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vtkDescriptiveStatistics.cxx
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vtkDescriptiveStatistics.cxx
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/*=========================================================================
Program: Visualization Toolkit
Module: vtkDescriptiveStatistics.cxx
Copyright (c) Ken Martin, Will Schroeder, Bill Lorensen
All rights reserved.
See Copyright.txt or http://www.kitware.com/Copyright.htm for details.
This software is distributed WITHOUT ANY WARRANTY; without even
the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR
PURPOSE. See the above copyright notice for more information.
=========================================================================*/
/*-------------------------------------------------------------------------
Copyright 2011 Sandia Corporation.
Under the terms of Contract DE-AC04-94AL85000 with Sandia Corporation,
the U.S. Government retains certain rights in this software.
-------------------------------------------------------------------------*/
#include "vtkToolkits.h"
#include "vtkDescriptiveStatistics.h"
#include "vtkStatisticsAlgorithmPrivate.h"
#include "vtkDataObjectCollection.h"
#include "vtkDoubleArray.h"
#include "vtkIdTypeArray.h"
#include "vtkInformation.h"
#include "vtkMath.h"
#include "vtkMultiBlockDataSet.h"
#include "vtkObjectFactory.h"
#include "vtkStringArray.h"
#include "vtkStdString.h"
#include "vtkTable.h"
#include "vtkVariantArray.h"
#include <set>
#include <sstream>
#include <limits>
vtkObjectFactoryNewMacro(vtkDescriptiveStatistics)
// ----------------------------------------------------------------------
vtkDescriptiveStatistics::vtkDescriptiveStatistics()
{
this->AssessNames->SetNumberOfValues( 1 );
this->AssessNames->SetValue( 0, "d" ); // relative deviation, i.e., when unsigned, 1D Mahalanobis distance
this->UnbiasedVariance = 1; // By default, use unbiased estimator of the variance (divided by cardinality-1)
this->G1Skewness = 0; // By default, use g1 estimator of the skewness (G1 otherwise)
this->G2Kurtosis = 0; // By default, use g2 estimator of the kurtosis (G2 otherwise)
this->SignedDeviations = 0; // By default, use unsigned deviation (1D Mahlanobis distance)
}
// ----------------------------------------------------------------------
vtkDescriptiveStatistics::~vtkDescriptiveStatistics()
{
}
// ----------------------------------------------------------------------
void vtkDescriptiveStatistics::PrintSelf( ostream &os, vtkIndent indent )
{
this->Superclass::PrintSelf( os, indent );
os << indent << "UnbiasedVariance: " << this->UnbiasedVariance << "\n";
os << indent << "G1Skewness: " << this->G1Skewness << "\n";
os << indent << "G2Kurtosis: " << this->G2Kurtosis << "\n";
os << indent << "SignedDeviations: " << this->SignedDeviations << "\n";
}
// ----------------------------------------------------------------------
void vtkDescriptiveStatistics::Aggregate( vtkDataObjectCollection* inMetaColl,
vtkMultiBlockDataSet* outMeta )
{
if ( ! outMeta )
{
return;
}
// Get hold of the first model (data object) in the collection
vtkCollectionSimpleIterator it;
inMetaColl->InitTraversal( it );
vtkDataObject *inMetaDO = inMetaColl->GetNextDataObject( it );
// Verify that the first input model is indeed contained in a multiblock data set
vtkMultiBlockDataSet* inMeta = vtkMultiBlockDataSet::SafeDownCast( inMetaDO );
if ( ! inMeta )
{
return;
}
// Verify that the first primary statistics are indeed contained in a table
vtkTable* primaryTab = vtkTable::SafeDownCast( inMeta->GetBlock( 0 ) );
if ( ! primaryTab )
{
return;
}
vtkIdType nRow = primaryTab->GetNumberOfRows();
if ( ! nRow )
{
// No statistics were calculated.
