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root/OpenMD/trunk/src/math/CubicSpline.cpp
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Comparing trunk/src/math/CubicSpline.cpp (file contents):
Revision 1928 by gezelter, Sat Aug 17 13:03:17 2013 UTC vs.
Revision 2057 by gezelter, Tue Mar 3 15:22:26 2015 UTC

# Line 45 | Line 45
45   #include <cassert>
46   #include <cstdio>
47   #include <algorithm>
48 + #include <numeric>
49  
50   using namespace OpenMD;
51   using namespace std;
52  
53   CubicSpline::CubicSpline() : generated(false), isUniform(true) {
54 <  data_.clear();
54 >  x_.clear();
55 >  y_.clear();
56   }
57  
58   void CubicSpline::addPoint(const RealType xp, const RealType yp) {
59 <  data_.push_back(make_pair(xp, yp));
59 >  x_.push_back(xp);
60 >  y_.push_back(yp);
61   }
62  
63   void CubicSpline::addPoints(const vector<RealType>& xps,
# Line 62 | Line 65 | void CubicSpline::addPoints(const vector<RealType>& xp
65    
66    assert(xps.size() == yps.size());
67    
68 <  for (unsigned int i = 0; i < xps.size(); i++)
69 <    data_.push_back(make_pair(xps[i], yps[i]));
68 >  for (unsigned int i = 0; i < xps.size(); i++){
69 >    x_.push_back(xps[i]);
70 >    y_.push_back(yps[i]);
71 >  }
72   }
73  
74   void CubicSpline::generate() {
# Line 71 | Line 76 | void CubicSpline::generate() {
76    //
77    // class values constructed:
78    //   n   = number of data_ points.
79 <  //   x   = vector of independent variable values
80 <  //   y   = vector of dependent variable values
81 <  //   b   = vector of S'(x[i]) values.
82 <  //   c   = vector of S"(x[i])/2 values.
83 <  //   d   = vector of S'''(x[i]+)/6 values (i < n).
79 >  //   x_  = vector of independent variable values
80 >  //   y_  = vector of dependent variable values
81 >  //   b   = vector of S'(x_[i]) values.
82 >  //   c   = vector of S"(x_[i])/2 values.
83 >  //   d   = vector of S'''(x_[i]+)/6 values (i < n).
84    // Local variables:  
85  
86    RealType fp1, fpn, h, p;
87    
88    // make sure the sizes match
89    
90 <  n = data_.size();  
90 >  n = x_.size();  
91    b.resize(n);
92    c.resize(n);
93    d.resize(n);
# Line 92 | Line 97 | void CubicSpline::generate() {
97    bool sorted = true;
98    
99    for (int i = 1; i < n; i++) {
100 <    if ( (data_[i].first - data_[i-1].first ) <= 0.0 ) sorted = false;
100 >    if ( (x_[i] - x_[i-1] ) <= 0.0 ) sorted = false;
101    }
102    
103    // sort if necessary
104    
105 <  if (!sorted) sort(data_.begin(), data_.end());  
105 >  if (!sorted) {
106 >    vector<int> p = sort_permutation(x_);
107 >    x_ = apply_permutation(x_, p);
108 >    y_ = apply_permutation(y_, p);
109 >  }
110    
111 +  
112    // Calculate coefficients for the tridiagonal system: store
113    // sub-diagonal in B, diagonal in D, difference quotient in C.  
114    
115 <  b[0] = data_[1].first - data_[0].first;
116 <  c[0] = (data_[1].second - data_[0].second) / b[0];
115 >  b[0] = x_[1] - x_[0];
116 >  c[0] = (y_[1] - y_[0]) / b[0];
117    
118    if (n == 2) {
119  
120      // Assume the derivatives at both endpoints are zero. Another
121      // assumption could be made to have a linear interpolant between
122      // the two points.  In that case, the b coefficients below would be
123 <    // (data_[1].second - data_[0].second) / (data_[1].first - data_[0].first)
123 >    // (y_[1] - y_[0]) / (x_[1] - x_[0])
124      // and the c and d coefficients would both be zero.
