def bssn_puncture_gauge(eta_damp, isStaged=False, prefix=""):
if (not isStaged):
C1 = dendro.get_first_christoffel()
C2 = dendro.get_second_christoffel()
C2_spatial = dendro.get_complete_christoffel(chi)
[R, Rt, Rphi, CalGt] = dendro.compute_ricci(Gt, chi)
a_rhs = l1 * dendro.lie(b, a) - 2 * a * K
b_rhs = [(Rational(3, 4) * (lf0 + lf1 * a) * B[i] +
l2 * dendro.vec_j_ad_j(b, b[i])) for i in dendro.e_i]
gt_rhs = dendro.lie(b, gt, weight) - 2 * a * At
chi_rhs = dendro.lie(b, chi, weight) + Rational(2, 3) * (chi * a * K)
AikAkj = Matrix([
sum([
At[i, k] *
sum([dendro.inv_metric[k, l] * At[l, j] for l in dendro.e_i])
for k in dendro.e_i
]) for i, j in dendro.e_ij
])
At_rhs = dendro.lie(b, At, weight) + chi * dendro.trace_free(
a * R - dendro.DiDj(a)) + a * (K * At - 2 * AikAkj.reshape(3, 3))
K_rhs = dendro.lie(b, K) - dendro.laplacian(
a, chi) + a * (K * K / 3 + dendro.sqr(At))
At_UU = dendro.up_up(At)
Gt_rhs = Matrix([sum(b[j]*ad(j,Gt[i]) for j in dendro.e_i) for i in dendro.e_i]) - \
Matrix([sum(CalGt[j]*d(j,b[i]) for j in dendro.e_i) for i in dendro.e_i]) + \
Rational(2,3)*Matrix([ CalGt[i] * sum(d(j,b[j]) for j in dendro.e_i) for i in dendro.e_i ]) + \
Matrix([sum([igt[j, k] * d2(j, k, b[i]) + igt[i, j] * d2(j, k, b[k])/3 for j, k in dendro.e_ij]) for i in dendro.e_i]) - \
Matrix([sum([2*At_UU[i, j]*d(j, a) for j in dendro.e_i]) for i in dendro.e_i]) + \
Matrix([sum([2*a*dendro.C2[i, j, k]*At_UU[j, k] for j,k in dendro.e_ij]) for i in dendro.e_i]) - \
Matrix([sum([a*(3/chi*At_UU[i,j]*d(j, chi) + Rational(4,3)*dendro.inv_metric[i, j]*d(j, K)) for j in dendro.e_i]) for i in dendro.e_i])
Gt_rhs = [item for sublist in Gt_rhs.tolist() for item in sublist]
B_rhs = [
(Gt_rhs[i] - eta_damp * B[i] + l3 * dendro.vec_j_ad_j(b, B[i]) -
l4 * dendro.vec_j_ad_j(b, Gt[i])) for i in dendro.e_i
]
###################################################################
# generate code
###################################################################
outs = [a_rhs, b_rhs, gt_rhs, chi_rhs, At_rhs, K_rhs, Gt_rhs, B_rhs]
vnames = [
'a_rhs', 'b_rhs', 'gt_rhs', 'chi_rhs', 'At_rhs', 'K_rhs', 'Gt_rhs',
'B_rhs'
]
dendro.generate_cpu(outs, vnames, '[pp]')
else:
# note: these are just the symbolic vars that is being used to generate the
# Gt_rhs by satges
_Gt_rhs_s1 = dendro.vec3("Gt_rhs_s1_", "[pp]")
_Gt_rhs_s2 = dendro.vec3("Gt_rhs_s2_", "[pp]")
_Gt_rhs_s3 = dendro.vec3("Gt_rhs_s3_", "[pp]")
_Gt_rhs_s4 = dendro.vec3("Gt_rhs_s4_", "[pp]")
_Gt_rhs_s5 = dendro.vec3("Gt_rhs_s5_", "[pp]")
_Gt_rhs_s6 = dendro.vec3("Gt_rhs_s6_", "[pp]")
_Gt_rhs_s7 = dendro.vec3("Gt_rhs_s7_", "[pp]")
_CalGt = dendro.vec3("CalGt", "[pp]")
_Gt_rhs = dendro.vec3("Gt_rhs", "[pp]")
