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1. Further optimisation in
Ostap::Math::ChebyshedSum
1. add new test `ostap/math/tests/test_math.poly.py`
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| #!/usr/bin/env python | ||
| # -*- coding: utf-8 -*- | ||
| # ============================================================================= | ||
| # Copyright (c) Ostap developpers. | ||
| # ============================================================================= | ||
| ## @file ostap/math/tests/test_math_poly.py | ||
| # Test script for polynomial functions | ||
| # @see Ostap::Math::LegendreSum | ||
| # @see Ostap::Math::HermiteSum | ||
| # @see Ostap::Math::ChebyshevSum | ||
| # @see Ostap::Math::Bernstein | ||
| # @see Ostap::Math::Polynomial | ||
| # ============================================================================= | ||
| """ Test script for 2&3-dimnsional polynomial functions | ||
| - see Ostap::Math::LegendreSum | ||
| - see Ostap::Math::HermiteSum | ||
| - see Ostap::Math::ChebyshevSum | ||
| - see Ostap::Math::Bernstein | ||
| - see Ostap::Math::Polynomial | ||
| """ | ||
| # ============================================================================= | ||
| from ostap.core.core import Ostap, SE | ||
| from ostap.logger.colorized import attention | ||
| from ostap.utils.progress_bar import progress_bar | ||
| import ostap.math.models | ||
| import ostap.math.integral as I | ||
| import ostap.math.derivative as D | ||
| import ostap.logger.table as T | ||
| import ROOT, random, math | ||
| # ============================================================================= | ||
| # logging | ||
| # ============================================================================= | ||
| from ostap.logger.logger import getLogger | ||
| if '__main__' == __name__ : logger = getLogger ( 'ostap.test_math_poly' ) | ||
| else : logger = getLogger ( __name__ ) | ||
| # ============================================================================= | ||
|
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| xmin = 0 | ||
| xmax = 10 | ||
| N = 5 | ||
| scale = 1.e+12 | ||
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| # ============================================================================= | ||
| ## test derivative | ||
| def test_poly_derivative () : | ||
| """Test derivative | ||
| """ | ||
| logger = getLogger ( 'test_poly_derivative') | ||
|
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| poly = ( | ||
| Ostap.Math.ChebyshevSum ( N , xmin , xmax ) , | ||
| Ostap.Math.LegendreSum ( N , xmin , xmax ) , | ||
| Ostap.Math.HermiteSum ( N , xmin , xmax ) , | ||
| Ostap.Math.Bernstein ( N , xmin , xmax ) , | ||
| Ostap.Math.Polynomial ( N , xmin , xmax ) , | ||
| ) | ||
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| for p in poly : | ||
| n = p.npars() | ||
| for i in range ( n ) : p [ i ] = random.uniform ( -10 , 10 ) | ||
|
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| ders = tuple ( [ p.derivative() for p in poly ] ) | ||
|
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| cnts = [ SE() for i in poly ] | ||
|
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| dx = 0.1 * ( xmax - xmin ) | ||
| for i in progress_bar ( range ( 1000 ) ) : | ||
|
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| x = random.uniform ( xmin + dx , xmax - dx ) | ||
|
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| for i, p in enumerate ( poly ) : | ||
| d1 = p.derivative ( x ) | ||
| d2 = ders [ i ] ( x ) | ||
| d3 = D.derivative ( p , x ) | ||
|
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| dd = max ( abs ( d1 - d2 ) / ( abs ( d1 ) + abs ( d2 ) ) , | ||
| abs ( d1 - d3 ) / ( abs ( d1 ) + abs ( d3 ) ) , | ||
| abs ( d2 - d3 ) / ( abs ( d2 ) + abs ( d3 ) ) ) | ||
|
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| ## dd = abs ( d2 - d3 ) / ( abs ( d2 ) + abs ( d3 ) ) | ||
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| cnts [ i ] += 2 * dd * scale | ||
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| names = 'Chebyshev' , 'Legendre' , 'Hermite' , 'Bernstein' , 'Polynomial' | ||
|
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| rows = [ ( 'Poly' , | ||
