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Comparing trunk/src/math/Vector.hpp (file contents):
Revision 253 by tim, Thu Jan 13 19:40:37 2005 UTC vs.
Revision 1390 by gezelter, Wed Nov 25 20:02:06 2009 UTC

# Line 1 | Line 1
1 < /*
1 > /*
2   * Copyright (c) 2005 The University of Notre Dame. All Rights Reserved.
3   *
4   * The University of Notre Dame grants you ("Licensee") a
# Line 6 | Line 6
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
9 > * 1. Redistributions of source code must retain the above copyright
10   *    notice, this list of conditions and the following disclaimer.
11   *
12 < * 3. Redistributions in binary form must reproduce the above copyright
12 > * 2. Redistributions in binary form must reproduce the above copyright
13   *    notice, this list of conditions and the following disclaimer in the
14   *    documentation and/or other materials provided with the
15   *    distribution.
# Line 37 | Line 28
28   * arising out of the use of or inability to use software, even if the
29   * University of Notre Dame has been advised of the possibility of
30   * such damages.
31 + *
32 + * SUPPORT OPEN SCIENCE!  If you use OpenMD or its source code in your
33 + * research, please cite the appropriate papers when you publish your
34 + * work.  Good starting points are:
35 + *                                                                      
36 + * [1]  Meineke, et al., J. Comp. Chem. 26, 252-271 (2005).            
37 + * [2]  Fennell & Gezelter, J. Chem. Phys. 124, 234104 (2006).          
38 + * [3]  Sun, Lin & Gezelter, J. Chem. Phys. 128, 24107 (2008).          
39 + * [4]  Vardeman & Gezelter, in progress (2009).                        
40   */
41  
42   /**
# Line 53 | Line 53
53   #include <cmath>
54   #include <iostream>
55   #include <math.h>
56 < namespace oopse {
56 > #include "config.h"
57 > namespace OpenMD {
58  
59 <    static const double epsilon = 0.000001;
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 <    }
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 <    }
66 >  //template<>
67 >  //inline bool equal(float e1, float e2) {
68 >  //  return fabs(e1 - e2) < epsilon;
69 >  //}
70  
71 <    template<>
72 <    inline bool equal(double e1, double e2) {
73 <        return fabs(e1 - e2) < epsilon;
74 <    }
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:
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;
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 <                    data_[i] = 0;
92 <            }
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 <            }
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;
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 <                    data_[i] = v[i];
104 >      for (unsigned int i = 0; i < Dim; i++)            
105 >        this->data_[i] = v[i];
106                  
107 <                return *this;
108 <            }
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 <                    data_[i] = s;
114 <            }
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 <                    data_[i] = v[i];
120 <            }
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 data_[i];
130 <            }
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 data_[i];
140 <            }
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 data_[i];
150 <            }
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 data_[i];
160 <            }
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] = data_[i];
166 <                }                
167 <            }
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 data_;
172 <            }
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) {
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(data_[i], v[i])) {
183 <                        return false;
184 <                    }
185 <                }
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 <            }
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 <            }
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 <                    data_[i] = -data_[i];
203 <            }
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 <                    data_[i] = -v1.data_[i];
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 <            }
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 <                    data_[i] += v1.data_[i];
222 <            }
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 <                    data_[i] = v1.data_[i] + v2.data_[i];
232 <            }
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 <                    data_[i] -= v1.data_[i];
241 <            }
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 <                    data_[i] = v1.data_[i] - v2.data_[i];
251 <            }
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 <                   data_[i] *= s;
260 <            }
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 <                    data_[i] = s * v1.data_[i];
271 <            }
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 <                    data_[i] /= s;
280 <            }
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 <                    data_[i] = v1.data_[i] / s;
290 <            }
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 <            }
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 <            }
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 <            }
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 <            }
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 <            }
316 >    /**
317 >     * Returns the sum of all elements of this vector.