# Gt_rhs staged vars that is being used to generate the code.
At_UU = dendro.sym_3x3("At_UU", "[pp]")
CalGt = dendro.vec3("CalGt", "[pp]")
Gt_rhs_s1 = dendro.vec3("Gt_rhs_s1_", "[pp]")
Gt_rhs_s2 = dendro.vec3("Gt_rhs_s2_", "[pp]")
Gt_rhs_s3 = dendro.vec3("Gt_rhs_s3_", "[pp]")
Gt_rhs_s4 = dendro.vec3("Gt_rhs_s4_", "[pp]")
Gt_rhs_s5 = dendro.vec3("Gt_rhs_s5_", "[pp]")
Gt_rhs_s6 = dendro.vec3("Gt_rhs_s6_", "[pp]")
Gt_rhs_s7 = dendro.vec3("Gt_rhs_s7_", "[pp]")
C1 = dendro.get_first_christoffel()
C2 = dendro.get_second_christoffel()
C2_spatial = dendro.get_complete_christoffel(chi)
[R, Rt, Rphi, CalGt] = dendro.compute_ricci(Gt, chi)
a_rhs = l1 * dendro.lie(b, a) - 2 * a * K
b_rhs = [(Rational(3, 4) * (lf0 + lf1 * a) * B[i] +
l2 * dendro.vec_j_ad_j(b, b[i])) for i in dendro.e_i]
gt_rhs = dendro.lie(b, gt, weight) - 2 * a * At
chi_rhs = dendro.lie(b, chi, weight) + Rational(2, 3) * (chi * a * K)
AikAkj = Matrix([
sum([
At[i, k] *
sum([dendro.inv_metric[k, l] * At[l, j] for l in dendro.e_i])
for k in dendro.e_i
]) for i, j in dendro.e_ij
])
At_rhs = dendro.lie(b, At, weight) + chi * dendro.trace_free(
a * R - dendro.DiDj(a)) + a * (K * At - 2 * AikAkj.reshape(3, 3))
K_rhs = dendro.lie(b, K) - dendro.laplacian(
a, chi) + a * (K * K / 3 + dendro.sqr(At))
At_UU = dendro.up_up(At)
Gt_rhs_s1 = ([
sum(b[j] * ad(j, Gt[i]) for j in dendro.e_i) for i in dendro.e_i
])
Gt_rhs_s2 = ([
sum(_CalGt[j] * d(j, b[i]) for j in dendro.e_i) for i in dendro.e_i
])
Gt_rhs_s3 = ([
_CalGt[i] * sum(d(j, b[j]) for j in dendro.e_i) for i in dendro.e_i
])
Gt_rhs_s4 = ([
sum([
igt[j, k] * d2(j, k, b[i]) + igt[i, j] * d2(j, k, b[k]) / 3
for j, k in dendro.e_ij
]) for i in dendro.e_i
])
Gt_rhs_s5 = ([
sum([2 * At_UU[i, j] * d(j, a) for j in dendro.e_i])
for i in dendro.e_i
])
Gt_rhs_s6 = ([
sum([
2 * a * dendro.C2[i, j, k] * At_UU[j, k]
for j, k in dendro.e_ij
]) for i in dendro.e_i
])
Gt_rhs_s7 = ([
sum([
a * (3 / chi * At_UU[i, j] * d(j, chi) +
Rational(4, 3) * dendro.inv_metric[i, j] * d(j, K))
for j in dendro.e_i
]) for i in dendro.e_i
])
Gt_rhs = Matrix(_Gt_rhs_s1) - \
Matrix(_Gt_rhs_s2) + \
Rational(2,3)*Matrix(_Gt_rhs_s3) + \
Matrix(_Gt_rhs_s4) - \
Matrix(_Gt_rhs_s5) + \
Matrix(_Gt_rhs_s6) - \
Matrix(_Gt_rhs_s7)
Gt_rhs = [item for sublist in Gt_rhs.tolist() for item in sublist]
B_rhs = [
(Gt_rhs[i] - eta_damp * B[i] + l3 * dendro.vec_j_ad_j(b, B[i]) -
l4 * dendro.vec_j_ad_j(b, Gt[i])) for i in dendro.e_i
]
outs = [
a_rhs, b_rhs, gt_rhs, chi_rhs, At_rhs, K_rhs, CalGt, Gt_rhs_s1,