| 'mean [%.0g]' % ( 1/scale ) , | ||
| 'rms [%.0g]' % ( 1/scale ) , | ||
| 'max [%.0g]' % ( 1/scale ) ) ] | ||
|
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| for name, cnt in zip ( names , cnts ) : | ||
|
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| row = name , \ | ||
| '%.3g' % cnt.mean () , \ | ||
| '%.3g' % cnt.rms () , \ | ||
| '%.3g' % cnt.max () | ||
|
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| rows.append ( row ) | ||
|
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| title = 'Derivatives (analytical&numerical)' | ||
| table = T.table ( rows , title = title , prefix = '# ' , alignment = 'lccc' ) | ||
| logger.info ( '%s\n%s' % ( title , table ) ) | ||
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| # ============================================================================= | ||
| ## test integrals | ||
| def test_poly_integral () : | ||
| """Test derivative | ||
| """ | ||
| logger = getLogger ( 'test_poly_integral') | ||
|
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| poly = ( | ||
| Ostap.Math.ChebyshevSum ( N , xmin , xmax ) , | ||
| Ostap.Math.LegendreSum ( N , xmin , xmax ) , | ||
| Ostap.Math.HermiteSum ( N , xmin , xmax ) , | ||
| Ostap.Math.Bernstein ( N , xmin , xmax ) , | ||
| Ostap.Math.Polynomial ( N , xmin , xmax ) , | ||
| ) | ||
|
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| for p in poly : | ||
| n = p.npars() | ||
| for i in range ( n ) : p [ i ] = random.uniform ( -10 , 10 ) | ||
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| ints = tuple ( [ p.indefinite_integral() for p in poly ] ) | ||
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| cnts = [ SE() for i in poly ] | ||
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| dx = 0.1 * ( xmax - xmin ) | ||
| for i in progress_bar ( range ( 1000 ) ) : | ||
|
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| x = random.uniform ( xmin , xmax ) | ||
| y = random.uniform ( xmin , xmax ) | ||
|
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| for i, p in enumerate ( poly ) : | ||
| d1 = p.integral ( x , y ) | ||
| d2 = ints [ i ] ( y ) - ints [ i ] ( x ) | ||
| d3 = I.integral ( p , x , y ) | ||
|
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| dd = max ( abs ( d1 - d2 ) / ( abs ( d1 ) + abs ( d2 ) ) , | ||
| abs ( d1 - d3 ) / ( abs ( d1 ) + abs ( d3 ) ) , | ||
| abs ( d2 - d3 ) / ( abs ( d2 ) + abs ( d3 ) ) ) | ||
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| ## dd = abs ( d2 - d3 ) / ( abs ( d2 ) + abs ( d3 ) ) | ||
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| cnts [ i ] += 2 * dd * scale | ||
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| names = 'Chebyshev' , 'Legendre' , 'Hermite' , 'Bernstein' , 'Polynomial' | ||
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| rows = [ ( 'Poly' , | ||
| 'mean [%.0g]' % ( 1/scale ) , | ||
| 'rms [%.0g]' % ( 1/scale ) , | ||
| 'max [%.0g]' % ( 1/scale ) ) ] | ||
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| for name, cnt in zip ( names , cnts ) : | ||
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| row = name , \ | ||
| '%.3g' % cnt.mean () , \ | ||
| '%.3g' % cnt.rms () , \ | ||
| '%.3g' % cnt.max () | ||
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| rows.append ( row ) | ||
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| title = 'Integrals (analytical&numerical)' | ||
| table = T.table ( rows , title = title , prefix = '# ' , alignment = 'lccc' ) | ||
| logger.info ( '%s\n%s' % ( title , table ) ) | ||
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| # ============================================================================= | ||
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| if '__main__' == __name__ : | ||
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| test_poly_derivative () | ||
| test_poly_integral () | ||
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| # ============================================================================= | ||
| ## The END | ||
| # ============================================================================= |
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