return;
}
// Use this first model to initialize the aggregated one
vtkTable* aggregatedTab = vtkTable::New();
aggregatedTab->DeepCopy( primaryTab );
// Now, loop over all remaining models and update aggregated each time
while ( ( inMetaDO = inMetaColl->GetNextDataObject( it ) ) )
{
// Verify that the current model is indeed contained in a multiblock data set
inMeta = vtkMultiBlockDataSet::SafeDownCast( inMetaDO );
if ( ! inMeta )
{
aggregatedTab->Delete();
return;
}
// Verify that the current primary statistics are indeed contained in a table
primaryTab = vtkTable::SafeDownCast( inMeta->GetBlock( 0 ) );
if ( ! primaryTab )
{
aggregatedTab->Delete();
return;
}
if ( primaryTab->GetNumberOfRows() != nRow )
{
// Models do not match
aggregatedTab->Delete();
return;
}
// Iterate over all model rows
for ( int r = 0; r < nRow; ++ r )
{
// Verify that variable names match each other
if ( primaryTab->GetValueByName( r, "Variable" ) != aggregatedTab->GetValueByName( r, "Variable" ) )
{
// Models do not match
aggregatedTab->Delete();
return;
}
// Get aggregated statistics
int n = aggregatedTab->GetValueByName( r, "Cardinality" ).ToInt();
double min = aggregatedTab->GetValueByName( r, "Minimum" ).ToDouble();
double max = aggregatedTab->GetValueByName( r, "Maximum" ).ToDouble();
double mean = aggregatedTab->GetValueByName( r, "Mean" ).ToDouble();
double M2 = aggregatedTab->GetValueByName( r, "M2" ).ToDouble();
double M3 = aggregatedTab->GetValueByName( r, "M3" ).ToDouble();
double M4 = aggregatedTab->GetValueByName( r, "M4" ).ToDouble();
// Get current model statistics
int n_c = primaryTab->GetValueByName( r, "Cardinality" ).ToInt();
double min_c = primaryTab->GetValueByName( r, "Minimum" ).ToDouble();
double max_c = primaryTab->GetValueByName( r, "Maximum" ).ToDouble();
double mean_c = primaryTab->GetValueByName( r, "Mean" ).ToDouble();
double M2_c = primaryTab->GetValueByName( r, "M2" ).ToDouble();
double M3_c = primaryTab->GetValueByName( r, "M3" ).ToDouble();
double M4_c = primaryTab->GetValueByName( r, "M4" ).ToDouble();
// Update global statics
int N = n + n_c;
if ( min_c < min )
{
aggregatedTab->SetValueByName( r, "Minimum", min_c );
}
if ( max_c > max )
{
aggregatedTab->SetValueByName( r, "Maximum", max_c );
}
double delta = mean_c - mean;
double delta_sur_N = delta / static_cast<double>( N );
double delta2_sur_N2 = delta_sur_N * delta_sur_N;
int n2 = n * n;
int n_c2 = n_c * n_c;
int prod_n = n * n_c;
M4 += M4_c
+ prod_n * ( n2 - prod_n + n_c2 ) * delta * delta_sur_N * delta2_sur_N2
+ 6. * ( n2 * M2_c + n_c2 * M2 ) * delta2_sur_N2
+ 4. * ( n * M3_c - n_c * M3 ) * delta_sur_N;
M3 += M3_c
+ prod_n * ( n - n_c ) * delta * delta2_sur_N2
+ 3. * ( n * M2_c - n_c * M2 ) * delta_sur_N;
M2 += M2_c
+ prod_n * delta * delta_sur_N;
mean += n_c * delta_sur_N;
// Store updated model
aggregatedTab->SetValueByName( r, "Cardinality", N );
aggregatedTab->SetValueByName( r, "Mean", mean );
aggregatedTab->SetValueByName( r, "M2", M2 );
aggregatedTab->SetValueByName( r, "M3", M3 );
aggregatedTab->SetValueByName( r, "M4", M4 );
}
}
// Finally set first block of aggregated model to primary statistics table
outMeta->SetNumberOfBlocks( 1 );
outMeta->GetMetaData( static_cast<unsigned>( 0 ) )->Set( vtkCompositeDataSet::NAME(), "Primary Statistics" );
outMeta->SetBlock( 0, aggregatedTab );
// Clean up
aggregatedTab->Delete();
}
// ----------------------------------------------------------------------
void vtkDescriptiveStatistics::Learn( vtkTable* inData,
vtkTable* vtkNotUsed( inParameters ),
vtkMultiBlockDataSet* outMeta )
{
if ( ! inData )
{
return;
