real, Dim>& v1 ) {
299	tim	70	sub(v1);
300			return *this;
301			}
302
303			/** @see #mul */
304	tim	110	inline Vector<Real, Dim>& operator *=( Real s) {
305	tim	70	mul(s);
306			return *this;
307			}
308
309			/** @see #div */
310	tim	110	inline Vector<Real, Dim>& operator /=( Real s ) {
311	tim	70	div(s);
312			return *this;
313			}
314
315			/**
316			* Returns the length of this vector.
317			* @return the length of this vector
318			*/
319	tim	110	inline Real length() {
320	tim	104	return sqrt(lengthSquare());
321	tim	70	}
322
323			/**
324			* Returns the squared length of this vector.
325			* @return the squared length of this vector
326			*/
327	tim	110	inline Real lengthSquare() {
328	tim	70	return dot(this, this);
329			}
330
331			/** Normalizes this vector in place */
332			inline void normalize() {
333	tim	110	Real len;
334	tim	70
335			len = length();
336	tim	102
337			//if (len < oopse:epsilon)
338			// throw();
339
340	tim	70	*this /= len;
341			}
342	tim	93
343			/**
344			* Tests if this vector is normalized
345			* @return true if this vector is normalized, otherwise return false
346			*/
347	tim	104	inline bool isNormalized() {
348			return equal(lengthSquare(), 1.0);
349	tim	93	}
350	tim	70
351			protected:
352	tim	110	Real data_[Dim];
353	tim	70
354			};
355
356			/** unary minus*/
357	tim	71	template<typename Real, unsigned int Dim>
358	tim	70	inline Vector<Real, Dim> operator -(const Vector<Real, Dim>& v1){
359	tim	101	Vector<Real, Dim> tmp(v1);
360			tmp.negate();
361			return tmp;
362	tim	70	}
363
364			/**
365			* Return the sum of two vectors (v1 - v2).
366			* @return the sum of two vectors
367			* @param v1 the first vector
368			* @param v2 the second vector
369			*/
370	tim	71	template<typename Real, unsigned int Dim>
371	tim	70	inline Vector<Real, Dim> operator +(const Vector<Real, Dim>& v1, const Vector<Real, Dim>& v2) {
372			Vector<Real, Dim> result;
373
374			result.add(v1, v2);
375			return result;
376			}
377
378			/**
379			* Return the difference of two vectors (v1 - v2).
380			* @return the difference of two vectors
381			* @param v1 the first vector
382			* @param v2 the second vector
383			*/
384	tim	71	template<typename Real, unsigned int Dim>
385	tim	70	Vector<Real, Dim> operator -(const Vector<Real, Dim>& v1, const Vector<Real, Dim>& v2) {
386			Vector<Real, Dim> result;
387			result.sub(v1, v2);
388			return result;
389			}
390
391			/**
392			* Returns the vaule of scalar multiplication of this vector v1 (v1 * r).
393			* @return the vaule of scalar multiplication of this vector
394			* @param v1 the source vector
395			* @param s the scalar value
396			*/
397	tim	71	template<typename Real, unsigned int Dim>
398	tim	110	Vector<Real, Dim> operator * ( const Vector<Real, Dim>& v1, Real s) {
399	tim	70	Vector<Real, Dim> result;
400	tim	101	result.mul(v1,s);
401	tim	70	return result;
402			}
403
404			/**
405			* Returns the vaule of scalar multiplication of this vector v1 (v1 * r).
406			* @return the vaule of scalar multiplication of this vector
407			* @param s the scalar value
408			* @param v1 the source vector
409			*/
410	tim	71	template<typename Real, unsigned int Dim>
411	tim	110	Vector<Real, Dim> operator * ( Real s, const Vector<Real, Dim>& v1 ) {
412	tim	70	Vector<Real, Dim> result;
413	tim	101	result.mul(v1, s);
414	tim	70	return result;
415			}
416
417			/**
418			* Returns the value of division of a vector by a scalar.
419			* @return the vaule of scalar division of this vector
420			* @param v1 the source vector
421			* @param s the scalar value
422			*/
423	tim	71	template<typename Real, unsigned int Dim>
424	tim	110	Vector<Real, Dim> operator / ( const Vector<Real, Dim>& v1, Real s) {
425	tim	70	Vector<Real, Dim> result;
426			result.div( v1,s);
427			return result;
428			}
429
430			/**
431			* Returns the dot product of two Vectors
432			* @param v1 first vector
433			* @param v2 second vector
434			* @return the dot product of v1 and v2
435			*/
436	tim	71	template<typename Real, unsigned int Dim>
437	tim	70	inline Real dot( const Vector<Real, Dim>& v1, const Vector<Real, Dim>& v2 ) {
438	tim	93	Real tmp;
439			tmp = 0;
440	tim	70
441	tim	93	for (unsigned int i = 0; i < Dim; i++)
442	tim	110	tmp += v1[i] * v2[i];
443	tim	93
444			return tmp;
445	tim	70	}
446
447			/**
448			* Returns the distance between two Vectors
449			* @param v1 first vector
450			* @param v2 second vector
451			* @return the distance between v1 and v2
452			*/
453	tim	71	template<typename Real, unsigned int Dim>
454	tim	70	inline Real distance( const Vector<Real, Dim>& v1, const Vector<Real, Dim>& v2 ) {
455			Vector<Real, Dim> tempVector = v1 - v2;
456			return tempVector.length();
457			}
458
459			/**
460			* Returns the squared distance between two Vectors
461			* @param v1 first vector
462			* @param v2 second vector
463			* @return the squared distance between v1 and v2
464			*/
465	tim	71	template<typename Real, unsigned int Dim>
466	tim	70	inline Real distanceSquare( const Vector<Real, Dim>& v1, const Vector<Real, Dim>& v2 ) {
467			Vector<Real, Dim> tempVector = v1 - v2;
468			return tempVector.lengthSquare();
469			}
470
471			/**
472			* Write to an output stream
473			*/
474	tim	71	template<typename Real, unsigned int Dim>
475	tim	93	std::ostream &operator<< ( std::ostream& o, const Vector<Real, Dim>& v) {
476
477	tim	110	o << "[ ";
478
479			for (unsigned int i = 0 ; i< Dim; i++) {
480			o << v[i];
481
482			if (i != Dim -1) {
483			o<< ", ";
484			}
485			}
486
487			o << " ]";
488	tim	70	return o;
489			}
490
491			}
492			#endif