125      b[0] = 0.0;
126 <    c[0] = -3.0 * pow((data_[1].second - data_[0].second) /
127 <                      (data_[1].first-data_[0].first), 2);
118 <    d[0] = -2.0 * pow((data_[1].second - data_[0].second) /
119 <                      (data_[1].first-data_[0].first), 3);
126 >    c[0] = -3.0 * pow((y_[1] - y_[0]) / (x_[1] - x_[0]), 2);
127 >    d[0] = -2.0 * pow((y_[1] - y_[0]) / (x_[1] - x_[0]), 3);
128      b[1] = b[0];
129      c[1] = 0.0;
130      d[1] = 0.0;
131 <    dx = 1.0 / (data_[1].first - data_[0].first);
131 >    dx = 1.0 / (x_[1] - x_[0]);
132      isUniform = true;
133      generated = true;
134      return;
# Line 129 | Line 137 | void CubicSpline::generate() {
137    d[0] = 2.0 * b[0];
138    
139    for (int i = 1; i < n-1; i++) {
140 <    b[i] = data_[i+1].first - data_[i].first;
140 >    b[i] = x_[i+1] - x_[i];
141      if ( fabs( b[i] - b[0] ) / b[0] > 1.0e-5) isUniform = false;
142 <    c[i] = (data_[i+1].second - data_[i].second) / b[i];
142 >    c[i] = (y_[i+1] - y_[i]) / b[i];
143      d[i] = 2.0 * (b[i] + b[i-1]);
144    }
145    
# Line 143 | Line 151 | void CubicSpline::generate() {
151    fp1 = c[0] - b[0]*(c[1] - c[0])/(b[0] + b[1]);
152    if (n > 3) fp1 = fp1 + b[0]*((b[0] + b[1]) * (c[2] - c[1]) /
153                                 (b[1] + b[2]) -
154 <                               c[1] + c[0]) / (data_[3].first - data_[0].first);
154 >                               c[1] + c[0]) / (x_[3] - x_[0]);
155    
156    fpn = c[n-2] + b[n-2]*(c[n-2] - c[n-3])/(b[n-3] + b[n-2]);
157    
158    if (n > 3)  fpn = fpn + b[n-2] *
159                  (c[n-2] - c[n-3] - (b[n-3] + b[n-2]) *
160                   (c[n-3] - c[n-4])/(b[n-3] + b[n-4])) /
161 <                (data_[n-1].first - data_[n-4].first);
161 >                (x_[n-1] - x_[n-4]);
162    
163    // Calculate the right hand side and store it in C.
164    
# Line 175 | Line 183 | void CubicSpline::generate() {
183    // Calculate the coefficients defining the spline.
184    
185    for (int i = 0; i < n-1; i++) {
186 <    h = data_[i+1].first - data_[i].first;
186 >    h = x_[i+1] - x_[i];
187      d[i] = (c[i+1] - c[i]) / (3.0 * h);
188 <    b[i] = (data_[i+1].second - data_[i].second)/h - h * (c[i] + h * d[i]);
188 >    b[i] = (y_[i+1] - y_[i])/h - h * (c[i] + h * d[i]);
189    }
190    
191    b[n-1] = b[n-2] + h * (2.0 * c[n-2] + h * 3.0 * d[n-2]);
192    
193 <  if (isUniform) dx = 1.0 / (data_[1].first - data_[0].first);
193 >  if (isUniform) dx = 1.0 / (x_[1] - x_[0]);
194    
195    generated = true;
196    return;
# Line 198 | Line 206 | RealType CubicSpline::getValueAt(const RealType& t) {
206    
207    if (!generated) generate();
208    
209 <  assert(t >= data_.front().first);
210 <  assert(t <= data_.back().first);
209 >  assert(t >= x_.front());
210 >  assert(t <= x_.back());
211  
212    //  Find the interval ( x[j], x[j+1] ) that contains or is nearest
213    //  to t.
214  
215    if (isUniform) {    
216      
217 <    j = max(0, min(n-1, int((t - data_[0].first) * dx)));  
217 >    j = max(0, min(n-1, int((t - x_[0]) * dx)));  
218  
219    } else {
220  
221      j = n-1;
222      
223      for (int i = 0; i < n; i++) {
224 <      if ( t < data_[i].first ) {
224 >      if ( t < x_[i] ) {
225          j = i-1;
226          break;
227        }      
# Line 222 | Line 230 | RealType CubicSpline::getValueAt(const RealType& t) {
230    
231    //  Evaluate the cubic polynomial.
232    
233 <  dt = t - data_[j].first;
234 <  return data_[j].second + dt*(b[j] + dt*(c[j] + dt*d[j]));  
233 >  dt = t - x_[j];
234 >  return y_[j] + dt*(b[j] + dt*(c[j] + dt*d[j]));  
235   }
236  
237  
# Line 234 | Line 242 | void CubicSpline::getValueAt(const RealType& t, RealTy
242    //   t = point where spline is to be evaluated.
243    // Output:
244    //   value of spline at t.
237 –  
238 –  if (!generated) generate();
239 –  
240 –  assert(t >= data_.front().first);
241 –  assert(t <= data_.back().first);
242 –
243 –  //  Find the interval ( x[j], x[j+1] ) that contains or is nearest
244 –  //  to t.
