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Fix jacobian format #21

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merged 2 commits into from
Nov 9, 2023
Merged

Fix jacobian format #21

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d7ec8e4
update equality_jac_6DoF_rate
A-Hayasaka Mar 1, 2023
bbf7e24
change jacobian matrix format
A-Hayasaka Nov 8, 2023
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247 changes: 156 additions & 91 deletions constraints.py
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Original file line number Diff line number Diff line change
Expand Up @@ -26,7 +26,6 @@
import sys
import numpy as np
from numpy.linalg import norm
from scipy import sparse
from numba import jit
from utils import *
from USStandardAtmosphere import *
Expand Down Expand Up @@ -115,36 +114,60 @@ def equality_jac_init(xdict, pdict, unitdict, condition):
jac = {}

if condition["OptimizationMode"] == "Payload":
rowcol_pos = (range(0, 3), range(0, 3))
rowcol_vel = (range(3, 6), range(0, 3))
rowcol_quat = (range(6, 10), range(0, 4))

jac["position"] = sparse.coo_matrix(
([1.0] * 3, rowcol_pos), shape=(10, pdict["M"] * 3)
)
jac["velocity"] = sparse.coo_matrix(
([1.0] * 3, rowcol_vel), shape=(10, pdict["M"] * 3)
)
jac["quaternion"] = sparse.coo_matrix(
([1.0] * 4, rowcol_quat), shape=(10, pdict["M"] * 4)
)
jac["position"] = {
"coo": [
np.arange(0, 3, dtype="i4"),
np.arange(0, 3, dtype="i4"),
np.ones(3),
],
"shape": (10, pdict["M"] * 3),
}
jac["velocity"] = {
"coo": [
np.arange(3, 6, dtype="i4"),
np.arange(0, 3, dtype="i4"),
np.ones(3),
],
"shape": (10, pdict["M"] * 3),
}
jac["quaternion"] = {
"coo": [
np.arange(6, 10, dtype="i4"),
np.arange(0, 4, dtype="i4"),
np.ones(4),
],
"shape": (10, pdict["M"] * 4),
}

else:
rowcol_mass = ([0], [0])
rowcol_pos = (range(1, 4), range(0, 3))
rowcol_vel = (range(4, 7), range(0, 3))
rowcol_quat = (range(7, 11), range(0, 4))

jac["mass"] = sparse.coo_matrix(([1.0], rowcol_mass), shape=(11, pdict["M"]))
jac["position"] = sparse.coo_matrix(
([1.0] * 3, rowcol_pos), shape=(11, pdict["M"] * 3)
)
jac["velocity"] = sparse.coo_matrix(
([1.0] * 3, rowcol_vel), shape=(11, pdict["M"] * 3)
)
jac["quaternion"] = sparse.coo_matrix(
([1.0] * 4, rowcol_quat), shape=(11, pdict["M"] * 4)
)
jac["mass"] = {
"coo": [np.zeros(1, dtype="i4"), np.zeros(1, dtype="i4"), np.ones(1)],
"shape": (11, pdict["M"]),
}
jac["position"] = {
"coo": [
np.arange(1, 4, dtype="i4"),
np.arange(0, 3, dtype="i4"),
np.ones(3),
],
"shape": (11, pdict["M"] * 3),
}
jac["velocity"] = {
"coo": [
np.arange(4, 7, dtype="i4"),
np.arange(0, 3, dtype="i4"),
np.ones(3),
],
"shape": (11, pdict["M"] * 3),
}
jac["quaternion"] = {
"coo": [
np.arange(7, 11, dtype="i4"),
np.arange(0, 4, dtype="i4"),
np.ones(4),
],
"shape": (11, pdict["M"] * 4),
}

return jac

Expand Down Expand Up @@ -191,7 +214,10 @@ def equality_jac_time(xdict, pdict, unitdict, condition):
col.extend([i, i_ref])
iRow += 1

jac["t"] = sparse.coo_matrix((data, (row, col)), shape=[iRow, len(xdict["t"])])
jac["t"] = {
"coo": [np.array(row, dtype="i4"), np.array(col, dtype="i4"), np.array(data)],
"shape": (iRow, len(xdict["t"])),
}

return jac

Expand Down Expand Up @@ -239,26 +265,45 @@ def equality_jac_dynamics_mass(xdict, pdict, unitdict, condition):
unit_t = unitdict["t"]
num_sections = pdict["num_sections"]

jac["mass"] = sparse.lil_matrix((pdict["N"], pdict["M"]))
jac["t"] = sparse.lil_matrix((pdict["N"], num_sections + 1))
jac["mass"] = {"coo": [[], [], []], "shape": (pdict["N"], pdict["M"])}
jac["t"] = {"coo": [[], [], []], "shape": (pdict["N"], num_sections + 1)}

