rf901_numintconfig

Numeric algorithm tuning: configuration and customization of how numeric (partial) integrals are executed

Author: Wouter Verkerke
This notebook tutorial was automatically generated with ROOTBOOK-izer from the macro found in the ROOT repository on Wednesday, November 30, 2022 at 11:24 AM.

In [1]:
%%cpp -d
#include "RooRealVar.h"
#include "RooDataSet.h"
#include "RooGaussian.h"
#include "RooConstVar.h"
#include "TCanvas.h"
#include "TAxis.h"
#include "RooPlot.h"
#include "RooNumIntConfig.h"
#include "RooLandau.h"
#include "RooArgSet.h"
#include <iomanip>
using namespace RooFit;

Adjust global 1D integration precision

Print current global default configuration for numeric integration strategies

In [2]:
RooAbsReal::defaultIntegratorConfig()->Print("v");
Requested precision: 1e-07 absolute, 1e-07 relative

1-D integration method: RooIntegrator1D (RooImproperIntegrator1D if open-ended)
2-D integration method: RooAdaptiveIntegratorND (N/A if open-ended)
N-D integration method: RooAdaptiveIntegratorND (N/A if open-ended)

Available integration methods:

*** RooBinIntegrator ***
Capabilities: [1-D] [2-D] [N-D] 
Configuration: 
  1)  numBins = 100

*** RooIntegrator1D ***
Capabilities: [1-D] 
Configuration: 
  1)        sumRule = Trapezoid(idx = 0)

  2)  extrapolation = Wynn-Epsilon(idx = 1)

  3)       maxSteps = 20
  4)       minSteps = 999
  5)       fixSteps = 0

*** RooIntegrator2D ***
Capabilities: [2-D] 
Configuration: 
(Depends on 'RooIntegrator1D')

*** RooSegmentedIntegrator1D ***
Capabilities: [1-D] 
Configuration: 
  1)  numSeg = 3
(Depends on 'RooIntegrator1D')

*** RooSegmentedIntegrator2D ***
Capabilities: [2-D] 
Configuration: 
(Depends on 'RooSegmentedIntegrator1D')

*** RooImproperIntegrator1D ***
Capabilities: [1-D] [OpenEnded] 
Configuration: 
(Depends on 'RooIntegrator1D')

*** RooMCIntegrator ***
Capabilities: [1-D] [2-D] [N-D] 
Configuration: 
  1)   samplingMode = Importance(idx = 0)

  2)        genType = QuasiRandom(idx = 0)

  3)        verbose = false(idx = 0)

  4)          alpha = 1.5
  5)    nRefineIter = 5
  6)  nRefinePerDim = 1000
  7)     nIntPerDim = 5000

*** RooAdaptiveIntegratorND ***
Capabilities: [2-D] [N-D] 
Configuration: 
  1)  maxEval2D = 100000
  2)  maxEval3D = 1e+06
  3)  maxEvalND = 1e+07
  4)    maxWarn = 5

*** RooAdaptiveGaussKronrodIntegrator1D ***
Capabilities: [1-D] [OpenEnded] 
Configuration: 
  1)  maxSeg = 100
  2)  method = 21Points(idx = 2)


*** RooGaussKronrodIntegrator1D ***
Capabilities: [1-D] [OpenEnded] 
Configuration: 

Example: Change global precision for 1D integrals from 1e-7 to 1e-6

The relative epsilon (change as fraction of current best integral estimate) and absolute epsilon (absolute change w.r.t last best integral estimate) can be specified separately. For most pdf integrals the relative change criterium is the most important, however for certain non-pdf functions that integrate out to zero a separate absolute change criterium is necessary to declare convergence of the integral

NB: This change is for illustration only. In general the precision should be at least 1e-7 for normalization integrals for MINUIT to succeed.

In [3]:
RooAbsReal::defaultIntegratorConfig()->setEpsAbs(1e-6);
RooAbsReal::defaultIntegratorConfig()->setEpsRel(1e-6);

Numeric integration of landau pdf

Construct pdf without support for analytical integrator for demonstration purposes

In [4]:
RooRealVar x("x", "x", -10, 10);
RooLandau landau("landau", "landau", x, RooConst(0), RooConst(0.1));

Activate debug-level messages for topic integration to be able to follow actions below

In [5]:
RooMsgService::instance().addStream(DEBUG, Topic(Integration));

Calculate integral over landau with default choice of numeric integrator

In [6]:
RooAbsReal *intLandau = landau.createIntegral(x);
double val = intLandau->getVal();
cout << " [1] int_dx landau(x) = " << setprecision(15) << val << endl;
[#3] INFO:Integration -- RooRealIntegral::ctor(landau_Int[x]) Constructing integral of function landau over observables(x) with normalization () with range identifier <none>
[#3] DEBUG:Integration -- landau: Adding observable x as shape dependent
[#3] DEBUG:Integration -- landau: Adding parameter 0 as value dependent
[#3] DEBUG:Integration -- landau: Adding parameter 0.1 as value dependent
[#3] INFO:Integration -- landau: Observable x is suitable for analytical integration (if supported by p.d.f)
[#3] INFO:Integration -- landau: Observables (x) are numerically integrated
[#1] INFO:NumericIntegration -- RooRealIntegral::init(landau_Int[x]) using numeric integrator RooIntegrator1D to calculate Int(x)
 [1] int_dx landau(x) = 0.0989653362054419

