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 <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:	1536
Committed:	Wed Jan 5 14:49:05 2011 UTC (14 years, 3 months ago) by gezelter
File size:	8747 byte(s)
Log Message:	compiles, builds and runs, but is very slow
#	User	Rev	Content
1	gezelter	1475	/*
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 <algorithm>
46
47			using namespace OpenMD;
48			using namespace std;
49
50	gezelter	1536	CubicSpline::CubicSpline() : generated(false), isUniform(true) {
51			data_.clear();
52			}
53	gezelter	1475
54	gezelter	1536	void CubicSpline::addPoint(const RealType xp, const RealType yp) {
55			data_.push_back(make_pair(xp, yp));
56	gezelter	1475	}
57
58			void CubicSpline::addPoints(const vector<RealType>& xps,
59			const vector<RealType>& yps) {
60
61			if (xps.size() != yps.size()) {
62			printf( painCave.errMsg,
63			"CubicSpline::addPoints was passed vectors of different length!\n");
64			painCave.severity = OPENMD_ERROR;
65			painCave.isFatal = 1;
66			simError();
67			}
68
69			for (int i = 0; i < xps.size(); i++)
70	gezelter	1536	data_.push_back(make_pair(xps[i], yps[i]));
71	gezelter	1475	}
72
73			void CubicSpline::generate() {
74			// Calculate coefficients defining a smooth cubic interpolatory spline.
75			//
76			// class values constructed:
77	gezelter	1536	// n = number of data_ points.
78	gezelter	1475	// x = vector of independent variable values
79			// y = vector of dependent variable values
80			// b = vector of S'(x[i]) values.
81			// c = vector of S"(x[i])/2 values.
82			// d = vector of S'''(x[i]+)/6 values (i < n).
83			// Local variables:
84	gezelter	1536
85	gezelter	1475	RealType fp1, fpn, h, p;
86
87			// make sure the sizes match
88
89	gezelter	1536	n = data_.size();
90	gezelter	1475	b.resize(n);
91			c.resize(n);
92			d.resize(n);
93
94			// make sure we are monotonically increasing in x:
95
96			bool sorted = true;
97
98			for (int i = 1; i < n; i++) {
99	gezelter	1536	if ( (data_[i].first - data_[i-1].first ) <= 0.0 ) sorted = false;
100	gezelter	1475	}
101
102			// sort if necessary
103
104	gezelter	1536	if (!sorted) sort(data_.begin(), data_.end());
105	gezelter	1475
106			// Calculate coefficients for the tridiagonal system: store
107			// sub-diagonal in B, diagonal in D, difference quotient in C.
108
109	gezelter	1536	b[0] = data_[1].first - data_[0].first;
110			c[0] = (data_[1].second - data_[0].second) / b[0];
111	gezelter	1475
112			if (n == 2) {
113
114			// Assume the derivatives at both endpoints are zero. Another
115			// assumption could be made to have a linear interpolant between
116			// the two points. In that case, the b coefficients below would be
117	gezelter	1536	// (data_[1].second - data_[0].second) / (data_[1].first - data_[0].first)
118	gezelter	1475	// and the c and d coefficients would both be zero.
119			b[0] = 0.0;
120	gezelter	1536	c[0] = -3.0 * pow((data_[1].second - data_[0].second) /
121			(data_[1].first-data_[0].first), 2);
122			d[0] = -2.0 * pow((data_[1].second - data_[0].second) /
123			(data_[1].first-data_[0].first), 3);
124	gezelter	1475	b[1] = b[0];
125			c[1] = 0.0;
126			d[1] = 0.0;
127	gezelter	1536	dx = 1.0 / (data_[1].first - data_[0].first);
128	gezelter	1475	isUniform = true;
129			generated = true;
130			return;
131			}
132
133			d[0] = 2.0 * b[0];
134
135			for (int i = 1; i < n-1; i++) {
136	gezelter	1536	b[i] = data_[i+1].first - data_[i].first;
137	gezelter	1475	if ( fabs( b[i] - b[0] ) / b[0] > 1.0e-5) isUniform = false;
138	gezelter	1536	c[i] = (data_[i+1].second - data_[i].second) / b[i];
139	gezelter	1475	d[i] = 2.0 * (b[i] + b[i-1]);
140			}
141
142			d[n-1] = 2.0 * b[n-2];
143
144			// Calculate estimates for the end slopes using polynomials
145	gezelter	1536	// that interpolate the data_ nearest the end.
146	gezelter	1475
147			fp1 = c[0] - b[0]*(c[1] - c[0])/(b[0] + b[1]);
148			if (n > 3) fp1 = fp1 + b[0]((b[0] + b[1]) (c[2] - c[1]) /
149			(b[1] + b[2]) -
150	gezelter	1536	c[1] + c[0]) / (data_[3].first - data_[0].first);
151	gezelter	1475
152			fpn = c[n-2] + b[n-2]*(c[n-2] - c[n-3])/(b[n-3] + b[n-2]);
153
154			if (n > 3) fpn = fpn + b[n-2] *
155			(c[n-2] - c[n-3] - (b[n-3] + b[n-2]) *
156	gezelter	1536	(c[n-3] - c[n-4])/(b[n-3] + b[n-4]))/(data_[n-1].first - data_[n-4].first);
157	gezelter	1475
158
159			// Calculate the right hand side and store it in C.