for i in range(num_sections):
a = pdict["ps_params"][i]["index_start"]
n = pdict["ps_params"][i]["nodes"]
b = a + n

if pdict["params"][i]["engineOn"]:
jac["mass"][a:b, a + i : b + i + 1] = pdict["ps_params"][i]["D"] # lh
jac["t"][a:b, i] = (
-pdict["params"][i]["massflow"] / unit_mass * unit_t / 2.0

jac["mass"]["coo"][0].extend(sum([[i] * (n + 1) for i in range(a, b)], []))
jac["mass"]["coo"][1].extend(list(range(a + i, b + i + 1)) * (n))
jac["mass"]["coo"][2].extend(
pdict["ps_params"][i]["D"].ravel(order="C").tolist()
)

jac["t"]["coo"][0].extend(list(range(a, b)))
jac["t"]["coo"][1].extend([i] * n)
jac["t"]["coo"][2].extend(
[-pdict["params"][i]["massflow"] / unit_mass * unit_t / 2.0] * n
) # rh(to)
jac["t"][a:b, i + 1] = (
pdict["params"][i]["massflow"] / unit_mass * unit_t / 2.0
jac["t"]["coo"][0].extend(list(range(a, b)))
jac["t"]["coo"][1].extend([i + 1] * n)
jac["t"]["coo"][2].extend(
[pdict["params"][i]["massflow"] / unit_mass * unit_t / 2.0] * n
) # rh(tf)

else:
jac["mass"][a:b, a + i] = -1.0
jac["mass"][a:b, a + i + 1 : b + i + 1] = np.eye(n)
jac["mass"]["coo"][0].extend(list(range(a, b)))
jac["mass"]["coo"][1].extend([a + i] * n)
jac["mass"]["coo"][2].extend([-1.0] * n)
jac["mass"]["coo"][0].extend(list(range(a, b)))
jac["mass"]["coo"][1].extend(list(range(a + i + 1, b + i + 1)))
jac["mass"]["coo"][2].extend([1.0] * n)

for key in jac.keys():
jac[key]["coo"][0] = np.array(jac[key]["coo"][0], dtype="i4")
jac[key]["coo"][1] = np.array(jac[key]["coo"][1], dtype="i4")
jac[key]["coo"][2] = np.array(jac[key]["coo"][2], dtype="f8")

return jac

Expand Down Expand Up @@ -977,30 +1022,23 @@ def equality_jac_6DoF_LGR_terminal(xdict, pdict, unitdict, condition):
else:
nRow = 1

jac_base = {
"position": np.zeros((nRow, pdict["M"] * 3)),
"velocity": np.zeros((nRow, pdict["M"] * 3)),
}
nCol = pdict["M"] * 3
jac["position"] = {"coo": [[], [], []], "shape": (nRow, nCol)}
jac["velocity"] = {"coo": [[], [], []], "shape": (nRow, nCol)}

for key in ["position", "velocity"]:

jac_base[key][:, -3:] = 1.0
jac_base_coo = sparse.coo_matrix(jac_base[key])
jac[key] = {
"coo": [jac_base_coo.row, jac_base_coo.col, jac_base_coo.data],
"shape": jac_base[key].shape,
}

for j in range(-3, 0):
for j in range(nCol - 3, nCol):
xdict[key][j] += dx
f_p = equality_6DoF_LGR_terminal(xdict, pdict, unitdict, condition)
xdict[key][j] -= dx
jac_base[key][:, j] = (f_p - f_center) / dx
jac[key]["coo"][0].extend(list(range(nRow)))
jac[key]["coo"][1].extend([j] * nRow)
jac[key]["coo"][2].extend(((f_p - f_center) / dx).tolist())

for i in range(len(jac[key]["coo"][0])):
jac[key]["coo"][2][i] = jac_base[key][
jac[key]["coo"][0][i], jac[key]["coo"][1][i]
]
jac[key]["coo"][0] = np.array(jac[key]["coo"][0], dtype="i4")
jac[key]["coo"][1] = np.array(jac[key]["coo"][1], dtype="i4")
jac[key]["coo"][2] = np.array(jac[key]["coo"][2], dtype="f8")

return jac

Expand Down Expand Up @@ -1080,9 +1118,9 @@ def equality_jac_6DoF_rate(xdict, pdict, unitdict, condition):

