Esempio n. 1
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 def general_linear_z(self, z):
     ez = self.phi(z)[0]
     one, ez, e2z = Polynomial.exponents(ez, 2)
     ez2 = self.phi(z / 2)[0]
     return ([[0, None, None, one, None],
              [1., 3 / 2 * ez, None, ez,
               -1 / 2 * e2z]], [[3 / 2 * ez, None, ez, -1 / 2 * ez2],
                                [one, None, None, None]])
Esempio n. 2
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 def general_linear_z(self, z):
     ez = self.phi(z)[0]
     one, ez, e2z, e3z = Polynomial.exponents(ez, 3)
     return ([[0, None, None, one, None, None],
              [1., 23 / 12 * ez, None, ez, -4 / 3 * e3z, 5 / 12 * e3z]], [
                  [23 / 12 * ez, None, ez, -4 / 3 * e2z, 5 / 12 * e3z],
                  [one, None, None, None, None],
                  [None, None, None, one, None],
              ])
Esempio n. 3
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 def general_linear_z(self, z):
     one = Polynomial.exponents(z, 0)[0]
     ez = self.phi(z)[0]
     ez2 = self.phi(z / 2)[0]
     return ([[0, None, None, None, None, one],
              [1 / 2, 1 / 2 * ez2, None, None, None, ez2],
              [1 / 2, None, 1 / 2 * one, None, None, ez2],
              [1., None, None, ez2, None, ez]],
             [[1 / 6 * ez, 1 / 3 * ez2, 1 / 3 * ez2, 1 / 6 * one, ez]])
Esempio n. 4
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	def general_linear_z(self, z):
		ez = self.phi(z)[0]
		one, ez, e2z = Polynomial.exponents(ez,2)
		ez2 = self.phi(z/2)[0]
		return ([	[0, None, None, one, None],
					[1., 3/2*ez, None, ez, -1/2*e2z]
				],
				[	[3/2*ez, None, ez, -1/2*ez2],
					[one, None, None, None]
				])
Esempio n. 5
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	def general_linear_z(self, z):
		one = Polynomial.exponents(z,0)[0]
		ez = self.phi(z)[0]
		ez2 = self.phi(z/2)[0]
		return ([	[0, None, None, None, None, one],
					[1/2, 1/2*ez2, None, None, None, ez2],
					[1/2, None, 1/2*one, None, None, ez2],
					[1., None, None, ez2, None, ez]
				],
				[[1/6*ez, 1/3*ez2, 1/3*ez2, 1/6*one, ez]])
Esempio n. 6
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	def general_linear_z(self, z):
		ez = self.phi(z)[0]
		one, ez, e2z, e3z = Polynomial.exponents(ez,3)
		return ([	[0, None, None, one, None, None],
					[1., 23/12*ez, None, ez,  -4/3*e3z,  5/12*e3z]
				],
				[	[23/12*ez, None, ez, -4/3*e2z, 5/12*e3z],
					[one, None, None, None, None],
					[None, None, None, one, None],
				])
Esempio n. 7
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	def general_linear_z(self, z):
		one = Polynomial.exponents(z,0)[0]
		ez, phi_1 = self.phi(z)
		ez2, phi_12 = self.phi(z/2)
		return ([	[0, None, None, None, None, one],
					[1/2, 1/2*phi_12, None, None, None, ez2],
					[1/2, 1/8*np.dot(z, phi_12), 1/2*np.dot(phi_12,one-1/4*z), None, None, ez2],
					[1, None, None, phi_1, None, ez]
				],
				[[1/6*np.dot(phi_1,one+1/2*z), 1/3*phi_1, 1/3*phi_1, 1/6*np.dot(phi_1,one-1/2*z), ez]]
				)
Esempio n. 8
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	def general_linear_z(self, z):
		ez, phi_1, phi_2, phi_3, phi_4 = self.phi(z)
		one = Polynomial.exponents(z,0)[0]
		return ([	[0, None, None, one, None, None, None],
					[1., phi_1 + 11/6*phi_2 + 2*phi_3 + phi_4, None, ez,   -3*phi_2 - 5*phi_3 - 3*phi_4, 3/2*phi_2 + 4*phi_3 + 3*phi_4,   -1/3*phi_2 - phi_3 - phi_4 ]
				],
				[	[phi_1 + 11/6*phi_2 + 2*phi_3 + phi_4, None, ez, -3*phi_2 - 5*phi_3 - 3*phi_4, 3/2*phi_2 + 4*phi_3 + 3*phi_4, -1/3*phi_2 - phi_3 - phi_4],
