libMesh::StatisticsVector< T > Class Template Reference

A std::vector derived class for implementing simple statistical algorithms. More...

#include <statistics.h>

Inheritance diagram for libMesh::StatisticsVector< T >:

Public Member Functions
	StatisticsVector (dof_id_type i=0)
	StatisticsVector (dof_id_type i, T val)
virtual	~StatisticsVector ()
virtual Real	l2_norm () const
virtual T	minimum () const
virtual T	maximum () const
virtual Real	mean () const
virtual Real	median ()
virtual Real	median () const
virtual Real	variance () const
virtual Real	variance (const Real known_mean) const
virtual Real	stddev () const
virtual Real	stddev (const Real known_mean) const
void	normalize ()
virtual void	histogram (std::vector< dof_id_type > &bin_members, unsigned int n_bins=10)
void	plot_histogram (const processor_id_type my_procid, const std::string &filename, unsigned int n_bins)
virtual void	histogram (std::vector< dof_id_type > &bin_members, unsigned int n_bins=10) const
virtual std::vector< dof_id_type >	cut_below (Real cut) const
virtual std::vector< dof_id_type >	cut_above (Real cut) const

Detailed Description

template<typename T>
class libMesh::StatisticsVector< T >

A std::vector derived class for implementing simple statistical algorithms.

The StatisticsVector class is derived from the std::vector<> and therefore has all of its useful features. It was designed to not have any internal state, i.e. no public or private data members. Also, it was only designed for classes and types for which the operators +,*,/ have meaning, specifically floats, doubles, ints, etc. The main reason for this design decision was to allow a std::vector<> to be successfully cast to a StatisticsVector, thereby enabling its additional functionality. We do not anticipate any problems with deriving from an stl container which lacks a virtual destructor in this case.

Where manipulation of the data set was necessary (for example sorting) two versions of member functions have been implemented. The non-const versions perform sorting directly in the data set, invalidating pointers and changing the entries. const versions of the same functions are generally available, and will be automatically invoked on const StatisticsVector objects. A draw-back to the const versions is that they simply make a copy of the original object and therefore double the original memory requirement for the data set.

Most of the actual code was copied or adapted from the GNU Scientific Library (GSL). More precisely, the recursion relations for computing the mean were implemented in order to avoid possible problems with buffer overruns.

Author

John W. Peterson

Date

2002

Definition at line 67 of file statistics.h.

Constructor & Destructor Documentation

StatisticsVector() [1/2]

template<typename T>

libMesh::StatisticsVector< T >::StatisticsVector ( dof_id_type  i = 0 )

inlineexplicit

Call the std::vector constructor.

Definition at line 75 of file statistics.h.

: std::vector<T> (i) {}

StatisticsVector() [2/2]

template<typename T>

libMesh::StatisticsVector< T >::StatisticsVector ( dof_id_type  i, T  val  )

inline

Call the std::vector constructor, fill each entry with val.

Definition at line 80 of file statistics.h.

: std::vector<T> (i,val) {}

~StatisticsVector()

template<typename T>

virtual libMesh::StatisticsVector< T >::~StatisticsVector ( )

inlinevirtual

Destructor. Virtual so we can derive from the StatisticsVector

Definition at line 85 of file statistics.h.

{}

Member Function Documentation

cut_above()

template<typename T >

std::vector< dof_id_type > libMesh::StatisticsVector< T >::cut_above ( Real  cut ) const

virtual

Returns

A vector of dof_id_types which corresponds to the indices of every member of the data set above the cutoff value cut.

I chose not to combine these two functions since the interface is cleaner with one passed parameter instead of two.

Reimplemented in libMesh::ErrorVector.

Definition at line 349 of file statistics.C.

{
  LOG_SCOPE ("cut_above()", "StatisticsVector");

  const dof_id_type n = cast_int<dof_id_type>(this->size());

  std::vector<dof_id_type> cut_indices;
  cut_indices.reserve(n/2);  // Arbitrary

  for (dof_id_type i=0; i<n; i++)
    if ((*this)[i] > cut)
      cut_indices.push_back(i);

  return cut_indices;
}

cut_below()

template<typename T >

std::vector< dof_id_type > libMesh::StatisticsVector< T >::cut_below ( Real  cut ) const

virtual

Returns

A vector of dof_id_types which corresponds to the indices of every member of the data set below the cutoff value "cut".

