src/math/CubicSpline.cpp

/*
 * 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. Redistributions of source code must retain the above copyright
 *    notice, this list of conditions and the following disclaimer.
 *
 * 2. 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.
 *
 * SUPPORT OPEN SCIENCE!  If you use OpenMD or its source code in your
 * research, please cite the appropriate papers when you publish your
 * work.  Good starting points are:
 *                                                                      
 * [1]  Meineke, et al., J. Comp. Chem. 26, 252-271 (2005).             
 * [2]  Fennell & Gezelter, J. Chem. Phys. 124, 234104 (2006).          
 * [3]  Sun, Lin & Gezelter, J. Chem. Phys. 128, 24107 (2008).          
 * [4]  Vardeman & Gezelter, in progress (2009).                        
 */
 
#include "math/CubicSpline.hpp"
#include "utils/simError.h"
#include <cmath>
#include <cstdio>
#include <algorithm>

using namespace OpenMD;
using namespace std;

CubicSpline::CubicSpline() : generated(false), isUniform(true) {
  data_.clear();
}

void CubicSpline::addPoint(const RealType xp, const RealType yp) {
  data_.push_back(make_pair(xp, yp));
}

void CubicSpline::addPoints(const vector<RealType>& xps, 
                            const vector<RealType>& yps) {
  
  if (xps.size() != yps.size()) {
    printf( painCave.errMsg,
            "CubicSpline::addPoints was passed vectors of different length!\n");
    painCave.severity = OPENMD_ERROR;
    painCave.isFatal = 1;
    simError();    
  }

  for (int i = 0; i < xps.size(); i++) 
    data_.push_back(make_pair(xps[i], yps[i]));
}

void CubicSpline::generate() { 
  // Calculate coefficients defining a smooth cubic interpolatory spline.
  //
  // class values constructed:
  //   n   = number of data_ points.
  //   x   = vector of independent variable values 
  //   y   = vector of dependent variable values
  //   b   = vector of S'(x[i]) values.
  //   c   = vector of S"(x[i])/2 values.
  //   d   = vector of S'''(x[i]+)/6 values (i < n).
  // Local variables:   
 
  RealType fp1, fpn, h, p;
  
  // make sure the sizes match
  
  n = data_.size();  
  b.resize(n);
  c.resize(n);
  d.resize(n);
  
  // make sure we are monotonically increasing in x:
  
  bool sorted = true;
  
  for (int i = 1; i < n; i++) {
    if ( (data_[i].first - data_[i-1].first ) <= 0.0 ) sorted = false;
  }
  
  // sort if necessary
  
  if (!sorted) sort(data_.begin(), data_.end());  
  
  // Calculate coefficients for the tridiagonal system: store
  // sub-diagonal in B, diagonal in D, difference quotient in C.  
  
  b[0] = data_[1].first - data_[0].first;
  c[0] = (data_[1].second - data_[0].second) / b[0];
  
  if (n == 2) {

    // Assume the derivatives at both endpoints are zero. Another
    // assumption could be made to have a linear interpolant between
    // the two points.  In that case, the b coefficients below would be
    // (data_[1].second - data_[0].second) / (data_[1].first - data_[0].first)
    // and the c and d coefficients would both be zero.
    b[0] = 0.0;
    c[0] = -3.0 * pow((data_[1].second - data_[0].second) /
                      (data_[1].first-data_[0].first), 2);
    d[0] = -2.0 * pow((data_[1].second - data_[0].second) / 
                      (data_[1].first-data_[0].first), 3);
    b[1] = b[0];
    c[1] = 0.0;
    d[1] = 0.0;
    dx = 1.0 / (data_[1].first - data_[0].first);
    isUniform = true;
    generated = true;
    return;
  }
  
  d[0] = 2.0 * b[0];
  
  for (int i = 1; i < n-1; i++) {
    b[i] = data_[i+1].first - data_[i].first;
    if ( fabs( b[i] - b[0] ) / b[0] > 1.0e-5) isUniform = false;
    c[i] = (data_[i+1].second - data_[i].second) / b[i];
    d[i] = 2.0 * (b[i] + b[i-1]);
  }
  
  d[n-1] = 2.0 * b[n-2];
  
  // Calculate estimates for the end slopes using polynomials
  // that interpolate the data_ nearest the end.
  
