def Newton(x0, function_Block, iter_limit=1000, threshold=0.01):
Expr = function_Block.expression_give()
Varbs = function_Block.variables_give()
Grad = function_Block.grad_give()
pointsN_file = open(r'/home/senex/Documents/2D Newton Point list.txt','a+')
start_Time = time.time()
k=0
xk = x0
print xk
var_Val_List = var_matcher(Varbs,xk)
for i in range(0,len(Grad)):
Grad[i]=-Grad[i].subs(var_Val_List)
Grad_Mag = normAr(Grad)
Hessian = function_Block.hessian_give()
for i in range(0,Hessian.shape[0]):
for j in range(0,Hessian.shape[1]):
Hessian[i,j] = float(Hessian[i,j].subs(var_Val_List))
Hessian = np.array(Hessian,dtype=np.float32)/float(np.amax(Hessian))
pointsN_file.write('\r\n'+str(xk)+'\r\n')
while Grad_Mag>threshold and k < iter_limit:
k += 1
if (np.linalg.eig(Hessian)[0]>np.zeros(Hessian.shape[1])).all():
dk = np.dot(-np.linalg.inv(Hessian),Grad)
else:
dk = -Grad
[a,b] = Bound_Find.multiVariableHalfOpen(xk, Expr, Varbs, dk)
step = OneD_Search.multiVariableGoldenSectionSearch(Expr, Varbs,a,b,xk,dk)
xk = xk + step*dk
print xk
pointsN_file.write(str(xk)+'\r\n')
Grad = function_Block.grad_give()
var_Val_List = var_matcher(Varbs,xk)
for i in range(0,len(Grad)):
Grad[i]=Grad[i].subs(var_Val_List)
Grad_Mag = normAr(Grad)
Hessian = function_Block.hessian_give()
for i in range(0,Hessian.shape[0]):
for j in range(0,Hessian.shape[1]):
Hessian[i,j] = Hessian[i,j].subs(var_Val_List)
Hessian = np.array(Hessian,dtype=np.float32)/float(np.amax(Hessian))
x_min = xk
if Grad_Mag>threshold and k==iter_limit:
iter_no = None
time_taken = None
else:
iter_no = k
time_taken = time.time() - start_Time
pointsN_file.close()
return [x_min,iter_no,time_taken]
def Steepest_Desc(x0, function_Block, iter_limit=1000, threshold=0.01):
'''Function block object must have a Grad in object and a function
value calculator given a coordinate. Hessian can be empty.
This works for symbolic functions and black box models'''
Expr = function_Block.expression_give()
Varbs = function_Block.variables_give()
Grad = function_Block.grad_give()
pointsSD_file = open(r'/home/senex/Documents/2D Steepest Descent Point list.txt','a+')
start_Time = time.time()
xk = x0
print xk
k=0
dk = function_Block.grad_give()
var_Val_List = var_matcher(Varbs,xk)
for i in range(0,len(Grad)):
dk[i]=-Grad[i].subs(var_Val_List)
Grad_Mag = normAr(dk)
pointsSD_file.write('\r\n'+str(xk)+'\r\n')
while Grad_Mag>threshold and k < iter_limit:
k+=1
[a,b] = Bound_Find.multiVariableHalfOpen(xk, Expr, Varbs, dk)
step = OneD_Search.multiVariableGoldenSectionSearch(Expr, Varbs,a,b,xk,dk)
xk = xk + step*dk
print xk
pointsSD_file.write(str(xk)+'\r\n')
Grad = function_Block.grad_give()
var_Val_List = var_matcher(Varbs,xk)
dk = function_Block.grad_give()
for i in range(0,len(dk)):
dk[i]=-Grad[i].subs(var_Val_List)
Grad_Mag = normAr(dk)
x_min = xk
if Grad_Mag>threshold and k==iter_limit:
iter_no = None
time_taken = None
else:
iter_no = k
time_taken = time.time() - start_Time
pointsSD_file.close()
return [x_min,iter_no,time_taken]
def BFGS(x0, function_Block, H0=None, iter_limit=1000, threshold=0.01):
Expr = function_Block.expression_give()
Varbs = function_Block.variables_give()
Grad = function_Block.grad_give()
if H0 == None:
H0=np.eye(len(Grad),dtype=np.float32)
pointsQ_file = open(r'/home/senex/Documents/2D BFGS Point list.txt','a+')
start_Time = time.time()
k=0
xk = x0
print xk
xk_old = x0
H_old = H0
var_Val_List = var_matcher(Varbs,xk)
for i in range(0,len(Grad)):
Grad[i]=Grad[i].subs(var_Val_List)
Grad_Mag = normAr(Grad)
pointsQ_file.write('\r\n'+str(xk)+'\r\n')
while Grad_Mag>threshold and k < iter_limit:
k += 1
H0 = np.array(H0,dtype=np.float32)/float(np.amax(H0))
dk = -np.dot(H_old,Grad)
[a,b] = Bound_Find.multiVariableHalfOpen(xk, Expr, Varbs, dk)
step = OneD_Search.multiVariableGoldenSectionSearch(Expr, Varbs,a,b,xk,dk)
xk = xk + step*dk
print xk
pointsQ_file.write(str(xk)+'\r\n')
xk_new = xk_old + step*dk
sk = xk_new - xk_old
Grad_New = function_Block.grad_give()
new_var_Val_List = var_matcher(Varbs,xk_new)
for i in range(0,len(Grad_New)):
Grad_New[i]=Grad_New[i].subs(new_var_Val_List)
Grad_Old = function_Block.grad_give()
old_var_Val_List = var_matcher(Varbs,xk_old)
for i in range(0,len(Grad_Old)):
Grad_Old[i]=Grad_Old[i].subs(old_var_Val_List)
gk = Grad_New - Grad_Old
rk = np.dot(H_old,gk)/np.dot(sk,gk)
H_new = H_old + ((1+np.dot(rk,gk))/np.dot(sk,gk))*np.outer(sk,sk) - np.outer(sk,rk) - np.outer(rk,sk)
xk_old = xk_new
H_old = H_new
Grad_Mag = normAr(Grad_New)
x_min = xk
if Grad_Mag>threshold and k==iter_limit:
iter_no = None
time_taken = None
else:
iter_no = k
time_taken = time.time() - start_Time
pointsQ_file.close()
return [x_min,iter_no,time_taken]