318 >     * @return the sum of all elements of this vector
319 >     */
320 >    inline Real sum() {
321 >      Real tmp;
322 >      tmp = 0;
323 >      for (unsigned int i = 0; i < Dim; i++)
324 >        tmp += this->data_[i];
325 >      return tmp;  
326 >    }
327              
328 <            /**
329 <             * Returns the squared length of this vector.
330 <             * @return the squared length of this vector
331 <             */
332 <             inline Real lengthSquare() {
333 <                return dot(*this, *this);
334 <            }
328 >    /**
329 >     * Returns the length of this vector.
330 >     * @return the length of this vector
331 >     */
332 >    inline Real length() {
333 >      return sqrt(lengthSquare());  
334 >    }
335              
336 <            /** Normalizes this vector in place */
337 <            inline void normalize() {
338 <                Real len;
336 >    /**
337 >     * Returns the squared length of this vector.
338 >     * @return the squared length of this vector
339 >     */
340 >    inline Real lengthSquare() {
341 >      return dot(*this, *this);
342 >    }
343 >            
344 >    /** Normalizes this vector in place */
345 >    inline void normalize() {
346 >      Real len;
347  
348 <                len = length();
348 >      len = length();
349                  
350 <                //if (len < oopse:epsilon)
351 <                //  throw();
350 >      //if (len < OpenMD::NumericConstant::epsilon)
351 >      //  throw();
352                  
353 <                *this /= len;
354 <            }
353 >      *this /= len;
354 >    }
355  
356 <            /**
357 <             * Tests if this vector is normalized
358 <             * @return true if this vector is normalized, otherwise return false
359 <             */
360 <            inline bool isNormalized() {
361 <                return equal(lengthSquare(), 1.0);
362 <            }          
363 <            
364 <        protected:
365 <            Real data_[Dim];
356 >    /**
357 >     * Tests if this vector is normalized
358 >     * @return true if this vector is normalized, otherwise return false
359 >     */
360 >    inline bool isNormalized() {
361 >      return equal(lengthSquare(), (RealType)1);
362 >    }          
363 >
364 >    unsigned int size() {return Dim;}
365 >  protected:
366 >    Real data_[Dim];
367          
368 <    };
368 >  };
369  
370 <    /** unary minus*/
371 <    template<typename Real, unsigned int Dim>    
372 <    inline Vector<Real, Dim> operator -(const Vector<Real, Dim>& v1){
373 <        Vector<Real, Dim> tmp(v1);
374 <        tmp.negate();
375 <        return tmp;
376 <    }
370 >  /** unary minus*/
371 >  template<typename Real, unsigned int Dim>    
372 >  inline Vector<Real, Dim> operator -(const Vector<Real, Dim>& v1){
373 >    Vector<Real, Dim> tmp(v1);
374 >    tmp.negate();
375 >    return tmp;
376 >  }
377  
378 <    /**
379 <     * Return the sum of two vectors  (v1 - v2).
380 <     * @return the sum of two vectors
381 <     * @param v1 the first vector
382 <     * @param v2 the second vector
383 <     */  
384 <    template<typename Real, unsigned int Dim>    
385 <    inline Vector<Real, Dim> operator +(const Vector<Real, Dim>& v1, const Vector<Real, Dim>& v2) {
386 <        Vector<Real, Dim> result;
378 >  /**
379 >   * Return the sum of two vectors  (v1 - v2).
380 >   * @return the sum of two vectors
381 >   * @param v1 the first vector
382 >   * @param v2 the second vector
383 >   */  
384 >  template<typename Real, unsigned int Dim>    
385 >  inline Vector<Real, Dim> operator +(const Vector<Real, Dim>& v1, const Vector<Real, Dim>& v2) {
386 >    Vector<Real, Dim> result;
387          
388 <        result.add(v1, v2);
389 <        return result;        
390 <    }
388 >    result.add(v1, v2);
389 >    return result;        
390 >  }
391  
392 <    /**
393 <     * Return the difference of two vectors  (v1 - v2).
