/usr/include/openvdb/math/Stats.h is in libopenvdb-dev 2.1.0-1ubuntu1.
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//
// Copyright (c) 2012-2013 DreamWorks Animation LLC
//
// All rights reserved. This software is distributed under the
// Mozilla Public License 2.0 ( http://www.mozilla.org/MPL/2.0/ )
//
// Redistributions of source code must retain the above copyright
// and license notice and the following restrictions and disclaimer.
//
// * Neither the name of DreamWorks Animation nor the names of
// its contributors may be used to endorse or promote products derived
// from this software without specific prior written permission.
//
// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
// OWNER OR CONTRIBUTORS BE LIABLE FOR ANY INDIRECT, INCIDENTAL,
// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
// LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
// DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
// THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
// IN NO EVENT SHALL THE COPYRIGHT HOLDERS' AND CONTRIBUTORS' AGGREGATE
// LIABILITY FOR ALL CLAIMS REGARDLESS OF THEIR BASIS EXCEED US$250.00.
//
///////////////////////////////////////////////////////////////////////////
//
/// @file Stats.h
///
/// @brief Classes to compute statistics and histograms
#ifndef OPENVDB_MATH_STATS_HAS_BEEN_INCLUDED
#define OPENVDB_MATH_STATS_HAS_BEEN_INCLUDED
#include <iosfwd> // for ostringstream
#include <openvdb/version.h>
#include <iostream>
#include <iomanip>
#include <sstream>
#include <vector>
#include "Math.h"
namespace openvdb {
OPENVDB_USE_VERSION_NAMESPACE
namespace OPENVDB_VERSION_NAME {
namespace math {
/// @brief This class computes statistics (minimum value, maximum
/// value, mean, variance and standard deviation) of a population
/// of floating-point values.
///
/// @details variance = Mean[ (X-Mean[X])^2 ] = Mean[X^2] - Mean[X]^2,
/// standard deviation = sqrt(variance)
///
/// @note This class employs incremental computation and double precision.
class Stats
{
public:
Stats(): mSize(0), mAvg(0.0), mAux(0.0),
mMin(std::numeric_limits<double>::max()), mMax(-mMin) {}
/// Add a single sample.
void add(double val)
{
mSize++;
mMin = std::min<double>(val, mMin);
mMax = std::max<double>(val, mMax);
const double delta = val - mAvg;
mAvg += delta/double(mSize);
mAux += delta*(val - mAvg);
}
/// Add @a n samples with constant value @a val.
void add(double val, uint64_t n)
{
mMin = std::min<double>(val, mMin);
mMax = std::max<double>(val, mMax);
const double denom = 1.0/double(mSize + n);
const double delta = val - mAvg;
mAvg += denom*delta*n;
mAux += denom*delta*delta*mSize*n;
mSize += n;
}
/// Add the samples from the other Stats instance.
void add(const Stats& other)
{
if (other.mSize > 0) {
mMin = std::min<double>(mMin, other.mMin);
mMax = std::max<double>(mMax, other.mMax);
const double denom = 1.0/double(mSize + other.mSize);
const double delta = other.mAvg - mAvg;
mAvg += denom*delta*other.mSize;
mAux += other.mAux + denom*delta*delta*mSize*other.mSize;
mSize += other.mSize;
}
}
/// Return the size of the population, i.e., the total number of samples.
inline uint64_t size() const { return mSize; }
/// Return the minimum value.
inline double min() const { return mMin; }
/// Return the maximum value.
inline double max() const { return mMax; }
//@{
/// Return the arithmetic mean, i.e. average, value.
inline double avg() const { return mAvg; }
inline double mean() const { return mAvg; }
//@}
//@{
/// @brief Return the population variance.
/// @note The unbiased sample variance = population variance *
//num/(num-1)
inline double var() const { return mSize<2 ? 0.0 : mAux/double(mSize); }
inline double variance() const { return this->var(); }
//@}
//@{
/// @brief Return the standard deviation (=Sqrt(variance)) as
/// defined from the (biased) population variance.
inline double std() const { return sqrt(this->var()); }
inline double stdDev() const { return this->std(); }
//@}
/// @brief Print statistics to the specified output stream.
void print(const std::string &name= "", std::ostream &strm=std::cout, int precision=3) const
{
// Write to a temporary string stream so as not to affect the state
// (precision, field width, etc.) of the output stream.
std::ostringstream os;
os << std::setprecision(precision) << std::setiosflags(std::ios::fixed);
os << "Statistics ";
if (!name.empty()) os << "for \"" << name << "\" ";
if (mSize>0) {
os << "with " << mSize << " samples:\n"
<< " Min=" << mMin
<< ", Max=" << mMax
<< ", Ave=" << mAvg
<< ", Std=" << this->stdDev()
<< ", Var=" << this->variance() << std::endl;
} else {
os << ": no samples were added." << std::endl;
}
strm << os.str();
}
private:
uint64_t mSize;
double mAvg, mAux, mMin, mMax;
}; // end Stats
////////////////////////////////////////
/// @brief This class computes a histogram, with a fixed interval width,
/// of a population of floating-point values.
class Histogram
{
public:
/// Construct with given minimum and maximum values and the given bin count.