  fp1 = c[0] - b[0]*(c[1] - c[0])/(b[0] + b[1]);
  if (n > 3) fp1 = fp1 + b[0]*((b[0] + b[1]) * (c[2] - c[1]) / 
                               (b[1] + b[2]) - 
                               c[1] + c[0]) / (data_[3].first - data_[0].first);
  
  fpn = c[n-2] + b[n-2]*(c[n-2] - c[n-3])/(b[n-3] + b[n-2]);

  if (n > 3)  fpn = fpn + b[n-2] * 
    (c[n-2] - c[n-3] - (b[n-3] + b[n-2]) * 
     (c[n-3] - c[n-4])/(b[n-3] + b[n-4]))/(data_[n-1].first - data_[n-4].first);
  
  
  // Calculate the right hand side and store it in C.
  
  c[n-1] = 3.0 * (fpn - c[n-2]);
  for (int i = n-2; i > 0; i--) 
    c[i] = 3.0 * (c[i] - c[i-1]);  
  c[0] = 3.0 * (c[0] - fp1);
  
  // Solve the tridiagonal system.
  
  for (int k = 1; k < n; k++) {
    p = b[k-1] / d[k-1];
    d[k] = d[k] - p*b[k-1];
    c[k] = c[k] - p*c[k-1];
  }
  
  c[n-1] = c[n-1] / d[n-1];
  
  for (int k = n-2; k >= 0; k--) 
    c[k] = (c[k] - b[k] * c[k+1]) / d[k];
  
  // Calculate the coefficients defining the spline.
  
  for (int i = 0; i < n-1; i++) {
    h = data_[i+1].first - data_[i].first;
    d[i] = (c[i+1] - c[i]) / (3.0 * h);
    b[i] = (data_[i+1].second - data_[i].second)/h - h * (c[i] + h * d[i]);
  }
  
  b[n-1] = b[n-2] + h * (2.0 * c[n-2] + h * 3.0 * d[n-2]);
  
  if (isUniform) dx = 1.0 / (data_[1].first - data_[0].first); 
  
  generated = true;
  return;
}

RealType CubicSpline::getValueAt(RealType t) {
  // Evaluate the spline at t using coefficients 
  //
  // Input parameters
  //   t = point where spline is to be evaluated.
  // Output:
  //   value of spline at t.
  
  if (!generated) generate();
  RealType dt;
  
  if ( t < data_[0].first || t > data_[n-1].first ) {    
    sprintf( painCave.errMsg,
             "CubicSpline::getValueAt was passed a value outside the range of the spline!\n");
    painCave.severity = OPENMD_ERROR;
    painCave.isFatal = 1;
    simError();    
  }

  //  Find the interval ( x[j], x[j+1] ) that contains or is nearest
  //  to t.

  int j;

  if (isUniform) {    
    
    j = max(0, min(n-1, int((t - data_[0].first) * dx)));   

  } else { 

    j = n-1;
    
    for (int i = 0; i < n; i++) {
      if ( t < data_[i].first ) {
        j = i-1;
        break;
      }      
    }
  }
  
  //  Evaluate the cubic polynomial.
  
  dt = t - data_[j].first;
  return data_[j].second + dt*(b[j] + dt*(c[j] + dt*d[j]));
  
}


pair<RealType, RealType> CubicSpline::getValueAndDerivativeAt(RealType t) {
  // Evaluate the spline and first derivative at t using coefficients 
  //
  // Input parameters
  //   t = point where spline is to be evaluated.
  // Output:
  //   pair containing value of spline at t and first derivative at t

  if (!generated) generate();
  RealType dt;
  
  if ( t < data_.front().first || t > data_.back().first ) {    
    sprintf( painCave.errMsg,
             "CubicSpline::getValueAndDerivativeAt was passed a value outside the range of the spline!\n");
    painCave.severity = OPENMD_ERROR;
    painCave.isFatal = 1;
    simError();    
  }

  //  Find the interval ( x[j], x[j+1] ) that contains or is nearest
  //  to t.

  int j;

  if (isUniform) {    
    
    j = max(0, min(n-1, int((t - data_[0].first) * dx)));   

  } else { 

    j = n-1;
    
    for (int i = 0; i < n; i++) {
      if ( t < data_[i].first ) {
        j = i-1;
        break;
      }      
    }
  }
  
  //  Evaluate the cubic polynomial.
  
  dt = t - data_[j].first;