394 <     * @return the difference of two vectors
395 <     * @param v1 the first vector
396 <     * @param v2 the second vector
397 <     */  
398 <    template<typename Real, unsigned int Dim>    
399 <    Vector<Real, Dim> operator -(const Vector<Real, Dim>& v1, const Vector<Real, Dim>& v2) {
400 <        Vector<Real, Dim> result;
401 <        result.sub(v1, v2);
402 <        return result;        
403 <    }
392 >  /**
393 >   * Return the difference of two vectors  (v1 - v2).
394 >   * @return the difference of two vectors
395 >   * @param v1 the first vector
396 >   * @param v2 the second vector
397 >   */  
398 >  template<typename Real, unsigned int Dim>    
399 >  Vector<Real, Dim> operator -(const Vector<Real, Dim>& v1, const Vector<Real, Dim>& v2) {
400 >    Vector<Real, Dim> result;
401 >    result.sub(v1, v2);
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 v1 the source vector
409 <     * @param s the scalar value
410 <     */
411 <    template<typename Real, unsigned int Dim>                
412 <    Vector<Real, Dim> operator * ( const Vector<Real, Dim>& v1, Real s) {      
413 <        Vector<Real, Dim> result;
414 <        result.mul(v1,s);
415 <        return result;          
416 <    }
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 v1 the source vector
409 >   * @param s the scalar value
410 >   */
411 >  template<typename Real, unsigned int Dim>                
412 >  Vector<Real, Dim> operator * ( const Vector<Real, Dim>& v1, Real s) {      
413 >    Vector<Real, Dim> result;
414 >    result.mul(v1,s);
415 >    return result;          
416 >  }
417      
418 <    /**
419 <     * Returns the vaule of scalar multiplication of this vector v1 (v1 * r).
420 <     * @return  the vaule of scalar multiplication of this vector
421 <     * @param s the scalar value
422 <     * @param v1 the source vector
423 <     */  
424 <    template<typename Real, unsigned int Dim>
425 <    Vector<Real, Dim> operator * ( Real s, const Vector<Real, Dim>& v1 ) {
426 <        Vector<Real, Dim> result;
427 <        result.mul(v1, s);
428 <        return result;          
429 <    }
418 >  /**
419 >   * Returns the vaule of scalar multiplication of this vector v1 (v1 * r).
420 >   * @return  the vaule of scalar multiplication of this vector
421 >   * @param s the scalar value
422 >   * @param v1 the source vector
423 >   */  
424 >  template<typename Real, unsigned int Dim>
425 >  Vector<Real, Dim> operator * ( Real s, const Vector<Real, Dim>& v1 ) {
426 >    Vector<Real, Dim> result;
427 >    result.mul(v1, s);
428 >    return result;          
429 >  }
430  
431 <    /**
432 <     * Returns the  value of division of a vector by a scalar.
433 <     * @return  the vaule of scalar division of this vector
434 <     * @param v1 the source vector
435 <     * @param s the scalar value
436 <     */
437 <    template<typename Real, unsigned int Dim>    
438 <    Vector<Real, Dim> operator / ( const Vector<Real, Dim>& v1, Real s) {      
439 <        Vector<Real, Dim> result;
440 <        result.div( v1,s);
441 <        return result;          
442 <    }
431 >  /**
432 >   * Returns the  value of division of a vector by a scalar.
