OpenVDB: openvdb/math/Stats.h Source File

OpenVDB 10.0.1

Stats.h
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1// Copyright Contributors to the OpenVDB Project
2// SPDX-License-Identifier: MPL-2.0
3//
4/// @file Stats.h
5///
6/// @author Ken Museth
7///
8/// @brief Classes to compute statistics and histograms
9
10#ifndef OPENVDB_MATH_STATS_HAS_BEEN_INCLUDED
11#define OPENVDB_MATH_STATS_HAS_BEEN_INCLUDED
12
13#include <iosfwd> // for ostringstream
14#include <openvdb/version.h>
15#include <openvdb/Exceptions.h>
16#include <iostream>
17#include <iomanip>
18#include <sstream>
19#include <vector>
20#include <functional>// for std::less
21#include "Math.h"
22
23namespace openvdb {
24 OPENVDB_USE_VERSION_NAMESPACE
25namespace OPENVDB_VERSION_NAME {
26namespace math {
27
28/// @brief Templated class to compute the minimum and maximum values.
29template <typename ValueType, typename Less = std::less<ValueType> >
30 class MinMax
31{
32 using Limits = std::numeric_limits<ValueType>;
33public:
34
35 /// @brief Empty constructor
36 ///
37 /// @warning Only use this constructor with POD types
38 MinMax() : mMin(Limits::max()), mMax(Limits::lowest())
39 {
40 static_assert(std::numeric_limits<ValueType>::is_specialized,
41 "openvdb::math::MinMax default constructor requires a std::numeric_limits specialization");
42 }
43
44 /// @brief Constructor
45 MinMax(const ValueType &min, const ValueType &max) : mMin(min), mMax(max)
46 {
47 }
48
49 /// @brief Default copy constructor
50 MinMax(const MinMax &other) = default;
51
52 /// Add a single sample.
53 inline void add(const ValueType &val, const Less &less = Less())
54 {
55 if (less(val, mMin)) mMin = val;
56 if (less(mMax, val)) mMax = val;
57 }
58
59 /// Return the minimum value.
60 inline const ValueType& min() const { return mMin; }
61
62 /// Return the maximum value.
63 inline const ValueType& max() const { return mMax; }
64
65 /// Add the samples from the other Stats instance.
66 inline void add(const MinMax& other, const Less &less = Less())
67 {
68 if (less(other.mMin, mMin)) mMin = other.mMin;
69 if (less(mMax, other.mMax)) mMax = other.mMax;
70 }
71
72 /// @brief Print MinMax to the specified output stream.
73 void print(const std::string &name= "", std::ostream &strm=std::cout, int precision=3) const
74 {
75 // Write to a temporary string stream so as not to affect the state
76 // (precision, field width, etc.) of the output stream.
77 std::ostringstream os;
78 os << std::setprecision(precision) << std::setiosflags(std::ios::fixed);
79 os << "MinMax ";
80 if (!name.empty()) os << "for \"" << name << "\" ";
81 os << " Min=" << mMin << ", Max=" << mMax << std::endl;
82 strm << os.str();
83 }
84
85protected:
86
87 ValueType mMin, mMax;
88};//end MinMax
89
90/// @brief This class computes the minimum and maximum values of a population
91/// of floating-point values.
92 class Extrema
93{
94public:
95
96 /// @brief Constructor
97 /// @warning The min/max values are initiated to extreme values
98 Extrema()
99 : mSize(0)
100 , mMin(std::numeric_limits<double>::max())
101 , mMax(-mMin)
102 {
103 }
104
105 /// Add a single sample.
106 void add(double val)
107 {
108 ++mSize;
109 mMin = std::min<double>(val, mMin);
110 mMax = std::max<double>(val, mMax);
111 }
112
113 /// Add @a n samples with constant value @a val.
114 void add(double val, uint64_t n)
115 {
116 mSize += n;
117 mMin = std::min<double>(val, mMin);
118 mMax = std::max<double>(val, mMax);
119 }
120
121 /// Return the size of the population, i.e., the total number of samples.
122 inline uint64_t size() const { return mSize; }
123
124 /// Return the minimum value.
125 inline double min() const { return mMin; }
126
127 /// Return the maximum value.
128 inline double max() const { return mMax; }
129
130 /// Return the range defined as the maximum value minus the minimum value.
131 inline double range() const { return mMax - mMin; }
132
133 /// Add the samples from the other Stats instance.