}
if ( ! outMeta )
{
return;
}
// The primary statistics table
vtkTable* primaryTab = vtkTable::New();
vtkStringArray* stringCol = vtkStringArray::New();
stringCol->SetName( "Variable" );
primaryTab->AddColumn( stringCol );
stringCol->Delete();
vtkIdTypeArray* idTypeCol = vtkIdTypeArray::New();
idTypeCol->SetName( "Cardinality" );
primaryTab->AddColumn( idTypeCol );
idTypeCol->Delete();
vtkDoubleArray* doubleCol = vtkDoubleArray::New();
doubleCol->SetName( "Minimum" );
primaryTab->AddColumn( doubleCol );
doubleCol->Delete();
doubleCol = vtkDoubleArray::New();
doubleCol->SetName( "Maximum" );
primaryTab->AddColumn( doubleCol );
doubleCol->Delete();
doubleCol = vtkDoubleArray::New();
doubleCol->SetName( "Mean" );
primaryTab->AddColumn( doubleCol );
doubleCol->Delete();
doubleCol = vtkDoubleArray::New();
doubleCol->SetName( "M2" );
primaryTab->AddColumn( doubleCol );
doubleCol->Delete();
doubleCol = vtkDoubleArray::New();
doubleCol->SetName( "M3" );
primaryTab->AddColumn( doubleCol );
doubleCol->Delete();
doubleCol = vtkDoubleArray::New();
doubleCol->SetName( "M4" );
primaryTab->AddColumn( doubleCol );
doubleCol->Delete();
// Loop over requests
vtkIdType nRow = inData->GetNumberOfRows();
for ( std::set<std::set<vtkStdString> >::const_iterator rit = this->Internals->Requests.begin();
rit != this->Internals->Requests.end(); ++ rit )
{
// Each request contains only one column of interest (if there are others, they are ignored)
std::set<vtkStdString>::const_iterator it = rit->begin();
vtkStdString varName = *it;
if ( ! inData->GetColumnByName( varName ) )
{
vtkWarningMacro( "InData table does not have a column "
<< varName.c_str()
<< ". Ignoring it." );
continue;
}
double minVal = inData->GetValueByName( 0, varName ).ToDouble();
double maxVal = minVal;
double mean = 0.;
double mom2 = 0.;
double mom3 = 0.;
double mom4 = 0.;
double n, inv_n, val, delta, A, B;
for ( vtkIdType r = 0; r < nRow; ++ r )
{
n = r + 1.;
inv_n = 1. / n;
val = inData->GetValueByName( r, varName ).ToDouble();
delta = val - mean;
A = delta * inv_n;
mean += A;
mom4 += A * ( A * A * delta * r * ( n * ( n - 3. ) + 3. ) + 6. * A * mom2 - 4. * mom3 );
B = val - mean;
mom3 += A * ( B * delta * ( n - 2. ) - 3. * mom2 );
mom2 += delta * B;
if ( val < minVal )
{
minVal = val;
}
else if ( val > maxVal )
{
maxVal = val;
}
}
vtkVariantArray* row = vtkVariantArray::New();
row->SetNumberOfValues( 8 );
row->SetValue( 0, varName );
row->SetValue( 1, nRow );
row->SetValue( 2, minVal );
row->SetValue( 3, maxVal );
row->SetValue( 4, mean );
row->SetValue( 5, mom2 );
row->SetValue( 6, mom3 );
row->SetValue( 7, mom4 );
primaryTab->InsertNextRow( row );
row->Delete();
} // rit
// Finally set first block of output meta port to primary statistics table
outMeta->SetNumberOfBlocks( 1 );
outMeta->GetMetaData( static_cast<unsigned>( 0 ) )->Set( vtkCompositeDataSet::NAME(), "Primary Statistics" );
outMeta->SetBlock( 0, primaryTab );
// Clean up
primaryTab->Delete();
}
// ----------------------------------------------------------------------
void vtkDescriptiveStatistics::Derive( vtkMultiBlockDataSet* inMeta )
{
if ( ! inMeta || inMeta->GetNumberOfBlocks() < 1 )
{
return;
}
vtkTable* primaryTab = vtkTable::SafeDownCast( inMeta->GetBlock( 0 ) );
if ( ! primaryTab )
{
return;
}
int numDoubles = 5;
vtkStdString doubleNames[] = { "Standard Deviation",
"Variance",
"Skewness",
"Kurtosis",
"Sum" };
// Create table for derived statistics
vtkIdType nRow = primaryTab->GetNumberOfRows();
vtkTable* derivedTab = vtkTable::New();
vtkDoubleArray* doubleCol;
for ( int j = 0; j < numDoubles; ++ j )