Histogram(double min, double max, size_t numBins = 10)
: mSize(0), mMin(min), mMax(max+1e-10),
mDelta(double(numBins)/(max-min)), mBins(numBins)
{
assert(numBins > 1);
assert(mMax-mMin > 1e-10);
for (size_t i=0; i<numBins; ++i) mBins[i]=0;
}
/// @brief Construct with the given bin count and with minimum and maximum values
/// taken from a Stats object.
Histogram(const Stats& s, size_t numBins = 10):
mSize(0), mMin(s.min()), mMax(s.max()+1e-10),
mDelta(double(numBins)/(mMax-mMin)), mBins(numBins)
{
assert(numBins > 1);
assert(mMax-mMin > 1e-10);
for (size_t i=0; i<numBins; ++i) mBins[i]=0;
}
/// @brief Add @a n samples with constant value @a val, provided that the
/// @a val falls within this histogram's value range.
/// @return @c true if the sample value falls within this histogram's value range.
inline bool add(double val, uint64_t n = 1)
{
if (val<mMin || val>mMax) return false;
mBins[size_t(mDelta*(val-mMin))] += n;
mSize += n;
return true;
}
/// @brief Add all the contributions from the other histogram, provided that
/// it has the same configuration as this histogram.
bool add(const Histogram& other)
{
if (!isApproxEqual(mMin, other.mMin) || !isApproxEqual(mMax, other.mMax) ||
mBins.size() != other.mBins.size()) return false;
for (size_t i=0, e=mBins.size(); i!=e; ++i) mBins[i] += other.mBins[i];
mSize += other.mSize;
return true;
}
/// Return the number of bins in this histogram.
inline size_t numBins() const { return mBins.size(); }
/// Return the lower bound of this histogram's value range.
inline double min() const { return mMin; }
/// Return the upper bound of this histogram's value range.
inline double max() const { return mMax; }
/// Return the minimum value in the <i>n</i>th bin.
inline double min(int n) const { return mMin+n/mDelta; }
/// Return the maximum value in the <i>n</i>th bin.
inline double max(int n) const { return mMin+(n+1)/mDelta; }
/// Return the number of samples in the <i>n</i>th bin.
inline uint64_t count(int n) const { return mBins[n]; }
/// Return the population size, i.e., the total number of samples.
inline uint64_t size() const { return mSize; }
/// Print the histogram to the specified output stream.
void print(const std::string& name = "", std::ostream& strm = std::cout) const
{
// Write to a temporary string stream so as not to affect the state
// (precision, field width, etc.) of the output stream.
std::ostringstream os;
os << std::setprecision(6) << std::setiosflags(std::ios::fixed) << std::endl;
os << "Histogram ";
if (!name.empty()) os << "for \"" << name << "\" ";
if (mSize > 0) {
os << "with " << mSize << " samples:\n";
os << "==============================================================\n";
os << "|| # | Min | Max | Frequency | % ||\n";
os << "==============================================================\n";
for (size_t i=0, e=mBins.size(); i!=e; ++i) {
os << "|| " << std::setw(4) << i << " | " << std::setw(14) << this->min(i) << " | "
<< std::setw(14) << this->max(i) << " | " << std::setw(9) << mBins[i] << " | "
<< std::setw(3) << (100*mBins[i]/mSize) << " ||\n";
}
os << "==============================================================\n";
} else {
os << ": no samples were added." << std::endl;
}
strm << os.str();
}
private:
uint64_t mSize;
double mMin, mMax, mDelta;
std::vector<uint64_t> mBins;
};
} // namespace math
} // namespace OPENVDB_VERSION_NAME
} // namespace openvdb
#endif // OPENVDB_MATH_STATS_HAS_BEEN_INCLUDED
// Copyright (c) 2012-2013 DreamWorks Animation LLC
// All rights reserved. This software is distributed under the
// Mozilla Public License 2.0 ( http://www.mozilla.org/MPL/2.0/ )
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