OpenVDB 5.1.0

Stats.h
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1 //
3 // Copyright (c) 2012-2018 DreamWorks Animation LLC
4 //
5 // All rights reserved. This software is distributed under the
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36
37 #ifndef OPENVDB_MATH_STATS_HAS_BEEN_INCLUDED
38 #define OPENVDB_MATH_STATS_HAS_BEEN_INCLUDED
39
40 #include <iosfwd> // for ostringstream
41 #include <openvdb/version.h>
42 #include <openvdb/Exceptions.h>
43 #include <iostream>
44 #include <iomanip>
45 #include <sstream>
46 #include <vector>
47 #include <functional>// for std::less
48 #include "Math.h"
49
50 namespace openvdb {
51 OPENVDB_USE_VERSION_NAMESPACE
52 namespace OPENVDB_VERSION_NAME {
53 namespace math {
54
56 template <typename ValueType, typename Less = std::less<ValueType> >
57 class MinMax
58 {
59 using Limits = std::numeric_limits<ValueType>;
60 public:
61
65 MinMax() : mMin(Limits::max()), mMax(Limits::lowest())
66 {
67 static_assert(std::numeric_limits<ValueType>::is_specialized,
68 "openvdb::math::MinMax default constructor requires a std::numeric_limits specialization");
69 }
70
72 MinMax(const ValueType &min, const ValueType &max) : mMin(min), mMax(max)
73 {
74 }
75
77 MinMax(const MinMax &other) = default;
78
80 inline void add(const ValueType &val, const Less &less = Less())
81 {
82 if (less(val, mMin)) mMin = val;
83 if (less(mMax, val)) mMax = val;
84 }
85
87 inline const ValueType& min() const { return mMin; }
88
90 inline const ValueType& max() const { return mMax; }
91
93 inline void add(const MinMax& other, const Less &less = Less())
94 {
95 if (less(other.mMin, mMin)) mMin = other.mMin;
96 if (less(mMax, other.mMax)) mMax = other.mMax;
97 }
98
100 void print(const std::string &name= "", std::ostream &strm=std::cout, int precision=3) const
101 {
102 // Write to a temporary string stream so as not to affect the state
103 // (precision, field width, etc.) of the output stream.
104 std::ostringstream os;
105 os << std::setprecision(precision) << std::setiosflags(std::ios::fixed);
106 os << "MinMax ";
107 if (!name.empty()) os << "for \"" << name << "\" ";
108 os << " Min=" << mMin << ", Max=" << mMax << std::endl;
109 strm << os.str();
110 }
111
112 protected:
113
114 ValueType mMin, mMax;
115 };//end MinMax
116
119 class Extrema
120 {
121 public:
122
125 Extrema()
126 : mSize(0)
127 , mMin(std::numeric_limits<double>::max())
128 , mMax(-mMin)
129 {
130 }
131
133 void add(double val)
134 {
135 ++mSize;
136 mMin = std::min<double>(val, mMin);
137 mMax = std::max<double>(val, mMax);
138 }
139
141 void add(double val, uint64_t n)
142 {
143 mSize += n;
144 mMin = std::min<double>(val, mMin);
145 mMax = std::max<double>(val, mMax);
146 }
147
149 inline uint64_t size() const { return mSize; }
150
152 inline double min() const { return mMin; }
153
155 inline double max() const { return mMax; }
156
158 inline double range() const { return mMax - mMin; }
159
161 void add(const Extrema& other)
162 {
163 if (other.mSize > 0) this->join(other);
164 }
165
167 void print(const std::string &name= "", std::ostream &strm=std::cout, int precision=3) const
168 {
169 // Write to a temporary string stream so as not to affect the state
170 // (precision, field width, etc.) of the output stream.