  RealType yval = data_[j].second + dt*(b[j] + dt*(c[j] + dt*d[j]));
  RealType dydx = b[j] + dt*(2.0 * c[j] + 3.0 * dt * d[j]);
  
  return make_pair(yval, dydx);
}
Revision:	1618
Committed:	Mon Sep 12 17:09:26 2011 UTC (14 years, 1 month ago) by gezelter
Original Path:	*branches/development/src/math/CubicSpline.cpp*
File size:	8765 byte(s)
Log Message:	Build fixes for qhull 2011, fixes for compilation with PGI.
#	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. Redistributions of source code must retain the above copyright
10	* notice, this list of conditions and the following disclaimer.
11	*
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.
16	*
17	* This software is provided "AS IS," without a warranty of any
18	* kind. All express or implied conditions, representations and
19	* warranties, including any implied warranty of merchantability,
20	* fitness for a particular purpose or non-infringement, are hereby
21	* excluded. The University of Notre Dame and its licensors shall not
22	* be liable for any damages suffered by licensee as a result of
23	* using, modifying or distributing the software or its
24	* derivatives. In no event will the University of Notre Dame or its
25	* licensors be liable for any lost revenue, profit or data, or for
26	* direct, indirect, special, consequential, incidental or punitive
27	* damages, however caused and regardless of the theory of liability,
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	#include "math/CubicSpline.hpp"
43	#include "utils/simError.h"
44	#include <cmath>
45	#include <cstdio>
46	#include <algorithm>
47
48	using namespace OpenMD;
49	using namespace std;
50
51	CubicSpline::CubicSpline() : generated(false), isUniform(true) {
52	data_.clear();
53	}
54
55	void CubicSpline::addPoint(const RealType xp, const RealType yp) {
56	data_.push_back(make_pair(xp, yp));
57	}
58
59	void CubicSpline::addPoints(const vector<RealType>& xps,
60	const vector<RealType>& yps) {
61
62	if (xps.size() != yps.size()) {
63	printf( painCave.errMsg,
64	"CubicSpline::addPoints was passed vectors of different length!\n");
65	painCave.severity = OPENMD_ERROR;
66	painCave.isFatal = 1;
67	simError();
68	}
69
70	for (int i = 0; i < xps.size(); i++)
71	data_.push_back(make_pair(xps[i], yps[i]));
72	}
73
74	void CubicSpline::generate() {
75	// Calculate coefficients defining a smooth cubic interpolatory spline.
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).
84	// Local variables:
85
86	RealType fp1, fpn, h, p;
87
88	// make sure the sizes match
89
90	n = data_.size();
91	b.resize(n);
92	c.resize(n);
93	d.resize(n);
94
95	// make sure we are monotonically increasing in x:
96
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;
101	}
102
103	// sort if necessary
104
105	if (!sorted) sort(data_.begin(), data_.end());
106
107	// Calculate coefficients for the tridiagonal system: store
108	// sub-diagonal in B, diagonal in D, difference quotient in C.
109
110	b[0] = data_[1].first - data_[0].first;
111	c[0] = (data_[1].second - data_[0].second) / b[0];
112
113	if (n == 2) {
114
115	// Assume the derivatives at both endpoints are zero. Another
116	// assumption could be made to have a linear interpolant between
117	// the two points. In that case, the b coefficients below would be
118	// (data_[1].second - data_[0].second) / (data_[1].first - data_[0].first)
119	// and the c and d coefficients would both be zero.
120	b[0] = 0.0;
121	c[0] = -3.0 * pow((data_[1].second - data_[0].second) /
122	(data_[1].first-data_[0].first), 2);
123	d[0] = -2.0 * pow((data_[1].second - data_[0].second) /
124	(data_[1].first-data_[0].first), 3);
125	b[1] = b[0];
126	c[1] = 0.0;
127	d[1] = 0.0;
128	dx = 1.0 / (data_[1].first - data_[0].first);
129	isUniform = true;
130	generated = true;
131	return;
132	}
133
134	d[0] = 2.0 * b[0];
135
136	for (int i = 1; i < n-1; i++) {
137	b[i] = data_[i+1].first - data_[i].first;
