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quadrature.py
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quadrature.py
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def gauss_legendre(k):
'''
tabulation of gauss legendre quadrature rules on [0,1]
solely for the purpose of making the 1d example standalone
'''
return __points[k],__weights[k]
__points = {}
__weights = {}
__points[1] = [0.50000000000000000]
__weights[1] = [ 1.00000000000000000]
__points[2] = [0.78867513459481287, 0.21132486540518713]
__weights[2] = [ 0.50000000000000011, 0.50000000000000011]
__points[3] = [0.88729833462074170, 0.50000000000000000, 0.11270166537925830]
__weights[3] = [ 0.27777777777777751, 0.44444444444444442, 0.27777777777777751]
__points[4] = [0.93056815579702623, 0.66999052179242813, 0.33000947820757187, 0.06943184420297371]
__weights[4] = [ 0.17392742256872701, 0.32607257743127305, 0.32607257743127305, 0.17392742256872701]
__points[5] = [0.95308992296933193, 0.76923465505284150, 0.50000000000000000, 0.23076534494715845, 0.04691007703066802]
__weights[5] = [ 0.11846344252809465, 0.23931433524968321, 0.28444444444444444, 0.23931433524968321, 0.11846344252809465]
__points[6] = [0.96623475710157603, 0.83060469323313224, 0.61930959304159849, 0.38069040695840156, 0.16939530676686776, 0.03376524289842397]
__weights[6] = [ 0.08566224618958508, 0.18038078652406936, 0.23395696728634546, 0.23395696728634546, 0.18038078652406936, 0.08566224618958508]
__points[7] = [0.97455395617137930, 0.87076559279969723, 0.70292257568869854, 0.50000000000000000, 0.29707742431130141, 0.12923440720030277, 0.02544604382862070]
__weights[7] = [ 0.06474248308443417, 0.13985269574463832, 0.19091502525255946, 0.20897959183673470, 0.19091502525255946, 0.13985269574463832, 0.06474248308443417]
__points[8] = [0.98014492824876809, 0.89833323870681336, 0.76276620495816450, 0.59171732124782495, 0.40828267875217511, 0.23723379504183550, 0.10166676129318664, 0.01985507175123191]
__weights[8] = [ 0.05061426814518921, 0.11119051722668717, 0.15685332293894369, 0.18134189168918102, 0.18134189168918102, 0.15685332293894369, 0.11119051722668717, 0.05061426814518921]
__points[9] = [0.98408011975381304, 0.91801555366331788, 0.80668571635029518, 0.66212671170190451, 0.50000000000000000, 0.33787328829809554, 0.19331428364970482, 0.08198444633668206, 0.01591988024618696]
__weights[9] = [ 0.04063719418078738, 0.09032408034742866, 0.13030534820146775, 0.15617353852000135, 0.16511967750062989, 0.15617353852000135, 0.13030534820146775, 0.09032408034742841, 0.04063719418078738]
__points[10] = [0.98695326425858587, 0.93253168334449232, 0.83970478414951222, 0.71669769706462361, 0.57443716949081558, 0.42556283050918442, 0.28330230293537639, 0.16029521585048778, 0.06746831665550773, 0.01304673574141413]
__weights[10] = [ 0.03333567215434403, 0.07472567457529021, 0.10954318125799088, 0.13463335965499817, 0.14776211235737641, 0.14776211235737641, 0.13463335965499817, 0.10954318125799088, 0.07472567457529021, 0.03333567215434403]
__points[11] = x = [0.98911432907302843, 0.94353129988404771, 0.86507600278702468, 0.75954806460340585, 0.63477157797617245, 0.50000000000000000, 0.36522842202382755, 0.24045193539659410, 0.13492399721297532, 0.05646870011595234, 0.01088567092697151]
__weights[11] = w = [ 0.02783428355808731, 0.06279018473245226, 0.09314510546386703, 0.11659688229599521, 0.13140227225512346, 0.13646254338895031, 0.13140227225512346, 0.11659688229599521, 0.09314510546386703, 0.06279018473245226, 0.02783428355808731]