433 >   * @return  the vaule of scalar division of this vector
434 >   * @param v1 the source vector
435 >   * @param s the scalar value
436 >   */
437 >  template<typename Real, unsigned int Dim>    
438 >  Vector<Real, Dim> operator / ( const Vector<Real, Dim>& v1, Real s) {      
439 >    Vector<Real, Dim> result;
440 >    result.div( v1,s);
441 >    return result;          
442 >  }
443      
444 <    /**
445 <     * Returns the dot product of two Vectors
446 <     * @param v1 first vector
447 <     * @param v2 second vector
448 <     * @return the dot product of v1 and v2
449 <     */
450 <    template<typename Real, unsigned int Dim>    
451 <    inline Real dot( const Vector<Real, Dim>& v1, const Vector<Real, Dim>& v2 ) {
452 <        Real tmp;
453 <        tmp = 0;
444 >  /**
445 >   * Returns the dot product of two Vectors
446 >   * @param v1 first vector
447 >   * @param v2 second vector
448 >   * @return the dot product of v1 and v2
449 >   */
450 >  template<typename Real, unsigned int Dim>    
451 >  inline Real dot( const Vector<Real, Dim>& v1, const Vector<Real, Dim>& v2 ) {
452 >    Real tmp;
453 >    tmp = 0;
454  
455 <        for (unsigned int i = 0; i < Dim; i++)
456 <            tmp += v1[i] * v2[i];
455 >    for (unsigned int i = 0; i < Dim; i++)
456 >      tmp += v1[i] * v2[i];
457  
458 <        return tmp;
459 <    }
458 >    return tmp;
459 >  }
460  
461 <    /**
462 <     * Returns the distance between  two Vectors
463 <     * @param v1 first vector
464 <     * @param v2 second vector
465 <     * @return the distance between v1 and v2
466 <     */
467 <    template<typename Real, unsigned int Dim>    
468 <    inline Real distance( const Vector<Real, Dim>& v1, const Vector<Real, Dim>& v2 ) {
469 <        Vector<Real, Dim> tempVector = v1 - v2;
470 <        return tempVector.length();
471 <    }
461 >  /**
462 >   * Returns the distance between  two Vectors
463 >   * @param v1 first vector
464 >   * @param v2 second vector
465 >   * @return the distance between v1 and v2
466 >   */  
467 >  template<typename Real, unsigned int Dim>    
468 >  inline Real distance( const Vector<Real, Dim>& v1, const Vector<Real, Dim>& v2 ) {
469 >    Vector<Real, Dim> tempVector = v1 - v2;
470 >    return tempVector.length();
471 >  }
472  
473 <    /**
474 <     * Returns the squared distance between  two Vectors
475 <     * @param v1 first vector
476 <     * @param v2 second vector
477 <     * @return the squared distance between v1 and v2
478 <     */
479 <    template<typename Real, unsigned int Dim>
480 <    inline Real distanceSquare( const Vector<Real, Dim>& v1, const Vector<Real, Dim>& v2 ) {
481 <        Vector<Real, Dim> tempVector = v1 - v2;
482 <        return tempVector.lengthSquare();
483 <    }
473 >  /**
474 >   * Returns the squared distance between  two Vectors
475 >   * @param v1 first vector
476 >   * @param v2 second vector
477 >   * @return the squared distance between v1 and v2
478 >   */
479 >  template<typename Real, unsigned int Dim>
480 >  inline Real distanceSquare( const Vector<Real, Dim>& v1, const Vector<Real, Dim>& v2 ) {
481 >    Vector<Real, Dim> tempVector = v1 - v2;
482 >    return tempVector.lengthSquare();
483 >  }
484  
485 <    /**
486 <     * Write to an output stream
487 <     */
488 <    template<typename Real, unsigned int Dim>
489 <    std::ostream &operator<< ( std::ostream& o, const Vector<Real, Dim>& v) {
485 >  /**
486 >   * Write to an output stream
487 >   */
488 >  template<typename Real, unsigned int Dim>
489 >  std::ostream &operator<< ( std::ostream& o, const Vector<Real, Dim>& v) {
490  
491 <        o << "[ ";
491 >    o << "[ ";
492          
493 <        for (unsigned int i = 0 ; i< Dim; i++) {
494 <            o << v[i];
493 >    for (unsigned int i = 0 ; i< Dim; i++) {
494 >      o << v[i];
495  
496 <            if (i  != Dim -1) {
497 <                o<< ", ";
498 <            }
485 <        }
486 <
487 <        o << " ]";
488 <        return o;        
496 >      if (i  != Dim -1) {
497 >        o<< ", ";
498 >      }
499      }
500 +
501 +    o << " ]";
502 +    return o;        
503 +  }
504      
505   }
506   #endif

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