171 std::ostringstream os;
172 os << std::setprecision(precision) << std::setiosflags(std::ios::fixed);
173 os << "Extrema ";
174 if (!name.empty()) os << "for \"" << name << "\" ";
175 if (mSize>0) {
176 os << "with " << mSize << " samples:\n"
177 << " Min=" << mMin
178 << ", Max=" << mMax
179 << ", Range="<< this->range() << std::endl;
180 } else {
181 os << ": no samples were added." << std::endl;
182 }
183 strm << os.str();
184 }
185
186 protected:
187
188 inline void join(const Extrema& other)
189 {
190 assert(other.mSize > 0);
191 mSize += other.mSize;
192 mMin = std::min<double>(mMin, other.mMin);
193 mMax = std::max<double>(mMax, other.mMax);
194 }
195
196 uint64_t mSize;
197 double mMin, mMax;
198 };//end Extrema
199
200
209 class Stats : public Extrema
210 {
211 public:
212 Stats()
213 : Extrema()
214 , mAvg(0.0)
215 , mAux(0.0)
216 {
217 }
218
220 void add(double val)
221 {
222 Extrema::add(val);
223 const double delta = val - mAvg;
224 mAvg += delta/double(mSize);
225 mAux += delta*(val - mAvg);
226 }
227
229 void add(double val, uint64_t n)
230 {
231 const double denom = 1.0/double(mSize + n);
232 const double delta = val - mAvg;
233 mAvg += denom * delta * double(n);
234 mAux += denom * delta * delta * double(mSize) * double(n);
235 Extrema::add(val, n);
236 }
237
239 void add(const Stats& other)
240 {
241 if (other.mSize > 0) {
242 const double denom = 1.0/double(mSize + other.mSize);
243 const double delta = other.mAvg - mAvg;
244 mAvg += denom * delta * double(other.mSize);
245 mAux += other.mAux + denom * delta * delta * double(mSize) * double(other.mSize);
246 Extrema::join(other);
247 }
248 }
249
251 inline double avg() const { return mAvg; }
253 inline double mean() const { return mAvg; }
255
257 //num/(num-1)
260 inline double var() const { return mSize<2 ? 0.0 : mAux/double(mSize); }
261 inline double variance() const { return this->var(); }
263
265 inline double std() const { return sqrt(this->var()); }
268 inline double stdDev() const { return this->std(); }
270
272 void print(const std::string &name= "", std::ostream &strm=std::cout, int precision=3) const
273 {
274 // Write to a temporary string stream so as not to affect the state
275 // (precision, field width, etc.) of the output stream.
276 std::ostringstream os;
277 os << std::setprecision(precision) << std::setiosflags(std::ios::fixed);
278 os << "Statistics ";
279 if (!name.empty()) os << "for \"" << name << "\" ";
280 if (mSize>0) {
281 os << "with " << mSize << " samples:\n"
282 << " Min=" << mMin
283 << ", Max=" << mMax
284 << ", Ave=" << mAvg
285 << ", Std=" << this->stdDev()
286 << ", Var=" << this->variance() << std::endl;
287 } else {
288 os << ": no samples were added." << std::endl;
289 }
290 strm << os.str();
291 }
292
293 protected:
294 using Extrema::mSize;
295 using Extrema::mMin;
296 using Extrema::mMax;
297 double mAvg, mAux;
298 }; // end Stats
299
300
302
303
306 class Histogram
307 {
308 public:
310 Histogram(double min, double max, size_t numBins = 10)
311 : mSize(0), mMin(min), mMax(max + 1e-10),
312 mDelta(double(numBins)/(max-min)), mBins(numBins)
313 {
314 if ( mMax <= mMin ) {
315 OPENVDB_THROW(ValueError, "Histogram: expected min < max");
316 } else if ( numBins == 0 ) {
317 OPENVDB_THROW(ValueError, "Histogram: expected at least one bin");
318 }
319 for (size_t i=0; i<numBins; ++i) mBins[i]=0;
320 }
321
324 Histogram(const Stats& s, size_t numBins = 10):
325 mSize(0), mMin(s.min()), mMax(s.max()+1e-10),
326 mDelta(double(numBins)/(mMax-mMin)), mBins(numBins)
327 {
328 if ( mMax <= mMin ) {
329 OPENVDB_THROW(ValueError, "Histogram: expected min < max");
330 } else if ( numBins == 0 ) {
331 OPENVDB_THROW(ValueError, "Histogram: expected at least one bin");
332 }
333 for (size_t i=0; i<numBins; ++i) mBins[i]=0;
334 }
335
339 inline bool add(double val, uint64_t n = 1)
340 {
341 if (val<mMin || val>mMax) return false;
342 mBins[size_t(mDelta*(val-mMin))] += n;
343 mSize += n;
344 return true;
345 }
346
349 bool add(const Histogram& other)
350 {
351 if (!isApproxEqual(mMin, other.mMin) || !isApproxEqual(mMax, other.mMax) ||
352 mBins.size() != other.mBins.size()) return false;
353 for (size_t i=0, e=mBins.size(); i!=e; ++i) mBins[i] += other.mBins[i];
354 mSize += other.mSize;
355 return true;
356 }
357
359 inline size_t numBins() const { return mBins.size(); }
361 inline double min() const { return mMin; }
363 inline double max() const { return mMax; }
365 inline double min(int n) const { return mMin+n/mDelta; }
367 inline double max(int n) const { return mMin+(n+1)/mDelta; }
369 inline uint64_t count(int n) const { return mBins[n]; }
371 inline uint64_t size() const { return mSize; }
372
374 void print(const std::string& name = "", std::ostream& strm = std::cout) const
375 {
376 // Write to a temporary string stream so as not to affect the state
377 // (precision, field width, etc.) of the output stream.
