def spa_derivT(i, j, k, V, g):
left_deriv = hcl.scalar(0, "left_deriv")
right_deriv = hcl.scalar(0, "right_deriv")
dim_idx = 2
u_i = V[i, j, k]
with hcl.if_(k == 0):
u_i_minus_1 = hcl.scalar(0, "u_i_minus_1")
u_i_minus_1[0] = V[i, j, V.shape[dim_idx] - 1]
u_i_plus_1 = V[i, j, k + 1]
u_i_plus_2 = V[i, j, k + 2]
D1_i_plus_half = (u_i_plus_1 - u_i) / g.dx[dim_idx]
D1_i_minus_half = (u_i - u_i_minus_1[0]) / g.dx[dim_idx]
Q1d_left = D1_i_minus_half
Q1d_right = D1_i_plus_half
D2_i = 0.5 * ((D1_i_plus_half - D1_i_minus_half) / g.dx[dim_idx])
u_i_plus_1_plus_1 = u_i_plus_2
D1_i_plus_1_plus_half = (u_i_plus_1_plus_1 -
u_i_plus_1) / g.dx[dim_idx]
D1_i_plus_1_minus_half = D1_i_plus_half
D2_i_plus_1 = 0.5 * (
(D1_i_plus_1_plus_half - D1_i_plus_1_minus_half) / g.dx[dim_idx])
with hcl.if_(my_abs(D2_i) <= my_abs(D2_i_plus_1)):
c = D2_i
Q2d = c * g.dx[dim_idx]
left_deriv[0] = Q1d_left + Q2d
right_deriv[0] = Q1d_right - Q2d
with hcl.else_():
c = D2_i_plus_1
Q2d = c * g.dx[dim_idx]
left_deriv[0] = Q1d_left + Q2d
right_deriv[0] = Q1d_right - Q2d
with hcl.elif_(k == V.shape[dim_idx] - 1):
u_i_plus_1 = hcl.scalar(0, "u_i_plus_1")
u_i_plus_2 = hcl.scalar(0, "u_i_plus_2")
u_i_plus_1[0] = V[i, j, 0]
u_i_plus_2[0] = V[i, j, 1]
u_i_minus_1 = V[i, j, k - 1]
D1_i_plus_half = (u_i_plus_1[0] - u_i) / g.dx[dim_idx]
D1_i_minus_half = (u_i - u_i_minus_1) / g.dx[dim_idx]
Q1d_left = D1_i_minus_half
Q1d_right = D1_i_plus_half
D2_i = 0.5 * ((D1_i_plus_half - D1_i_minus_half) / g.dx[dim_idx])
u_i_plus_1_plus_1 = u_i_plus_2[0]
D1_i_plus_1_plus_half = (u_i_plus_1_plus_1 -
u_i_plus_1[0]) / g.dx[dim_idx]
D1_i_plus_1_minus_half = D1_i_plus_half
D2_i_plus_1 = 0.5 * (
(D1_i_plus_1_plus_half - D1_i_plus_1_minus_half) / g.dx[dim_idx])
with hcl.if_(my_abs(D2_i) <= my_abs(D2_i_plus_1)):
c = D2_i
Q2d = c * g.dx[dim_idx]
left_deriv[0] = Q1d_left + Q2d
right_deriv[0] = Q1d_right - Q2d
with hcl.else_():
c = D2_i_plus_1
Q2d = c * g.dx[dim_idx]
left_deriv[0] = Q1d_left + Q2d
right_deriv[0] = Q1d_right - Q2d
with hcl.elif_(k == V.shape[dim_idx] - 2):
u_i_plus_2 = hcl.scalar(0, "u_i_plus_2")
u_i_plus_1 = V[i, j, k + 1]
u_i_plus_2[0] = V[i, j, 0]
u_i_minus_1 = V[i, j, k - 1]
D1_i_plus_half = (u_i_plus_1 - u_i) / g.dx[dim_idx]
D1_i_minus_half = (u_i - u_i_minus_1) / g.dx[dim_idx]
Q1d_left = D1_i_minus_half
Q1d_right = D1_i_plus_half
D2_i = 0.5 * ((D1_i_plus_half - D1_i_minus_half) / g.dx[dim_idx])
u_i_plus_1_plus_1 = u_i_plus_2[0]
D1_i_plus_1_plus_half = (u_i_plus_1_plus_1 -
u_i_plus_1) / g.dx[dim_idx]
D1_i_plus_1_minus_half = D1_i_plus_half
D2_i_plus_1 = 0.5 * (
(D1_i_plus_1_plus_half - D1_i_plus_1_minus_half) / g.dx[dim_idx])
with hcl.if_(my_abs(D2_i) <= my_abs(D2_i_plus_1)):
c = D2_i
Q2d = c * g.dx[dim_idx]
left_deriv[0] = Q1d_left + Q2d
right_deriv[0] = Q1d_right - Q2d
with hcl.else_():
c = D2_i_plus_1
Q2d = c * g.dx[dim_idx]
left_deriv[0] = Q1d_left + Q2d
right_deriv[0] = Q1d_right - Q2d
with hcl.else_():
u_i_minus_1 = V[i, j, k - 1]
u_i_plus_1 = V[i, j, k + 1]
u_i_plus_2 = V[i, j, k + 2]
D1_i_plus_half = (u_i_plus_1 - u_i) / g.dx[dim_idx]
D1_i_minus_half = (u_i - u_i_minus_1) / g.dx[dim_idx]
Q1d_left = D1_i_minus_half
Q1d_right = D1_i_plus_half
D2_i = 0.5 * ((D1_i_plus_half - D1_i_minus_half) / g.dx[dim_idx])
u_i_plus_1_plus_1 = u_i_plus_2
D1_i_plus_1_plus_half = (u_i_plus_1_plus_1 -
u_i_plus_1) / g.dx[dim_idx]
D1_i_plus_1_minus_half = D1_i_plus_half
D2_i_plus_1 = 0.5 * (
(D1_i_plus_1_plus_half - D1_i_plus_1_minus_half) / g.dx[dim_idx])
with hcl.if_(my_abs(D2_i) <= my_abs(D2_i_plus_1)):
c = D2_i
Q2d = c * g.dx[dim_idx]
left_deriv[0] = Q1d_left + Q2d
right_deriv[0] = Q1d_right - Q2d
with hcl.else_():
c = D2_i_plus_1
Q2d = c * g.dx[dim_idx]
left_deriv[0] = Q1d_left + Q2d
right_deriv[0] = Q1d_right - Q2d
return left_deriv[0], right_deriv[0]
def maxVWithCStraint(i, j, k, l, m, n):
with hcl.if_(V_new[i, j, k, l, m, n] < obstacle[i, j, k, l, m, n]):
V_new[i, j, k, l, m, n] = obstacle[i, j, k, l, m, n]
def maxVWithV0(i, j, k, l, m, n): # Take the max
with hcl.if_(V_new[i, j, k, l, m, n] < l0[i, j, k, l, m, n]):
V_new[i, j, k, l, m, n] = l0[i, j, k, l, m, n]
def maxVWithCStraint(i, j, k, l, m, n):
with hcl.if_(V_new[i, j, k, l, m, n] < 5.0):
V_new[i, j, k, l, m, n] = 1.0
def update(l, prototype, prototypeCounter, max):
hcl.print((l + 1),
"%d:Use hard examples to update the prototype counters.\n")
###data preparation
distance = hcl.compute((pack_train.shape[1], ),
lambda x: 0,
'distance',
dtype=hcl.UInt(bw))
pre_dist = hcl.compute((pack_train.shape[1], ), lambda x: 0,
"pre_dist")
hamming_dist = hcl.compute((numClasses, ), lambda x: 0, "hamming_dist")
m = hcl.reduce_axis(0, pack_train.shape[1], "m")
###
with hcl.for_(0, pack_train.shape[0]) as i:
hcl.print((i), "%d suc\n")
pack_proto = hcl.pack(prototype,
axis=1,
dtype=hcl.UInt(bw),
name="pack_proto")
with hcl.for_(0, numClasses) as n:
#Do hdc multiplication(XOR) on sample[i]'s hdv and prototype[n]'s hdv (elementwise on the high-bit data)
hcl.update(distance,
lambda x: pack_train[i][x] ^ pack_proto[n][x])
#Calculate the hamming distance of the two vectors by adding 1s
hcl.update(pre_dist, lambda x: popcount(distance[x]))
hcl.print((), "sum of 1s suc")
hamming_dist[n] = hcl.sum(pre_dist[m], axis=m)
#Find the one having the least hamming distance and choose it's label as the predicted label
pred = hcl.scalar(0, 'pred')
with hcl.for_(0, hamming_dist.shape[0]) as j:
with hcl.if_(hamming_dist[j] < hamming_dist[pred]):
pred.v = j
#Adjust the proto vectors by adding the sample vector on its label proto hdv and substrct it on its predicted proto hdv
with hcl.if_(pred.v != trainLabels[i]):
max[trainLabels[i]] += 1
max[pred] -= 1
with hcl.for_(0, dim) as m:
with hcl.if_(hdTrainData[i][m] == 1):
###########
prototypeCounter[trainLabels[i]][m] += 1
prototypeCounter[pred][m] -= 1
# prototypeCounter[trainLabels[i]][m] += hdTrainData[i][m]
# prototypeCounter[pred][m] -= hdTrainData[i][m]
with hcl.if_(max[trainLabels[i]] % 2 == 0):
with hcl.if_(prototypeCounter[trainLabels[i]][m] -
max[trainLabels[i]] / 2 == 0):
prototype[trainLabels[i]][m] &= 1
with hcl.else_():
prototype[trainLabels[i]][m] = hcl.select(
prototypeCounter[trainLabels[i]][m] -
max[trainLabels[i]] / 2 > 0, 1, 0)
with hcl.if_(max[pred] % 2 == 0):
with hcl.if_(prototypeCounter[pred][m] -
max[pred] / 2 == 0):
prototype[pred][m] &= 1
with hcl.else_():
prototype[pred][m] = hcl.select(
prototypeCounter[pred][m] - max[pred] / 2 > 0, 1,
0)
#print the accuracy
hcl.mutate(
(1, ),
lambda x: test_hdc_accu(prototype, pack_train, trainLabels, 1),
'training_update')
hcl.mutate(
(1, ),
lambda x: test_hdc_accu(prototype, pack_test, testLabels, 2),
'testing_update')
def kernel(A):
with hcl.for_(0, 10) as i:
with hcl.if_(i > 5):
hcl.break_()
A[i] = i
def kernel(A):
with hcl.if_(A[0] > 5):
A[0] = 5
def spa_derivX1_5d(i, j, k, l, m, V,
g): # Left -> right == Outer Most -> Inner Most
left_deriv = hcl.scalar(0, "left_deriv")
right_deriv = hcl.scalar(0, "right_deriv")
dim_idx = 0
u_i = V[i, j, k, l, m]
with hcl.if_(i == 0):
u_i_minus_1 = hcl.scalar(0, "u_i_minus_1")
u_i_plus_1 = V[i + 1, j, k, l, m]
u_i_plus_2 = V[i + 2, j, k, l, m]
u_i_minus_1[0] = u_i + my_abs(u_i_plus_1 - u_i) * my_sign(u_i)
D1_i_plus_half = (u_i_plus_1 - u_i) / g.dx[dim_idx]
D1_i_minus_half = (u_i - u_i_minus_1[0]) / g.dx[dim_idx]
Q1d_left = D1_i_minus_half
Q1d_right = D1_i_plus_half
D2_i = 0.5 * ((D1_i_plus_half - D1_i_minus_half) / g.dx[dim_idx])
u_i_plus_1_plus_1 = u_i_plus_2
D1_i_plus_1_plus_half = (u_i_plus_1_plus_1 -
u_i_plus_1) / g.dx[dim_idx]
D1_i_plus_1_minus_half = D1_i_plus_half
D2_i_plus_1 = 0.5 * (
(D1_i_plus_1_plus_half - D1_i_plus_1_minus_half) / g.dx[dim_idx])
with hcl.if_(my_abs(D2_i) <= my_abs(D2_i_plus_1)):
c = D2_i
Q2d = c * g.dx[dim_idx]
left_deriv[0] = Q1d_left + Q2d
right_deriv[0] = Q1d_right - Q2d
with hcl.else_():
c = D2_i_plus_1
Q2d = c * g.dx[dim_idx]
left_deriv[0] = Q1d_left + Q2d
right_deriv[0] = Q1d_right - Q2d
with hcl.elif_(i == V.shape[dim_idx] - 1):
u_i_plus_1 = hcl.scalar(0, "u_i_plus_1")
u_i_plus_2 = hcl.scalar(0, "u_i_plus_2")
u_i_minus_1 = V[i - 1, j, k, l, m]
u_i_plus_1[0] = u_i + my_abs(u_i - u_i_minus_1) * my_sign(u_i)
u_i_plus_2[0] = u_i_plus_1[0] + my_abs(u_i_plus_1[0] - u_i) * my_sign(
