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BCHOL.py
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BCHOL.py
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import numpy as np
import math
import copy
import scipy.linalg as linalg
try:
# Attempt relative import (for when the file is part of a package)
from .utils import *
except ImportError:
# Fallback to absolute import (for when running as a standalone script)
from utils import *
def BCHOL(knot_points,control_size, state_size,
Q,R,q,r,A,B,d):
#KKT constants
depth = int(np.log2(knot_points))
binary_tree =initBTlevel(knot_points)
#negate q_r and d vectors
q[:]=-q #state vector
r[:]= -r # input vector/ control vector
d[:]= -d #lambda /lagrange multiplies
#Set F_lambda,F_state, and F_input
F_lambda = np.zeros((knot_points*depth,state_size,state_size))
F_state = np.zeros((knot_points*depth,state_size,state_size))
F_input = np.zeros((knot_points*depth,control_size,state_size))
epsln = 1e-6
for i in range(Q.shape[0]):
Q[i]+= np.diag(np.full(Q.shape[1], epsln))
R[i]+=np.diag(np.full(R.shape[1], epsln))
for ind in range (knot_points):
solveLeaf(binary_tree,ind, state_size,knot_points,Q,R,q,r,A,B,d,F_lambda,F_state, F_input)
#Starting the factorization of recursive algorithm
for level in range (depth):
#get the indxs for curr level
indx_atlevel =getValuesAtLevel(binary_tree,level)
count =len(indx_atlevel)
L = int(np.power(2.0,(depth-level-1)))
cur_depth = depth-level
upper_levels = cur_depth-1
num_factors = knot_points*upper_levels
num_perblock = num_factors//L
# print(f"level {level}, leaves {L}\n")
#calc inner products Bbar and bbar (to solve y in Schur)
for b_ind in range (L):
for t_ind in range(cur_depth):
# print(f"calcinner {level}\n")
ind = b_ind * cur_depth + t_ind
leaf = ind // cur_depth
upper_level = level + (ind % cur_depth)
lin_ind = int(np.power(2.0, level)) * (2 * leaf + 1) - 1
factorInnerProduct(A,B, F_state, F_input, F_lambda, lin_ind, upper_level, knot_points)
#cholesky fact for Bbar/bbar
for leaf in range (L):
# print(f"cholfact {level}\n")
index = int(np.power(2.0, level)) * (2 * leaf + 1) - 1
lin_ind = index + knot_points * level
if(is_choleskysafe(F_lambda[lin_ind+1])):
F_lambda[lin_ind+1]=linalg.cho_factor(F_lambda[lin_ind+1],lower =True)[0]
else:
print(f"Can't factor Cholesky {lin_ind} :\n")
print(F_lambda[lin_ind])
#solve with Chol solve for y SHUR compliment
for b_id in range(L):
for t_id in range(upper_levels):
# print(f"chol solve {level}\n")
i = b_id*upper_levels+t_id
leaf = i//upper_levels
upper_level = level+1+(i%upper_levels)
lin_ind = int(np.power(2,level)*(2*leaf+1))
# print(f"lin_ind {lin_ind}, sbar {(lin_ind)+knot_points*level}")
Sbar = F_lambda[(lin_ind)+knot_points*level]
f = F_lambda[(lin_ind)+knot_points*upper_level]
# print(f"level {level}, b_id {b_id} Sbar {Sbar} \n f {f}")
f[:]=linalg.cho_solve((Sbar,True),f,overwrite_b=True)
# while(is_choleskysafe(Sbar)==False):
# Sbar+=Sbar+10*np.eye(2)
# update SHUR - update x and z compliments
for b_id in range(L):
for t_id in range(num_perblock):
# print(f"update shur {level}\n")
i = (b_id*4)+t_id
k = i//upper_levels
upper_level = level+1+(i%upper_levels)
index = getIndexFromLevel(knot_points,depth,level,k,binary_tree)
calc_lambda = shouldCalcLambda(index, k,binary_tree)
g = k+knot_points*upper_level
updateShur(F_state,F_input,F_lambda,index,k,level,upper_level,calc_lambda,knot_points)
# breakpoint()
#soln vector loop, use factorized matrices for a fast solver
for level in range (depth):
L = int(np.power(2.0,(depth-level-1)))
indx_atlevel = getValuesAtLevel(binary_tree,level)
count = len(indx_atlevel)
num_perblock = knot_points // count
#calculate inner products with rhc - seems to be CORRECT
for leaf in range(L):
lin_ind = int(np.power(2,level)*(2*leaf+1)-1)
factorInnerProduct(A,B,q,r,d,lin_ind,0,knot_points,sol=True)
#solve for separator vars with Cached cholesky
for leaf in range(L):
lin_ind = int(np.power(2,level)*(2*leaf+1)-1)
Sbar = F_lambda[level * knot_points + (lin_ind + 1)]
zy = d[lin_ind+1]
zy[:]=linalg.cho_solve((Sbar,True),zy,overwrite_b=True)
#propogate info to soln vector
for b_id in range(L):
for t_id in range(num_perblock):
k = b_id * num_perblock + t_id
index = getIndexFromLevel(knot_points,depth,level,k,binary_tree)
calc_lambda = shouldCalcLambda(index,k,binary_tree)
updateShur(F_state,F_input,F_lambda,index,k,level,upper_level,
calc_lambda,knot_points,sol=True,d=d,q=q,r=r)
#construct dxul
dxul = np.zeros(knot_points*(state_size*2+control_size))
#first add all x,u (q,r)
lambda_st = (knot_points-1)*(state_size+control_size)+state_size
for i in range(knot_points):
start = i*(state_size+control_size)
dxul[start:start+state_size] = q[i]
start+=state_size
if(i!=knot_points-1):
dxul[start:start+control_size] = r[i]
l_start = lambda_st+i*state_size
dxul[l_start:l_start+state_size] = d[i]
dxul=dxul[:-control_size]
dxul=dxul.reshape(knot_points*(state_size)+(knot_points-1)*(state_size+control_size)+state_size,1)
# print("KKT soln BCHOL")
# with np.printoptions(precision=4, suppress=True):
# print(dxul)
return dxul