{
if ( ! derivedTab->GetColumnByName( doubleNames[j] ) )
{
doubleCol = vtkDoubleArray::New();
doubleCol->SetName( doubleNames[j] );
doubleCol->SetNumberOfTuples( nRow );
derivedTab->AddColumn( doubleCol );
doubleCol->Delete();
}
}
// Storage for standard deviation, variance, skewness, kurtosis, sum
double* derivedVals = new double[numDoubles];
for ( int i = 0; i < nRow; ++ i )
{
double mom2 = primaryTab->GetValueByName( i, "M2" ).ToDouble();
double mom3 = primaryTab->GetValueByName( i, "M3" ).ToDouble();
double mom4 = primaryTab->GetValueByName( i, "M4" ).ToDouble();
int numSamples = primaryTab->GetValueByName( i, "Cardinality" ).ToInt();
if ( numSamples == 1 || mom2 < 1.e-150 )
{
derivedVals[0] = 0.;
derivedVals[1] = 0.;
derivedVals[2] = 0.;
derivedVals[3] = 0.;
derivedVals[4] = 0.;
}
else
{
double n = static_cast<double>( numSamples );
double inv_n = 1. / n;
double nm1 = n - 1.;
// Variance
if ( this->UnbiasedVariance )
{
derivedVals[1] = mom2 / nm1;
}
else // use population variance
{
derivedVals[1] = mom2 * inv_n;
}
// Standard deviation
derivedVals[0] = sqrt( derivedVals[1] );
// Skeweness and kurtosis
double var_inv = nm1 / mom2;
double nvar_inv = var_inv * inv_n;
derivedVals[2] = nvar_inv * sqrt( var_inv ) * mom3;
derivedVals[3] = nvar_inv * var_inv * mom4 - 3.;
if ( this->G1Skewness && n > 2 )
{
// G1 skewness estimate
derivedVals[2] *= ( n * n ) / ( nm1 * ( nm1 - 1. ) );
}
if ( this->G2Kurtosis && n > 3 )
{
// G2 kurtosis estimate
derivedVals[3] *= ( ( n + 1. ) * derivedVals[4] + 6. ) * nm1 / ( ( nm1 - 1. ) * ( nm1 - 2. ) );
}
}
// Sum
derivedVals[4] = numSamples * primaryTab->GetValueByName( i, "Mean" ).ToDouble();
for ( int j = 0; j < numDoubles; ++ j )
{
derivedTab->SetValueByName( i, doubleNames[j], derivedVals[j] );
}
}
// Finally set second block of output meta port to derived statistics table
inMeta->SetNumberOfBlocks( 2 );
inMeta->GetMetaData( static_cast<unsigned>( 0 ) )->Set( vtkCompositeDataSet::NAME(), "Derived Statistics" );
inMeta->SetBlock( 1, derivedTab );
// Clean up
derivedTab->Delete();
delete [] derivedVals;
}
// ----------------------------------------------------------------------
// Use the invalid value of -1 for p-values if R is absent
vtkDoubleArray* vtkDescriptiveStatistics::CalculatePValues(vtkDoubleArray *statCol)
{
// A column must be created first
vtkDoubleArray* testCol = vtkDoubleArray::New();
// Fill this column
vtkIdType n = statCol->GetNumberOfTuples();
testCol->SetNumberOfTuples( n );
for ( vtkIdType r = 0; r < n; ++ r )
{
testCol->SetTuple1( r, -1 );
}
return testCol;
}
// ----------------------------------------------------------------------
void vtkDescriptiveStatistics::Test( vtkTable* inData,
vtkMultiBlockDataSet* inMeta,
vtkTable* outMeta )
{
if ( ! inMeta )
{
return;
}
vtkTable* primaryTab = vtkTable::SafeDownCast( inMeta->GetBlock( 0 ) );
if ( ! primaryTab )
{
return;
}
vtkTable* derivedTab = vtkTable::SafeDownCast( inMeta->GetBlock( 1 ) );
if ( ! derivedTab )
{
return;
}
vtkIdType nRowPrim = primaryTab->GetNumberOfRows();
if ( nRowPrim != derivedTab->GetNumberOfRows() )
{
vtkErrorMacro( "Inconsistent input: primary model has "
<< nRowPrim
<< " rows but derived model has "
<< derivedTab->GetNumberOfRows()
<<". Cannot test." );
return;
}
if ( ! outMeta )
{
return;
}
// Prepare columns for the test:
// 0: variable name
// 1: Jarque-Bera statistic
// 2: Jarque-Bera p-value (calculated only if R is available, filled with -1 otherwise)
// NB: These are not added to the output table yet, for they will be filled individually first
// in order that R be invoked only once.