u_i_plus_1[0])
D1_i_plus_half = (u_i_plus_1[0] - u_i) / g.dx[dim_idx]
D1_i_minus_half = (u_i - u_i_minus_1) / g.dx[dim_idx]
Q1d_left = D1_i_minus_half
Q1d_right = D1_i_plus_half
D2_i = 0.5 * ((D1_i_plus_half - D1_i_minus_half) / g.dx[dim_idx])
u_i_plus_1_plus_1 = u_i_plus_2[0]
D1_i_plus_1_plus_half = (u_i_plus_1_plus_1 -
u_i_plus_1[0]) / g.dx[dim_idx]
D1_i_plus_1_minus_half = D1_i_plus_half
D2_i_plus_1 = 0.5 * (
(D1_i_plus_1_plus_half - D1_i_plus_1_minus_half) / g.dx[dim_idx])
with hcl.if_(my_abs(D2_i) <= my_abs(D2_i_plus_1)):
c = D2_i
Q2d = c * g.dx[dim_idx]
left_deriv[0] = Q1d_left + Q2d
right_deriv[0] = Q1d_right - Q2d
with hcl.else_():
c = D2_i_plus_1
Q2d = c * g.dx[dim_idx]
left_deriv[0] = Q1d_left + Q2d
right_deriv[0] = Q1d_right - Q2d
with hcl.elif_(i == V.shape[dim_idx] - 2):
u_i_plus_2 = hcl.scalar(0, "u_i_plus_2")
u_i_plus_1 = V[i + 1, j, k, l, m]
u_i_minus_1 = V[i - 1, j, k, l, m]
u_i_plus_2[0] = u_i_plus_1 + my_abs(u_i_plus_1 -
u_i) * my_sign(u_i_plus_1)
D1_i_plus_half = (u_i_plus_1 - u_i) / g.dx[dim_idx]
D1_i_minus_half = (u_i - u_i_minus_1) / g.dx[dim_idx]
Q1d_left = D1_i_minus_half
Q1d_right = D1_i_plus_half
D2_i = 0.5 * ((D1_i_plus_half - D1_i_minus_half) / g.dx[dim_idx])
u_i_plus_1_plus_1 = u_i_plus_2[0]
D1_i_plus_1_plus_half = (u_i_plus_1_plus_1 -
u_i_plus_1) / g.dx[dim_idx]
D1_i_plus_1_minus_half = D1_i_plus_half
D2_i_plus_1 = 0.5 * (
(D1_i_plus_1_plus_half - D1_i_plus_1_minus_half) / g.dx[dim_idx])
with hcl.if_(my_abs(D2_i) <= my_abs(D2_i_plus_1)):
c = D2_i
Q2d = c * g.dx[dim_idx]
left_deriv[0] = Q1d_left + Q2d
right_deriv[0] = Q1d_right - Q2d
with hcl.else_():
c = D2_i_plus_1
Q2d = c * g.dx[dim_idx]
left_deriv[0] = Q1d_left + Q2d
right_deriv[0] = Q1d_right - Q2d
with hcl.else_():
u_i_minus_1 = V[i - 1, j, k, l, m]
u_i_plus_1 = V[i + 1, j, k, l, m]
u_i_plus_2 = V[i + 2, j, k, l, m]
D1_i_plus_half = (u_i_plus_1 - u_i) / g.dx[dim_idx]
D1_i_minus_half = (u_i - u_i_minus_1) / g.dx[dim_idx]
Q1d_left = D1_i_minus_half
Q1d_right = D1_i_plus_half
D2_i = 0.5 * ((D1_i_plus_half - D1_i_minus_half) / g.dx[dim_idx])
u_i_plus_1_plus_1 = u_i_plus_2
D1_i_plus_1_plus_half = (u_i_plus_1_plus_1 -
u_i_plus_1) / g.dx[dim_idx]
D1_i_plus_1_minus_half = D1_i_plus_half
D2_i_plus_1 = 0.5 * (
(D1_i_plus_1_plus_half - D1_i_plus_1_minus_half) / g.dx[dim_idx])
with hcl.if_(my_abs(D2_i) <= my_abs(D2_i_plus_1)):
c = D2_i
Q2d = c * g.dx[dim_idx]
left_deriv[0] = Q1d_left + Q2d
right_deriv[0] = Q1d_right - Q2d
with hcl.else_():
c = D2_i_plus_1
Q2d = c * g.dx[dim_idx]
left_deriv[0] = Q1d_left + Q2d
right_deriv[0] = Q1d_right - Q2d
return left_deriv[0], right_deriv[0]
def graph_create(V_new, V_init, x1, x2, x3, x4, t, l0, probe):
# Specify intermediate tensors
deriv_diff1 = hcl.compute(V_init.shape, lambda *x:0, "deriv_diff1")
deriv_diff2 = hcl.compute(V_init.shape, lambda *x:0, "deriv_diff2")
deriv_diff3 = hcl.compute(V_init.shape, lambda *x:0, "deriv_diff3")
deriv_diff4 = hcl.compute(V_init.shape, lambda *x:0, "deriv_diff4")
# Maximum derivative for each dim
max_deriv1 = hcl.scalar(-1e9, "max_deriv1")
max_deriv2 = hcl.scalar(-1e9, "max_deriv2")
max_deriv3 = hcl.scalar(-1e9, "max_deriv3")
max_deriv4 = hcl.scalar(-1e9, "max_deriv4")
# Min derivative for each dim
min_deriv1 = hcl.scalar(1e9, "min_deriv1")
min_deriv2 = hcl.scalar(1e9, "min_deriv2")
min_deriv3 = hcl.scalar(1e9, "min_deriv3")
min_deriv4 = hcl.scalar(1e9, "min_deriv4")
# These variables are used to dissipation calculation
max_alpha1 = hcl.scalar(-1e9, "max_alpha1")
max_alpha2 = hcl.scalar(-1e9, "max_alpha2")
max_alpha3 = hcl.scalar(-1e9, "max_alpha3")
max_alpha4 = hcl.scalar(-1e9, "max_alpha4")
def step_bound(): # Function to calculate time step
stepBoundInv = hcl.scalar(0, "stepBoundInv")
stepBound = hcl.scalar(0, "stepBound")
stepBoundInv[0] = max_alpha1[0] / g.dx[0] + max_alpha2[0] / g.dx[1] + max_alpha3[0] / g.dx[2] + max_alpha4[0] / \
g.dx[3]
stepBound[0] = 0.8 / stepBoundInv[0]
with hcl.if_(stepBound > t[1] - t[0]):
stepBound[0] = t[1] - t[0]
# Update the lower time ranges
t[0] = t[0] + stepBound[0]
# t[0] = min_deriv2[0]
return stepBound[0]
# Min with V_before
def minVWithVInit(i, j, k, l):
with hcl.if_(V_new[i, j, k, l] > V_init[i, j, k, l]):
V_new[i, j, k, l] = V_init[i, j, k, l]
def maxVWithVInit(i, j, k, l):
with hcl.if_(V_new[i, j, k, l] < V_init[i, j, k, l]):
V_new[i, j, k, l] = V_init[i, j, k, l]
def maxVWithV0(i, j, k, l): # Take the max
with hcl.if_(V_new[i, j, k, l] < l0[i, j, k, l]):
V_new[i, j, k, l] = l0[i, j, k, l]
def minVWithV0(i, j, k, l):
with hcl.if_(V_new[i, j, k, l] > l0[i, j, k, l]):
V_new[i, j, k, l] = l0[i, j, k, l]
# Calculate Hamiltonian for every grid point in V_init
with hcl.Stage("Hamiltonian"):
with hcl.for_(0, V_init.shape[0], name="i") as i:
with hcl.for_(0, V_init.shape[1], name="j") as j:
with hcl.for_(0, V_init.shape[2], name="k") as k:
with hcl.for_(0, V_init.shape[3], name="l") as l:
# Variables to calculate dV_dx
dV_dx1_L = hcl.scalar(0, "dV_dx1_L")
dV_dx1_R = hcl.scalar(0, "dV_dx1_R")
dV_dx1 = hcl.scalar(0, "dV_dx1")
dV_dx2_L = hcl.scalar(0, "dV_dx2_L")
dV_dx2_R = hcl.scalar(0, "dV_dx2_R")
dV_dx2 = hcl.scalar(0, "dV_dx2")
dV_dx3_L = hcl.scalar(0, "dV_dx3_L")
dV_dx3_R = hcl.scalar(0, "dV_dx3_R")
dV_dx3 = hcl.scalar(0, "dV_dx3")
dV_dx4_L = hcl.scalar(0, "dV_dx4_L")
dV_dx4_R = hcl.scalar(0, "dV_dx4_R")
dV_dx4 = hcl.scalar(0, "dV_dx4")
# No tensor slice operation
# dV_dx_L[0], dV_dx_R[0] = spa_derivX(i, j, k)
dV_dx1_L[0], dV_dx1_R[0] = spa_derivX1_4d(i, j, k, l, V_init, g)
dV_dx2_L[0], dV_dx2_R[0] = spa_derivX2_4d(i, j, k, l, V_init, g)
dV_dx3_L[0], dV_dx3_R[0] = spa_derivX3_4d(i, j, k, l, V_init, g)
dV_dx4_L[0], dV_dx4_R[0] = spa_derivX4_4d(i, j, k, l, V_init, g)
# Saves spatial derivative diff into tables
deriv_diff1[i, j, k, l] = dV_dx1_R[0] - dV_dx1_L[0]
deriv_diff2[i, j, k, l] = dV_dx2_R[0] - dV_dx2_L[0]
deriv_diff3[i, j, k, l] = dV_dx3_R[0] - dV_dx3_L[0]
deriv_diff4[i, j, k, l] = dV_dx4_R[0] - dV_dx4_L[0]
# Calculate average gradient
dV_dx1[0] = (dV_dx1_L + dV_dx1_R) / 2
dV_dx2[0] = (dV_dx2_L + dV_dx2_R) / 2
dV_dx3[0] = (dV_dx3_L + dV_dx3_R) / 2
dV_dx4[0] = (dV_dx4_L + dV_dx4_R) / 2
#probe[i,j,k,l] = dV_dx2[0]
# Find optimal control
uOpt = my_object.opt_ctrl(t, (x1[i], x2[j], x3[k], x4[l]),
(dV_dx1[0], dV_dx2[0], dV_dx3[0], dV_dx4[0]))
# Find optimal disturbance
dOpt = my_object.optDstb((dV_dx1[0], dV_dx2[0], dV_dx3[0], dV_dx4[0]))
# Find rates of changes based on dynamics equation
dx1_dt, dx2_dt, dx3_dt, dx4_dt = my_object.dynamics(t, (x1[i], x2[j], x3[k], x4[l]), uOpt, dOpt)
# Calculate Hamiltonian terms:
V_new[i, j, k, l] = -(
dx1_dt * dV_dx1[0] + dx2_dt * dV_dx2[0] + dx3_dt * dV_dx3[0] + dx4_dt * dV_dx4[0])
# Debugging
# V_new[i, j, k, l] = dV_dx2[0]
probe[i, j, k, l] = V_init[i, j, k, l]
# Get derivMin
with hcl.if_(dV_dx1_L[0] < min_deriv1[0]):
min_deriv1[0] = dV_dx1_L[0]
with hcl.if_(dV_dx1_R[0] < min_deriv1[0]):
min_deriv1[0] = dV_dx1_R[0]
with hcl.if_(dV_dx2_L[0] < min_deriv2[0]):
min_deriv2[0] = dV_dx2_L[0]
with hcl.if_(dV_dx2_R[0] < min_deriv2[0]):
min_deriv2[0] = dV_dx2_R[0]
with hcl.if_(dV_dx3_L[0] < min_deriv3[0]):
min_deriv3[0] = dV_dx3_L[0]
with hcl.if_(dV_dx3_R[0] < min_deriv3[0]):
min_deriv3[0] = dV_dx3_R[0]
with hcl.if_(dV_dx4_L[0] < min_deriv4[0]):
min_deriv4[0] = dV_dx4_L[0]
with hcl.if_(dV_dx4_R[0] < min_deriv4[0]):
min_deriv4[0] = dV_dx4_R[0]
# Get derivMax
with hcl.if_(dV_dx1_L[0] > max_deriv1[0]):
max_deriv1[0] = dV_dx1_L[0]
with hcl.if_(dV_dx1_R[0] > max_deriv1[0]):
max_deriv1[0] = dV_dx1_R[0]
with hcl.if_(dV_dx2_L[0] > max_deriv2[0]):
max_deriv2[0] = dV_dx2_L[0]
with hcl.if_(dV_dx2_R[0] > max_deriv2[0]):
max_deriv2[0] = dV_dx2_R[0]
with hcl.if_(dV_dx3_L[0] > max_deriv3[0]):
max_deriv3[0] = dV_dx3_L[0]
with hcl.if_(dV_dx3_R[0] > max_deriv3[0]):
max_deriv3[0] = dV_dx3_R[0]
with hcl.if_(dV_dx4_L[0] > max_deriv4[0]):
max_deriv4[0] = dV_dx4_L[0]
with hcl.if_(dV_dx4_R[0] > max_deriv4[0]):
max_deriv4[0] = dV_dx4_R[0]
# Calculate dissipation amount
with hcl.Stage("Dissipation"):
#dOptU = hcl.compute((4,), lambda x: 0, "dOptU")
# Storing alphas
dOptL1 = hcl.scalar(0, "dOptL1")
dOptL2 = hcl.scalar(0, "dOptL2")
dOptL3 = hcl.scalar(0, "dOptL3")
