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# $Id$ |
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""" |
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Test a grad, interpolate and integrate over the unit square. |
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|
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The tests are very basic. |
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|
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by Lutz Gross, ACcESS, University of Queensland, Australia, 2003. |
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""" |
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|
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import sys |
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import os |
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import unittest |
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|
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from esys.escript import * |
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from esys.linearPDEs import * |
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from esys import finley |
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|
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from math import * |
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from numarray import array |
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|
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numElements=10 |
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max_error=0. |
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max_error_text="" |
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|
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for dim in [2,3]: |
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for order in [1,2]: |
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for onFace in [True,False]: |
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|
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print "\n" |
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print "-----------------------------------------------------------------------------------------------------" |
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print "dim: %d, order: %i, onFace: %s." % (dim, order, onFace) |
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print "-----------------------------------------------------------------------------------------------------" |
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|
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if onFace: |
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onFaceText=", on elements" |
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else: |
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onFaceText="" |
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|
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case="dim=%d, order=%d%s" % (dim,order,onFaceText) |
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|
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if dim==2: |
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mydomain=finley.Rectangle(numElements,numElements,order=order,useElementsOnFace=onFace) |
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m00=[[1,0],[0,0]] |
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m01=[[0,1],[0,0]] |
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m11=[[0,0],[0,1]] |
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h=5 |
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else: |
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mydomain=finley.Brick(numElements,numElements,numElements,order=order,useElementsOnFace=onFace) |
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m00=[[1,0,0],[0,0,0]] |
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m01=[[0,1,0],[0,0,0]] |
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m11=[[0,0,0],[0,1,0]] |
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h=7 |
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|
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n=ContinuousFunction(mydomain) |
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e=Function(mydomain) |
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f=FunctionOnBoundary(mydomain) |
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d=Solution(mydomain) |
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r=ReducedSolution(mydomain) |
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|
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# |
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# test gradient |
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# |
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|
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test="error gradient in interior (nodes)" |
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|
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x=n.getX()[0:2] |
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g=grad(x**order+x[1]*[1,0]) |
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ref=order*x[0]**(order-1)*m00+m01+order*x[1]**(order-1)*m11 |
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error_norm=Lsup(ref-g) |
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|
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text="%s: %55s = %e" % (case, test, error_norm) |
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print "%s" % text |
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|
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if error_norm>max_error: |
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max_error_text=text |
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max_error=error_norm |
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|
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# |
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# test gradient on degrees of freedom |
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# |
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|
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test="error gradient in interior (degrees of freedom)" |
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|
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x=n.getX()[0:2].interpolate(d) |
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g=grad(x**order+x[1]*[1,0]) |
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ref=order*x[0]**(order-1)*m00+m01+order*x[1]**(order-1)*m11 |
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error_norm=Lsup(ref-g)/Lsup(ref) |
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|
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text="%s: %55s = %e" % (case, test, error_norm) |
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print "%s" % text |
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|
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if error_norm>max_error: |
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max_error_text=text |
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max_error=error_norm |
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|
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# |
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# test gradient on reduced degrees of freedom |
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# |
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|
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test="error gradient in interior (reduced degrees of freedom)" |
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|
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x=n.getX()[0:2].interpolate(r) |
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g=grad(x+x[1]*[1,0]) |
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ref=Scalar(1,what=r)*m00+m01+Scalar(1,what=r)*m11 |
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error_norm=Lsup(ref-g)/Lsup(ref) |
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|
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text="%s: %55s = %e" % (case, test, error_norm) |
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print "%s" % text |
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|
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if error_norm>max_error: |
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max_error_text=text |
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max_error=error_norm |
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|
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# |
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# test integration over volume |
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# |
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|
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test="error volume integration" |
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|
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x=e.getX()[0:2] |
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error=integrate(x**2+[0,2.]*x)-array([1./3.,1./3.+2*1./2.]) |