Gt_rhs_s2, Gt_rhs_s3, Gt_rhs_s4, Gt_rhs_s5, Gt_rhs_s6, Gt_rhs_s7,
Gt_rhs, B_rhs
]
vnames = [
'a_rhs', 'b_rhs', 'gt_rhs', 'chi_rhs', 'At_rhs', 'K_rhs', 'CalGt',
'Gt_rhs_s1_', 'Gt_rhs_s2_', 'Gt_rhs_s3_', 'Gt_rhs_s4_',
'Gt_rhs_s5_', 'Gt_rhs_s6_', 'Gt_rhs_s7_', 'Gt_rhs', 'B_rhs'
]
###################################################################
# generate code
###################################################################
numVars = len(outs)
for i in range(0, numVars):
dendro.generate_separate([outs[i]], [vnames[i]], '[pp]')
AikAkj = Matrix([
sum([
At[i, k] *
sum([dendro.inv_metric[k, l] * At[l, j] for l in dendro.e_i])
for k in dendro.e_i
]) for i, j in dendro.e_ij
])
#ewh2 At_rhs = dendro.lie(b, At, weight) + dendro.trace_free(chi*(dendro.DiDj(a) + a*R)) + a*(K*At - 2*AikAkj.reshape(3, 3))
At_rhs = dendro.lie(
b, At, weight) + chi * dendro.trace_free(a * R - dendro.DiDj(a)) + a * (
K * At - 2 * AikAkj.reshape(3, 3)) + 0 * dendro.kodiss(At)
#K_rhs = dendro.vec_k_del_k(b, K) - dendro.laplacian(a) + a*(1/3*K*K + dendro.sqr(At))
K_rhs = dendro.lie(b, K) - dendro.laplacian(
a, chi) + a * (K * K / 3 + dendro.sqr(At)) + 0 * dendro.kodiss(K)
At_UU = dendro.up_up(At)
Gt_rhs_s1 = ([
sum(b[j] * ad(j, Gt[i]) for j in dendro.e_i) for i in dendro.e_i
])
Gt_rhs_s2 = ([
sum(_CalGt[j] * d(j, b[i]) for j in dendro.e_i) for i in dendro.e_i
])
Gt_rhs_s3 = ([
_CalGt[i] * sum(d(j, b[j]) for j in dendro.e_i) for i in dendro.e_i
])
Gt_rhs_s4 = ([
sum([
igt[j, k] * d2(j, k, b[i]) + igt[i, j] * d2(j, k, b[k]) / 3
(m_img_A_vec - 0.5 * m_img_d_chi) +
m_img_A_vec *
(m_real_A_vec - 0.5 * m_real_d_chi))
# Adding previous auxilary Psi4 calculations
psi4_real = psi4_1_real + psi4_2_real - psi4_3_real - psi4_4_real
psi4_img = -(psi4_1_img + psi4_2_img - psi4_3_img - psi4_4_img)
###################################################################
# Constraint Equations
###################################################################
# The Hamiltonian constraint
ham = sum(chi * igt[j, k] * R[j, k]
for j, k in dendro.e_ij) - dendro.sqr(At) + Rational(2, 3) * K**2
# The momentum constraints
mom = Matrix([sum([igt[j,k]*( d(k,At[i,j]) - \
sum(dendro.C2[m,k,i]*At[j,m] for m in dendro.e_i)) \
for j,k in dendro.e_ij]) for i in dendro.e_i]) - \
Matrix([sum([Gt[j]*At[i,j] for j in dendro.e_i]) for i in dendro.e_i]) -\
Rational(3,2)*Matrix([ \
sum([igt[j,k]*At[k,i]*d(j,chi)/chi for j,k in dendro.e_ij]) \
for i in dendro.e_i]) -\
Rational(2,3)*Matrix([d(i,K) for i in dendro.e_i])