f_center = equality_6DoF_rate(xdict, pdict, unitdict, condition)
nRow = len(f_center)
jac["position"] = sparse.lil_matrix((nRow, pdict["M"] * 3))
jac["quaternion"] = sparse.lil_matrix((nRow, pdict["M"] * 4))
jac["u"] = sparse.lil_matrix((nRow, pdict["N"] * 3))
jac["position"] = {"coo": [[], [], []], "shape": (nRow, pdict["M"] * 3)}
jac["quaternion"] = {"coo": [[], [], []], "shape": (nRow, pdict["M"] * 4)}
jac["u"] = {"coo": [[], [], []], "shape": (nRow, pdict["N"] * 3)}

iRow = 0

Expand All @@ -1098,86 +1136,113 @@ def equality_jac_6DoF_rate(xdict, pdict, unitdict, condition):
att = pdict["params"][i]["attitude"]
# attitude hold : angular velocity is zero
if att in ["hold", "vertical"]:
jac["u"][iRow : iRow + n * 3, a * 3 : (a + n) * 3] = np.eye(n * 3)
jac["u"]["coo"][0].extend(list(range(iRow, iRow + n * 3)))
jac["u"]["coo"][1].extend(list(range(a * 3, (a + n) * 3)))
jac["u"]["coo"][2].extend([1.0] * (n * 3))
iRow += n * 3

# kick-turn : pitch rate constant, roll/yaw rate is zero
elif att == "kick-turn" or att == "pitch":
jac["u"][iRow : iRow + n, a * 3 : (a + n) * 3 : 3] = np.eye(n)
jac["u"]["coo"][0].extend(list(range(iRow, iRow + n)))
jac["u"]["coo"][1].extend(list(range(a * 3, (a + n) * 3, 3)))
jac["u"]["coo"][2].extend([1.0] * n)
iRow += n
jac["u"][iRow : iRow + n, a * 3 + 2 : (a + n) * 3 + 2 : 3] = np.eye(n)
jac["u"]["coo"][0].extend(list(range(iRow, iRow + n)))
jac["u"]["coo"][1].extend(list(range(a * 3 + 2, (a + n) * 3 + 2, 3)))
jac["u"]["coo"][2].extend([1.0] * n)
iRow += n
jac["u"][iRow : iRow + n - 1, a * 3 + 1] = -1.0
jac["u"][
iRow : iRow + n - 1, (a + 1) * 3 + 1 : (a + n) * 3 + 1 : 3
] = np.eye(n - 1)
jac["u"]["coo"][0].extend(list(range(iRow, iRow + n - 1)))
jac["u"]["coo"][1].extend([a * 3 + 1] * (n - 1))
jac["u"]["coo"][2].extend([-1.0] * (n - 1))
jac["u"]["coo"][0].extend(list(range(iRow, iRow + n - 1)))
jac["u"]["coo"][1].extend(list(range((a + 1) * 3 + 1, (a + n) * 3 + 1, 3)))
jac["u"]["coo"][2].extend([1.0] * (n - 1))
iRow += n - 1

# pitch-yaw : pitch/yaw constant, roll ANGLE is zero
elif att == "pitch-yaw":
jac["u"][iRow : iRow + n - 1, a * 3 + 1] = -1.0
jac["u"][
iRow : iRow + n - 1, (a + 1) * 3 + 1 : (a + n) * 3 + 1 : 3
] = np.eye(n - 1)
jac["u"]["coo"][0].extend(list(range(iRow, iRow + n - 1)))
jac["u"]["coo"][1].extend([a * 3 + 1] * (n - 1))
jac["u"]["coo"][2].extend([-1.0] * (n - 1))
jac["u"]["coo"][0].extend(list(range(iRow, iRow + n - 1)))
jac["u"]["coo"][1].extend(list(range((a + 1) * 3 + 1, (a + n) * 3 + 1, 3)))
jac["u"]["coo"][2].extend([1.0] * (n - 1))
iRow += n - 1
jac["u"][iRow : iRow + n - 1, a * 3 + 2] = -1.0
jac["u"][
iRow : iRow + n - 1, (a + 1) * 3 + 2 : (a + n) * 3 + 2 : 3
] = np.eye(n - 1)
jac["u"]["coo"][0].extend(list(range(iRow, iRow + n - 1)))
jac["u"]["coo"][1].extend([a * 3 + 2] * (n - 1))
jac["u"]["coo"][2].extend([-1.0] * (n - 1))
jac["u"]["coo"][0].extend(list(range(iRow, iRow + n - 1)))
jac["u"]["coo"][1].extend(list(range((a + 1) * 3 + 2, (a + n) * 3 + 2, 3)))
jac["u"]["coo"][2].extend([1.0] * (n - 1))
iRow += n - 1
for k in range(n):
f_c = yb_r_dot(pos_i_[k + 1] * unit_pos, quat_i_[k + 1])
for j in range(3):
pos_i_[k + 1, j] += dx
f_p = yb_r_dot(pos_i_[k + 1] * unit_pos, quat_i_[k + 1])
pos_i_[k + 1, j] -= dx
jac["position"][iRow + k, (a + i + 1 + k) * 3 + j] = (
f_p - f_c
) / dx
jac["position"]["coo"][0].append(iRow + k)
jac["position"]["coo"][1].append((a + i + 1 + k) * 3 + j)
jac["position"]["coo"][2].append((f_p - f_c) / dx)
for j in range(4):
quat_i_[k + 1, j] += dx
f_p = yb_r_dot(pos_i_[k + 1] * unit_pos, quat_i_[k + 1])
quat_i_[k + 1, j] -= dx
jac["quaternion"][iRow + k, (a + i + 1 + k) * 4 + j] = (
f_p - f_c
) / dx
jac["quaternion"]["coo"][0].append(iRow + k)
jac["quaternion"]["coo"][1].append((a + i + 1 + k) * 4 + j)
jac["quaternion"]["coo"][2].append((f_p - f_c) / dx)
iRow += n

