src/utils/Accumulator.hpp

/*
 * Copyright (c) 2012 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, 234107 (2008).          
 * [4]  Kuang & Gezelter,  J. Chem. Phys. 133, 164101 (2010).
 * [5]  Vardeman, Stocker & Gezelter, J. Chem. Theory Comput. 7, 834 (2011).
 */

#ifndef UTILS_ACCUMULATOR_HPP
#define UTILS_ACCUMULATOR_HPP

#include <cmath>
#include <cassert>
#include "math/Vector3.hpp"

namespace OpenMD {


  class BaseAccumulator {
  public:
    virtual void clear() = 0;
    /**
     * get the number of accumulated values
     */
    virtual size_t count()  {
      return Count_;
    }
  protected:
    size_t Count_;

  };   


  /** 
   * Basic Accumulator class for numbers. 
   */  
  class Accumulator : public BaseAccumulator {    

    typedef RealType ElementType;
    typedef RealType ResultType;

  public:
    
    Accumulator() : BaseAccumulator() {
      this->clear();
    }

    /**
     * Accumulate another value
     */
    virtual void add(ElementType const& val) {
      Count_++;
      Avg_  += (val       - Avg_ ) / Count_;
      Avg2_ += (val * val - Avg2_) / Count_;
      Val_   = val;
      if (Count_ <= 1) {
        Max_ = val;
        Min_ = val;
      } else {
        Max_ = val > Max_ ? val : Max_;
        Min_ = val < Min_ ? val : Min_;
      }
    }
    
    /**
     * reset the Accumulator to the empty state
     */
    void clear() {
      Count_ = 0;
      Avg_   = 0;
      Avg2_  = 0;
      Val_   = 0;
    }
    

    /**
     * return the most recently added value
     */
    void getLastValue(ElementType &ret)  {
      ret = Val_;
      return;
    }    

    /**
     * compute the Mean
     */
    void getAverage(ResultType &ret)  {
      assert(Count_ != 0);
      ret = Avg_;
      return;
    }

    /**
     * compute the Variance
     */
    void getVariance(ResultType &ret)  {
      assert(Count_ != 0);
      ret = (Avg2_ - Avg_  * Avg_);
      return;
    }
    
    /**
     * compute error of average value
     */
    void getStdDev(ResultType &ret)  {
      assert(Count_ != 0);
      RealType var;
      this->getVariance(var);
      ret = sqrt(var);
      return;
    }

    /**
     * return the largest value
     */
    void getMax(ElementType &ret)  {
      assert(Count_ != 0);
      ret = Max_;
      return;
    }

    /**
     * return the smallest value
     */
    void getMin(ElementType &ret)  {
      assert(Count_ != 0);
      ret = Max_;
      return;
    }

    /**
     * return the 95% confidence interval:
     *
     * That is returns c, such that we have 95% confidence that the
     * true mean is within 2c of the Average (x):
     *
     *   x - c <= true mean <= x + c
     *
     */
    void get95percentConfidenceInterval(ResultType &ret) {
      assert(Count_ != 0);
      RealType sd;
      this->getStdDev(sd);
      ret = 1.960 * sd / sqrt(Count_);
      return;
    }

  private:
    ElementType Val_;
    ResultType Avg_;
    ResultType Avg2_;
    ElementType Min_;
    ElementType Max_;
  };

  class VectorAccumulator : public BaseAccumulator {
    
    typedef Vector3d ElementType;
    typedef Vector3d ResultType;
    
  public:
    VectorAccumulator() : BaseAccumulator() {
      this->clear();
    }

    /**
     * Accumulate another value
     */
    void add(ElementType const& val) {
      Count_++;
      RealType len(0.0);
      for (unsigned int i =0; i < 3; i++) {
        Avg_[i]  += (val[i]       - Avg_[i] ) / Count_;
        Avg2_[i] += (val[i] * val[i] - Avg2_[i]) / Count_;
        Val_[i]   = val[i];
        len += val[i]*val[i];
      }
      len = sqrt(len);
      AvgLen_  += (len       - AvgLen_ ) / Count_;
      AvgLen2_ += (len * len - AvgLen2_) / Count_;

      if (Count_ <= 1) {
        Max_ = len;
        Min_ = len;
      } else {
        Max_ = len > Max_ ? len : Max_;
        Min_ = len < Min_ ? len : Min_;
      }
    }

