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]])
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],
])
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]])
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] ])
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]])
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], ])
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]] )
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], ])
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] ])
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]])
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
]])
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], ])
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],
])
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
],
])
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], ], )
def general_linear_z(self, z):
ez = self.phi(z)[0]
one = Polynomial.exponents(z, 0)[0]
return [[0., None, one]], [[ez, ez]]
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],
],
)
def general_linear_z(self, z): ez = self.phi(z)[0] one = Polynomial.exponents(z,0)[0] return [[0., None, one]], [[ez, ez]]