378 std::ostringstream os;
379 os << std::setprecision(6) << std::setiosflags(std::ios::fixed) << std::endl;
380 os << "Histogram ";
381 if (!name.empty()) os << "for \"" << name << "\" ";
382 if (mSize > 0) {
383 os << "with " << mSize << " samples:\n";
384 os << "==============================================================\n";
385 os << "|| # | Min | Max | Frequency | % ||\n";
386 os << "==============================================================\n";
387 for (int i = 0, e = int(mBins.size()); i != e; ++i) {
388 os << "|| " << std::setw(4) << i << " | " << std::setw(14) << this->min(i) << " | "
389 << std::setw(14) << this->max(i) << " | " << std::setw(9) << mBins[i] << " | "
390 << std::setw(3) << (100*mBins[i]/mSize) << " ||\n";
391 }
392 os << "==============================================================\n";
393 } else {
394 os << ": no samples were added." << std::endl;
395 }
396 strm << os.str();
397 }
398
399 private:
400 uint64_t mSize;
401 double mMin, mMax, mDelta;
402 std::vector<uint64_t> mBins;
403 };// end Histogram
404
405 } // namespace math
406 } // namespace OPENVDB_VERSION_NAME
407 } // namespace openvdb
408
409 #endif // OPENVDB_MATH_STATS_HAS_BEEN_INCLUDED
410
411 // Copyright (c) 2012-2018 DreamWorks Animation LLC
412 // All rights reserved. This software is distributed under the
413 // Mozilla Public License 2.0 ( http://www.mozilla.org/MPL/2.0/ )
openvdb::v5_1::math::Histogram::max
double max() const
Return the upper bound of this histogram&#39;s value range.
Definition: Stats.h:363
openvdb::v5_1::math::Extrema::mMin
double mMin
Definition: Stats.h:197
openvdb::v5_1::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:310
openvdb::v5_1::math::Stats
This class computes statistics (minimum value, maximum value, mean, variance and standard deviation) ...
Definition: Stats.h:209
Math.h
General-purpose arithmetic and comparison routines, most of which accept arbitrary value types (or at...
openvdb::v5_1::math::MinMax
Templated class to compute the minimum and maximum values.
Definition: Stats.h:57
openvdb::v5_1::math::Stats::stdDev
double stdDev() const
Return the standard deviation (=Sqrt(variance)) as defined from the (biased) population variance...
Definition: Stats.h:268
openvdb::v5_1::math::Extrema::mMax
double mMax
Definition: Stats.h:197
openvdb::v5_1::math::MinMax::max
const ValueType & max() const
Return the maximum value.
Definition: Stats.h:90
openvdb::v5_1::math::Stats::mSize
uint64_t mSize
Definition: Stats.h:196
openvdb::v5_1::math::Histogram::count
uint64_t count(int n) const
Return the number of samples in the nth bin.
Definition: Stats.h:369
openvdb::v5_1::math::Extrema::join
void join(const Extrema &other)
Definition: Stats.h:188
openvdb::v5_1::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:100
OPENVDB_THROW
#define OPENVDB_THROW(exception, message)
Definition: Exceptions.h:109
openvdb::v5_1::math::MinMax::mMin
ValueType mMin
Definition: Stats.h:114
openvdb::v5_1::math::Extrema::add
void add(double val)
Add a single sample.
Definition: Stats.h:133
openvdb::v5_1::math::Stats::add
void add(const Stats &other)
Add the samples from the other Stats instance.
Definition: Stats.h:239
openvdb::v5_1::math::Stats::mAvg
double mAvg
Definition: Stats.h:297
openvdb::v5_1::math::Stats::add
void add(double val)
Add a single sample.
Definition: Stats.h:220
openvdb::v5_1::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:324
openvdb::v5_1::math::Stats::mAux
double mAux
Definition: Stats.h:297
openvdb::v5_1::math::Histogram::max
double max(int n) const
Return the maximum value in the nth bin.