    /**
     * reset the Accumulator to the empty state
     */
    void clear() {
      Count_ = 0;
      Avg_ = V3Zero;
      Avg2_ = V3Zero;
      Val_ = V3Zero;
      AvgLen_   = 0;
      AvgLen2_  = 0;
    }
    
    /**
     * return the most recently added value
     */
    void getLastValue(ElementType &ret) {
      ret = Val_;
      return;
    }
    
    /**
     * compute the Mean
     */
    void getAverage(ResultType &ret) {
      assert(Count_ != 0);
      ret = Avg_;
      return;
    }
    
    /**
     * compute the Variance
     */
    void getVariance(ResultType &ret) {
      assert(Count_ != 0);
      for (unsigned int i =0; i < 3; i++) {
        ret[i] = (Avg2_[i] - Avg_[i]  * Avg_[i]);
      }
      return;
    }
    
    /**
     * compute error of average value
     */
    void getStdDev(ResultType &ret) {
      assert(Count_ != 0);
      ResultType var;
      this->getVariance(var);
      ret[0] = sqrt(var[0]);
      ret[1] = sqrt(var[1]);
      ret[2] = sqrt(var[2]);
      return;
    }

    /**
     * return the 95% confidence interval:
     *
     * That is returns c, such that we have 95% confidence that the
     * true mean is within 2c of the Average (x):
     *
     *   x - c <= true mean <= x + c
     *
     */
    void get95percentConfidenceInterval(ResultType &ret) {
      assert(Count_ != 0);
      ResultType sd;
      this->getStdDev(sd);
      ret[0] = 1.960 * sd[0] / sqrt(Count_);
      ret[1] = 1.960 * sd[1] / sqrt(Count_);
      ret[2] = 1.960 * sd[2] / sqrt(Count_);
      return;
    }

    /**
     * return the largest length
     */
    void getMaxLength(RealType &ret) {
      assert(Count_ != 0);
      ret = Max_;
      return;
    }

    /**
     * return the smallest length
     */
    void getMinLength(RealType &ret) {
      assert(Count_ != 0);
      ret = Min_;
      return;
    }

    /**
     * return the largest length
     */
    void getAverageLength(RealType &ret) {
      assert(Count_ != 0);
      ret = AvgLen_;
      return;
    }

    /**
     * compute the Variance of the length
     */
    void getLengthVariance(RealType &ret) {
      assert(Count_ != 0);      
      ret= (AvgLen2_ - AvgLen_ * AvgLen_);
      return;
    }
    
    /**
     * compute error of average value
     */
    void getLengthStdDev(RealType &ret) {
      assert(Count_ != 0);
      RealType var;
      this->getLengthVariance(var);
      ret = sqrt(var);
      return;
    }

    /**
     * return the 95% confidence interval:
     *
     * That is returns c, such that we have 95% confidence that the
     * true mean is within 2c of the Average (x):
     *
     *   x - c <= true mean <= x + c
     *
     */
    void getLength95percentConfidenceInterval(ResultType &ret) {
      assert(Count_ != 0);
      RealType sd;
      this->getLengthStdDev(sd);
      ret = 1.960 * sd / sqrt(Count_);
      return;
    }


  private:
    ResultType Val_;
    ResultType Avg_;
    ResultType Avg2_;
    RealType AvgLen_;
    RealType AvgLen2_;
    RealType Min_;
    RealType Max_;

  };

  class MatrixAccumulator : public BaseAccumulator {
    
    typedef Mat3x3d ElementType;
    typedef Mat3x3d ResultType;
    
  public:
    MatrixAccumulator() : BaseAccumulator() {
      this->clear();
    }

    /**
     * Accumulate another value
     */
    void add(ElementType const& val) {
      Count_++;
      for (unsigned int i = 0; i < 3; i++) {
        for (unsigned int j = 0; j < 3; j++) {          
          Avg_(i,j)  += (val(i,j)       - Avg_(i,j) ) / Count_;
          Avg2_(i,j) += (val(i,j) * val(i,j) - Avg2_(i,j)) / Count_;
          Val_(i,j)   = val(i,j);
        }
      }
    }

    /**
     * reset the Accumulator to the empty state
     */
    void clear() {
      Count_ = 0;
      Avg_ *= 0.0;
      Avg2_ *= 0.0;
      Val_ *= 0.0;
    }
    
    /**
     * return the most recently added value
     */
    void getLastValue(ElementType &ret) {
      ret = Val_;
      return;
    }
    
    /**
     * compute the Mean
     */
    void getAverage(ResultType &ret) {
      assert(Count_ != 0);
      ret = Avg_;
      return;
    }