245 –
246 –  if (isUniform) {    
247 –    
248 –    j = max(0, min(n-1, int((t - data_[0].first) * dx)));  
249 –
250 –  } else {
251 –
252 –    j = n-1;
253 –    
254 –    for (int i = 0; i < n; i++) {
255 –      if ( t < data_[i].first ) {
256 –        j = i-1;
257 –        break;
258 –      }      
259 –    }
260 –  }
245    
262 –  //  Evaluate the cubic polynomial.
263 –  
264 –  dt = t - data_[j].first;
265 –  v = data_[j].second + dt*(b[j] + dt*(c[j] + dt*d[j]));  
266 – }
267 –
268 –
269 – pair<RealType, RealType> CubicSpline::getValueAndDerivativeAt(const RealType& t){
270 –  // Evaluate the spline and first derivative at t using coefficients
271 –  //
272 –  // Input parameters
273 –  //   t = point where spline is to be evaluated.
274 –  // Output:
275 –  //   pair containing value of spline at t and first derivative at t
276 –
246    if (!generated) generate();
247    
248 <  assert(t >= data_.front().first);
249 <  assert(t <= data_.back().first);
248 >  assert(t >= x_.front());
249 >  assert(t <= x_.back());
250  
251    //  Find the interval ( x[j], x[j+1] ) that contains or is nearest
252    //  to t.
253  
254    if (isUniform) {    
255      
256 <    j = max(0, min(n-1, int((t - data_[0].first) * dx)));  
256 >    j = max(0, min(n-1, int((t - x_[0]) * dx)));  
257  
258    } else {
259  
260      j = n-1;
261      
262      for (int i = 0; i < n; i++) {
263 <      if ( t < data_[i].first ) {
263 >      if ( t < x_[i] ) {
264          j = i-1;
265          break;
266        }      
# Line 300 | Line 269 | pair<RealType, RealType> CubicSpline::getValueAndDeriv
269    
270    //  Evaluate the cubic polynomial.
271    
272 <  dt = t - data_[j].first;
273 <
305 <  yval = data_[j].second + dt*(b[j] + dt*(c[j] + dt*d[j]));
306 <  dydx = b[j] + dt*(2.0 * c[j] + 3.0 * dt * d[j]);
307 <
308 <  return make_pair(yval, dydx);
272 >  dt = t - x_[j];
273 >  v = y_[j] + dt*(b[j] + dt*(c[j] + dt*d[j]));  
274   }
275  
276   pair<RealType, RealType> CubicSpline::getLimits(){
277    if (!generated) generate();
278 <  return make_pair( data_.front().first, data_.back().first );
278 >  return make_pair( x_.front(), x_.back() );
279   }
280  
281   void CubicSpline::getValueAndDerivativeAt(const RealType& t, RealType& v,
# Line 322 | Line 287 | void CubicSpline::getValueAndDerivativeAt(const RealTy
287  
288    if (!generated) generate();
289    
290 <  assert(t >= data_.front().first);
291 <  assert(t <= data_.back().first);
290 >  assert(t >= x_.front());
291 >  assert(t <= x_.back());
292  
293    //  Find the interval ( x[j], x[j+1] ) that contains or is nearest
294    //  to t.
295  
296    if (isUniform) {    
297      
298 <    j = max(0, min(n-1, int((t - data_[0].first) * dx)));  
298 >    j = max(0, min(n-1, int((t - x_[0]) * dx)));  
299  
300    } else {
301  
302      j = n-1;
303      
304      for (int i = 0; i < n; i++) {
305 <      if ( t < data_[i].first ) {
305 >      if ( t < x_[i] ) {
306          j = i-1;
307          break;
308        }      
# Line 346 | Line 311 | void CubicSpline::getValueAndDerivativeAt(const RealTy
311    
312    //  Evaluate the cubic polynomial.
313    
314 <  dt = t - data_[j].first;
314 >  dt = t - x_[j];
315  
316 <  v = data_[j].second + dt*(b[j] + dt*(c[j] + dt*d[j]));
316 >  v = y_[j] + dt*(b[j] + dt*(c[j] + dt*d[j]));
317    dv = b[j] + dt*(2.0 * c[j] + 3.0 * dt * d[j]);
318   }
319 +
320 + std::vector<int> CubicSpline::sort_permutation(std::vector<RealType>& v) {
321 +  std::vector<int> p(v.size());
322 +  std::iota(p.begin(), p.end(), 0);
323 +  std::sort(p.begin(), p.end(), OpenMD::Comparator(v) );
324 +  return p;
325 + }
326 +
327 + std::vector<RealType> CubicSpline::apply_permutation(std::vector<RealType> const& v,
328 +                                                     std::vector<int> const& p) {
329 +  int n = p.size();
330 +  std::vector<double> sorted_vec(n);
331 +  for (int i = 0; i < n; ++i) {
332 +    sorted_vec[i] = v[p[i]];
333 +  }
334 +  return sorted_vec;
335 + }

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