160
161			c[n-1] = 3.0 * (fpn - c[n-2]);
162			for (int i = n-2; i > 0; i--)
163			c[i] = 3.0 * (c[i] - c[i-1]);
164			c[0] = 3.0 * (c[0] - fp1);
165
166			// Solve the tridiagonal system.
167
168			for (int k = 1; k < n; k++) {
169			p = b[k-1] / d[k-1];
170			d[k] = d[k] - p*b[k-1];
171			c[k] = c[k] - p*c[k-1];
172			}
173
174			c[n-1] = c[n-1] / d[n-1];
175
176			for (int k = n-2; k >= 0; k--)
177			c[k] = (c[k] - b[k] * c[k+1]) / d[k];
178
179			// Calculate the coefficients defining the spline.
180
181			for (int i = 0; i < n-1; i++) {
182	gezelter	1536	h = data_[i+1].first - data_[i].first;
183	gezelter	1475	d[i] = (c[i+1] - c[i]) / (3.0 * h);
184	gezelter	1536	b[i] = (data_[i+1].second - data_[i].second)/h - h * (c[i] + h * d[i]);
185	gezelter	1475	}
186
187			b[n-1] = b[n-2] + h * (2.0 * c[n-2] + h * 3.0 * d[n-2]);
188
189	gezelter	1536	if (isUniform) dx = 1.0 / (data_[1].first - data_[0].first);
190	gezelter	1475
191			generated = true;
192			return;
193			}
194
195			RealType CubicSpline::getValueAt(RealType t) {
196			// Evaluate the spline at t using coefficients
197			//
198			// Input parameters
199			// t = point where spline is to be evaluated.
200			// Output:
201			// value of spline at t.
202
203			if (!generated) generate();
204			RealType dt;
205
206	gezelter	1536	if ( t < data_[0].first \|\| t > data_[n-1].first ) {
207	gezelter	1475	sprintf( painCave.errMsg,
208			"CubicSpline::getValueAt was passed a value outside the range of the spline!\n");
209			painCave.severity = OPENMD_ERROR;
210			painCave.isFatal = 1;
211			simError();
212			}
213
214			// Find the interval ( x[j], x[j+1] ) that contains or is nearest
215			// to t.
216
217			int j;
218
219			if (isUniform) {
220
221	gezelter	1536	j = max(0, min(n-1, int((t - data_[0].first) * dx)));
222	gezelter	1475
223			} else {
224
225			j = n-1;
226
227			for (int i = 0; i < n; i++) {
228	gezelter	1536	if ( t < data_[i].first ) {
229	gezelter	1475	j = i-1;
230			break;
231			}
232			}
233			}
234
235			// Evaluate the cubic polynomial.
236
237	gezelter	1536	dt = t - data_[j].first;
238			return data_[j].second + dt(b[j] + dt(c[j] + dt*d[j]));
239	gezelter	1475
240			}
241
242
243			pair<RealType, RealType> CubicSpline::getValueAndDerivativeAt(RealType t) {
244			// Evaluate the spline and first derivative at t using coefficients
245			//
246			// Input parameters
247			// t = point where spline is to be evaluated.
248			// Output:
249			// pair containing value of spline at t and first derivative at t
250
251			if (!generated) generate();
252			RealType dt;
253
254	gezelter	1536	if ( t < data_.front().first \|\| t > data_.back().first ) {
255	gezelter	1475	sprintf( painCave.errMsg,
256			"CubicSpline::getValueAndDerivativeAt was passed a value outside the range of the spline!\n");
257			painCave.severity = OPENMD_ERROR;
258			painCave.isFatal = 1;
259			simError();
260			}
261
262			// Find the interval ( x[j], x[j+1] ) that contains or is nearest
263			// to t.
264
265			int j;
266
267			if (isUniform) {
268
269	gezelter	1536	j = max(0, min(n-1, int((t - data_[0].first) * dx)));
270	gezelter	1475
271			} else {
272
273			j = n-1;
274
275			for (int i = 0; i < n; i++) {
276	gezelter	1536	if ( t < data_[i].first ) {
277	gezelter	1475	j = i-1;
278			break;
279			}
280			}
281			}
282
283			// Evaluate the cubic polynomial.
284
285	gezelter	1536	dt = t - data_[j].first;
286	gezelter	1475
287	gezelter	1536	RealType yval = data_[j].second + dt(b[j] + dt(c[j] + dt*d[j]));
288	gezelter	1475	RealType dydx = b[j] + dt(2.0 c[j] + 3.0 * dt * d[j]);
289
290			return make_pair(yval, dydx);
291			}