134 void add(const Extrema& other)
135 {
136 if (other.mSize > 0) this->join(other);
137 }
138
139 /// @brief Print extrema to the specified output stream.
140 void print(const std::string &name= "", std::ostream &strm=std::cout, int precision=3) const
141 {
142 // Write to a temporary string stream so as not to affect the state
143 // (precision, field width, etc.) of the output stream.
144 std::ostringstream os;
145 os << std::setprecision(precision) << std::setiosflags(std::ios::fixed);
146 os << "Extrema ";
147 if (!name.empty()) os << "for \"" << name << "\" ";
148 if (mSize>0) {
149 os << "with " << mSize << " samples:\n"
150 << " Min=" << mMin
151 << ", Max=" << mMax
152 << ", Range="<< this->range() << std::endl;
153 } else {
154 os << ": no samples were added." << std::endl;
155 }
156 strm << os.str();
157 }
158
159protected:
160
161 inline void join(const Extrema& other)
162 {
163 assert(other.mSize > 0);
164 mSize += other.mSize;
165 mMin = std::min<double>(mMin, other.mMin);
166 mMax = std::max<double>(mMax, other.mMax);
167 }
168
169 uint64_t mSize;
170 double mMin, mMax;
171};//end Extrema
172
173
174/// @brief This class computes statistics (minimum value, maximum
175/// value, mean, variance and standard deviation) of a population
176/// of floating-point values.
177///
178/// @details variance = Mean[ (X-Mean[X])^2 ] = Mean[X^2] - Mean[X]^2,
179/// standard deviation = sqrt(variance)
180///
181/// @note This class employs incremental computation and double precision.
182 class Stats : public Extrema
183{
184public:
185 Stats()
186 : Extrema()
187 , mAvg(0.0)
188 , mAux(0.0)
189 {
190 }
191
192 /// Add a single sample.
193 void add(double val)
194 {
195 Extrema::add(val);
196 const double delta = val - mAvg;
197 mAvg += delta/double(mSize);
198 mAux += delta*(val - mAvg);
199 }
200
201 /// Add @a n samples with constant value @a val.
202 void add(double val, uint64_t n)
203 {
204 const double denom = 1.0/double(mSize + n);
205 const double delta = val - mAvg;
206 mAvg += denom * delta * double(n);
207 mAux += denom * delta * delta * double(mSize) * double(n);
208 Extrema::add(val, n);
209 }
210
211 /// Add the samples from the other Stats instance.
212 void add(const Stats& other)
213 {
214 if (other.mSize > 0) {
215 const double denom = 1.0/double(mSize + other.mSize);
216 const double delta = other.mAvg - mAvg;
217 mAvg += denom * delta * double(other.mSize);
218 mAux += other.mAux + denom * delta * delta * double(mSize) * double(other.mSize);
219 Extrema::join(other);
220 }
221 }
222
223 //@{
224 /// Return the arithmetic mean, i.e. average, value.
225 inline double avg() const { return mAvg; }
226 inline double mean() const { return mAvg; }
227 //@}
228
229 //@{
230 /// @brief Return the population variance.
231 /// @note The unbiased sample variance = population variance *
232 //num/(num-1)
233 inline double var() const { return mSize<2 ? 0.0 : mAux/double(mSize); }
234 inline double variance() const { return this->var(); }
235 //@}
236
237 //@{
238 /// @brief Return the standard deviation (=Sqrt(variance)) as
239 /// defined from the (biased) population variance.
240 inline double std() const { return sqrt(this->var()); }
241 inline double stdDev() const { return this->std(); }
242 //@}
243
244 /// @brief Print statistics to the specified output stream.
245 void print(const std::string &name= "", std::ostream &strm=std::cout, int precision=3) const
246 {
247 // Write to a temporary string stream so as not to affect the state
248 // (precision, field width, etc.) of the output stream.
249 std::ostringstream os;
250 os << std::setprecision(precision) << std::setiosflags(std::ios::fixed);
251 os << "Statistics ";
252 if (!name.empty()) os << "for \"" << name << "\" ";
253 if (mSize>0) {
254 os << "with " << mSize << " samples:\n"
255 << " Min=" << mMin
256 << ", Max=" << mMax
257 << ", Ave=" << mAvg
258 << ", Std=" << this->stdDev()
259 << ", Var=" << this->variance() << std::endl;
260 } else {
261 os << ": no samples were added." << std::endl;
262 }
263 strm << os.str();
264 }
265
266protected:
267 using Extrema::mSize;
268 using Extrema::mMin;
269 using Extrema::mMax;
270 double mAvg, mAux;
271}; // end Stats
272
273
274////////////////////////////////////////
275
276
277/// @brief This class computes a histogram, with a fixed interval width,
278/// of a population of floating-point values.