					[one, None, None, None, None, None],
					[None, None, None, one, None, None],
					[None, None, None, None, one, None],
				])
Esempio n. 9
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	def general_linear_z(self, z):
		ez = self.phi(z)[0]
		one, ez, e2z, e3z, e4z = Polynomial.exponents(ez, 4)
		return ([	[0, None, None, one, None, None, None],
					[1, 55/24*ez, None, ez, -59/24*e2z, 37/24*e3z, -3/8*e4z]
				],
				[	[55/24*ez, None, ez, -59/24*e2z, 37/24*e3z, -3/8*e4z],
					[one, None, None, None, None, None],
					[None, None, None, one, None, None],
					[None, None, None, None, one, None]
				])
Esempio n. 10
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 def general_linear_z(self, z):
     ez = self.phi(z)[0]
     one, ez, e2z, e3z, e4z = Polynomial.exponents(ez, 4)
     return ([[0, None, None, one, None, None, None],
              [
                  1, 55 / 24 * ez, None, ez, -59 / 24 * e2z, 37 / 24 * e3z,
                  -3 / 8 * e4z
              ]], [[
                  55 / 24 * ez, None, ez, -59 / 24 * e2z, 37 / 24 * e3z,
                  -3 / 8 * e4z
              ], [one, None, None, None, None, None],
                   [None, None, None, one, None, None],
                   [None, None, None, None, one, None]])
Esempio n. 11
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 def general_linear_z(self, z):
     one = Polynomial.exponents(z, 0)[0]
     ez, phi_1 = self.phi(z)
     ez2, phi_12 = self.phi(z / 2)
     return ([[0, None, None, None, None, one],
              [1 / 2, 1 / 2 * phi_12, None, None, None, ez2],
              [
                  1 / 2, 1 / 8 * np.dot(z, phi_12),
                  1 / 2 * np.dot(phi_12, one - 1 / 4 * z), None, None, ez2
              ], [1, None, None, phi_1, None, ez]], [[
                  1 / 6 * np.dot(phi_1, one + 1 / 2 * z), 1 / 3 * phi_1,
                  1 / 3 * phi_1, 1 / 6 * np.dot(phi_1, one - 1 / 2 * z), ez
              ]])
Esempio n. 12
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	def general_linear_z(self, z):
		one = Polynomial.exponents(z,0)[0]
		ez, phi_1, phi_2, phi_3 = self.phi(z)
		ez2, phi_12, phi_22, phi_32 = self.phi(z/2)
		a_52 = 1/2*phi_22 - phi_3 + 1/4*phi_2 - 1/2*phi_32
		a_54 = 1/4*phi_22 - a_52
		return ([	[0, None, None, None, None, None, one],
					[1/2, 1/2*phi_12, None, None, None, None, ez2],
					[1/2, 1/2*phi_12 - phi_22, phi_22, None, None, None, ez2],
					[1, phi_1-2*phi_2, phi_2, phi_2, None, None, ez],
					[1/2, 1/2*phi_12 - 2*a_52 - a_54, a_52, a_52, a_54, None, ez2]
				],
				[	[phi_1 - 3*phi_2 + 4*phi_3, None, None, -phi_2 + 4*phi_3, 4*phi_2 - 8*phi_3, ez],
				])
Esempio n. 13
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 def general_linear_z(self, z):
     ez, phi_1, phi_2, phi_3, phi_4 = self.phi(z)
     one = Polynomial.exponents(z, 0)[0]
     return ([[0, None, None, one, None, None, None],
              [
                  1., phi_1 + 11 / 6 * phi_2 + 2 * phi_3 + phi_4, None, ez,
                  -3 * phi_2 - 5 * phi_3 - 3 * phi_4,
                  3 / 2 * phi_2 + 4 * phi_3 + 3 * phi_4,
                  -1 / 3 * phi_2 - phi_3 - phi_4
              ]], [
                  [
                      phi_1 + 11 / 6 * phi_2 + 2 * phi_3 + phi_4, None, ez,
                      -3 * phi_2 - 5 * phi_3 - 3 * phi_4,
                      3 / 2 * phi_2 + 4 * phi_3 + 3 * phi_4,
                      -1 / 3 * phi_2 - phi_3 - phi_4
                  ],