dOptL4 = hcl.scalar(0, "dOptL4")
# Find UPPER BOUND optimal disturbance
dOptU1 = hcl.scalar(0, "dOptL1")
dOptU2 = hcl.scalar(0, "dOptL2")
dOptU3 = hcl.scalar(0, "dOptL3")
dOptU4 = hcl.scalar(0, "dOptL4")
alpha1 = hcl.scalar(0, "alpha1")
alpha2 = hcl.scalar(0, "alpha2")
alpha3 = hcl.scalar(0, "alpha3")
alpha4 = hcl.scalar(0, "alpha4")
# Find LOWER BOUND optimal disturbance
dOptL1[0], dOptL2[0], dOptL3[0], dOptL4[0] = my_object.optDstb((min_deriv1[0], min_deriv2[0], \
min_deriv3[0], min_deriv4[0]))
dOptU1[0], dOptL2[0], dOptL3[0], dOptL4[0] = my_object.optDstb((max_deriv1[0], max_deriv2[0], \
max_deriv3[0], max_deriv4[0]))
uOptL1 = hcl.scalar(0, "uOptL1")
uOptL2 = hcl.scalar(0, "uOptL2")
uOptL3 = hcl.scalar(0, "uOptL3")
uOptL4 = hcl.scalar(0, "uOptL4")
# Find UPPER BOUND optimal disturbance
uOptU1 = hcl.scalar(0, "uOptU1")
uOptU2 = hcl.scalar(0, "uOptU2")
uOptU3 = hcl.scalar(0, "uOptU3")
uOptU4 = hcl.scalar(0, "uOptU4")
with hcl.for_(0, V_init.shape[0], name="i") as i:
with hcl.for_(0, V_init.shape[1], name="j") as j:
with hcl.for_(0, V_init.shape[2], name="k") as k:
with hcl.for_(0, V_init.shape[3], name="l") as l:
dx_LL1 = hcl.scalar(0, "dx_LL1")
dx_LL2 = hcl.scalar(0, "dx_LL2")
dx_LL3 = hcl.scalar(0, "dx_LL3")
dx_LL4 = hcl.scalar(0, "dx_LL4")
dx_UL1 = hcl.scalar(0, "dx_UL1")
dx_UL2 = hcl.scalar(0, "dx_UL2")
dx_UL3 = hcl.scalar(0, "dx_UL3")
dx_UL4 = hcl.scalar(0, "dx_UL4")
dx_UU1 = hcl.scalar(0, "dx_UU1")
dx_UU2 = hcl.scalar(0, "dx_UU2")
dx_UU3 = hcl.scalar(0, "dx_UU3")
dx_UU4 = hcl.scalar(0, "dx_UU4")
dx_LU1 = hcl.scalar(0, "dx_LU1")
dx_LU2 = hcl.scalar(0, "dx_LU2")
dx_LU3 = hcl.scalar(0, "dx_LU3")
dx_LU4 = hcl.scalar(0, "dx_LU4")
# Find LOWER BOUND optimal control
uOptL1[0], uOptL2[0], uOptL3[0], uOptL4[0]= my_object.opt_ctrl(t, (x1[i], x2[j], x3[k], x4[l]),
(min_deriv1[0], min_deriv2[0], min_deriv3[0],
min_deriv4[0]))
# Find UPPER BOUND optimal control
uOptU1[0], uOptU2[0], uOptU3[0], uOptU4[0] = my_object.opt_ctrl(t, (x1[i], x2[j], x3[k], x4[l]),
(max_deriv1[0], max_deriv2[0], max_deriv3[0],
max_deriv4[0]))
# Find magnitude of rates of changes
dx_LL1[0], dx_LL2[0], dx_LL3[0], dx_LL4[0] = my_object.dynamics(t, (x1[i], x2[j], x3[k], x4[l]),
(uOptL1[0], uOptL2[0],uOptL3[0], uOptL4[0]),\
(dOptL1[0], dOptL2[0], dOptL3[0], dOptL4[0]))
dx_LL1[0] = my_abs(dx_LL1[0])
dx_LL2[0] = my_abs(dx_LL2[0])
dx_LL3[0] = my_abs(dx_LL3[0])
dx_LL4[0] = my_abs(dx_LL4[0])
dx_LU1[0], dx_LU2[0], dx_LU3[0], dx_LU4[0] = my_object.dynamics(t, (x1[i], x2[j], x3[k], x4[l]),
(uOptL1[0], uOptL2[0],uOptL3[0], uOptL4[0]), \
(dOptU1[0], dOptU2[0], dOptU3[0], dOptU4[0]))
dx_LU1[0] = my_abs(dx_LU1[0])
dx_LU2[0] = my_abs(dx_LU2[0])
dx_LU3[0] = my_abs(dx_LU3[0])
dx_LU4[0] = my_abs(dx_LU4[0])
# Calculate alpha
alpha1[0] = my_max(dx_LL1[0], dx_LU1[0])
alpha2[0] = my_max(dx_LL2[0], dx_LU2[0])
alpha3[0] = my_max(dx_LL3[0], dx_LU3[0])
alpha4[0] = my_max(dx_LL4[0], dx_LU4[0])
#dx_UL3 = hcl.scalar(0, "dx_UL3")
# dx_UL1[0], dx_UL2[0], dx_UL3[0], dx_UL4[0] = my_object.dynamics(t, (x1[i], x2[j], x3[k], x4[l]),
# uOptU, dOptL)
dx_UL1[0], dx_UL2[0], dx_UL3[0], dx_UL4[0] = my_object.dynamics(t, (x1[i], x2[j], x3[k], x4[l]),\
(uOptU1[0], uOptU2[0], uOptU3[0], uOptU4[0]), \
(dOptL1[0], dOptL2[0], dOptL3[0], dOptL4[0]))
dx_UL1[0] = my_abs(dx_UL1[0])
dx_UL2[0] = my_abs(dx_UL2[0])
dx_UL3[0] = my_abs(dx_UL3[0])
dx_UL4[0] = my_abs(dx_UL4[0])
# Calculate alpha
alpha1[0] = my_max(alpha1[0], dx_UL1[0])
alpha2[0] = my_max(alpha2[0], dx_UL2[0])
alpha3[0] = my_max(alpha3[0], dx_UL3[0])
alpha4[0] = my_max(alpha4[0], dx_UL4[0])
dx_UU1[0], dx_UU2[0], dx_UU3[0], dx_UU4[0] = my_object.dynamics(t, (x1[i], x2[j], x3[k], x4[l]),
(uOptU1[0], uOptU2[0], uOptU3[0], uOptU4[0]),\
(dOptU1[0], dOptU2[0], dOptU3[0], dOptU4[0]))
dx_UU1[0] = my_abs(dx_UU1[0])
dx_UU2[0] = my_abs(dx_UU2[0])
dx_UU3[0] = my_abs(dx_UU3[0])
dx_UU4[0] = my_abs(dx_UU4[0])
# Calculate alpha
alpha1[0] = my_max(alpha1[0], dx_UU1[0])
alpha2[0] = my_max(alpha2[0], dx_UU2[0])
alpha3[0] = my_max(alpha3[0], dx_UU3[0])
alpha4[0] = my_max(alpha4[0], dx_UU4[0])
diss = hcl.scalar(0, "diss")
diss[0] = 0.5 * (
deriv_diff1[i, j, k, l] * alpha1[0] + deriv_diff2[i, j, k, l] * alpha2[0] + deriv_diff3[
i, j, k, l] * alpha3[0] + deriv_diff4[i, j, k, l] * alpha4[0])
#probe[i, j, k, l] = alpha1[0]
#V_init[i, j, k, l] + 0.00749716 * V_new[i,j,k,l]
# Finally
V_new[i, j, k, l] = -(V_new[i, j, k, l] - diss[0])
#probe[i, j, k, l] = V_new[i, j, k, l]*0.00749716
#probe[i, j, k, l] = V_init[i, j, k, l] + V_new[i, j, k, l] *0.00749716
# Get maximum alphas in each dimension
# Calculate alphas
with hcl.if_(alpha1[0] > max_alpha1[0]):
max_alpha1[0] = alpha1[0]
with hcl.if_(alpha2[0] > max_alpha2[0]):
max_alpha2[0] = alpha2[0]
with hcl.if_(alpha3[0] > max_alpha3[0]):
max_alpha3[0] = alpha3[0]
with hcl.if_(alpha4[0] > max_alpha4[0]):
max_alpha4[0] = alpha4[0]
# Determine time step
delta_t = hcl.compute((1,), lambda x: step_bound(), name="delta_t")
# Integrate
result = hcl.update(V_new, lambda i, j, k, l: V_init[i, j, k, l] + V_new[i, j, k, l] * delta_t[0])
# Different computation method check
if compMethod == 'maxVWithV0':
result = hcl.update(V_new, lambda i, j, k, l: maxVWithV0(i, j, k, l))
if compMethod == 'minVWithV0':
result = hcl.update(V_new, lambda i, j, k, l: minVWithV0(i, j, k, l))
if compMethod == 'minVWithVInit':
result = hcl.update(V_new, lambda i, j, k, l: minVWithVInit(i, j, k, l))
if compMethod == 'maxVWithVInit':
result = hcl.update(V_new, lambda i, j, k, l: maxVWithVInit(i, j, k, l))
# Copy V_new to V_init
hcl.update(V_init, lambda i, j, k, l: V_new[i, j, k, l])
return result
def maxVWithV0(i, j, k): # Take the max
with hcl.if_(V_new[i, j, k] < l0[i, j, k]):
V_new[i, j, k] = l0[i, j, k]
def minVWithV0(i, j, k):
with hcl.if_(V_new[i, j, k] > l0[i, j, k]):
V_new[i, j, k] = l0[i, j, k]
def maxVWithVInit(i, j, k):
with hcl.if_(V_new[i, j, k] < V_init[i, j, k]):
V_new[i, j, k] = V_init[i, j, k]
def minVWithVInit(i, j, k):
with hcl.if_(V_new[i, j, k] > V_init[i, j, k]):
V_new[i, j, k] = V_init[i, j, k]
def graph_create(V_new, V_init, x1, x2, x3, t, l0):
# Specify intermediate tensors
deriv_diff1 = hcl.compute(V_init.shape, lambda *x: 0, "deriv_diff1")
deriv_diff2 = hcl.compute(V_init.shape, lambda *x: 0, "deriv_diff2")
deriv_diff3 = hcl.compute(V_init.shape, lambda *x: 0, "deriv_diff3")
# Maximum derivative for each dim
max_deriv1 = hcl.scalar(-1e9, "max_deriv1")
max_deriv2 = hcl.scalar(-1e9, "max_deriv2")
max_deriv3 = hcl.scalar(-1e9, "max_deriv3")
# Min derivative for each dim
min_deriv1 = hcl.scalar(1e9, "min_deriv1")
min_deriv2 = hcl.scalar(1e9, "min_deriv2")
min_deriv3 = hcl.scalar(1e9, "min_deriv3")
# These variables are used to dissipation calculation
max_alpha1 = hcl.scalar(-1e9, "max_alpha1")
max_alpha2 = hcl.scalar(-1e9, "max_alpha2")
max_alpha3 = hcl.scalar(-1e9, "max_alpha3")
def step_bound(): # Function to calculate time step
stepBoundInv = hcl.scalar(0, "stepBoundInv")
stepBound = hcl.scalar(0, "stepBound")
stepBoundInv[0] = max_alpha1[0] / g.dx[0] + max_alpha2[0] / g.dx[
1] + max_alpha3[0] / g.dx[2]
stepBound[0] = 0.8 / stepBoundInv[0]
with hcl.if_(stepBound > t[1] - t[0]):
stepBound[0] = t[1] - t[0]
t[0] = t[0] + stepBound[0]
return stepBound[0]
# Min with V_before
def minVWithVInit(i, j, k):
with hcl.if_(V_new[i, j, k] > V_init[i, j, k]):
V_new[i, j, k] = V_init[i, j, k]
def maxVWithVInit(i, j, k):
with hcl.if_(V_new[i, j, k] < V_init[i, j, k]):
V_new[i, j, k] = V_init[i, j, k]
def maxVWithV0(i, j, k): # Take the max
with hcl.if_(V_new[i, j, k] < l0[i, j, k]):
V_new[i, j, k] = l0[i, j, k]
def minVWithV0(i, j, k):
with hcl.if_(V_new[i, j, k] > l0[i, j, k]):
V_new[i, j, k] = l0[i, j, k]
# Calculate Hamiltonian for every grid point in V_init
with hcl.Stage("Hamiltonian"):
with hcl.for_(
0, V_init.shape[0], name="i"
) as i: # Plus 1 as for loop count stops at V_init.shape[0]
with hcl.for_(0, V_init.shape[1], name="j") as j:
with hcl.for_(0, V_init.shape[2], name="k") as k:
# Variables to calculate dV_dx
dV_dx_L = hcl.scalar(0, "dV_dx_L")
dV_dx_R = hcl.scalar(0, "dV_dx_R")
dV_dx = hcl.scalar(0, "dV_dx")
# Variables to calculate dV_dy
dV_dy_L = hcl.scalar(0, "dV_dy_L")
dV_dy_R = hcl.scalar(0, "dV_dy_R")