vtkStringArray* nameCol = vtkStringArray::New();
nameCol->SetName( "Variable" );
vtkDoubleArray* statCol = vtkDoubleArray::New();
statCol->SetName( "Jarque-Bera" );
// Downcast columns to string arrays for efficient data access
vtkStringArray* vars = vtkArrayDownCast<vtkStringArray>( primaryTab->GetColumnByName( "Variable" ) );
// Loop over requests
for ( std::set<std::set<vtkStdString> >::const_iterator rit = this->Internals->Requests.begin();
rit != this->Internals->Requests.end(); ++ rit )
{
// Each request contains only one column of interest (if there are others, they are ignored)
std::set<vtkStdString>::const_iterator it = rit->begin();
vtkStdString varName = *it;
if ( ! inData->GetColumnByName( varName ) )
{
vtkWarningMacro( "InData table does not have a column "
<< varName.c_str()
<< ". Ignoring it." );
continue;
}
// Find the model row that corresponds to the variable of the request
vtkIdType r = 0;
while ( r < nRowPrim && vars->GetValue( r ) != varName )
{
++ r;
}
if ( r >= nRowPrim )
{
vtkWarningMacro( "Incomplete input: model does not have a row "
<< varName.c_str()
<<". Cannot test." );
continue;
}
// Retrieve model statistics necessary for Jarque-Bera testing
double n = primaryTab->GetValueByName( r, "Cardinality" ).ToDouble();
double skew = derivedTab->GetValueByName( r, "Skewness" ).ToDouble();
double kurt = derivedTab->GetValueByName( r, "Kurtosis" ).ToDouble();
// Now calculate Jarque-Bera statistic
double jb = n * ( skew * skew + .25 * kurt * kurt ) / 6.;
// Insert variable name and calculated Jarque-Bera statistic
// NB: R will be invoked only once at the end for efficiency
nameCol->InsertNextValue( varName );
statCol->InsertNextTuple1( jb );
} // rit
// Now, add the already prepared columns to the output table
outMeta->AddColumn( nameCol );
outMeta->AddColumn( statCol );
// Last phase: compute the p-values or assign invalid value if they cannot be computed
// If available, use R to obtain the p-values for the Chi square distribution with 2 DOFs
vtkDoubleArray* testCol = this->CalculatePValues( statCol );
// The test column name can only be set after the column has been obtained from R
testCol->SetName( "P" );
// Now add the column of invalid values to the output table
outMeta->AddColumn( testCol );
testCol->Delete();
// Clean up
nameCol->Delete();
statCol->Delete();
}
// ----------------------------------------------------------------------
class TableColumnDeviantFunctor : public vtkStatisticsAlgorithm::AssessFunctor
{
public:
vtkDataArray* Data;
double Nominal;
double Deviation;
};
// When the deviation is 0, we can't normalize. Instead, a non-zero value (1)
// is returned only when the nominal value is matched exactly.