mom = [item for sublist in mom.tolist() for item in sublist]
# Output for this should be included psi4_real and psi4_img as double precision
###################################################################
# generate code
# l2 * dendro.vec_j_del_j(b, b[i])
b_rhs = [ S(3)/4 * (lf0 + lf1*a) * B[i] +
l2 * dendro.vec_j_ad_j(b, b[i])
for i in dendro.e_i ] + dendro.kodiss(b)
gt_rhs = dendro.lie(b, gt, weight) - 2*a*At + 0*dendro.kodiss(gt)
chi_rhs = dendro.lie(b, chi, weight) + Rational(2,3) * (chi*a*K) + 0*dendro.kodiss(chi)
AikAkj = Matrix([sum([At[i, k] * sum([dendro.inv_metric[k, l]*At[l, j] for l in dendro.e_i]) for k in dendro.e_i]) for i, j in dendro.e_ij])
#ewh2 At_rhs = dendro.lie(b, At, weight) + dendro.trace_free(chi*(dendro.DiDj(a) + a*R)) + a*(K*At - 2*AikAkj.reshape(3, 3))
At_rhs = dendro.lie(b, At, weight) + chi*dendro.trace_free( a*R - dendro.DiDj(a)) + a*(K*At - 2*AikAkj.reshape(3, 3)) + 0*dendro.kodiss(At)
#K_rhs = dendro.vec_k_del_k(b, K) - dendro.laplacian(a) + a*(1/3*K*K + dendro.sqr(At))
K_rhs = dendro.lie(b, K) - dendro.laplacian(a,chi) + a*(K*K/3 + dendro.sqr(At)) + 0*dendro.kodiss(K)
At_UU = dendro.up_up(At)
Gt_rhs = Matrix([sum(b[j]*ad(j,Gt[i]) for j in dendro.e_i) for i in dendro.e_i]) - \
Matrix([sum(CalGt[j]*d(j,b[i]) for j in dendro.e_i) for i in dendro.e_i]) + \
Rational(2,3)*Matrix([ CalGt[i] * sum(d(j,b[j]) for j in dendro.e_i) for i in dendro.e_i ]) + \
Matrix([sum([igt[j, k] * d2(j, k, b[i]) + igt[i, j] * d2(j, k, b[k])/3 for j, k in dendro.e_ij]) for i in dendro.e_i]) - \
Matrix([sum([2*At_UU[i, j]*d(j, a) for j in dendro.e_i]) for i in dendro.e_i]) + \
Matrix([sum([2*a*dendro.C2[i, j, k]*At_UU[j, k] for j,k in dendro.e_ij]) for i in dendro.e_i]) - \
Matrix([sum([a*(3/chi*At_UU[i,j]*d(j, chi) + Rational(4,3)*dendro.inv_metric[i, j]*d(j, K)) for j in dendro.e_i]) for i in dendro.e_i])
# + kod(i,Gt[i])
Gt_rhs = [item for sublist in Gt_rhs.tolist() for item in sublist]
eta_func = R0*sqrt(sum([igt[i,j]*d(i,chi)*d(j,chi) for i,j in dendro.e_ij]))/((1-chi**ep1)**ep2)
AikAkj = Matrix([
sum([
At[i, k] *
sum([dendro.inv_metric[k, l] * At[l, j] for l in dendro.e_i])
for k in dendro.e_i
]) for i, j in dendro.e_ij
])
#ewh2 At_rhs = dendro.lie(b, At, weight) + dendro.trace_free(chi*(dendro.DiDj(a) + a*R)) + a*(K*At - 2*AikAkj.reshape(3, 3))
At_rhs = dendro.lie(b, At, weight) + chi * dendro.trace_free(
a * R - dendro.DiDj(a)) + a * (K * At - 2 * AikAkj.reshape(3, 3))