dV_dy = hcl.scalar(0, "dV_dy")
# Variables to calculate dV_dtheta
dV_dT_L = hcl.scalar(0, "dV_dT_L")
dV_dT_R = hcl.scalar(0, "dV_dT_R")
dV_dT = hcl.scalar(0, "dV_dT")
# Variables to keep track of dynamics
# dx_dt = hcl.scalar(0, "dx_dt")
# dy_dt = hcl.scalar(0, "dy_dt")
# dtheta_dt = hcl.scalar(0, "dtheta_dt")
# No tensor slice operation
dV_dx_L[0], dV_dx_R[0] = spa_derivX(i, j, k, V_init, g)
dV_dy_L[0], dV_dy_R[0] = spa_derivY(i, j, k, V_init, g)
dV_dT_L[0], dV_dT_R[0] = spa_derivT(i, j, k, V_init, g)
# Saves spatial derivative diff into tables
deriv_diff1[i, j, k] = dV_dx_R[0] - dV_dx_L[0]
deriv_diff2[i, j, k] = dV_dy_R[0] - dV_dy_L[0]
deriv_diff3[i, j, k] = dV_dT_R[0] - dV_dT_L[0]
# Calculate average gradient
dV_dx[0] = (dV_dx_L + dV_dx_R) / 2
dV_dy[0] = (dV_dy_L + dV_dy_R) / 2
dV_dT[0] = (dV_dT_L + dV_dT_R) / 2
# Use method of DubinsCar to solve optimal control instead
uOpt = my_object.opt_ctrl(
t, (x1[i], x2[j], x3[k]),
(dV_dx[0], dV_dy[0], dV_dT[0]))
dOpt = my_object.optDstb(
t, (x1[i], x2[j], x3[k]),
(dV_dx[0], dV_dy[0], dV_dT[0]))
# Calculate dynamical rates of changes
dx_dt, dy_dt, dtheta_dt = my_object.dynamics(
t, (x1[i], x2[j], x3[k]), uOpt, dOpt)
# Calculate Hamiltonian terms:
V_new[i, j,
k] = -(dx_dt * dV_dx[0] + dy_dt * dV_dy[0] +
dtheta_dt * dV_dT[0])
#probe[i, j, k] = V_new[i, j, k]
# Get derivMin
with hcl.if_(dV_dx_L[0] < min_deriv1[0]):
min_deriv1[0] = dV_dx_L[0]
with hcl.if_(dV_dx_R[0] < min_deriv1[0]):
min_deriv1[0] = dV_dx_R[0]
with hcl.if_(dV_dy_L[0] < min_deriv2[0]):
min_deriv2[0] = dV_dy_L[0]
with hcl.if_(dV_dy_R[0] < min_deriv2[0]):
min_deriv2[0] = dV_dy_R[0]
with hcl.if_(dV_dT_L[0] < min_deriv3[0]):
min_deriv3[0] = dV_dT_L[0]
with hcl.if_(dV_dT_R[0] < min_deriv3[0]):
min_deriv3[0] = dV_dT_R[0]
# Get derivMax
with hcl.if_(dV_dx_L[0] > max_deriv1[0]):
max_deriv1[0] = dV_dx_L[0]
with hcl.if_(dV_dx_R[0] > max_deriv1[0]):
max_deriv1[0] = dV_dx_R[0]
with hcl.if_(dV_dy_L[0] > max_deriv2[0]):
max_deriv2[0] = dV_dy_L[0]
with hcl.if_(dV_dy_R[0] > max_deriv2[0]):
max_deriv2[0] = dV_dy_R[0]
with hcl.if_(dV_dT_L[0] > max_deriv3[0]):
max_deriv3[0] = dV_dT_L[0]
with hcl.if_(dV_dT_R[0] > max_deriv3[0]):
max_deriv3[0] = dV_dT_R[0]
# Calculate the dissipation
with hcl.Stage("Dissipation"):
# Storing alphas
dOptL1 = hcl.scalar(0, "dOptL1")
dOptL2 = hcl.scalar(0, "dOptL2")
dOptL3 = hcl.scalar(0, "dOptL3")
# Find UPPER BOUND optimal disturbance
dOptU1 = hcl.scalar(0, "dOptU1")
dOptU2 = hcl.scalar(0, "dOptU2")
dOptU3 = hcl.scalar(0, "dOptU3")
alpha1 = hcl.scalar(0, "alpha1")
alpha2 = hcl.scalar(0, "alpha2")
alpha3 = hcl.scalar(0, "alpha3")
# Lower bound optimal control
uOptL1 = hcl.scalar(0, "uOptL1")
uOptL2 = hcl.scalar(0, "uOptL2")
uOptL3 = hcl.scalar(0, "uOptL3")
# Find UPPER BOUND optimal disturbance
uOptU1 = hcl.scalar(0, "uOptU1")
uOptU2 = hcl.scalar(0, "uOptU2")
uOptU3 = hcl.scalar(0, "uOptU3")
with hcl.for_(0, V_init.shape[0], name="i") as i:
with hcl.for_(0, V_init.shape[1], name="j") as j:
with hcl.for_(0, V_init.shape[2], name="k") as k:
dx_LL1 = hcl.scalar(0, "dx_LL1")
dx_LL2 = hcl.scalar(0, "dx_LL2")
dx_LL3 = hcl.scalar(0, "dx_LL3")
dx_UL1 = hcl.scalar(0, "dx_UL1")
dx_UL2 = hcl.scalar(0, "dx_UL2")
dx_UL3 = hcl.scalar(0, "dx_UL3")
dx_UU1 = hcl.scalar(0, "dx_UU1")
dx_UU2 = hcl.scalar(0, "dx_UU2")
dx_UU3 = hcl.scalar(0, "dx_UU3")
dx_LU1 = hcl.scalar(0, "dx_LU1")
dx_LU2 = hcl.scalar(0, "dx_LU2")
dx_LU3 = hcl.scalar(0, "dx_LU3")
# Find LOWER BOUND optimal disturbance
dOptL1[0], dOptL2[0], dOptL3[0] = my_object.optDstb(t, (x1[i], x2[j], x3[k]),\
(min_deriv1[0], min_deriv2[0],min_deriv3[0]))
# probe[i, j, k] = dOptL1[0] + dOptL2[0] + dOptL3[0]
dOptU1[0], dOptU2[0], dOptU3[0] = my_object.optDstb(t, (x1[i], x2[j], x3[k]),\
(max_deriv1[0], max_deriv2[0],max_deriv3[0]))
# probe[i, j, k] = dOptL1[0] + dOptL2[0] + dOptL3[0]
# Find LOWER BOUND optimal control
uOptL1[0], uOptL2[0], uOptL3[0] = my_object.opt_ctrl(t, (x1[i], x2[j], x3[k]), \
(min_deriv1[0], min_deriv2[0],min_deriv3[0]))
# probe[i, j, k] = uOptL1[0] + uOptL2[0] + uOptL3[0]
# Find UPPER BOUND optimal control
uOptU1[0], uOptU2[0], uOptU3[0] = my_object.opt_ctrl(
t, (x1[i], x2[j], x3[k]),
(max_deriv1[0], max_deriv2[0], max_deriv3[0]))
#probe[i, j, k] = uOptU1[0] + uOptU2[0] + uOptU3[0]
# Find magnitude of rates of changes
dx_LL1[0], dx_LL2[0], dx_LL3[0] = my_object.dynamics(t, (x1[i], x2[j], x3[k]),
(uOptL1[0], uOptL2[0], uOptL3[0]), \
(dOptL1[0], dOptL2[0], dOptL3[0]))
dx_LL1[0] = my_abs(dx_LL1[0])
dx_LL2[0] = my_abs(dx_LL2[0])
dx_LL3[0] = my_abs(dx_LL3[0])
#probe[i, j, k] = dx_LL1[0] + dx_LL2[0] + dx_LL3[0]
dx_LU1[0], dx_LU2[0], dx_LU3[0] = my_object.dynamics(t, (x1[i], x2[j], x3[k]),
(uOptL1[0], uOptL2[0], uOptL3[0]), \
(dOptU1[0], dOptU2[0], dOptU3[0]))
dx_LU1[0] = my_abs(dx_LU1[0])
dx_LU2[0] = my_abs(dx_LU2[0])
dx_LU3[0] = my_abs(dx_LU3[0])
# Calculate alpha
alpha1[0] = my_max(dx_LL1[0], dx_LU1[0])
alpha2[0] = my_max(dx_LL2[0], dx_LU2[0])
alpha3[0] = my_max(dx_LL3[0], dx_LU3[0])
# dx_UL3 = hcl.scalar(0, "dx_UL3")
# dx_UL1[0], dx_UL2[0], dx_UL3[0], dx_UL4[0] = my_object.dynamics(t, (x1[i], x2[j], x3[k], x4[l]),
# uOptU, dOptL)
dx_UL1[0], dx_UL2[0], dx_UL3[0]= my_object.dynamics(t, (x1[i], x2[j], x3[k]),\
(uOptU1[0], uOptU2[0], uOptU3[0]), \
(dOptL1[0], dOptL2[0], dOptL3[0]))
dx_UL1[0] = my_abs(dx_UL1[0])
dx_UL2[0] = my_abs(dx_UL2[0])
dx_UL3[0] = my_abs(dx_UL3[0])
# Calculate alpha
alpha1[0] = my_max(alpha1[0], dx_UL1[0])
alpha2[0] = my_max(alpha2[0], dx_UL2[0])
alpha3[0] = my_max(alpha3[0], dx_UL3[0])
dx_UU1[0], dx_UU2[0], dx_UU3[0] = my_object.dynamics(t, (x1[i], x2[j], x3[k]),
(uOptU1[0], uOptU2[0], uOptU3[0]),\
(dOptU1[0], dOptU2[0], dOptU3[0]))
dx_UU1[0] = my_abs(dx_UU1[0])
dx_UU2[0] = my_abs(dx_UU2[0])
dx_UU3[0] = my_abs(dx_UU3[0])
# Calculate alpha
alpha1[0] = my_max(alpha1[0], dx_UU1[0])
alpha2[0] = my_max(alpha2[0], dx_UU2[0])
alpha3[0] = my_max(alpha3[0], dx_UU3[0])
#probe[i, j, k] = alpha1[0] + alpha2[0] + alpha3[0]
diss = hcl.scalar(0, "diss")
diss[0] = 0.5 * (deriv_diff1[i, j, k] * alpha1[0] +
deriv_diff2[i, j, k] * alpha2[0] +
deriv_diff3[i, j, k] * alpha3[0])
# probe[i, j, k] = alpha2[0]
# Finally
V_new[i, j, k] = -(V_new[i, j, k] - diss[0])
# probe[i, j, k] = alpha3[0]
# Get maximum alphas in each dimension
# Calculate alphas
with hcl.if_(alpha1[0] > max_alpha1[0]):
max_alpha1[0] = alpha1[0]
with hcl.if_(alpha2[0] > max_alpha2[0]):
max_alpha2[0] = alpha2[0]
with hcl.if_(alpha3[0] > max_alpha3[0]):
max_alpha3[0] = alpha3[0]
# Determine time step
delta_t = hcl.compute((1, ), lambda x: step_bound(), name="delta_t")
# Integrate
result = hcl.update(
V_new,
lambda i, j, k: V_init[i, j, k] + V_new[i, j, k] * delta_t[0])
# Different computation method check
if compMethod == 'maxVWithV0':
result = hcl.update(V_new, lambda i, j, k: maxVWithV0(i, j, k))
if compMethod == 'minVWithV0':
result = hcl.update(V_new, lambda i, j, k: minVWithV0(i, j, k))
if compMethod == 'minVWithVInit':
result = hcl.update(V_new, lambda i, j, k: minVWithVInit(i, j, k))
if compMethod == 'maxVWithVInit':
result = hcl.update(V_new, lambda i, j, k: maxVWithVInit(i, j, k))
# Copy V_new to V_init
hcl.update(V_init, lambda i, j, k: V_new[i, j, k])
return result
def maxVWithVInit(i, j, k, l, m):
with hcl.if_(V_new[i, j, k, l, m] < V_init[i, j, k, l, m]):
V_new[i, j, k, l, m] = V_init[i, j, k, l, m]
def minVWithVInit(i, j, k, l):
with hcl.if_(V_new[i, j, k, l] > V_init[i, j, k, l]):
V_new[i, j, k, l] = V_init[i, j, k, l]
def kernel(A):
with hcl.if_(A[0] > 5):
A[0] = 5
with hcl.elif_(A[0] > 3):
A[0] = 3
def maxVWithVInit(i, j, k, l):
with hcl.if_(V_new[i, j, k, l] < V_init[i, j, k, l]):
V_new[i, j, k, l] = V_init[i, j, k, l]
def kernel(A):
with hcl.for_(0, 10) as i:
with hcl.for_(0, 10) as j:
with hcl.if_(j >= i):
hcl.break_()
A[i] += j
def maxVWithV0(i, j, k, l): # Take the max
with hcl.if_(V_new[i, j, k, l] < l0[i, j, k, l]):
V_new[i, j, k, l] = l0[i, j, k, l]
def kernel(A):
with hcl.if_(A[0] > 5):
A[0] = 5
with hcl.else_():
A[0] = -1
def minVWithV0(i, j, k, l):
with hcl.if_(V_new[i, j, k, l] > l0[i, j, k, l]):
V_new[i, j, k, l] = l0[i, j, k, l]
def minVWithVInit(i, j, k, l, m, n):
with hcl.if_(V_new[i, j, k, l, m, n] > V_init[i, j, k, l, m, n]):