                  [one, None, None, None, None, None],
                  [None, None, None, one, None, None],
                  [None, None, None, None, one, None],
              ])
Esempio n. 14
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 def general_linear_z(self, z):
     one = Polynomial.exponents(z, 0)[0]
     ez, phi_1, phi_2, phi_3 = self.phi(z)
     ez2, phi_12, phi_22, phi_32 = self.phi(z / 2)
     a_52 = 1 / 2 * phi_22 - phi_3 + 1 / 4 * phi_2 - 1 / 2 * phi_32
     a_54 = 1 / 4 * phi_22 - a_52
     return ([[0, None, None, None, None, None, one],
              [1 / 2, 1 / 2 * phi_12, None, None, None, None, ez2],
              [
                  1 / 2, 1 / 2 * phi_12 - phi_22, phi_22, None, None, None,
                  ez2
              ], [1, phi_1 - 2 * phi_2, phi_2, phi_2, None, None, ez],
              [
                  1 / 2, 1 / 2 * phi_12 - 2 * a_52 - a_54, a_52, a_52, a_54,
                  None, ez2
              ]], [
                  [
                      phi_1 - 3 * phi_2 + 4 * phi_3, None, None,
                      -phi_2 + 4 * phi_3, 4 * phi_2 - 8 * phi_3, ez
                  ],
              ])
Esempio n. 15
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	def general_linear_z(self, z):
		one = Polynomial.exponents(z,0)[0]
		ez, phi_1, phi_2, phi_3, phi_4, phi_5 = self.phi(z)
		ez2, phi_12, phi_22, phi_32, phi_42, phi_52 = self.phi(z/2)
		return ([	[0,None,None,None,None,
						one,None,None,None,None],
					[1/2,1/2*phi_12 + 25/48*phi_22 + 35/96*phi_32 + 5/32*phi_42 + 1/32*phi_52, None,None,None,
						ez2, -phi_22 - 13/12*phi_32 - 9/16*phi_42 - 1/8*phi_52, 3/4*phi_22 + 19/16*phi_32 + 3/4*phi_42 + 3/16*phi_52, -1/3*phi_22 - 7/12*phi_32 - 7/16*phi_42 - 1/8*phi_52, 1/16*phi_22 + 11/96*phi_32 + 3/32*phi_42 + 1/32*phi_52,],
					[1/2,1/2*phi_12 + 25/48*phi_22 + 35/96*phi_32 + 5/32*phi_42 + 1/32*phi_52 - 315/256*one, 1/2*one,None,None,
						ez2, -phi_22 - 13/12*phi_32 - 9/16*phi_42 - 1/8*phi_52 + 105/64*one, 3/4*phi_22 + 19/16*phi_32 + 3/4*phi_42 + 3/16*phi_52 - 189/128*one,   -1/3*phi_22 - 7/12*phi_32 - 7/16*phi_42 - 1/8*phi_52 + 45/64*one,       1/16*phi_22 + 11/96*phi_32 + 3/32*phi_42 + 1/32*phi_52 - 35/256*one],
					[1.,phi_1 + 25/12*phi_2 + 35/12*phi_3 + 5/2*phi_4 + phi_5 - 315/128*ez2, None,
						ez2, None,  ez, -4*phi_2 - 26/3*phi_3 - 9*phi_4 - 4*phi_5 + 105/32*ez2,  3*phi_2 + 19/2*phi_3 + 12*phi_4 + 6*phi_5 - 189/64*ez2,      -4/3*phi_2 - 14/3*phi_3 - 7*phi_4 - 4*phi_5 + 45/32*ez2,       1/4*phi_2 + 11/12*phi_3 + 3/2*phi_4 + phi_5 - 35/128*ez2],],
				[	[phi_1 + 25/12*phi_2 + 35/12*phi_3 + 5/2*phi_4 + phi_5 - 5/6*one - 105/64*ez2, 1/3*ez2, 1/3*ez2, 1/6*one,
							ez,  -4*phi_2 - 26/3*phi_3 - 9*phi_4 - 4*phi_5 + 5/3*one + 35/16*ez2, 3*phi_2 + 19/2*phi_3 + 12*phi_4 + 6*phi_5 - 5/3*one - 63/32*ez2, -4/3*phi_2 - 14/3*phi_3 - 7*phi_4 - 4*phi_5 + 5/6*one + 15/16*ez2, 1/4*phi_2 + 11/12*phi_3 + 3/2*phi_4 + phi_5 - 1/6*one - 35/192*ez2],
					[one, None,None,None,None,
						None,None,None,None,],
					[None,None,None,None,
						None,one,None,None,None],
					[None,None,None,None,
						None,None,one,None,None],
					[None,None,None,None,
						None,None,None,one,None],
				],
				)
Esempio n. 16
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 def general_linear_z(self, z):
     ez = self.phi(z)[0]
     one = Polynomial.exponents(z, 0)[0]
     return [[0., None, one]], [[ez, ez]]
Esempio n. 17
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 def general_linear_z(self, z):
     one = Polynomial.exponents(z, 0)[0]