class ZedDeviationDeviantFunctor : public TableColumnDeviantFunctor
{
public:
ZedDeviationDeviantFunctor( vtkDataArray* vals,
double nominal )
{
this->Data = vals;
this->Nominal = nominal;
}
~ZedDeviationDeviantFunctor() VTK_OVERRIDE { }
void operator() ( vtkDoubleArray* result,
vtkIdType id ) VTK_OVERRIDE
{
result->SetNumberOfValues( 1 );
result->SetValue( 0, ( this->Data->GetTuple1( id ) == this->Nominal ) ? 0. : 1. );
}
};
class SignedTableColumnDeviantFunctor : public TableColumnDeviantFunctor
{
public:
SignedTableColumnDeviantFunctor( vtkDataArray* vals,
double nominal,
double deviation )
{
this->Data = vals;
this->Nominal = nominal;
this->Deviation = deviation;
}
~SignedTableColumnDeviantFunctor() VTK_OVERRIDE { }
void operator() ( vtkDoubleArray* result,
vtkIdType id ) VTK_OVERRIDE
{
result->SetNumberOfValues( 1 );
result->SetValue( 0, ( this->Data->GetTuple1( id ) - this->Nominal ) / this->Deviation );
}
};
class UnsignedTableColumnDeviantFunctor : public TableColumnDeviantFunctor
{
public:
UnsignedTableColumnDeviantFunctor( vtkDataArray* vals,
double nominal,
double deviation )
{
this->Data = vals;
this->Nominal = nominal;
this->Deviation = deviation;
}
~UnsignedTableColumnDeviantFunctor() VTK_OVERRIDE { }
void operator() ( vtkDoubleArray* result,
vtkIdType id ) VTK_OVERRIDE
{
result->SetNumberOfValues( 1 );
result->SetValue( 0, fabs ( this->Data->GetTuple1( id ) - this->Nominal ) / this->Deviation );
}
};
// ----------------------------------------------------------------------
void vtkDescriptiveStatistics::SelectAssessFunctor( vtkTable* outData,
vtkDataObject* inMetaDO,
vtkStringArray* rowNames,
AssessFunctor*& dfunc )
{
dfunc = 0;
vtkMultiBlockDataSet* inMeta = vtkMultiBlockDataSet::SafeDownCast( inMetaDO );
if ( ! inMeta )
{
return;
}
vtkTable* primaryTab= vtkTable::SafeDownCast( inMeta->GetBlock( 0 ) );
if ( ! primaryTab )
{
return;
}
vtkTable* derivedTab = vtkTable::SafeDownCast( inMeta->GetBlock( 1 ) );
if ( ! derivedTab )
{
return;
}
vtkIdType nRowPrim = primaryTab->GetNumberOfRows();
if ( nRowPrim != derivedTab->GetNumberOfRows() )
{
return;
}
vtkStdString varName = rowNames->GetValue( 0 );
// Downcast meta columns to string arrays for efficient data access
vtkStringArray* vars = vtkArrayDownCast<vtkStringArray>( primaryTab->GetColumnByName( "Variable" ) );
if ( ! vars )
{
return;
}
// Loop over primary statistics table until the requested variable is found
for ( int r = 0; r < nRowPrim; ++ r )
{
if ( vars->GetValue( r ) == varName )
{
// Grab the data for the requested variable
vtkAbstractArray* arr = outData->GetColumnByName( varName );
if ( ! arr )
{
return;
}
// For descriptive statistics, type must be convertible to DataArray
// E.g., StringArrays do not fit here
vtkDataArray* vals = vtkArrayDownCast<vtkDataArray>( arr );
if ( ! vals )
{
return;
}
// Fetch necessary value from primary model
double mean = primaryTab->GetValueByName( r, "Mean" ).ToDouble();
// Fetch necessary value from derived model
double stdv = derivedTab->GetValueByName( r, "Standard Deviation" ).ToDouble();
// NB: If derived values were specified (and not calculated by Derive)
// and are inconsistent, then incorrect assessments will be produced
if ( stdv < VTK_DBL_MIN )
{
dfunc = new ZedDeviationDeviantFunctor( vals, mean );
}
else
{
if ( this->GetSignedDeviations() )
{
dfunc = new SignedTableColumnDeviantFunctor( vals, mean, stdv );
}
else
{
dfunc = new UnsignedTableColumnDeviantFunctor( vals, mean, stdv );
}
}
return;
}
}
// If arrived here it means that the variable of interest was not found in the parameter table
}