V_new[i, j, k, l, m, n] = V_init[i, j, k, l, m, n]
def graph_create(V_new, V_init, x1, x2, x3, x4, x5, t, l0):
# Specify intermediate tensors
deriv_diff1 = hcl.compute(V_init.shape, lambda *x: 0, "deriv_diff1")
deriv_diff2 = hcl.compute(V_init.shape, lambda *x: 0, "deriv_diff2")
deriv_diff3 = hcl.compute(V_init.shape, lambda *x: 0, "deriv_diff3")
deriv_diff4 = hcl.compute(V_init.shape, lambda *x: 0, "deriv_diff4")
deriv_diff5 = hcl.compute(V_init.shape, lambda *x: 0, "deriv_diff5")
# Maximum derivative for each dim
max_deriv1 = hcl.scalar(-1e9, "max_deriv1")
max_deriv2 = hcl.scalar(-1e9, "max_deriv2")
max_deriv3 = hcl.scalar(-1e9, "max_deriv3")
max_deriv4 = hcl.scalar(-1e9, "max_deriv4")
max_deriv5 = hcl.scalar(-1e9, "max_deriv5")
# Min derivative for each dim
min_deriv1 = hcl.scalar(1e9, "min_deriv1")
min_deriv2 = hcl.scalar(1e9, "min_deriv2")
min_deriv3 = hcl.scalar(1e9, "min_deriv3")
min_deriv4 = hcl.scalar(1e9, "min_deriv4")
min_deriv5 = hcl.scalar(1e9, "min_deriv5")
# These variables are used to dissipation calculation
max_alpha1 = hcl.scalar(-1e9, "max_alpha1")
max_alpha2 = hcl.scalar(-1e9, "max_alpha2")
max_alpha3 = hcl.scalar(-1e9, "max_alpha3")
max_alpha4 = hcl.scalar(-1e9, "max_alpha4")
max_alpha5 = hcl.scalar(-1e9, "max_alpha5")
def step_bound(): # Function to calculate time step
stepBoundInv = hcl.scalar(0, "stepBoundInv")
stepBound = hcl.scalar(0, "stepBound")
stepBoundInv[0] = max_alpha1[0] / g.dx[0] + max_alpha2[0] / g.dx[1] + max_alpha3[0] / g.dx[2] + max_alpha4[
0] / g.dx[3] \
+ max_alpha5[0] / g.dx[4]
stepBound[0] = 0.8 / stepBoundInv[0]
with hcl.if_(stepBound > t[1] - t[0]):
stepBound[0] = t[1] - t[0]
# Update the lower time ranges
t[0] = t[0] + stepBound[0]
# t[0] = min_deriv2[0]
return stepBound[0]
def maxVWithV0(i, j, k, l, m): # Take the max
with hcl.if_(V_new[i, j, k, l, m] < l0[i, j, k, l, m]):
V_new[i, j, k, l, m] = l0[i, j, k, l, m]
def minVWithV0(i, j, k, l, m): # Take the max
with hcl.if_(V_new[i, j, k, l, m] > l0[i, j, k, l, m]):
V_new[i, j, k, l, m] = l0[i, j, k, l, m]
# Min with V_before
def minVWithVInit(i, j, k, l, m):
with hcl.if_(V_new[i, j, k, l, m] > V_init[i, j, k, l, m]):
V_new[i, j, k, l, m] = V_init[i, j, k, l, m]
def maxVWithVInit(i, j, k, l, m):
with hcl.if_(V_new[i, j, k, l, m] < V_init[i, j, k, l, m]):
V_new[i, j, k, l, m] = V_init[i, j, k, l, m]
# Calculate Hamiltonian for every grid point in V_init
with hcl.Stage("Hamiltonian"):
with hcl.for_(0, V_init.shape[0], name="i") as i:
with hcl.for_(0, V_init.shape[1], name="j") as j:
with hcl.for_(0, V_init.shape[2], name="k") as k:
with hcl.for_(0, V_init.shape[3], name="l") as l:
with hcl.for_(0, V_init.shape[4], name="m") as m:
# Variables to calculate dV_dx
dV_dx1_L = hcl.scalar(0, "dV_dx1_L")
dV_dx1_R = hcl.scalar(0, "dV_dx1_R")
dV_dx1 = hcl.scalar(0, "dV_dx1")
dV_dx2_L = hcl.scalar(0, "dV_dx2_L")
dV_dx2_R = hcl.scalar(0, "dV_dx2_R")
dV_dx2 = hcl.scalar(0, "dV_dx2")
dV_dx3_L = hcl.scalar(0, "dV_dx3_L")
dV_dx3_R = hcl.scalar(0, "dV_dx3_R")
dV_dx3 = hcl.scalar(0, "dV_dx3")
dV_dx4_L = hcl.scalar(0, "dV_dx4_L")
dV_dx4_R = hcl.scalar(0, "dV_dx4_R")
dV_dx4 = hcl.scalar(0, "dV_dx4")
dV_dx5_L = hcl.scalar(0, "dV_dx5_L")
dV_dx5_R = hcl.scalar(0, "dV_dx5_R")
dV_dx5 = hcl.scalar(0, "dV_dx5")
# No tensor slice operation
# dV_dx_L[0], dV_dx_R[0] = spa_derivX(i, j, k)
if accuracy == "low":
dV_dx1_L[0], dV_dx1_R[0] = spa_derivX1_5d(
i, j, k, l, m, V_init, g)
dV_dx2_L[0], dV_dx2_R[0] = spa_derivX2_5d(
i, j, k, l, m, V_init, g)
dV_dx3_L[0], dV_dx3_R[0] = spa_derivX3_5d(
i, j, k, l, m, V_init, g)
dV_dx4_L[0], dV_dx4_R[0] = spa_derivX4_5d(
i, j, k, l, m, V_init, g)
dV_dx5_L[0], dV_dx5_R[0] = spa_derivX5_5d(
i, j, k, l, m, V_init, g)
if accuracy == "high":
dV_dx1_L[0], dV_dx1_R[
0] = secondOrderX1_5d(
i, j, k, l, m, V_init, g)
dV_dx2_L[0], dV_dx2_R[
0] = secondOrderX2_5d(
i, j, k, l, m, V_init, g)
dV_dx3_L[0], dV_dx3_R[
0] = secondOrderX3_5d(
i, j, k, l, m, V_init, g)
dV_dx4_L[0], dV_dx4_R[
0] = secondOrderX4_5d(
i, j, k, l, m, V_init, g)
dV_dx5_L[0], dV_dx5_R[
0] = secondOrderX5_5d(
i, j, k, l, m, V_init, g)
# Saves spatial derivative diff into tables
deriv_diff1[i, j, k, l,
m] = dV_dx1_R[0] - dV_dx1_L[0]
deriv_diff2[i, j, k, l,
m] = dV_dx2_R[0] - dV_dx2_L[0]
deriv_diff3[i, j, k, l,
m] = dV_dx3_R[0] - dV_dx3_L[0]
deriv_diff4[i, j, k, l,
m] = dV_dx4_R[0] - dV_dx4_L[0]
deriv_diff5[i, j, k, l,
m] = dV_dx5_R[0] - dV_dx5_L[0]
# Calculate average gradient
dV_dx1[0] = (dV_dx1_L + dV_dx1_R) / 2
dV_dx2[0] = (dV_dx2_L + dV_dx2_R) / 2
dV_dx3[0] = (dV_dx3_L + dV_dx3_R) / 2
dV_dx4[0] = (dV_dx4_L + dV_dx4_R) / 2
dV_dx5[0] = (dV_dx5_L + dV_dx5_R) / 2
# Find optimal control
uOpt = my_object.opt_ctrl(t, (x1[i], x2[j], x3[k], x4[l], x5[m]), \
(dV_dx1[0], dV_dx2[0], dV_dx3[0], dV_dx4[0], dV_dx5[0]))
# Find optimal disturbance
dOpt = my_object.opt_dstb(t, (x1[i], x2[j], x3[k], x4[l], x5[m]), \
(dV_dx1[0], dV_dx2[0], dV_dx3[0], dV_dx4[0], dV_dx5[0]))
# Find rates of changes based on dynamics equation
dx1_dt, dx2_dt, dx3_dt, dx4_dt, dx5_dt = my_object.dynamics(
t, (x1[i], x2[j], x3[k], x4[l], x5[m]),
uOpt, dOpt)
# Calculate Hamiltonian terms:
V_new[i, j, k, l, m] = -(
dx1_dt * dV_dx1[0] + dx2_dt * dV_dx2[0] +
dx3_dt * dV_dx3[0] + dx4_dt * dV_dx4[0] +
dx5_dt * dV_dx5[0])
# Get derivMin
with hcl.if_(dV_dx1_L[0] < min_deriv1[0]):
min_deriv1[0] = dV_dx1_L[0]
with hcl.if_(dV_dx1_R[0] < min_deriv1[0]):
min_deriv1[0] = dV_dx1_R[0]
with hcl.if_(dV_dx2_L[0] < min_deriv2[0]):
min_deriv2[0] = dV_dx2_L[0]
with hcl.if_(dV_dx2_R[0] < min_deriv2[0]):
min_deriv2[0] = dV_dx2_R[0]
with hcl.if_(dV_dx3_L[0] < min_deriv3[0]):
min_deriv3[0] = dV_dx3_L[0]
with hcl.if_(dV_dx3_R[0] < min_deriv3[0]):
min_deriv3[0] = dV_dx3_R[0]
with hcl.if_(dV_dx4_L[0] < min_deriv4[0]):
min_deriv4[0] = dV_dx4_L[0]
with hcl.if_(dV_dx4_R[0] < min_deriv4[0]):
min_deriv4[0] = dV_dx4_R[0]
with hcl.if_(dV_dx5_L[0] < min_deriv5[0]):
min_deriv5[0] = dV_dx5_L[0]
with hcl.if_(dV_dx5_R[0] < min_deriv5[0]):
min_deriv5[0] = dV_dx5_R[0]
# Get derivMax
with hcl.if_(dV_dx1_L[0] > max_deriv1[0]):
max_deriv1[0] = dV_dx1_L[0]
with hcl.if_(dV_dx1_R[0] > max_deriv1[0]):
max_deriv1[0] = dV_dx1_R[0]
with hcl.if_(dV_dx2_L[0] > max_deriv2[0]):
max_deriv2[0] = dV_dx2_L[0]
with hcl.if_(dV_dx2_R[0] > max_deriv2[0]):
max_deriv2[0] = dV_dx2_R[0]
with hcl.if_(dV_dx3_L[0] > max_deriv3[0]):
max_deriv3[0] = dV_dx3_L[0]
with hcl.if_(dV_dx3_R[0] > max_deriv3[0]):
max_deriv3[0] = dV_dx3_R[0]
with hcl.if_(dV_dx4_L[0] > max_deriv4[0]):
max_deriv4[0] = dV_dx4_L[0]
with hcl.if_(dV_dx4_R[0] > max_deriv4[0]):
max_deriv4[0] = dV_dx4_R[0]
with hcl.if_(dV_dx5_L[0] > max_deriv5[0]):
max_deriv5[0] = dV_dx5_L[0]
with hcl.if_(dV_dx5_R[0] > max_deriv5[0]):
max_deriv5[0] = dV_dx5_R[0]
# Calculate dissipation amount
with hcl.Stage("Dissipation"):
uOptL1 = hcl.scalar(0, "uOptL1")
uOptL2 = hcl.scalar(0, "uOptL2")
uOptL3 = hcl.scalar(0, "uOptL3")
uOptL4 = hcl.scalar(0, "uOptL4")
uOptL5 = hcl.scalar(0, "uOptL5")
uOptU1 = hcl.scalar(0, "uOptU1")
uOptU2 = hcl.scalar(0, "uOptU2")
uOptU3 = hcl.scalar(0, "uOptU3")
uOptU4 = hcl.scalar(0, "uOptU4")
uOptU5 = hcl.scalar(0, "uOptU5")
dOptL1 = hcl.scalar(0, "dOptL1")
dOptL2 = hcl.scalar(0, "dOptL2")
dOptL3 = hcl.scalar(0, "dOptL3")
dOptL4 = hcl.scalar(0, "dOptL4")
dOptL5 = hcl.scalar(0, "dOptL5")
dOptU1 = hcl.scalar(0, "dOptU1")
dOptU2 = hcl.scalar(0, "dOptU2")
dOptU3 = hcl.scalar(0, "dOptU3")
dOptU4 = hcl.scalar(0, "dOptU4")
dOptU5 = hcl.scalar(0, "dOptU5")
# Storing alphas
alpha1 = hcl.scalar(0, "alpha1")
alpha2 = hcl.scalar(0, "alpha2")
alpha3 = hcl.scalar(0, "alpha3")
alpha4 = hcl.scalar(0, "alpha4")
alpha5 = hcl.scalar(0, "alpha5")
"""
NOTE: If optimal adversarial disturbance is not dependent on states
, the below approximate LOWER/UPPER BOUND optimal disturbance is accurate.
If that's not the case, move the next two statements into the nested loops and modify the states passed in
as my_object.opt_dstb(t, (x1[i], x2[j], x3[k], x4[l], ...), ...).
The reason we don't have this line in the nested loop by default is to avoid redundant computations
for certain systems where disturbance are not dependent on states.
In general, dissipation amount can just be approximates.