     ez, phi_1, phi_2, phi_3, phi_4, phi_5 = self.phi(z)
     ez2, phi_12, phi_22, phi_32, phi_42, phi_52 = self.phi(z / 2)
     return (
         [
             [0, None, None, None, None, one, None, None, None, None],
             [
                 1 / 2,
                 1 / 2 * phi_12 + 25 / 48 * phi_22 + 35 / 96 * phi_32 +
                 5 / 32 * phi_42 + 1 / 32 * phi_52,
                 None,
                 None,
                 None,
                 ez2,
                 -phi_22 - 13 / 12 * phi_32 - 9 / 16 * phi_42 -
                 1 / 8 * phi_52,
                 3 / 4 * phi_22 + 19 / 16 * phi_32 + 3 / 4 * phi_42 +
                 3 / 16 * phi_52,
                 -1 / 3 * phi_22 - 7 / 12 * phi_32 - 7 / 16 * phi_42 -
                 1 / 8 * phi_52,
                 1 / 16 * phi_22 + 11 / 96 * phi_32 + 3 / 32 * phi_42 +
                 1 / 32 * phi_52,
             ],
             [
                 1 / 2,
                 1 / 2 * phi_12 + 25 / 48 * phi_22 + 35 / 96 * phi_32 +
                 5 / 32 * phi_42 + 1 / 32 * phi_52 - 315 / 256 * one,
                 1 / 2 * one, None, None, ez2, -phi_22 - 13 / 12 * phi_32 -
                 9 / 16 * phi_42 - 1 / 8 * phi_52 + 105 / 64 * one,
                 3 / 4 * phi_22 + 19 / 16 * phi_32 + 3 / 4 * phi_42 +
                 3 / 16 * phi_52 - 189 / 128 * one, -1 / 3 * phi_22 -
                 7 / 12 * phi_32 - 7 / 16 * phi_42 - 1 / 8 * phi_52 +
                 45 / 64 * one, 1 / 16 * phi_22 + 11 / 96 * phi_32 +
                 3 / 32 * phi_42 + 1 / 32 * phi_52 - 35 / 256 * one
             ],
             [
                 1., phi_1 + 25 / 12 * phi_2 + 35 / 12 * phi_3 +
                 5 / 2 * phi_4 + phi_5 - 315 / 128 * ez2, None, ez2, None,
                 ez, -4 * phi_2 - 26 / 3 * phi_3 - 9 * phi_4 - 4 * phi_5 +
                 105 / 32 * ez2, 3 * phi_2 + 19 / 2 * phi_3 + 12 * phi_4 +
                 6 * phi_5 - 189 / 64 * ez2, -4 / 3 * phi_2 -
                 14 / 3 * phi_3 - 7 * phi_4 - 4 * phi_5 + 45 / 32 * ez2,
                 1 / 4 * phi_2 + 11 / 12 * phi_3 + 3 / 2 * phi_4 + phi_5 -
                 35 / 128 * ez2
             ],
         ],
         [
             [
                 phi_1 + 25 / 12 * phi_2 + 35 / 12 * phi_3 + 5 / 2 * phi_4 +
                 phi_5 - 5 / 6 * one - 105 / 64 * ez2, 1 / 3 * ez2,
                 1 / 3 * ez2, 1 / 6 * one, ez, -4 * phi_2 - 26 / 3 * phi_3 -
                 9 * phi_4 - 4 * phi_5 + 5 / 3 * one + 35 / 16 * ez2,
                 3 * phi_2 + 19 / 2 * phi_3 + 12 * phi_4 + 6 * phi_5 -
                 5 / 3 * one - 63 / 32 * ez2,
                 -4 / 3 * phi_2 - 14 / 3 * phi_3 - 7 * phi_4 - 4 * phi_5 +
                 5 / 6 * one + 15 / 16 * ez2,
                 1 / 4 * phi_2 + 11 / 12 * phi_3 + 3 / 2 * phi_4 + phi_5 -
                 1 / 6 * one - 35 / 192 * ez2
             ],
             [
                 one,
                 None,
                 None,
                 None,
                 None,
                 None,
                 None,
                 None,
                 None,
             ],
             [None, None, None, None, None, one, None, None, None],
             [None, None, None, None, None, None, one, None, None],
             [None, None, None, None, None, None, None, one, None],
         ],
     )
Esempio n. 18
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	def general_linear_z(self, z):
		ez = self.phi(z)[0]
		one = Polynomial.exponents(z,0)[0]
		return [[0., None, one]], [[ez, ez]]