Reimplemented in libMesh::ErrorVector.

Definition at line 325 of file statistics.C.

{
  LOG_SCOPE ("cut_below()", "StatisticsVector");

  const dof_id_type n = cast_int<dof_id_type>(this->size());

  std::vector<dof_id_type> cut_indices;
  cut_indices.reserve(n/2);  // Arbitrary

  for (dof_id_type i=0; i<n; i++)
    {
      if ((*this)[i] < cut)
        {
          cut_indices.push_back(i);
        }
    }

  return cut_indices;
}

histogram() [1/2]

template<typename T >

void libMesh::StatisticsVector< T >::histogram ( std::vector< dof_id_type > &  bin_members, unsigned int  n_bins = 10  )

virtual

Returns

A histogram with n_bins bins for the data set.

For simplicity, the bins are assumed to be of uniform size. Upon return, the bin_members vector will contain unsigned integers which give the number of members in each bin. WARNING: This non-const function sorts the vector, changing its order. Source: GNU Scientific Library.

Definition at line 178 of file statistics.C.

Referenced by libMesh::StatisticsVector< ErrorVectorReal >::histogram().

{
  // Must have at least 1 bin
  libmesh_assert (n_bins>0);

  const dof_id_type n = cast_int<dof_id_type>(this->size());

  std::sort(this->begin(), this->end());

  // The StatisticsVector can hold both integer and float types.
  // We will define all the bins, etc. using Reals.
  Real min      = static_cast<Real>(this->minimum());
  Real max      = static_cast<Real>(this->maximum());
  Real bin_size = (max - min) / static_cast<Real>(n_bins);

  LOG_SCOPE ("histogram()", "StatisticsVector");

  std::vector<Real> bin_bounds(n_bins+1);
  for (std::size_t i=0; i<bin_bounds.size(); i++)
    bin_bounds[i] = min + Real(i) * bin_size;

  // Give the last bin boundary a little wiggle room: we don't want
  // it to be just barely less than the max, otherwise our bin test below
  // may fail.
  bin_bounds.back() += 1.e-6 * bin_size;

  // This vector will store the number of members each bin has.
  bin_members.resize(n_bins);

  dof_id_type data_index = 0;
  for (std::size_t j=0; j<bin_members.size(); j++) // bin vector indexing
    {
      // libMesh::out << "(debug) Filling bin " << j << std::endl;

      for (dof_id_type i=data_index; i<n; i++) // data vector indexing
        {
          //libMesh::out << "(debug) Processing index=" << i << std::endl;
          Real current_val = static_cast<Real>( (*this)[i] );

          // There may be entries in the vector smaller than the value
          // reported by this->minimum().  (e.g. inactive elements in an
          // ErrorVector.)  We just skip entries like that.
          if (current_val < min)
            {
              //     libMesh::out << "(debug) Skipping entry v[" << i << "]="
              //       << (*this)[i]
              //       << " which is less than the min value: min="
              //       << min << std::endl;
              continue;
            }

          if (current_val > bin_bounds[j+1]) // if outside the current bin (bin[j] is bounded
            // by bin_bounds[j] and bin_bounds[j+1])
            {
              // libMesh::out.precision(16);
              //     libMesh::out.setf(std::ios_base::fixed);
              //     libMesh::out << "(debug) (*this)[i]= " << (*this)[i]
              //       << " is greater than bin_bounds[j+1]="
              //      << bin_bounds[j+1] << std::endl;
              data_index = i; // start searching here for next bin
              break; // go to next bin
            }

          // Otherwise, increment current bin's count
          bin_members[j]++;
          // libMesh::out << "(debug) Binned index=" << i << std::endl;
        }
    }

#ifdef DEBUG
  // Check the number of binned entries
  const dof_id_type n_binned = std::accumulate(bin_members.begin(),
                                               bin_members.end(),
                                               static_cast<dof_id_type>(0),
                                               std::plus<dof_id_type>());

  if (n != n_binned)
    {
      libMesh::out << "Warning: The number of binned entries, n_binned="
                   << n_binned
                   << ", did not match the total number of entries, n="
                   << n << "." << std::endl;
    }
#endif
}

histogram() [2/2]

template<typename T >

void libMesh::StatisticsVector< T >::histogram ( std::vector< dof_id_type > &  bin_members, unsigned int  n_bins = 10  ) const

virtual

A const version of the histogram function.