"""
# Find LOWER BOUND optimal disturbance
dOptL1[0], dOptL2[0], dOptL3[0], dOptL4[0], dOptL5[0] = my_object.opt_dstb(t, (x1[0], x2[0], x3[0], x4[0], x5[0]), \
(min_deriv1[0], min_deriv2[0], min_deriv3[0], min_deriv4[0], min_deriv5[0]))
# Find UPPER BOUND optimal disturbance
dOptU1[0], dOptU2[0], dOptU3[0], dOptU4[0], dOptU5[0] = my_object.opt_dstb(t, (x1[0], x2[0], x3[0], x4[0], x5[0]), \
(max_deriv1[0], max_deriv2[0], max_deriv3[0], max_deriv4[0], max_deriv5[0]))
with hcl.for_(0, V_init.shape[0], name="i") as i:
with hcl.for_(0, V_init.shape[1], name="j") as j:
with hcl.for_(0, V_init.shape[2], name="k") as k:
with hcl.for_(0, V_init.shape[3], name="l") as l:
with hcl.for_(0, V_init.shape[4], name="m") as m:
dx_LL1 = hcl.scalar(0, "dx_LL1")
dx_LL2 = hcl.scalar(0, "dx_LL2")
dx_LL3 = hcl.scalar(0, "dx_LL3")
dx_LL4 = hcl.scalar(0, "dx_LL4")
dx_LL5 = hcl.scalar(0, "dx_LL5")
dx_UL1 = hcl.scalar(0, "dx_UL1")
dx_UL2 = hcl.scalar(0, "dx_UL2")
dx_UL3 = hcl.scalar(0, "dx_UL3")
dx_UL4 = hcl.scalar(0, "dx_UL4")
dx_UL5 = hcl.scalar(0, "dx_UL5")
#
dx_LU1 = hcl.scalar(0, "dx_LU1")
dx_LU2 = hcl.scalar(0, "dx_LU2")
dx_LU3 = hcl.scalar(0, "dx_LU3")
dx_LU4 = hcl.scalar(0, "dx_LU4")
dx_LU5 = hcl.scalar(0, "dx_LU5")
dx_UU1 = hcl.scalar(0, "dx_UU1")
dx_UU2 = hcl.scalar(0, "dx_UU2")
dx_UU3 = hcl.scalar(0, "dx_UU3")
dx_UU4 = hcl.scalar(0, "dx_UU4")
dx_UU5 = hcl.scalar(0, "dx_UU5")
# Find LOWER BOUND optimal control
uOptL1[0], uOptL2[0], uOptL3[0], uOptL4[0], uOptL5[0] = my_object.opt_ctrl(t, (x1[i], x2[j], x3[k], x4[l], x5[m]), \
(min_deriv1[0], min_deriv2[0], min_deriv3[0], min_deriv4[0], min_deriv5[0]))
# Find UPPER BOUND optimal control
uOptU1[0], uOptU2[0], uOptU3[0], uOptU4[0], uOptU5[0] = my_object.opt_ctrl(t, (x1[i], x2[j], x3[k], x4[l], x5[m]), \
(max_deriv1[0], max_deriv2[0], max_deriv3[0], max_deriv4[0], max_deriv5[0]))
# Get upper bound and lower bound rates of changes
dx_LL1[0], dx_LL2[0], dx_LL3[0], dx_LL4[0], dx_LL5[0] = my_object.dynamics(t, \
(x1[i], x2[j], x3[k], x4[l], x5[m]), (uOptL1[0], uOptL2[0], uOptL3[0], uOptL4[0], uOptL5[0]),
(dOptL1[0], dOptL2[0], dOptL3[0], dOptL4[0], dOptL5[0]))
# Get absolute value of each
dx_LL1[0] = my_abs(dx_LL1[0])
dx_LL2[0] = my_abs(dx_LL2[0])
dx_LL3[0] = my_abs(dx_LL3[0])
dx_LL4[0] = my_abs(dx_LL4[0])
dx_LL5[0] = my_abs(dx_LL5[0])
dx_UL1[0], dx_UL2[0], dx_UL3[0], dx_UL4[0], dx_UL5[0] = my_object.dynamics(t, \
(x1[i], x2[j], x3[k], x4[l], x5[m]), (uOptU1[0], uOptU2[0], uOptU3[0], uOptU4[0], uOptU5[0]),
(dOptL1[0], dOptL2[0], dOptL3[0], dOptL4[0], dOptL5[0]))
# Get absolute value of each
dx_UL1[0] = my_abs(dx_UL1[0])
dx_UL2[0] = my_abs(dx_UL2[0])
dx_UL3[0] = my_abs(dx_UL3[0])
dx_UL4[0] = my_abs(dx_UL4[0])
dx_UL5[0] = my_abs(dx_UL5[0])
# Set maximum alphas
alpha1[0] = my_max(dx_UL1[0], dx_LL1[0])
alpha2[0] = my_max(dx_UL2[0], dx_LL2[0])
alpha3[0] = my_max(dx_UL3[0], dx_LL3[0])
alpha4[0] = my_max(dx_UL4[0], dx_LL4[0])
alpha5[0] = my_max(dx_UL5[0], dx_LL5[0])
dx_LU1[0], dx_LU2[0], dx_LU3[0], dx_LU4[0], dx_LU5[0] = my_object.dynamics(t, \
(x1[i], x2[j], x3[k], x4[l], x5[m]), (uOptL1[0], uOptL2[0], uOptL3[0], uOptL4[0], uOptL5[0]),
(dOptU1[0], dOptU2[0], dOptU3[0], dOptU4[0], dOptU5[0]))
# Get absolute value of each
dx_LU1[0] = my_abs(dx_LU1[0])
dx_LU2[0] = my_abs(dx_LU2[0])
dx_LU3[0] = my_abs(dx_LU3[0])
dx_LU4[0] = my_abs(dx_LU4[0])
dx_LU5[0] = my_abs(dx_LU5[0])
alpha1[0] = my_max(alpha1[0], dx_LU1[0])
alpha2[0] = my_max(alpha2[0], dx_LU2[0])
alpha3[0] = my_max(alpha3[0], dx_LU3[0])
alpha4[0] = my_max(alpha4[0], dx_LU4[0])
alpha5[0] = my_max(alpha5[0], dx_LU5[0])
dx_UU1[0], dx_UU2[0], dx_UU3[0], dx_UU4[0], dx_UU5[0] = my_object.dynamics(t, \
(x1[i], x2[j], x3[k], x4[l], x5[m]), (uOptU1[0], uOptU2[0], uOptU3[0], uOptU4[0], uOptU5[0]),
(dOptU1[0], dOptU2[0], dOptU3[0], dOptU4[0], dOptU5[0]))
dx_UU1[0] = my_abs(dx_UU1[0])
dx_UU2[0] = my_abs(dx_UU2[0])
dx_UU3[0] = my_abs(dx_UU3[0])
dx_UU4[0] = my_abs(dx_UU4[0])
dx_UU5[0] = my_abs(dx_UU5[0])
alpha1[0] = my_max(alpha1[0], dx_UU1[0])
alpha2[0] = my_max(alpha2[0], dx_UU2[0])
alpha3[0] = my_max(alpha3[0], dx_UU3[0])
alpha4[0] = my_max(alpha4[0], dx_UU4[0])
alpha5[0] = my_max(alpha5[0], dx_UU5[0])
diss = hcl.scalar(0, "diss")
diss[0] = 0.5 * (deriv_diff1[i, j, k, l, m] * alpha1[0] + deriv_diff2[
i, j, k, l, m] * alpha2[0] \
+ deriv_diff3[i, j, k, l, m] * alpha3[0] + deriv_diff4[
i, j, k, l, m] * alpha4[0] \
+ deriv_diff5[i, j, k, l, m] * alpha5[0] )
# Finally
V_new[i, j, k, l,
m] = -(V_new[i, j, k, l, m] - diss[0])
# Get maximum alphas in each dimension
# Calculate alphas
with hcl.if_(alpha1 > max_alpha1):
max_alpha1[0] = alpha1[0]
with hcl.if_(alpha2 > max_alpha2):
max_alpha2[0] = alpha2[0]
with hcl.if_(alpha3 > max_alpha3):
max_alpha3[0] = alpha3[0]
with hcl.if_(alpha4 > max_alpha4):
max_alpha4[0] = alpha4[0]
with hcl.if_(alpha5 > max_alpha5):
max_alpha5[0] = alpha5[0]
# Determine time step
delta_t = hcl.compute((1, ), lambda x: step_bound(), name="delta_t")
# hcl.update(t, lambda x: t[x] + delta_t[x])
# Integrate
# if compMethod == 'HJ_PDE':
result = hcl.update(
V_new, lambda i, j, k, l, m: V_init[i, j, k, l, m] + V_new[
i, j, k, l, m] * delta_t[0])
if compMethod == 'maxVWithV0':
result = hcl.update(
V_new, lambda i, j, k, l, m: maxVWithV0(i, j, k, l, m))
if compMethod == 'minVWithV0':
result = hcl.update(
V_new, lambda i, j, k, l, m: minVWithV0(i, j, k, l, m))
if compMethod == 'maxVWithVInit':
result = hcl.update(
V_new, lambda i, j, k, l, m: maxVWithVInit(i, j, k, l, m))
if compMethod == 'minVWithVInit':
result = hcl.update(
V_new, lambda i, j, k, l, m: minVWithVInit(i, j, k, l, m))
# Copy V_new to V_init
hcl.update(V_init, lambda i, j, k, l, m: V_new[i, j, k, l, m])
return result
def reducer_body(x, y):
with hcl.if_(x > 5):
hcl.return_(y + 1)
with hcl.else_():
hcl.return_(y + 2)
def minVWithV0(i, j, k, l, m): # Take the max
with hcl.if_(V_new[i, j, k, l, m] > l0[i, j, k, l, m]):
V_new[i, j, k, l, m] = l0[i, j, k, l, m]
def graph_6D(V_new, V_init, deriv_diff1, deriv_diff2, deriv_diff3, deriv_diff4, deriv_diff5, deriv_diff6,
x1, x2, x3, x4, x5, x6 ,t , l0, obstacle):
# Maximum derivative for each dim
max_deriv1 = hcl.scalar(-1e9, "max_deriv1")
max_deriv2 = hcl.scalar(-1e9, "max_deriv2")
max_deriv3 = hcl.scalar(-1e9, "max_deriv3")
max_deriv4 = hcl.scalar(-1e9, "max_deriv4")
max_deriv5 = hcl.scalar(-1e9, "max_deriv5")
max_deriv6 = hcl.scalar(-1e9, "max_deriv6")
# Min derivative for each dim
min_deriv1 = hcl.scalar(1e9, "min_deriv1")
min_deriv2 = hcl.scalar(1e9, "min_deriv2")
min_deriv3 = hcl.scalar(1e9, "min_deriv3")
min_deriv4 = hcl.scalar(1e9, "min_deriv4")
min_deriv5 = hcl.scalar(1e9, "min_deriv5")
min_deriv6 = hcl.scalar(1e9, "min_deriv6")
# These variables are used to dissipation calculation
max_alpha1 = hcl.scalar(-1e9, "max_alpha1")
max_alpha2 = hcl.scalar(-1e9, "max_alpha2")
max_alpha3 = hcl.scalar(-1e9, "max_alpha3")
max_alpha4 = hcl.scalar(-1e9, "max_alpha4")
max_alpha5 = hcl.scalar(-1e9, "max_alpha5")
max_alpha6 = hcl.scalar(-1e9, "max_alpha6")
def step_bound(): # Function to calculate time step
stepBoundInv = hcl.scalar(0, "stepBoundInv")
stepBound = hcl.scalar(0, "stepBound")
stepBoundInv[0] = max_alpha1[0]/g.dx[0] + max_alpha2[0]/g.dx[1] + max_alpha3[0]/g.dx[2] + max_alpha4[0]/g.dx[3] \
+ max_alpha5[0]/g.dx[4] + max_alpha6[0]/g.dx[5]
stepBound[0] = 0.8/stepBoundInv[0]
with hcl.if_(stepBound > t[1] - t[0]):
stepBound[0] = t[1] - t[0]
# Update the lower time ranges
t[0] = t[0] + stepBound[0]
#t[0] = min_deriv2[0]
return stepBound[0]
def maxVWithV0(i, j, k, l, m, n): # Take the max
with hcl.if_(V_new[i, j, k, l, m, n] < l0[i, j, k, l, m, n]):
V_new[i, j, k, l, m, n] = l0[i, j, k, l, m, n]
# Max(V, g )
def maxVWithCStraint(i, j, k, l, m, n):
with hcl.if_(V_new[i, j, k, l, m, n] < obstacle[i, j, k, l, m, n]):
V_new[i, j, k, l, m, n] = obstacle[i, j, k, l, m, n]
# Calculate Hamiltonian for every grid point in V_init
with hcl.Stage("Hamiltonian"):
with hcl.for_(0, V_init.shape[0], name="i") as i:
with hcl.for_(0, V_init.shape[1], name="j") as j:
with hcl.for_(0, V_init.shape[2], name="k") as k:
with hcl.for_(0, V_init.shape[3], name="l") as l:
with hcl.for_(0, V_init.shape[4], name="m") as m:
with hcl.for_(0, V_init.shape[5], name="n") as n:
#Variables to calculate dV_dx
dV_dx1_L = hcl.scalar(0, "dV_dx1_L")
dV_dx1_R = hcl.scalar(0, "dV_dx1_R")
dV_dx1 = hcl.scalar(0, "dV_dx1")
dV_dx2_L = hcl.scalar(0, "dV_dx2_L")
dV_dx2_R = hcl.scalar(0, "dV_dx2_R")
dV_dx2 = hcl.scalar(0, "dV_dx2")
dV_dx3_L = hcl.scalar(0, "dV_dx3_L")
dV_dx3_R = hcl.scalar(0, "dV_dx3_R")
dV_dx3 = hcl.scalar(0, "dV_dx3")
dV_dx4_L = hcl.scalar(0, "dV_dx4_L")
dV_dx4_R = hcl.scalar(0, "dV_dx4_R")
dV_dx4 = hcl.scalar(0, "dV_dx4")
dV_dx5_L = hcl.scalar(0, "dV_dx5_L")
dV_dx5_R = hcl.scalar(0, "dV_dx5_R")
dV_dx5 = hcl.scalar(0, "dV_dx5")
dV_dx6_L = hcl.scalar(0, "dV_dx6_L")
dV_dx6_R = hcl.scalar(0, "dV_dx6_R")
dV_dx6 = hcl.scalar(0, "dV_dx6")
# No tensor slice operation
#dV_dx_L[0], dV_dx_R[0] = spa_derivX(i, j, k)
dV_dx1_L[0], dV_dx1_R[0] = spa_derivX6_6d(i, j, k, l, m, n, V_init, g)
dV_dx2_L[0], dV_dx2_R[0] = spa_derivX5_6d(i, j, k, l, m, n, V_init, g)
dV_dx3_L[0], dV_dx3_R[0] = spa_derivX4_6d(i, j, k, l, m, n, V_init, g)