Same with custom configuration

Construct a custom configuration which uses the adaptive Gauss-Kronrod technique for closed 1D integrals

In [7]:
RooNumIntConfig customConfig(*RooAbsReal::defaultIntegratorConfig());
#ifdef R__HAS_MATHMORE
customConfig.method1D().setLabel("RooAdaptiveGaussKronrodIntegrator1D");
#else
Warning("rf901_numintconfig","ROOT is built without Mathmore (GSL) support. Cannot use RooAdaptiveGaussKronrodIntegrator1D");
#endif
Unbalanced braces. This cell was not processed.

Calculate integral over landau with custom integral specification

In [8]:
RooAbsReal *intLandau2 = landau.createIntegral(x, NumIntConfig(customConfig));
double val2 = intLandau2->getVal();
cout << " [2] int_dx landau(x) = " << val2 << endl;
input_line_57:2:109: error: use of undeclared identifier 'customConfig'
 (((*(class RooLandau*)0x7fbb340f5438)).createIntegral(((*(class RooRealVar*)0x7fbb340f5050)), NumIntConfig(customConfig)))
                                                                                                            ^
Error in <HandleInterpreterException>: Error evaluating expression (((*(class RooLandau*)0x7fbb340f5438)).createIntegral(((*(class RooRealVar*)0x7fbb340f5050)), NumIntConfig(customConfig)))
Execution of your code was aborted.

Adjusting default config for a specific pdf

Another possibility: associate custom numeric integration configuration as default for object 'landau'

In [9]:
landau.setIntegratorConfig(customConfig);
input_line_59:2:61: error: use of undeclared identifier 'customConfig'
 (((*(class RooLandau*)0x7fbb340f5438)).setIntegratorConfig(customConfig))
                                                            ^
Error in <HandleInterpreterException>: Error evaluating expression (((*(class RooLandau*)0x7fbb340f5438)).setIntegratorConfig(customConfig))
Execution of your code was aborted.

Calculate integral over landau custom numeric integrator specified as object default

In [10]:
RooAbsReal *intLandau3 = landau.createIntegral(x);
double val3 = intLandau3->getVal();
cout << " [3] int_dx landau(x) = " << val3 << endl;
[#3] INFO:Integration -- RooRealIntegral::ctor(landau_Int[x]) Constructing integral of function landau over observables(x) with normalization () with range identifier <none>
[#3] DEBUG:Integration -- landau: Adding observable x as shape dependent
[#3] DEBUG:Integration -- landau: Adding parameter 0 as value dependent
[#3] DEBUG:Integration -- landau: Adding parameter 0.1 as value dependent
[#3] INFO:Integration -- landau: Observable x is suitable for analytical integration (if supported by p.d.f)
[#3] INFO:Integration -- landau: Observables (x) are numerically integrated
[#1] INFO:NumericIntegration -- RooRealIntegral::init(landau_Int[x]) using numeric integrator RooIntegrator1D to calculate Int(x)
 [3] int_dx landau(x) = 0.0989653362054419

Another possibility: Change global default for 1D numeric integration strategy on finite domains

In [11]:
#ifdef R__HAS_MATHMORE
RooAbsReal::defaultIntegratorConfig()->method1D().setLabel("RooAdaptiveGaussKronrodIntegrator1D");
Unbalanced braces. This cell was not processed.

Adjusting parameters of a specific technique

Adjust maximum number of steps of RooIntegrator1D in the global default configuration

In [12]:
RooAbsReal::defaultIntegratorConfig()->getConfigSection("RooIntegrator1D").setRealValue("maxSteps", 30);

Example of how to change the parameters of a numeric integrator (Each config section is a RooArgSet with RooRealVars holding real-valued parameters and RooCategories holding parameters with a finite set of options)

In [13]:
customConfig.getConfigSection("RooAdaptiveGaussKronrodIntegrator1D").setRealValue("maxSeg", 50);
customConfig.getConfigSection("RooAdaptiveGaussKronrodIntegrator1D").setCatLabel("method", "15Points");
input_line_64:2:3: error: use of undeclared identifier 'customConfig'
 (customConfig.getConfigSection("RooAdaptiveGaussKronrodIntegrator1D").setRealValue("maxSeg", 50))
  ^
Error in <HandleInterpreterException>: Error evaluating expression (customConfig.getConfigSection("RooAdaptiveGaussKronrodIntegrator1D").setRealValue("maxSeg", 50))
Execution of your code was aborted.

Example of how to print set of possible values for "method" category

In [14]:
customConfig.getConfigSection("RooAdaptiveGaussKronrodIntegrator1D").find("method")->Print("v");
#endif
input_line_65:3:2: error: #endif without #if
#endif
 ^