279 class Histogram
280{
281public:
282 /// Construct with given minimum and maximum values and the given bin count.
283 Histogram(double min, double max, size_t numBins = 10)
284 : mSize(0), mMin(min), mMax(max + 1e-10),
285 mDelta(double(numBins)/(max-min)), mBins(numBins)
286 {
287 if ( mMax <= mMin ) {
288 OPENVDB_THROW(ValueError, "Histogram: expected min < max");
289 } else if ( numBins == 0 ) {
290 OPENVDB_THROW(ValueError, "Histogram: expected at least one bin");
291 }
292 for (size_t i=0; i<numBins; ++i) mBins[i]=0;
293 }
294
295 /// @brief Construct with the given bin count and with minimum and maximum values
296 /// taken from a Stats object.
297 Histogram(const Stats& s, size_t numBins = 10):
298 mSize(0), mMin(s.min()), mMax(s.max()+1e-10),
299 mDelta(double(numBins)/(mMax-mMin)), mBins(numBins)
300 {
301 if ( mMax <= mMin ) {
302 OPENVDB_THROW(ValueError, "Histogram: expected min < max");
303 } else if ( numBins == 0 ) {
304 OPENVDB_THROW(ValueError, "Histogram: expected at least one bin");
305 }
306 for (size_t i=0; i<numBins; ++i) mBins[i]=0;
307 }
308
309 /// @brief Add @a n samples with constant value @a val, provided that the
310 /// @a val falls within this histogram's value range.
311 /// @return @c true if the sample value falls within this histogram's value range.
312 inline bool add(double val, uint64_t n = 1)
313 {
314 if (val<mMin || val>mMax) return false;
315 mBins[size_t(mDelta*(val-mMin))] += n;
316 mSize += n;
317 return true;
318 }
319
320 /// @brief Add all the contributions from the other histogram, provided that
321 /// it has the same configuration as this histogram.
322 bool add(const Histogram& other)
323 {
324 if (!isApproxEqual(mMin, other.mMin) || !isApproxEqual(mMax, other.mMax) ||
325 mBins.size() != other.mBins.size()) return false;
326 for (size_t i=0, e=mBins.size(); i!=e; ++i) mBins[i] += other.mBins[i];
327 mSize += other.mSize;
328 return true;
329 }
330
331 /// Return the number of bins in this histogram.
332 inline size_t numBins() const { return mBins.size(); }
333 /// Return the lower bound of this histogram's value range.
334 inline double min() const { return mMin; }
335 /// Return the upper bound of this histogram's value range.
336 inline double max() const { return mMax; }
337 /// Return the minimum value in the <i>n</i>th bin.
338 inline double min(int n) const { return mMin+n/mDelta; }
339 /// Return the maximum value in the <i>n</i>th bin.
340 inline double max(int n) const { return mMin+(n+1)/mDelta; }
341 /// Return the number of samples in the <i>n</i>th bin.
342 inline uint64_t count(int n) const { return mBins[n]; }
343 /// Return the population size, i.e., the total number of samples.
344 inline uint64_t size() const { return mSize; }
345
346 /// Print the histogram to the specified output stream.
347 void print(const std::string& name = "", std::ostream& strm = std::cout) const
348 {
349 // Write to a temporary string stream so as not to affect the state
350 // (precision, field width, etc.) of the output stream.
351 std::ostringstream os;
352 os << std::setprecision(6) << std::setiosflags(std::ios::fixed) << std::endl;
353 os << "Histogram ";
354 if (!name.empty()) os << "for \"" << name << "\" ";
355 if (mSize > 0) {
356 os << "with " << mSize << " samples:\n";
357 os << "==============================================================\n";
358 os << "|| # | Min | Max | Frequency | % ||\n";
359 os << "==============================================================\n";
360 for (int i = 0, e = int(mBins.size()); i != e; ++i) {
361 os << "|| " << std::setw(4) << i << " | " << std::setw(14) << this->min(i) << " | "
362 << std::setw(14) << this->max(i) << " | " << std::setw(9) << mBins[i] << " | "
363 << std::setw(3) << (100*mBins[i]/mSize) << " ||\n";
364 }
365 os << "==============================================================\n";
366 } else {
367 os << ": no samples were added." << std::endl;
368 }
369 strm << os.str();
370 }
371
372private:
373 uint64_t mSize;
374 double mMin, mMax, mDelta;
375 std::vector<uint64_t> mBins;
376};// end Histogram
377
378} // namespace math
379} // namespace OPENVDB_VERSION_NAME
380} // namespace openvdb
381
382#endif // OPENVDB_MATH_STATS_HAS_BEEN_INCLUDED
Math.h
General-purpose arithmetic and comparison routines, most of which accept arbitrary value types (or at...