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error_norm=sqrt(numarray.innerproduct(error,error)) |
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|
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text="%s: %55s = %e" % (case, test, error_norm) |
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print "%s" % text |
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|
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if error_norm>max_error: |
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max_error_text=text |
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max_error=error_norm |
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|
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if onFace: |
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|
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# |
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# gradient on the boundary: |
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# |
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|
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test="error gradient on boundary" |
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|
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x=n.getX()[0:2] |
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g=grad(x**order+x[1]*[1,0],where=f) |
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x=f.getX()[0:2] |
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ref=order*x[0]**(order-1)*m00+m01+order*x[1]**(order-1)*m11 |
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error_norm=Lsup(g-ref) |
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|
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text="%s: %55s = %e" % (case, test, error_norm) |
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print "%s" % text |
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|
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if error_norm>max_error: |
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max_error_text=text |
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max_error=error_norm |
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|
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# |
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# test gradient on degrees of freedom |
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# |
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|
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test="error gradient on boundary (degrees of freedom)" |
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|
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x=n.getX()[0:2].interpolate(d) |
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g=grad(x**order+x[1]*[1,0],where=f) |
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x=f.getX()[0:2] |
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ref=order*x[0]**(order-1)*m00+m01+order*x[1]**(order-1)*m11 |
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error_norm=Lsup(ref-g)/Lsup(ref) |
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|
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text="%s: %55s = %e" % (case, test, error_norm) |
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print "%s" % text |
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|
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if error_norm>max_error: |
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max_error_text=text |
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max_error=error_norm |
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|
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# |
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# test gradient on reduced degrees of freedom |
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# |
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|
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test="error gradient on boundary (reduced degrees of freedom)" |
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|
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x=n.getX()[0:2].interpolate(r) |
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g=grad(x+x[1]*[1,0],where=f) |
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ref=Scalar(1,what=r)*m00+m01+Scalar(1,what=r)*m11 |
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error_norm=Lsup(ref-g)/Lsup(ref) |
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|
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text="%s: %55s = %e" % (case, test, error_norm) |
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print "%s" % text |
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|
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if error_norm>max_error: |
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max_error_text=text |
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max_error=error_norm |
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|
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# |
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# test integration over boundary |
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# |
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|
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test="error boundary integration" |
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|
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x=f.getX()[0:2] |
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error=integrate(x**2+[0,2.]*x)-array([h/3.,h/3.+2*(h-1)/2.]) |
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error_norm=sqrt(numarray.innerproduct(error,error)) |
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|
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text="%s: %55s = %e" % (case, test, error_norm) |
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print "%s" % text |
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|
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if error_norm>max_error: |
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max_error_text=text |
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max_error=error_norm |
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|
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# |
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# normal test: |
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# |
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|
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test="error normals" |
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|
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refNormal=Vector(0,what=f) |
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if dim==3: |
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refNormal.setTaggedValue(2,[1,0,0]) |
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refNormal.setTaggedValue(1,[-1,0,0]) |
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refNormal.setTaggedValue(20,[0,1,0]) |
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refNormal.setTaggedValue(10,[0,-1,0]) |
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refNormal.setTaggedValue(200,[0,0,1]) |
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refNormal.setTaggedValue(100,[0,0,-1]) |
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else: |
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refNormal.setTaggedValue(2,[1,0]) |
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refNormal.setTaggedValue(1,[-1,0]) |
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refNormal.setTaggedValue(20,[0,1]) |
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refNormal.setTaggedValue(10,[0,-1]) |
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error_norm=Lsup(f.getNormal()-refNormal) |
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|
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text="%s: %55s = %e" % (case, test, error_norm) |
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print "%s" % text |
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|
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if error_norm>max_error: |
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max_error_text=text |
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max_error=error_norm |
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|
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print "-----------------------------------------------------------------------------------------------------" |
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|
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print "\n\n" |
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print "******************************************************************************************************************" |
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print "maximal error:", max_error_text |
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print "******************************************************************************************************************" |
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