dV_dx4_L[0], dV_dx4_R[0] = spa_derivX3_6d(i, j, k, l, m, n, V_init, g)
dV_dx5_L[0], dV_dx5_R[0] = spa_derivX2_6d(i, j, k, l, m, n, V_init, g)
dV_dx6_L[0], dV_dx6_R[0] = spa_derivX1_6d(i, j, k, l, m, n, V_init, g)
# Saves spatial derivative diff into tables
deriv_diff1[i, j, k, l, m, n] = dV_dx1_R[0] - dV_dx1_L[0]
deriv_diff2[i, j, k, l, m, n] = dV_dx2_R[0] - dV_dx2_L[0]
deriv_diff3[i, j, k, l, m, n] = dV_dx3_R[0] - dV_dx3_L[0]
deriv_diff4[i, j, k, l, m, n] = dV_dx4_R[0] - dV_dx4_L[0]
deriv_diff5[i, j, k, l, m, n] = dV_dx5_R[0] - dV_dx5_L[0]
deriv_diff6[i, j, k, l, m, n] = dV_dx6_R[0] - dV_dx6_L[0]
#Calculate average gradient
dV_dx1[0] = (dV_dx1_L + dV_dx1_R) / 2
dV_dx2[0] = (dV_dx2_L + dV_dx2_R) / 2
dV_dx3[0] = (dV_dx3_L + dV_dx3_R) / 2
dV_dx4[0] = (dV_dx4_L + dV_dx4_R) / 2
dV_dx5[0] = (dV_dx5_L + dV_dx5_R) / 2
dV_dx6[0] = (dV_dx6_L + dV_dx6_R) / 2
# Find optimal control
uOpt = my_object.opt_ctrl(t,(x1[i], x2[j], x3[k], x4[l], x5[m], x6[n]), (dV_dx1[0], dV_dx2[0], dV_dx3[0], dV_dx4[0], dV_dx5[0], dV_dx6[0]))
# Find optimal disturbance
dOpt = my_object.opt_dstb((dV_dx1[0], dV_dx2[0], dV_dx3[0], dV_dx4[0], dV_dx5[0], dV_dx6[0]))
# Find rates of changes based on dynamics equation
dx1_dt, dx2_dt, dx3_dt, dx4_dt, dx5_dt, dx6_dt = my_object.dynamics(t, (x1[i], x2[j], x3[k], x4[l], x5[m], x6[n]), uOpt, dOpt)
# Calculate Hamiltonian terms:
V_new[i, j, k, l, m, n] = -(dx1_dt * dV_dx1[0] + dx2_dt * dV_dx2[0] + dx3_dt * dV_dx3[0] + dx4_dt * dV_dx4[0] + dx5_dt * dV_dx5[0] + dx6_dt * dV_dx6[0])
# Get derivMin
with hcl.if_(dV_dx1_L[0] < min_deriv1[0]):
min_deriv1[0] = dV_dx1_L[0]
with hcl.if_(dV_dx1_R[0] < min_deriv1[0]):
min_deriv1[0] = dV_dx1_R[0]
with hcl.if_(dV_dx2_L[0] < min_deriv2[0]):
min_deriv2[0] = dV_dx2_L[0]
with hcl.if_(dV_dx2_R[0] < min_deriv2[0]):
min_deriv2[0] = dV_dx2_R[0]
with hcl.if_(dV_dx3_L[0] < min_deriv3[0]):
min_deriv3[0] = dV_dx3_L[0]
with hcl.if_(dV_dx3_R[0] < min_deriv3[0]):
min_deriv3[0] = dV_dx3_R[0]
with hcl.if_(dV_dx4_L[0] < min_deriv4[0]):
min_deriv4[0] = dV_dx4_L[0]
with hcl.if_(dV_dx4_R[0] < min_deriv4[0]):
min_deriv4[0] = dV_dx4_R[0]
with hcl.if_(dV_dx5_L[0] < min_deriv5[0]):
min_deriv5[0] = dV_dx5_L[0]
with hcl.if_(dV_dx5_R[0] < min_deriv5[0]):
min_deriv5[0] = dV_dx5_R[0]
with hcl.if_(dV_dx6_L[0] < min_deriv6[0]):
min_deriv6[0] = dV_dx6_L[0]
with hcl.if_(dV_dx6_R[0] < min_deriv6[0]):
min_deriv6[0] = dV_dx6_R[0]
# Get derivMax
with hcl.if_(dV_dx1_L[0] > max_deriv1[0]):
max_deriv1[0] = dV_dx1_L[0]
with hcl.if_(dV_dx1_R[0] > max_deriv1[0]):
max_deriv1[0] = dV_dx1_R[0]
with hcl.if_(dV_dx2_L[0] > max_deriv2[0]):
max_deriv2[0] = dV_dx2_L[0]
with hcl.if_(dV_dx2_R[0] > max_deriv2[0]):
max_deriv2[0] = dV_dx2_R[0]
with hcl.if_(dV_dx3_L[0] > max_deriv3[0]):
max_deriv3[0] = dV_dx3_L[0]
with hcl.if_(dV_dx3_R[0] > max_deriv3[0]):
max_deriv3[0] = dV_dx3_R[0]
with hcl.if_(dV_dx4_L[0] > max_deriv4[0]):
max_deriv4[0] = dV_dx4_L[0]
with hcl.if_(dV_dx4_R[0] > max_deriv4[0]):
max_deriv4[0] = dV_dx4_R[0]
with hcl.if_(dV_dx5_L[0] > max_deriv5[0]):
max_deriv5[0] = dV_dx5_L[0]
with hcl.if_(dV_dx5_R[0] > max_deriv5[0]):
max_deriv5[0] = dV_dx5_R[0]
with hcl.if_(dV_dx6_L[0] > max_deriv6[0]):
max_deriv6[0] = dV_dx6_L[0]
with hcl.if_(dV_dx6_R[0] > max_deriv6[0]):
max_deriv6[0] = dV_dx6_R[0]
# Calculate dissipation amount
with hcl.Stage("Dissipation"):
uOptL1 = hcl.scalar(0, "uOptL1")
uOptL2 = hcl.scalar(0, "uOptL2")
uOptL3 = hcl.scalar(0, "uOptL3")
uOptL4 = hcl.scalar(0, "uOptL4")
uOptU1 = hcl.scalar(0, "uOptU1")
uOptU2 = hcl.scalar(0, "uOptU2")
uOptU3 = hcl.scalar(0, "uOptU3")
uOptU4 = hcl.scalar(0, "uOptU4")
dOptL1 = hcl.scalar(0, "dOptL1")
dOptL2 = hcl.scalar(0, "dOptL2")
dOptL3 = hcl.scalar(0, "dOptL3")
dOptL4 = hcl.scalar(0, "dOptL4")
dOptU1 = hcl.scalar(0, "dOptU1")
dOptU2 = hcl.scalar(0, "dOptU2")
dOptU3 = hcl.scalar(0, "dOptU3")
dOptU4 = hcl.scalar(0, "dOptU4")
# Storing alphas
alpha1 = hcl.scalar(0, "alpha1")
alpha2 = hcl.scalar(0, "alpha2")
alpha3 = hcl.scalar(0, "alpha3")
alpha4 = hcl.scalar(0, "alpha4")
alpha5 = hcl.scalar(0, "alpha5")
alpha6 = hcl.scalar(0, "alpha6")
# Find LOWER BOUND optimal disturbance
dOptL = my_object.opt_dstb((min_deriv1[0], min_deriv2[0], min_deriv3[0], min_deriv4[0], min_deriv5[0], min_deriv6[0]))
# Find UPPER BOUND optimal disturbance
dOptU = my_object.opt_dstb((max_deriv1[0], max_deriv2[0], max_deriv3[0], max_deriv4[0], min_deriv5[0], min_deriv6[0]))
with hcl.for_(0, V_init.shape[0], name="i") as i:
with hcl.for_(0, V_init.shape[1], name="j") as j:
with hcl.for_(0, V_init.shape[2], name="k") as k:
with hcl.for_(0, V_init.shape[3], name="l") as l:
with hcl.for_(0, V_init.shape[4], name="m") as m:
with hcl.for_(0, V_init.shape[5], name="n") as n:
dx_LL1 = hcl.scalar(0, "dx_LL1")
dx_LL2 = hcl.scalar(0, "dx_LL2")
dx_LL3 = hcl.scalar(0, "dx_LL3")
dx_LL4 = hcl.scalar(0, "dx_LL4")
dx_LL5 = hcl.scalar(0, "dx_LL5")
dx_LL6 = hcl.scalar(0, "dx_LL6")
dx_UL1 = hcl.scalar(0, "dx_UL1")
dx_UL2 = hcl.scalar(0, "dx_UL2")
dx_UL3 = hcl.scalar(0, "dx_UL3")
dx_UL4 = hcl.scalar(0, "dx_UL4")
dx_UL5 = hcl.scalar(0, "dx_UL5")
dx_UL6 = hcl.scalar(0, "dx_UL6")
#
dx_LU1 = hcl.scalar(0, "dx_LU1")
dx_LU2 = hcl.scalar(0, "dx_LU2")
dx_LU3 = hcl.scalar(0, "dx_LU3")
dx_LU4 = hcl.scalar(0, "dx_LU4")
dx_LU5 = hcl.scalar(0, "dx_LU5")
dx_LU6 = hcl.scalar(0, "dx_LU6")
dx_UU1 = hcl.scalar(0, "dx_UU1")
dx_UU2 = hcl.scalar(0, "dx_UU2")
dx_UU3 = hcl.scalar(0, "dx_UU3")
dx_UU4 = hcl.scalar(0, "dx_UU4")
dx_UU5 = hcl.scalar(0, "dx_UU5")
dx_UU6 = hcl.scalar(0, "dx_UU6")
# Find LOWER BOUND optimal control
uOptL = my_object.opt_ctrl(t, (x1[i], x2[j], x3[k], x4[l], x5[m], x6[n]), (min_deriv1[0], min_deriv2[0], min_deriv3[0], min_deriv4[0], min_deriv5[0], min_deriv6[0]))
# Find UPPER BOUND optimal control
uOptU = my_object.opt_ctrl(t, (x1[i], x2[j], x3[k], x4[l], x5[m], x6[n]), (max_deriv1[0], max_deriv2[0], max_deriv3[0], max_deriv4[0], max_deriv5[0], max_deriv6[0]))
# Get upper bound and lower bound rates of changes
dx_LL1[0], dx_LL2[0], dx_LL3[0], dx_LL4[0], dx_LL5[0], dx_LL6[0] = my_object.dynamics(t, (x1[i], x2[j], x3[k], x4[l], x5[m], x6[n]), uOptL, dOptL)
# Get absolute value of each
dx_LL1[0] = my_abs(dx_LL1[0])
dx_LL2[0] = my_abs(dx_LL2[0])
dx_LL3[0] = my_abs(dx_LL3[0])
dx_LL4[0] = my_abs(dx_LL4[0])
dx_LL5[0] = my_abs(dx_LL5[0])
dx_LL6[0] = my_abs(dx_LL6[0])
dx_UL1[0], dx_UL2[0], dx_UL3[0], dx_UL4[0], dx_UL5[0], dx_UL6[0] = my_object.dynamics(t, (x1[i], x2[j], x3[k], x4[l], x5[m], x6[n]), uOptU, dOptL)
# Get absolute value of each
dx_UL1[0] = my_abs(dx_UL1[0])
dx_UL2[0] = my_abs(dx_UL2[0])
dx_UL3[0] = my_abs(dx_UL3[0])
dx_UL4[0] = my_abs(dx_UL4[0])
dx_UL5[0] = my_abs(dx_UL5[0])
dx_UL6[0] = my_abs(dx_UL6[0])
# Set maximum alphas
alpha1[0] = my_max(dx_UL1[0], dx_LL1[0])
alpha2[0] = my_max(dx_UL2[0], dx_LL2[0])
alpha3[0] = my_max(dx_UL3[0], dx_LL3[0])
alpha4[0] = my_max(dx_UL4[0], dx_LL4[0])
alpha5[0] = my_max(dx_UL5[0], dx_LL5[0])
alpha6[0] = my_max(dx_UL6[0], dx_LL6[0])
dx_LU1[0], dx_LU2[0], dx_LU3[0], dx_LU4[0], dx_LU5[0], dx_LU6[0] = my_object.dynamics(t, (x1[i], x2[j], x3[k], x4[l], x5[m], x6[n]), uOptL, dOptU)
# Get absolute value of each
dx_LU1[0] = my_abs(dx_LU1[0])
dx_LU2[0] = my_abs(dx_LU2[0])
dx_LU3[0] = my_abs(dx_LU3[0])
dx_LU4[0] = my_abs(dx_LU4[0])
dx_LU5[0] = my_abs(dx_LU5[0])
dx_LU6[0] = my_abs(dx_LU6[0])
alpha1[0] = my_max(alpha1[0], dx_LU1[0])
alpha2[0] = my_max(alpha2[0], dx_LU2[0])
alpha3[0] = my_max(alpha3[0], dx_LU3[0])
alpha4[0] = my_max(alpha4[0], dx_LU4[0])
alpha5[0] = my_max(alpha5[0], dx_LU5[0])
alpha6[0] = my_max(alpha6[0], dx_LU6[0])
dx_UU1[0], dx_UU2[0], dx_UU3[0], dx_UU4[0], dx_UU5[0], dx_UU6[0] = my_object.dynamics(t, (x1[i], x2[j], x3[k], x4[l], x5[m], x6[n]), uOptU, dOptU)
dx_UU1[0] = my_abs(dx_UU1[0])
dx_UU2[0] = my_abs(dx_UU2[0])
dx_UU3[0] = my_abs(dx_UU3[0])
dx_UU4[0] = my_abs(dx_UU4[0])
dx_UU5[0] = my_abs(dx_UU5[0])
dx_UU6[0] = my_abs(dx_UU6[0])
alpha1[0] = my_max(alpha1[0], dx_UU1[0])
alpha2[0] = my_max(alpha2[0], dx_UU2[0])
alpha3[0] = my_max(alpha3[0], dx_UU3[0])
alpha4[0] = my_max(alpha4[0], dx_UU4[0])
alpha5[0] = my_max(alpha5[0], dx_UU5[0])
alpha6[0] = my_max(alpha6[0], dx_UU6[0])
diss = hcl.scalar(0, "diss")
diss[0] = 0.5*(deriv_diff1[i, j, k, l, m, n]*alpha1[0] + deriv_diff2[i, j, k, l, m, n]*alpha2[0] \
+ deriv_diff3[i, j, k, l, m, n]* alpha3[0] + deriv_diff4[i, j, k, l, m, n]* alpha4[0] \
+ deriv_diff5[i, j, k, l, m, n]* alpha5[0] + deriv_diff6[i, j, k, l, m, n]* alpha6[0])
# Finally
V_new[i, j, k, l, m, n] = -(V_new[i, j, k, l, m, n] - diss[0])
# Get maximum alphas in each dimension
# Calculate alphas
with hcl.if_(alpha1 > max_alpha1):
max_alpha1[0] = alpha1[0]
with hcl.if_(alpha2 > max_alpha2):
max_alpha2[0] = alpha2[0]
with hcl.if_(alpha3 > max_alpha3):
max_alpha3[0] = alpha3[0]
with hcl.if_(alpha4 > max_alpha4):
max_alpha4[0] = alpha4[0]
with hcl.if_(alpha5 > max_alpha5):
max_alpha5[0] = alpha5[0]
with hcl.if_(alpha6 > max_alpha6):
max_alpha6[0] = alpha6[0]
# Determine time step
delta_t = hcl.compute((1,), lambda x: step_bound(), name="delta_t")
#hcl.update(t, lambda x: t[x] + delta_t[x])
# Integrate
#if compMethod == 'HJ_PDE':
result = hcl.update(V_new, lambda i, j, k, l, m, n: V_init[i, j, k, l, m, n] + V_new[i, j, k, l, m, n] * delta_t[0])