    /**
     * compute the Variance
     */
    void getVariance(ResultType &ret) {
      assert(Count_ != 0);
      for (unsigned int i = 0; i < 3; i++) {
        for (unsigned int j = 0; j < 3; j++) {          
          ret(i,j) = (Avg2_(i,j) - Avg_(i,j)  * Avg_(i,j));
        }
      }
      return;
    }
    
    /**
     * compute error of average value
     */
    void getStdDev(ResultType &ret) {
      assert(Count_ != 0);
      Mat3x3d var;
      this->getVariance(var);
      for (unsigned int i = 0; i < 3; i++) {
        for (unsigned int j = 0; j < 3; j++) {
          ret(i,j) = sqrt(var(i,j));  
        }
      }
      return;
    }
      
    /**
     * return the 95% confidence interval:
     *
     * That is returns c, such that we have 95% confidence that the
     * true mean is within 2c of the Average (x):
     *
     *   x - c <= true mean <= x + c
     *
     */
    void get95percentConfidenceInterval(ResultType &ret) {
      assert(Count_ != 0);
      Mat3x3d sd;
      this->getStdDev(sd);
      for (unsigned int i = 0; i < 3; i++) {
        for (unsigned int j = 0; j < 3; j++) {
          ret(i,j) = 1.960 * sd(i,j) / sqrt(Count_);
        }
      }
      return;
    }

  private:
    ElementType Val_;
    ResultType Avg_;
    ResultType Avg2_;
  };