Definition: Stats.h:367
openvdb::v5_1::math::Extrema::add
void add(const Extrema &other)
Add the samples from the other Stats instance.
Definition: Stats.h:161
openvdb::v5_1::math::Histogram::numBins
size_t numBins() const
Return the number of bins in this histogram.
Definition: Stats.h:359
openvdb::v5_1::math::Stats::var
double var() const
Return the population variance.
Definition: Stats.h:260
openvdb::v5_1::math::Stats::Stats
Stats()
Definition: Stats.h:212
Exceptions.h
OPENVDB_VERSION_NAME
#define OPENVDB_VERSION_NAME
The version namespace name for this library version.
Definition: version.h:136
openvdb::v5_1::ValueError
Definition: Exceptions.h:92
openvdb::v5_1::math::Extrema::min
double min() const
Return the minimum value.
Definition: Stats.h:152
openvdb::v5_1::math::MinMax::MinMax
MinMax(const ValueType &min, const ValueType &max)
Constructor.
Definition: Stats.h:72
openvdb::v5_1::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:272
openvdb::v5_1::math::Stats::variance
double variance() const
Return the population variance.
Definition: Stats.h:261
openvdb::v5_1::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&#39;s value rang...
Definition: Stats.h:339
openvdb
Definition: Exceptions.h:40
openvdb::v5_1::math::Histogram::min
double min() const
Return the lower bound of this histogram&#39;s value range.
Definition: Stats.h:361
openvdb::v5_1::math::MinMax::min
const ValueType & min() const
Return the minimum value.
Definition: Stats.h:87
openvdb::v5_1::math::Histogram::size
uint64_t size() const
Return the population size, i.e., the total number of samples.
Definition: Stats.h:371
openvdb::v5_1::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:167
openvdb::v5_1::math::Extrema
This class computes the minimum and maximum values of a population of floating-point values...
Definition: Stats.h:119
openvdb::v5_1::math::MinMax::add
void add(const MinMax &other, const Less &less=Less())
Add the samples from the other Stats instance.
Definition: Stats.h:93
version.h
Library and file format version numbers.
openvdb::v5_1::math::Extrema::mSize
uint64_t mSize
Definition: Stats.h:196
openvdb::v5_1::math::Histogram::min
double min(int n) const
Return the minimum value in the nth bin.
Definition: Stats.h:365
openvdb::v5_1::math::Extrema::max
double max() const
Return the maximum value.
Definition: Stats.h:155
openvdb::v5_1::math::Stats::add
void add(double val, uint64_t n)
Add n samples with constant value val.
Definition: Stats.h:229
openvdb::v5_1::math::Histogram
This class computes a histogram, with a fixed interval width, of a population of floating-point value...
Definition: Stats.h:306
openvdb::v5_1::tools::composite::min
const std::enable_if<!VecTraits< T >::IsVec, T >::type & min(const T &a, const T &b)
Definition: Composite.h:129
openvdb::v5_1::math::Stats::mean
double mean() const
Return the arithmetic mean, i.e. average, value.
Definition: Stats.h:253
openvdb::v5_1::math::MinMax::mMax
ValueType mMax
Definition: Stats.h:114
openvdb::v5_1::math::isApproxEqual
bool isApproxEqual(const Type &a, const Type &b)
Return true if a is equal to b to within the default floating-point comparison tolerance.
Definition: Math.h:358
openvdb::v5_1::math::Extrema::size
uint64_t size() const
Return the size of the population, i.e., the total number of samples.
Definition: Stats.h:149
openvdb::v5_1::math::MinMax::add
void add(const ValueType &val, const Less &less=Less())
Add a single sample.
Definition: Stats.h:80
openvdb::v5_1::math::Extrema::Extrema
Extrema()
Constructor.
Definition: Stats.h:125
openvdb::v5_1::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:349
OPENVDB_USE_VERSION_NAMESPACE
#define OPENVDB_USE_VERSION_NAMESPACE
Definition: version.h:188
openvdb::v5_1::math::Extrema::add
void add(double val, uint64_t n)
Add n samples with constant value val.
Definition: Stats.h:141
openvdb::v5_1::tools::composite::max
const std::enable_if<!VecTraits< T >::IsVec, T >::type & max(const T &a, const T &b)
Definition: Composite.h:133
openvdb::v5_1::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:374
openvdb::v5_1::math::MinMax::MinMax
MinMax()
Empty constructor.
Definition: Stats.h:65
openvdb::v5_1::math::Extrema::range
double range() const
Return the range defined as the maximum value minus the minimum value.
Definition: Stats.h:158