Definition at line 313 of file statistics.C.

{
  StatisticsVector<T> sv = (*this);

  return sv.histogram(bin_members, n_bins);
}

l2_norm()

template<typename T >

Real libMesh::StatisticsVector< T >::l2_norm ( ) const

virtual

Returns

The l2 norm of the data set.

Definition at line 36 of file statistics.C.

{
  Real normsq = 0.;
  const dof_id_type n = cast_int<dof_id_type>(this->size());
  for (dof_id_type i = 0; i != n; ++i)
    normsq += ((*this)[i] * (*this)[i]);

  return std::sqrt(normsq);
}

maximum()

template<typename T >

T libMesh::StatisticsVector< T >::maximum ( ) const

virtual

Returns

The maximum value in the data set.

Definition at line 61 of file statistics.C.

{
  LOG_SCOPE ("maximum()", "StatisticsVector");

  const T max = *(std::max_element(this->begin(), this->end()));

  return max;
}

mean()

template<typename T >

Real libMesh::StatisticsVector< T >::mean ( ) const

virtual

Returns

The mean value of the data set using a recurrence relation.

Source: GNU Scientific Library

Reimplemented in libMesh::ErrorVector.

Definition at line 74 of file statistics.C.

Referenced by libMesh::StatisticsVector< ErrorVectorReal >::variance().

{
  LOG_SCOPE ("mean()", "StatisticsVector");

  const dof_id_type n = cast_int<dof_id_type>(this->size());

  Real the_mean = 0;

  for (dof_id_type i=0; i<n; i++)
    {
      the_mean += ( static_cast<Real>((*this)[i]) - the_mean ) /
        static_cast<Real>(i + 1);
    }

  return the_mean;
}

median() [1/2]

template<typename T >

Real libMesh::StatisticsVector< T >::median ( )

virtual

Returns

The median (e.g. the middle) value of the data set.

This function modifies the original data by sorting, so it can't be called on const objects. Source: GNU Scientific Library.

Reimplemented in libMesh::ErrorVector.

Definition at line 95 of file statistics.C.

Referenced by libMesh::ErrorVector::median(), and libMesh::StatisticsVector< ErrorVectorReal >::median().

{
  const dof_id_type n = cast_int<dof_id_type>(this->size());

  if (n == 0)
    return 0.;

  LOG_SCOPE ("median()", "StatisticsVector");

  std::sort(this->begin(), this->end());

  const dof_id_type lhs = (n-1) / 2;
  const dof_id_type rhs = n / 2;

  Real the_median = 0;


  if (lhs == rhs)
    {
      the_median = static_cast<Real>((*this)[lhs]);
    }

  else
    {
      the_median = ( static_cast<Real>((*this)[lhs]) +
                     static_cast<Real>((*this)[rhs]) ) / 2.0;
    }

  return the_median;
}

median() [2/2]

template<typename T >

Real libMesh::StatisticsVector< T >::median ( ) const

virtual

A const version of the median function. Requires twice the memory of original data set but does not change the original.

Reimplemented in libMesh::ErrorVector.

Definition at line 130 of file statistics.C.

{
  StatisticsVector<T> sv = (*this);

  return sv.median();
}

minimum()

template<typename T >

T libMesh::StatisticsVector< T >::minimum ( ) const

virtual

Returns

The minimum value in the data set.

Reimplemented in libMesh::ErrorVector.

Definition at line 48 of file statistics.C.

{
  LOG_SCOPE ("minimum()", "StatisticsVector");

  const T min = *(std::min_element(this->begin(), this->end()));

  return min;
}

normalize()

template<typename T >

void libMesh::StatisticsVector< T >::normalize

(

)

Divides all entries by the largest entry and stores the result.

Definition at line 164 of file statistics.C.