} 

#endif
Revision:	1979
Committed:	Sat Apr 5 20:56:01 2014 UTC (11 years ago) by gezelter
File size:	11216 byte(s)
Log Message:	* Changed the stdDev printouts in RNEMD stats to the 95% confidence intervals * Added the ability to specify non-bonded constraints in a molecule * Added the ability to do selection offsets in the pAngle staticProps module
#	Content
1	/*
2	* Copyright (c) 2012 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, 234107 (2008).
39	* [4] Kuang & Gezelter, J. Chem. Phys. 133, 164101 (2010).
40	* [5] Vardeman, Stocker & Gezelter, J. Chem. Theory Comput. 7, 834 (2011).
41	*/
42
43	#ifndef UTILS_ACCUMULATOR_HPP
44	#define UTILS_ACCUMULATOR_HPP
45
46	#include <cmath>
47	#include <cassert>
48	#include "math/Vector3.hpp"
49
50	namespace OpenMD {
51
52
53	class BaseAccumulator {
54	public:
55	virtual void clear() = 0;
56	/**
57	* get the number of accumulated values
58	*/
59	virtual size_t count() {
60	return Count_;
61	}
62	protected:
63	size_t Count_;
64
65	};
66
67
68
69	/**
70	* Basic Accumulator class for numbers.
71	*/
72	class Accumulator : public BaseAccumulator {
73
74	typedef RealType ElementType;
75	typedef RealType ResultType;
76
77	public:
78
79	Accumulator() : BaseAccumulator() {
80	this->clear();
81	}
82
83	/**
84	* Accumulate another value
85	*/
86	virtual void add(ElementType const& val) {
87	Count_++;
88	Avg_ += (val - Avg_ ) / Count_;
89	Avg2_ += (val * val - Avg2_) / Count_;
90	Val_ = val;
91	if (Count_ <= 1) {
92	Max_ = val;
93	Min_ = val;
94	} else {
95	Max_ = val > Max_ ? val : Max_;
96	Min_ = val < Min_ ? val : Min_;
97	}
98	}
99
100	/**
101	* reset the Accumulator to the empty state
102	*/
103	void clear() {
104	Count_ = 0;
105	Avg_ = 0;
106	Avg2_ = 0;
107	Val_ = 0;
108	}
109
110
111	/**
112	* return the most recently added value
113	*/
114	void getLastValue(ElementType &ret) {
115	ret = Val_;
116	return;
117	}
118
119	/**
120	* compute the Mean
121	*/
122	void getAverage(ResultType &ret) {
123	assert(Count_ != 0);
124	ret = Avg_;
125	return;
126	}
127
128	/**
129	* compute the Variance
130	*/
131	void getVariance(ResultType &ret) {
132	assert(Count_ != 0);
133	ret = (Avg2_ - Avg_ * Avg_);
134	return;
135	}
136
137	/**
138	* compute error of average value
139	*/
140	void getStdDev(ResultType &ret) {
141	assert(Count_ != 0);
142	RealType var;
143	this->getVariance(var);
144	ret = sqrt(var);
145	return;
146	}
147
148	/**
149	* return the largest value
150	*/
151	void getMax(ElementType &ret) {
152	assert(Count_ != 0);
153	ret = Max_;
154	return;
155	}
156
157	/**
158	* return the smallest value
159	*/
160	void getMin(ElementType &ret) {
161	assert(Count_ != 0);
162	ret = Max_;
163	return;
164	}
165
166	/**
167	* return the 95% confidence interval:
168	*
169	* That is returns c, such that we have 95% confidence that the
170	* true mean is within 2c of the Average (x):
171	*
172	* x - c <= true mean <= x + c
173	*
174	*/
175	void get95percentConfidenceInterval(ResultType &ret) {
176	assert(Count_ != 0);
177	RealType sd;
178	this->getStdDev(sd);
179	ret = 1.960 * sd / sqrt(Count_);
180	return;
181	}
182
183	private:
184	ElementType Val_;
185	ResultType Avg_;
186	ResultType Avg2_;
187	ElementType Min_;
188	ElementType Max_;
189	};
190
191	class VectorAccumulator : public BaseAccumulator {
192
193	typedef Vector3d ElementType;
194	typedef Vector3d ResultType;
195
196	public:
197	VectorAccumulator() : BaseAccumulator() {
198	this->clear();
199	}
200
201	/**
202	* Accumulate another value
203	*/
204	void add(ElementType const& val) {
205	Count_++;
206	RealType len(0.0);
207	for (unsigned int i =0; i < 3; i++) {
208	Avg_[i] += (val[i] - Avg_[i] ) / Count_;
209	Avg2_[i] += (val[i] * val[i] - Avg2_[i]) / Count_;
210	Val_[i] = val[i];
211	len += val[i]*val[i];
212	}
213	len = sqrt(len);
214	AvgLen_ += (len - AvgLen_ ) / Count_;
215	AvgLen2_ += (len * len - AvgLen2_) / Count_;
216
217	if (Count_ <= 1) {
218	Max_ = len;
219	Min_ = len;
220	} else {
221	Max_ = len > Max_ ? len : Max_;
222	Min_ = len < Min_ ? len : Min_;
223	}
224	}
225
226	/**
227	* reset the Accumulator to the empty state
228	*/
229	void clear() {
230	Count_ = 0;
231	Avg_ = V3Zero;
232	Avg2_ = V3Zero;
233	Val_ = V3Zero;
234	AvgLen_ = 0;
235	AvgLen2_ = 0;
236	}
237
238	/**
239	* return the most recently added value
240	*/
241	void getLastValue(ElementType &ret) {
242	ret = Val_;
243	return;
244	}
245
246	/**
247	* compute the Mean
248	*/
249	void getAverage(ResultType &ret) {
250	assert(Count_ != 0);
251	ret = Avg_;
252	return;
253	}
254
255	/**
256	* compute the Variance
257	*/
258	void getVariance(ResultType &ret) {