#K_rhs = dendro.vec_k_del_k(b, K) - dendro.laplacian(a) + a*(1/3*K*K + dendro.sqr(At))
K_rhs = dendro.lie(b, K) - dendro.laplacian(
a, chi) + a * (K * K / 3 + dendro.sqr(At))
At_UU = dendro.up_up(At)
Gt_rhs = Matrix([sum(b[j]*ad(j,Gt[i]) for j in dendro.e_i) for i in dendro.e_i]) - \
Matrix([sum(CalGt[j]*d(j,b[i]) for j in dendro.e_i) for i in dendro.e_i]) + \
2/3*Matrix([ CalGt[i] * sum(d(j,b[j]) for j in dendro.e_i) for i in dendro.e_i ]) + \
Matrix([sum([igt[j, k] * d2(j, k, b[i]) + igt[i, j] * d2(j, k, b[k])/3 for j, k in dendro.e_ij]) for i in dendro.e_i]) - \
Matrix([sum([2*At_UU[i, j]*d(j, a) for j in dendro.e_i]) for i in dendro.e_i]) + \
Matrix([sum([2*a*dendro.C2[i, j, k]*At_UU[j, k] for j,k in dendro.e_ij]) for i in dendro.e_i]) - \
Matrix([sum([a*(3/chi*At_UU[i,j]*d(j, chi) + (4/3)*dendro.inv_metric[i, j]*d(j, K)) for j in dendro.e_i]) for i in dendro.e_i])
Gt_rhs = [item for sublist in Gt_rhs.tolist() for item in sublist]
B_rhs = [
Gt_rhs[i] - eta * B[i] + l3 * dendro.vec_j_ad_j(b, B[i]) -
psi4_3_img = inv_chi * sum([sum([NR[i,j]* Uu[i,j] + MR[i,j]*Vv[i,j] for i in dendro.e_i]) for j in dendro.e_i])
psi4_4_real = inv_chi * inv_chi * (m_real_A_vec * (m_real_A_vec + 0.5 * m_real_d_chi) - m_img_A_vec * (m_img_A_vec + 0.5 * m_img_d_chi))
psi4_4_img = inv_chi * inv_chi * (m_real_A_vec * (m_img_A_vec - 0.5 * m_img_d_chi ) + m_img_A_vec * (m_real_A_vec - 0.5 * m_real_d_chi))
# Adding previous auxilary Psi4 calculations
psi4_real = psi4_1_real + psi4_2_real - psi4_3_real - psi4_4_real
psi4_img = - ( psi4_1_img + psi4_2_img - psi4_3_img - psi4_4_img )
###################################################################
# Constraint Equations
###################################################################
# The Hamiltonian constraint
ham = sum(chi*igt[j,k]*R[j,k] for j,k in dendro.e_ij) - dendro.sqr(At) + Rational(2,3)*K**2
# The momentum constraints
mom = Matrix([sum([igt[j,k]*( d(k,At[i,j]) - \
sum(dendro.C2[m,k,i]*At[j,m] for m in dendro.e_i)) \
for j,k in dendro.e_ij]) for i in dendro.e_i]) - \
Matrix([sum([Gt[j]*At[i,j] for j in dendro.e_i]) for i in dendro.e_i]) -\
Rational(3,2)*Matrix([ \
sum([igt[j,k]*At[k,i]*d(j,chi)/chi for j,k in dendro.e_ij]) \
for i in dendro.e_i]) -\
Rational(2,3)*Matrix([d(i,K) for i in dendro.e_i])
mom = [item for sublist in mom.tolist() for item in sublist]
# Output for this should be included psi4_real and psi4_img as double precision
###################################################################
# generate code