# same-rate : pitch/yaw is the same as previous section, roll ANGLE is zero
elif att == "same-rate":
jac["u"][iRow : iRow + n, a * 3 - 2] = -1.0
jac["u"][iRow : iRow + n, a * 3 + 1 : (a + n) * 3 + 1 : 3] = np.eye(n)
jac["u"]["coo"][0].extend(list(range(iRow, iRow + n)))
jac["u"]["coo"][1].extend([a * 3 - 2] * n)
jac["u"]["coo"][2].extend([-1.0] * n)
jac["u"]["coo"][0].extend(list(range(iRow, iRow + n)))
jac["u"]["coo"][1].extend(list(range(a * 3 + 1, (a + n) * 3 + 1, 3)))
jac["u"]["coo"][2].extend([1.0] * n)
iRow += n
jac["u"][iRow : iRow + n, a * 3 - 1] = -1.0
jac["u"][iRow : iRow + n, a * 3 + 2 : (a + n) * 3 + 2 : 3] = np.eye(n)
jac["u"]["coo"][0].extend(list(range(iRow, iRow + n)))
jac["u"]["coo"][1].extend([a * 3 - 1] * n)
jac["u"]["coo"][2].extend([-1.0] * n)
jac["u"]["coo"][0].extend(list(range(iRow, iRow + n)))
jac["u"]["coo"][1].extend(list(range(a * 3 + 2, (a + n) * 3 + 2, 3)))
jac["u"]["coo"][2].extend([1.0] * n)
iRow += n
for k in range(n):
f_c = yb_r_dot(pos_i_[k + 1] * unit_pos, quat_i_[k + 1])
for j in range(3):
pos_i_[k + 1, j] += dx
f_p = yb_r_dot(pos_i_[k + 1] * unit_pos, quat_i_[k + 1])
pos_i_[k + 1, j] -= dx
jac["position"][iRow + k, (a + i + 1 + k) * 3 + j] = (
f_p - f_c
) / dx
jac["position"]["coo"][0].append(iRow + k)
jac["position"]["coo"][1].append((a + i + 1 + k) * 3 + j)
jac["position"]["coo"][2].append((f_p - f_c) / dx)
for j in range(4):
quat_i_[k + 1, j] += dx
f_p = yb_r_dot(pos_i_[k + 1] * unit_pos, quat_i_[k + 1])
quat_i_[k + 1, j] -= dx
jac["quaternion"][iRow + k, (a + i + 1 + k) * 4 + j] = (
f_p - f_c
) / dx
jac["quaternion"]["coo"][0].append(iRow + k)
jac["quaternion"]["coo"][1].append((a + i + 1 + k) * 4 + j)
jac["quaternion"]["coo"][2].append((f_p - f_c) / dx)
iRow += n

# zero-lift-turn or free : roll hold
elif att == "zero-lift-turn" or att == "free":
jac["u"][iRow : iRow + n, a * 3 : (a + n) * 3 : 3] = np.eye(n)
jac["u"]["coo"][0].extend(list(range(iRow, iRow + n)))
jac["u"]["coo"][1].extend(list(range(a * 3, (a + n) * 3, 3)))
jac["u"]["coo"][2].extend([1.0] * n)
iRow += n

else:
print("ERROR: UNKNOWN ATTITUDE OPTION! ({})".format(att))
sys.exit()

for key in jac.keys():
jac[key]["coo"][0] = np.array(jac[key]["coo"][0], dtype="i4")
jac[key]["coo"][1] = np.array(jac[key]["coo"][1], dtype="i4")
jac[key]["coo"][2] = np.array(jac[key]["coo"][2], dtype="f8")

return jac


Expand Down
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