openvdb::v10_0::ValueError
Definition: Exceptions.h:65
openvdb::v10_0::math::Extrema
This class computes the minimum and maximum values of a population of floating-point values.
Definition: Stats.h:93
openvdb::v10_0::math::Extrema::add
void add(double val)
Add a single sample.
Definition: Stats.h:106
openvdb::v10_0::math::Extrema::add
void add(const Extrema &other)
Add the samples from the other Stats instance.
Definition: Stats.h:134
openvdb::v10_0::math::Extrema::Extrema
Extrema()
Constructor.
Definition: Stats.h:98
openvdb::v10_0::math::Extrema::mMax
double mMax
Definition: Stats.h:170
openvdb::v10_0::math::Extrema::mSize
uint64_t mSize
Definition: Stats.h:169
openvdb::v10_0::math::Extrema::range
double range() const
Return the range defined as the maximum value minus the minimum value.
Definition: Stats.h:131
openvdb::v10_0::math::Extrema::min
double min() const
Return the minimum value.
Definition: Stats.h:125
openvdb::v10_0::math::Extrema::size
uint64_t size() const
Return the size of the population, i.e., the total number of samples.
Definition: Stats.h:122
openvdb::v10_0::math::Extrema::add
void add(double val, uint64_t n)
Add n samples with constant value val.
Definition: Stats.h:114
openvdb::v10_0::math::Extrema::join
void join(const Extrema &other)
Definition: Stats.h:161
openvdb::v10_0::math::Extrema::mMin
double mMin
Definition: Stats.h:170
openvdb::v10_0::math::Extrema::print
void print(const std::string &name="", std::ostream &strm=std::cout, int precision=3) const
Print extrema to the specified output stream.
Definition: Stats.h:140
openvdb::v10_0::math::Extrema::max
double max() const
Return the maximum value.
Definition: Stats.h:128
openvdb::v10_0::math::Histogram
This class computes a histogram, with a fixed interval width, of a population of floating-point value...
Definition: Stats.h:280
openvdb::v10_0::math::Histogram::print
void print(const std::string &name="", std::ostream &strm=std::cout) const
Print the histogram to the specified output stream.
Definition: Stats.h:347
openvdb::v10_0::math::Histogram::count
uint64_t count(int n) const
Return the number of samples in the nth bin.
Definition: Stats.h:342
openvdb::v10_0::math::Histogram::add
bool add(double val, uint64_t n=1)
Add n samples with constant value val, provided that the val falls within this histogram's value rang...
Definition: Stats.h:312
openvdb::v10_0::math::Histogram::min
double min(int n) const
Return the minimum value in the nth bin.
Definition: Stats.h:338
openvdb::v10_0::math::Histogram::min
double min() const
Return the lower bound of this histogram's value range.
Definition: Stats.h:334
openvdb::v10_0::math::Histogram::size
uint64_t size() const
Return the population size, i.e., the total number of samples.
Definition: Stats.h:344
openvdb::v10_0::math::Histogram::Histogram
Histogram(const Stats &s, size_t numBins=10)
Construct with the given bin count and with minimum and maximum values taken from a Stats object.
Definition: Stats.h:297
openvdb::v10_0::math::Histogram::max
double max(int n) const
Return the maximum value in the nth bin.
Definition: Stats.h:340
openvdb::v10_0::math::Histogram::numBins
size_t numBins() const
Return the number of bins in this histogram.
Definition: Stats.h:332
openvdb::v10_0::math::Histogram::add
bool add(const Histogram &other)
Add all the contributions from the other histogram, provided that it has the same configuration as th...
Definition: Stats.h:322
openvdb::v10_0::math::Histogram::max
double max() const
Return the upper bound of this histogram's value range.
Definition: Stats.h:336
openvdb::v10_0::math::Histogram::Histogram
Histogram(double min, double max, size_t numBins=10)
Construct with given minimum and maximum values and the given bin count.