{
  const dof_id_type n = cast_int<dof_id_type>(this->size());
  const Real max = this->maximum();

  for (dof_id_type i=0; i<n; i++)
    (*this)[i] = static_cast<T>((*this)[i] / max);
}

plot_histogram()

template<typename T >

void libMesh::StatisticsVector< T >::plot_histogram	(	const processor_id_type	my_procid,
		const std::string &	filename,
		unsigned int	n_bins
	)

Generates a Matlab/Octave style file which can be used to make a plot of the histogram having the desired number of bins. Uses the histogram(...) function in this class WARNING: The histogram(...) function is non-const, and changes the order of the vector.

Definition at line 270 of file statistics.C.

{
  // First generate the histogram with the desired number of bins
  std::vector<dof_id_type> bin_members;
  this->histogram(bin_members, n_bins);

  // The max, min and bin size are used to generate x-axis values.
  T min      = this->minimum();
  T max      = this->maximum();
  T bin_size = (max - min) / static_cast<T>(n_bins);

  // On processor 0: Write histogram to file
  if (my_procid==0)
    {
      std::ofstream out_stream (filename.c_str());

      out_stream << "clear all\n";
      out_stream << "clf\n";
      //out_stream << "x=linspace(" << min << "," << max << "," << n_bins+1 << ");\n";

      // abscissa values are located at the center of each bin.
      out_stream << "x=[";
      for (std::size_t i=0; i<bin_members.size(); ++i)
        {
          out_stream << min + (Real(i)+0.5)*bin_size << " ";
        }
      out_stream << "];\n";

      out_stream << "y=[";
      for (std::size_t i=0; i<bin_members.size(); ++i)
        {
          out_stream << bin_members[i] << " ";
        }
      out_stream << "];\n";
      out_stream << "bar(x,y);\n";
    }
}

stddev() [1/2]

template<typename T>

virtual Real libMesh::StatisticsVector< T >::stddev ( ) const

inlinevirtual

Returns

The standard deviation of the data set, which is simply the square-root of the variance.

Definition at line 154 of file statistics.h.

  { return std::sqrt(this->variance()); }

stddev() [2/2]

template<typename T>

virtual Real libMesh::StatisticsVector< T >::stddev ( const Real  known_mean ) const

inlinevirtual

Returns

Computes the standard deviation of the data set, which is simply the square-root of the variance.

This method can be used for efficiency when the mean has already been computed.

Definition at line 164 of file statistics.h.

  { return std::sqrt(this->variance(known_mean)); }

variance() [1/2]

template<typename T>

virtual Real libMesh::StatisticsVector< T >::variance ( ) const

inlinevirtual

Returns

The variance of the data set.

Uses a recurrence relation to prevent data overflow for large sums.

Note

The variance is equal to the standard deviation squared. Source: GNU Scientific Library.

Reimplemented in libMesh::ErrorVector.

Definition at line 134 of file statistics.h.

Referenced by libMesh::StatisticsVector< ErrorVectorReal >::stddev(), and libMesh::StatisticsVector< ErrorVectorReal >::variance().

  { return this->variance(this->mean()); }

variance() [2/2]

template<typename T >

Real libMesh::StatisticsVector< T >::variance ( const Real  known_mean ) const

virtual

Returns

The variance of the data set where the mean is provided.

This is useful for efficiency when you have already calculated the mean. Uses a recurrence relation to prevent data overflow for large sums.

Note

The variance is equal to the standard deviation squared. Source: GNU Scientific Library.

Reimplemented in libMesh::ErrorVector.

Definition at line 141 of file statistics.C.

{
  const dof_id_type n = cast_int<dof_id_type>(this->size());

  LOG_SCOPE ("variance()", "StatisticsVector");

  Real the_variance = 0;

  for (dof_id_type i=0; i<n; i++)
    {
      const Real delta = ( static_cast<Real>((*this)[i]) - mean_in );
      the_variance += (delta * delta - the_variance) /
        static_cast<Real>(i + 1);
    }

  if (n > 1)
    the_variance *= static_cast<Real>(n) / static_cast<Real>(n - 1);

  return the_variance;
}

---

The documentation for this class was generated from the following files:

• statistics.h
• statistics.C