259	assert(Count_ != 0);
260	for (unsigned int i =0; i < 3; i++) {
261	ret[i] = (Avg2_[i] - Avg_[i] * Avg_[i]);
262	}
263	return;
264	}
265
266	/**
267	* compute error of average value
268	*/
269	void getStdDev(ResultType &ret) {
270	assert(Count_ != 0);
271	ResultType var;
272	this->getVariance(var);
273	ret[0] = sqrt(var[0]);
274	ret[1] = sqrt(var[1]);
275	ret[2] = sqrt(var[2]);
276	return;
277	}
278
279	/**
280	* return the 95% confidence interval:
281	*
282	* That is returns c, such that we have 95% confidence that the
283	* true mean is within 2c of the Average (x):
284	*
285	* x - c <= true mean <= x + c
286	*
287	*/
288	void get95percentConfidenceInterval(ResultType &ret) {
289	assert(Count_ != 0);
290	ResultType sd;
291	this->getStdDev(sd);
292	ret[0] = 1.960 * sd[0] / sqrt(Count_);
293	ret[1] = 1.960 * sd[1] / sqrt(Count_);
294	ret[2] = 1.960 * sd[2] / sqrt(Count_);
295	return;
296	}
297
298	/**
299	* return the largest length
300	*/
301	void getMaxLength(RealType &ret) {
302	assert(Count_ != 0);
303	ret = Max_;
304	return;
305	}
306
307	/**
308	* return the smallest length
309	*/
310	void getMinLength(RealType &ret) {
311	assert(Count_ != 0);
312	ret = Min_;
313	return;
314	}
315
316	/**
317	* return the largest length
318	*/
319	void getAverageLength(RealType &ret) {
320	assert(Count_ != 0);
321	ret = AvgLen_;
322	return;
323	}
324
325	/**
326	* compute the Variance of the length
327	*/
328	void getLengthVariance(RealType &ret) {
329	assert(Count_ != 0);
330	ret= (AvgLen2_ - AvgLen_ * AvgLen_);
331	return;
332	}
333
334	/**
335	* compute error of average value
336	*/
337	void getLengthStdDev(RealType &ret) {
338	assert(Count_ != 0);
339	RealType var;
340	this->getLengthVariance(var);
341	ret = sqrt(var);
342	return;
343	}
344
345	/**
346	* return the 95% confidence interval:
347	*
348	* That is returns c, such that we have 95% confidence that the
349	* true mean is within 2c of the Average (x):
350	*
351	* x - c <= true mean <= x + c
352	*
353	*/
354	void getLength95percentConfidenceInterval(ResultType &ret) {
355	assert(Count_ != 0);
356	RealType sd;
357	this->getLengthStdDev(sd);
358	ret = 1.960 * sd / sqrt(Count_);
359	return;
360	}
361
362
363	private:
364	ResultType Val_;
365	ResultType Avg_;
366	ResultType Avg2_;
367	RealType AvgLen_;
368	RealType AvgLen2_;
369	RealType Min_;
370	RealType Max_;
371
372	};
373
374	class MatrixAccumulator : public BaseAccumulator {
375
376	typedef Mat3x3d ElementType;
377	typedef Mat3x3d ResultType;
378
379	public:
380	MatrixAccumulator() : BaseAccumulator() {
381	this->clear();
382	}
383
384	/**
385	* Accumulate another value
386	*/
387	void add(ElementType const& val) {
388	Count_++;
389	for (unsigned int i = 0; i < 3; i++) {
390	for (unsigned int j = 0; j < 3; j++) {
391	Avg_(i,j) += (val(i,j) - Avg_(i,j) ) / Count_;
392	Avg2_(i,j) += (val(i,j) * val(i,j) - Avg2_(i,j)) / Count_;
393	Val_(i,j) = val(i,j);
394	}
395	}
396	}
397
398	/**
399	* reset the Accumulator to the empty state
400	*/
401	void clear() {
402	Count_ = 0;
403	Avg_ *= 0.0;
404	Avg2_ *= 0.0;
405	Val_ *= 0.0;
406	}
407
408	/**
409	* return the most recently added value
410	*/
411	void getLastValue(ElementType &ret) {
412	ret = Val_;
413	return;
414	}
415
416	/**
417	* compute the Mean
418	*/
419	void getAverage(ResultType &ret) {
420	assert(Count_ != 0);
421	ret = Avg_;
422	return;
423	}
424
425	/**
426	* compute the Variance
427	*/
428	void getVariance(ResultType &ret) {
429	assert(Count_ != 0);
430	for (unsigned int i = 0; i < 3; i++) {
431	for (unsigned int j = 0; j < 3; j++) {
432	ret(i,j) = (Avg2_(i,j) - Avg_(i,j) * Avg_(i,j));
433	}
434	}
435	return;
436	}
437
438	/**
439	* compute error of average value
440	*/
441	void getStdDev(ResultType &ret) {
442	assert(Count_ != 0);
443	Mat3x3d var;
444	this->getVariance(var);
445	for (unsigned int i = 0; i < 3; i++) {
446	for (unsigned int j = 0; j < 3; j++) {
447	ret(i,j) = sqrt(var(i,j));
448	}
449	}
450	return;
451	}
452
453	/**
454	* return the 95% confidence interval:
455	*
456	* That is returns c, such that we have 95% confidence that the
457	* true mean is within 2c of the Average (x):
458	*
459	* x - c <= true mean <= x + c
460	*
461	*/
462	void get95percentConfidenceInterval(ResultType &ret) {
463	assert(Count_ != 0);
464	Mat3x3d sd;
465	this->getStdDev(sd);
466	for (unsigned int i = 0; i < 3; i++) {
467	for (unsigned int j = 0; j < 3; j++) {
468	ret(i,j) = 1.960 * sd(i,j) / sqrt(Count_);
469	}
470	}
471	return;
472	}
473
474	private:
475	ElementType Val_;
476	ResultType Avg_;
477	ResultType Avg2_;
478	};
479
480
481	}
482
483	#endif