if compMethod == 'maxVWithV0':
result = hcl.update(V_new, lambda i, j, k, l, m, n: maxVWithV0(i, j, k, l, m, n))
if compMethod == 'maxVWithCStraint':
result = hcl.update(V_new, lambda i, j, k, l, m, n: maxVWithCStraint(i, j, k, l, m, n))
# Copy V_new to V_init
hcl.update(V_init, lambda i, j, k, l, m, n: V_new[i, j, k, l, m, n])
return result
def minVWithVInit(i, j, k, l, m):
with hcl.if_(V_new[i, j, k, l, m] > V_init[i, j, k, l, m]):
V_new[i, j, k, l, m] = V_init[i, j, k, l, m]
def solve_Vopt(Vopt, actions, intermeds, trans, interpV, gamma, epsilon,
iVals, sVals, bounds, goal, ptsEachDim, count, maxIters,
useNN, fillVal):
reSweep = hcl.scalar(1, "reSweep")
oldV = hcl.scalar(0, "oldV")
newV = hcl.scalar(0, "newV")
with hcl.while_(hcl.and_(reSweep[0] == 1, count[0] < maxIters[0])):
reSweep[0] = 0
# Perform value iteration by sweeping in direction 1
with hcl.Stage("Sweep_1"):
with hcl.for_(0, Vopt.shape[0], name="i") as i:
with hcl.for_(0, Vopt.shape[1], name="j") as j:
with hcl.for_(0, Vopt.shape[2], name="k") as k:
oldV[0] = Vopt[i, j, k]
updateVopt(MDP_object, i, j, k, iVals, sVals,
actions, Vopt, intermeds, trans,
interpV, gamma, bounds, goal,
ptsEachDim, useNN, fillVal)
newV[0] = Vopt[i, j, k]
evaluateConvergence(newV, oldV, epsilon, reSweep)
count[0] += 1
# Perform value iteration by sweeping in direction 2
with hcl.Stage("Sweep_2"):
with hcl.if_(useNN[0] == 1):
with hcl.for_(1, Vopt.shape[0] + 1, name="i") as i:
with hcl.for_(1, Vopt.shape[1] + 1, name="j") as j:
with hcl.for_(1, Vopt.shape[2] + 1, name="k") as k:
i2 = Vopt.shape[0] - i
j2 = Vopt.shape[1] - j
k2 = Vopt.shape[2] - k
oldV[0] = Vopt[i2, j2, k2]
updateVopt(MDP_object, i2, j2, k2, iVals,
sVals, actions, Vopt, intermeds,
trans, interpV, gamma, bounds, goal,
ptsEachDim, useNN, fillVal)
newV[0] = Vopt[i2, j2, k2]
evaluateConvergence(newV, oldV, epsilon,
reSweep)
count[0] += 1
# Perform value iteration by sweeping in direction 3
with hcl.Stage("Sweep_3"):
with hcl.if_(useNN[0] == 1):
with hcl.for_(1, Vopt.shape[0] + 1, name="i") as i:
with hcl.for_(0, Vopt.shape[1], name="j") as j:
with hcl.for_(0, Vopt.shape[2], name="k") as k:
i2 = Vopt.shape[0] - i
oldV[0] = Vopt[i2, j, k]
updateVopt(MDP_object, i2, j, k, iVals, sVals,
actions, Vopt, intermeds, trans,
interpV, gamma, bounds, goal,
ptsEachDim, useNN, fillVal)
newV[0] = Vopt[i2, j, k]
evaluateConvergence(newV, oldV, epsilon,
reSweep)
count[0] += 1
# Perform value iteration by sweeping in direction 4
with hcl.Stage("Sweep_4"):
with hcl.if_(useNN[0] == 1):
with hcl.for_(0, Vopt.shape[0], name="i") as i:
with hcl.for_(1, Vopt.shape[1] + 1, name="j") as j:
with hcl.for_(0, Vopt.shape[2], name="k") as k:
j2 = Vopt.shape[1] - j
oldV[0] = Vopt[i, j2, k]
updateVopt(MDP_object, i, j2, k, iVals, sVals,
actions, Vopt, intermeds, trans,
interpV, gamma, bounds, goal,
ptsEachDim, useNN, fillVal)
newV[0] = Vopt[i, j2, k]
evaluateConvergence(newV, oldV, epsilon,
reSweep)
count[0] += 1
# Perform value iteration by sweeping in direction 5
with hcl.Stage("Sweep_5"):
with hcl.if_(useNN[0] == 1):
with hcl.for_(0, Vopt.shape[0], name="i") as i:
with hcl.for_(0, Vopt.shape[1], name="j") as j:
with hcl.for_(1, Vopt.shape[2] + 1, name="k") as k:
k2 = Vopt.shape[2] - k
oldV[0] = Vopt[i, j, k2]
updateVopt(MDP_object, i, j, k2, iVals, sVals,
actions, Vopt, intermeds, trans,
interpV, gamma, bounds, goal,
ptsEachDim, useNN, fillVal)
newV[0] = Vopt[i, j, k2]
evaluateConvergence(newV, oldV, epsilon,
reSweep)
count[0] += 1
# Perform value iteration by sweeping in direction 6
with hcl.Stage("Sweep_6"):
with hcl.if_(useNN[0] == 1):
with hcl.for_(1, Vopt.shape[0] + 1, name="i") as i:
with hcl.for_(1, Vopt.shape[1] + 1, name="j") as j:
with hcl.for_(0, Vopt.shape[2], name="k") as k:
i2 = Vopt.shape[0] - i
j2 = Vopt.shape[1] - j
oldV[0] = Vopt[i2, j2, k]
updateVopt(MDP_object, i2, j2, k, iVals, sVals,
actions, Vopt, intermeds, trans,
interpV, gamma, bounds, goal,
ptsEachDim, useNN, fillVal)
newV[0] = Vopt[i2, j2, k]
evaluateConvergence(newV, oldV, epsilon,
reSweep)
count[0] += 1
# Perform value iteration by sweeping in direction 7
with hcl.Stage("Sweep_7"):
with hcl.if_(useNN[0] == 1):
with hcl.for_(1, Vopt.shape[0] + 1, name="i") as i:
with hcl.for_(0, Vopt.shape[1], name="j") as j:
with hcl.for_(1, Vopt.shape[2] + 1, name="k") as k:
i2 = Vopt.shape[0] - i
k2 = Vopt.shape[2] - k
oldV[0] = Vopt[i2, j, k2]
updateVopt(MDP_object, i2, j, k2, iVals, sVals,
actions, Vopt, intermeds, trans,
interpV, gamma, bounds, goal,
ptsEachDim, useNN, fillVal)
newV[0] = Vopt[i2, j, k2]
evaluateConvergence(newV, oldV, epsilon,
reSweep)
count[0] += 1
# Perform value iteration by sweeping in direction 8
with hcl.Stage("Sweep_8"):
with hcl.if_(useNN[0] == 1):
with hcl.for_(0, Vopt.shape[0], name="i") as i:
with hcl.for_(1, Vopt.shape[1] + 1, name="j") as j:
with hcl.for_(1, Vopt.shape[2] + 1, name="k") as k:
j2 = Vopt.shape[1] - j
k2 = Vopt.shape[2] - k
oldV[0] = Vopt[i, j2, k2]
updateVopt(MDP_object, i, j2, k2, iVals, sVals,
actions, Vopt, intermeds, trans,
interpV, gamma, bounds, goal,
ptsEachDim, useNN, fillVal)
newV[0] = Vopt[i, j2, k2]
evaluateConvergence(newV, oldV, epsilon,
reSweep)
count[0] += 1
def spa_derivY(i, j, k, V, g):
left_deriv = hcl.scalar(0, "left_deriv")
right_deriv = hcl.scalar(0, "right_deriv")
dim_idx = 1
u_i = V[i, j, k]
with hcl.if_(j == 0):
u_i_minus_1 = hcl.scalar(0, "u_i_minus_1")
u_i_plus_1 = V[i, j + 1, k]
u_i_plus_2 = V[i, j + 2, k]
u_i_minus_1[0] = u_i + my_abs(u_i_plus_1 - u_i) * my_sign(u_i)
D1_i_plus_half = (u_i_plus_1 - u_i) / g.dx[dim_idx]
D1_i_minus_half = (u_i - u_i_minus_1[0]) / g.dx[dim_idx]
Q1d_left = D1_i_minus_half
Q1d_right = D1_i_plus_half
D2_i = 0.5 * ((D1_i_plus_half - D1_i_minus_half) / g.dx[dim_idx])
u_i_plus_1_plus_1 = u_i_plus_2
D1_i_plus_1_plus_half = (u_i_plus_1_plus_1 -
u_i_plus_1) / g.dx[dim_idx]
D1_i_plus_1_minus_half = D1_i_plus_half
D2_i_plus_1 = 0.5 * (
(D1_i_plus_1_plus_half - D1_i_plus_1_minus_half) / g.dx[dim_idx])
with hcl.if_(my_abs(D2_i) <= my_abs(D2_i_plus_1)):
c = D2_i
Q2d = c * g.dx[dim_idx]
left_deriv[0] = Q1d_left + Q2d
right_deriv[0] = Q1d_right - Q2d
with hcl.else_():
c = D2_i_plus_1
Q2d = c * g.dx[dim_idx]
left_deriv[0] = Q1d_left + Q2d
right_deriv[0] = Q1d_right - Q2d
with hcl.elif_(j == V.shape[dim_idx] - 1):
u_i_plus_1 = hcl.scalar(0, "u_i_plus_1")
u_i_plus_2 = hcl.scalar(0, "u_i_plus_2")
u_i_minus_1 = V[i, j - 1, k]
u_i_plus_1[0] = u_i + my_abs(u_i - u_i_minus_1) * my_sign(u_i)
u_i_plus_2[0] = u_i_plus_1[0] + my_abs(u_i_plus_1[0] - u_i) * my_sign(
u_i_plus_1[0])
D1_i_plus_half = (u_i_plus_1[0] - u_i) / g.dx[dim_idx]
D1_i_minus_half = (u_i - u_i_minus_1) / g.dx[dim_idx]
Q1d_left = D1_i_minus_half
Q1d_right = D1_i_plus_half
D2_i = 0.5 * ((D1_i_plus_half - D1_i_minus_half) / g.dx[dim_idx])
u_i_plus_1_plus_1 = u_i_plus_2[0]
D1_i_plus_1_plus_half = (u_i_plus_1_plus_1 -
u_i_plus_1[0]) / g.dx[dim_idx]
D1_i_plus_1_minus_half = D1_i_plus_half
D2_i_plus_1 = 0.5 * (
(D1_i_plus_1_plus_half - D1_i_plus_1_minus_half) / g.dx[dim_idx])
with hcl.if_(my_abs(D2_i) <= my_abs(D2_i_plus_1)):
c = D2_i
Q2d = c * g.dx[dim_idx]
left_deriv[0] = Q1d_left + Q2d
right_deriv[0] = Q1d_right - Q2d
with hcl.else_():
c = D2_i_plus_1
Q2d = c * g.dx[dim_idx]
left_deriv[0] = Q1d_left + Q2d
right_deriv[0] = Q1d_right - Q2d
with hcl.elif_(j == V.shape[dim_idx] - 2):
u_i_plus_2 = hcl.scalar(0, "u_i_plus_2")
u_i_plus_1 = V[i, j + 1, k]
u_i_minus_1 = V[i, j - 1, k]
u_i_plus_2[0] = u_i_plus_1 + my_abs(u_i_plus_1 -
u_i) * my_sign(u_i_plus_1)
D1_i_plus_half = (u_i_plus_1 - u_i) / g.dx[dim_idx]
D1_i_minus_half = (u_i - u_i_minus_1) / g.dx[dim_idx]
Q1d_left = D1_i_minus_half
Q1d_right = D1_i_plus_half
D2_i = 0.5 * ((D1_i_plus_half - D1_i_minus_half) / g.dx[dim_idx])
u_i_plus_1_plus_1 = u_i_plus_2[0]
D1_i_plus_1_plus_half = (u_i_plus_1_plus_1 -
u_i_plus_1) / g.dx[dim_idx]
D1_i_plus_1_minus_half = D1_i_plus_half
D2_i_plus_1 = 0.5 * (
(D1_i_plus_1_plus_half - D1_i_plus_1_minus_half) / g.dx[dim_idx])
with hcl.if_(my_abs(D2_i) <= my_abs(D2_i_plus_1)):
c = D2_i
Q2d = c * g.dx[dim_idx]
left_deriv[0] = Q1d_left + Q2d
right_deriv[0] = Q1d_right - Q2d
with hcl.else_():
c = D2_i_plus_1
Q2d = c * g.dx[dim_idx]
left_deriv[0] = Q1d_left + Q2d
right_deriv[0] = Q1d_right - Q2d
with hcl.else_():
u_i_minus_1 = V[i, j - 1, k]
u_i_plus_1 = V[i, j + 1, k]
u_i_plus_2 = V[i, j + 2, k]
D1_i_plus_half = (u_i_plus_1 - u_i) / g.dx[dim_idx]
D1_i_minus_half = (u_i - u_i_minus_1) / g.dx[dim_idx]
Q1d_left = D1_i_minus_half
Q1d_right = D1_i_plus_half
D2_i = 0.5 * ((D1_i_plus_half - D1_i_minus_half) / g.dx[dim_idx])
u_i_plus_1_plus_1 = u_i_plus_2
D1_i_plus_1_plus_half = (u_i_plus_1_plus_1 -
u_i_plus_1) / g.dx[dim_idx]
D1_i_plus_1_minus_half = D1_i_plus_half
D2_i_plus_1 = 0.5 * (
(D1_i_plus_1_plus_half - D1_i_plus_1_minus_half) / g.dx[dim_idx])
with hcl.if_(my_abs(D2_i) <= my_abs(D2_i_plus_1)):
c = D2_i
Q2d = c * g.dx[dim_idx]
left_deriv[0] = Q1d_left + Q2d
right_deriv[0] = Q1d_right - Q2d
with hcl.else_():
c = D2_i_plus_1
Q2d = c * g.dx[dim_idx]
left_deriv[0] = Q1d_left + Q2d
right_deriv[0] = Q1d_right - Q2d
return left_deriv[0], right_deriv[0]