Definition: Stats.h:283
openvdb::v10_0::math::MinMax
Templated class to compute the minimum and maximum values.
Definition: Stats.h:31
openvdb::v10_0::math::MinMax::mMin
ValueType mMin
Definition: Stats.h:87
openvdb::v10_0::math::MinMax::MinMax
MinMax(const MinMax &other)=default
Default copy constructor.
openvdb::v10_0::math::MinMax::mMax
ValueType mMax
Definition: Stats.h:87
openvdb::v10_0::math::MinMax::max
const ValueType & max() const
Return the maximum value.
Definition: Stats.h:63
openvdb::v10_0::math::MinMax::add
void add(const ValueType &val, const Less &less=Less())
Add a single sample.
Definition: Stats.h:53
openvdb::v10_0::math::MinMax::MinMax
MinMax(const ValueType &min, const ValueType &max)
Constructor.
Definition: Stats.h:45
openvdb::v10_0::math::MinMax::print
void print(const std::string &name="", std::ostream &strm=std::cout, int precision=3) const
Print MinMax to the specified output stream.
Definition: Stats.h:73
openvdb::v10_0::math::MinMax::MinMax
MinMax()
Empty constructor.
Definition: Stats.h:38
openvdb::v10_0::math::MinMax::min
const ValueType & min() const
Return the minimum value.
Definition: Stats.h:60
openvdb::v10_0::math::MinMax::add
void add(const MinMax &other, const Less &less=Less())
Add the samples from the other Stats instance.
Definition: Stats.h:66
openvdb::v10_0::math::Stats
This class computes statistics (minimum value, maximum value, mean, variance and standard deviation) ...
Definition: Stats.h:183
openvdb::v10_0::math::Stats::var
double var() const
Return the population variance.
Definition: Stats.h:233
openvdb::v10_0::math::Stats::add
void add(double val)
Add a single sample.
Definition: Stats.h:193
openvdb::v10_0::math::Stats::mAvg
double mAvg
Definition: Stats.h:270
openvdb::v10_0::math::Stats::add
void add(const Stats &other)
Add the samples from the other Stats instance.
Definition: Stats.h:212
openvdb::v10_0::math::Stats::mSize
uint64_t mSize
Definition: Stats.h:169
openvdb::v10_0::math::Stats::mean
double mean() const
Definition: Stats.h:226
openvdb::v10_0::math::Stats::variance
double variance() const
Definition: Stats.h:234
openvdb::v10_0::math::Stats::add
void add(double val, uint64_t n)
Add n samples with constant value val.
Definition: Stats.h:202
openvdb::v10_0::math::Stats::stdDev
double stdDev() const
Definition: Stats.h:241
openvdb::v10_0::math::Stats::mAux
double mAux
Definition: Stats.h:270
openvdb::v10_0::math::Stats::std
double std() const
Return the standard deviation (=Sqrt(variance)) as defined from the (biased) population variance.
Definition: Stats.h:240
openvdb::v10_0::math::Stats::print
void print(const std::string &name="", std::ostream &strm=std::cout, int precision=3) const
Print statistics to the specified output stream.
Definition: Stats.h:245
openvdb::v10_0::math::Stats::avg
double avg() const
Return the arithmetic mean, i.e. average, value.
Definition: Stats.h:225
openvdb::v10_0::math::Stats::Stats
Stats()
Definition: Stats.h:185
openvdb::v10_0::math::isApproxEqual
bool isApproxEqual(const Type &a, const Type &b, const Type &tolerance)
Return true if a is equal to b to within the given tolerance.
Definition: Math.h:406
openvdb::v10_0::tools::composite::min
const std::enable_if<!VecTraits< T >::IsVec, T >::type & min(const T &a, const T &b)
Definition: Composite.h:106
openvdb::v10_0::tools::composite::max
const std::enable_if<!VecTraits< T >::IsVec, T >::type & max(const T &a, const T &b)
Definition: Composite.h:110
openvdb
Definition: Exceptions.h:13
std
Definition: Coord.h:587
Exceptions.h
OPENVDB_THROW
#define OPENVDB_THROW(exception, message)
Definition: Exceptions.h:74
OPENVDB_VERSION_NAME
#define OPENVDB_VERSION_NAME
The version namespace name for this library version.
Definition: version.h.in:121
OPENVDB_USE_VERSION_NAMESPACE
#define OPENVDB_USE_VERSION_NAMESPACE
Definition: version.h.in:212