138	if ( fabs( b[i] - b[0] ) / b[0] > 1.0e-5) isUniform = false;
139	c[i] = (data_[i+1].second - data_[i].second) / b[i];
140	d[i] = 2.0 * (b[i] + b[i-1]);
141	}
142
143	d[n-1] = 2.0 * b[n-2];
144
145	// Calculate estimates for the end slopes using polynomials
146	// that interpolate the data_ nearest the end.
147
148	fp1 = c[0] - b[0]*(c[1] - c[0])/(b[0] + b[1]);
149	if (n > 3) fp1 = fp1 + b[0]((b[0] + b[1]) (c[2] - c[1]) /
150	(b[1] + b[2]) -
151	c[1] + c[0]) / (data_[3].first - data_[0].first);
152
153	fpn = c[n-2] + b[n-2]*(c[n-2] - c[n-3])/(b[n-3] + b[n-2]);
154
155	if (n > 3) fpn = fpn + b[n-2] *
156	(c[n-2] - c[n-3] - (b[n-3] + b[n-2]) *
157	(c[n-3] - c[n-4])/(b[n-3] + b[n-4]))/(data_[n-1].first - data_[n-4].first);
158
159
160	// Calculate the right hand side and store it in C.
161
162	c[n-1] = 3.0 * (fpn - c[n-2]);
163	for (int i = n-2; i > 0; i--)
164	c[i] = 3.0 * (c[i] - c[i-1]);
165	c[0] = 3.0 * (c[0] - fp1);
166
167	// Solve the tridiagonal system.
168
169	for (int k = 1; k < n; k++) {
170	p = b[k-1] / d[k-1];
171	d[k] = d[k] - p*b[k-1];
172	c[k] = c[k] - p*c[k-1];
173	}
174
175	c[n-1] = c[n-1] / d[n-1];
176
177	for (int k = n-2; k >= 0; k--)
178	c[k] = (c[k] - b[k] * c[k+1]) / d[k];
179
180	// Calculate the coefficients defining the spline.
181
182	for (int i = 0; i < n-1; i++) {
183	h = data_[i+1].first - data_[i].first;
184	d[i] = (c[i+1] - c[i]) / (3.0 * h);
185	b[i] = (data_[i+1].second - data_[i].second)/h - h * (c[i] + h * d[i]);
186	}
187
188	b[n-1] = b[n-2] + h * (2.0 * c[n-2] + h * 3.0 * d[n-2]);
189
190	if (isUniform) dx = 1.0 / (data_[1].first - data_[0].first);
191
192	generated = true;
193	return;
194	}
195
196	RealType CubicSpline::getValueAt(RealType t) {
197	// Evaluate the spline at t using coefficients
198	//
199	// Input parameters
200	// t = point where spline is to be evaluated.
201	// Output:
202	// value of spline at t.
203
204	if (!generated) generate();
205	RealType dt;
206
207	if ( t < data_[0].first \|\| t > data_[n-1].first ) {
208	sprintf( painCave.errMsg,
209	"CubicSpline::getValueAt was passed a value outside the range of the spline!\n");
210	painCave.severity = OPENMD_ERROR;
211	painCave.isFatal = 1;
212	simError();
213	}
214
215	// Find the interval ( x[j], x[j+1] ) that contains or is nearest
216	// to t.
217
218	int j;
219
220	if (isUniform) {
221
222	j = max(0, min(n-1, int((t - data_[0].first) * dx)));
223
224	} else {
225
226	j = n-1;
227
228	for (int i = 0; i < n; i++) {
229	if ( t < data_[i].first ) {
230	j = i-1;
231	break;
232	}
233	}
234	}
235
236	// Evaluate the cubic polynomial.
237
238	dt = t - data_[j].first;
239	return data_[j].second + dt(b[j] + dt(c[j] + dt*d[j]));
240
241	}
242
243
244	pair<RealType, RealType> CubicSpline::getValueAndDerivativeAt(RealType t) {
245	// Evaluate the spline and first derivative at t using coefficients
246	//
247	// Input parameters
248	// t = point where spline is to be evaluated.
249	// Output:
250	// pair containing value of spline at t and first derivative at t
251
252	if (!generated) generate();
253	RealType dt;
254
255	if ( t < data_.front().first \|\| t > data_.back().first ) {
256	sprintf( painCave.errMsg,
257	"CubicSpline::getValueAndDerivativeAt was passed a value outside the range of the spline!\n");
258	painCave.severity = OPENMD_ERROR;
259	painCave.isFatal = 1;
260	simError();
261	}
262
263	// Find the interval ( x[j], x[j+1] ) that contains or is nearest
264	// to t.
265
266	int j;
267
268	if (isUniform) {
269
270	j = max(0, min(n-1, int((t - data_[0].first) * dx)));
271
272	} else {
273
274	j = n-1;
275
276	for (int i = 0; i < n; i++) {
277	if ( t < data_[i].first ) {
278	j = i-1;
279	break;
280	}
281	}
282	}
283
284	// Evaluate the cubic polynomial.
285
286	dt = t - data_[j].first;
287
288	RealType yval = data_[j].second + dt(b[j] + dt(c[j] + dt*d[j]));
289	RealType dydx = b[j] + dt(2.0 c[j] + 3.0 * dt * d[j]);
290
291	return make_pair(yval, dydx);
292	}