I want to find the value of the parameter m that minimizes my variable x subject to a system of differential equations. I have the following code
from gekko import GEKKO
def run_model_m(days, population, case, k_val, b_val, u0_val, sigma_val, Kmax0, a_val, c_val):
list_x =[]
list_u =[]
list_Kmax =[]
for i in range(len(days)):
list_xi=[]
list_ui=[]
list_Ki=[]
for j in range(len(days[i])):
#try:
m = GEKKO(remote=False)
#m.time= days[i][j]
eval = np.linspace(days[i][j][0], days[i][j][-1], 100, endpoint=True)
m.time = eval
x_data= population[i][j]
variable= np.linspace(population[i][j][0], population[i][j][-1], 100, endpoint=True)
x = m.Var(value=population[i][j][0], lb=0)
sigma= m.Param(sigma_val)
d = m.Param(c_val)
k = m.Param(k_val)
b = m.Param(b_val)
r = m.Param(a_val)
step = np.ones(len(eval))
step= 0.2*step
step[0]=1
m_param = m.CV(value=1, lb=0, ub=1, integer=True); m_param.STATUS=1
u = m.Var(value=u0_val, lb=0, ub=1)
#m.free(u)
a = m.Param(a_val)
c= m.Param(c_val)
Kmax= m.Param(Kmax0)
if case == 'case0':
m.Equations([x.dt()== x*(r*(1-x/(Kmax))-m_param/(k+b*u)-d), u.dt()== sigma*(m_param*b/((k+b*u)**2))])
elif case == 'case4':
m.Equations([x.dt()== x*(r*(1-u**2)*(1-x/(Kmax))-m_param/(k+b*u)-d), u.dt() == sigma*(-2*u*r*(1-x/(Kmax))+(b*m_param)/(b*u+k)**2)])
p = np.zeros(len(eval))
p[-1] = 1.0
final = m.Param(value=p)
m.Obj(x)
m.options.IMODE = 6
m.options.MAX_ITER=15000
m.options.SOLVER=1
# optimize
m.solve(disp=False, GUI=False)
#m.open_folder(dataset_path+'inf')
list_xi.append(x.value)
list_ui.append(u.value)
list_Ki.append(m_param.value)
list_x.append(list_xi)
list_Kmax.append(list_Ki)
list_u.append(list_ui)
return list_x, list_u, list_Kmax, m.options.OBJFCNVAL
scaled_days[i][j] =[-7.0, 42.0, 83.0, 125.0, 167.0, 217.0, 258.0, 300.0, 342.0]
scaled_pop[i][j] = [0.01762491277346285, 0.020592540360308997, 0.017870838266697213, 0.01690069378982034,0.015512320147187675,0.01506701796298272,0.014096420738841563,0.013991224004743027,0.010543380664478205]
k0,b0,group, case0, u0, sigma0, K0, a0, c0 = (100, 20, 'Size3, Inc', 'case0', 0.1, 0.05, 2, 0, 0.01)
list_x2, list_u2, list_Kmax2,final =run_model_m(days=[[scaled_days[i][j]]], population=
[[scaled_pop[i][j]]],case=case1, k_val=list_b1[i0][0], b_val=b1, u0_val=list_u1[i0][j0],
sigma_val=sigma1, Kmax0=K1, a_val=list_Kmax1[0][0], c_val=c1)
I get the error Data arrays must have the same length, and match time discretization in dynamic problems error but I don't understand why. I have tried making x and m_param arrays, with x=m.Var, m_param =m.MV... But still get the same error, even if they are all arrays of the same length. Is this the right way to find the solution of the minimization problem?
I think the error was just that in run_model_m I was passing a list as u0_val and it didn't have the same dimensions as m.time. So it should be u0_val=list_u1[0][0][0]
Related
I would like to use my calculated y[0] (x-values) and y[1] (y-values) from sol_3 using the solve_ivp to find the radius(r) and plot r(t).
How can I calculate r using x and y values from sol_r? I keep getting TypeError: only size-1 arrays can be converted to Python scalars.
It seems like I am having issues with data type.
Please find my code below:
timing = np.array([0,2*math.pi]) #t0 = 0 tf=2pi
sol_3 = solve_ivp(fun = motion, t_span=[-math.pi, 2*math.pi], y0 = initial, method='RK23')
x = (sol_3.y[0, :])
y = (sol_3.y[1, :])
r = math.sqrt(sol_3.y[1,:]**2+sol_3.y[0,:]**2)
The array of the sol_3 looks like this:
message: 'The solver successfully reached the end of the integration interval.'
nfev: 599
njev: 0
nlu: 0
sol: None
status: 0
success: True
t: array([-3.14159265, -3.14155739, -3.14120473, -3.13767817, -3.12223578,
-3.09595606, -3.0602884 , -3.01493539, -2.96220999, -2.90868487,
-2.86527118, -2.82204945, -2.76814683, -2.69499434, -2.61108567,
-2.51943819, -2.44000487, -2.36057156, -2.28852194, -2.20054302,
-2.10648128, -2.03001656, -1.97695204, -1.92388751, -1.87465566,
-1.82156056, -1.76673945, -1.73011416, -1.70585555, -1.68159695,
-1.64979671, -1.60847127, -1.55783888, -1.50388809, -1.45063319,
-1.40126952, -1.3488944 , -1.27797028, -1.19501887, -1.1039372 ,
-1.02086808, -0.95113058, -0.88636741, -0.80259334, -0.70932861,
-0.61584263, -0.55777683, -0.50936554, -0.46344206, -0.4113168 ,
-0.35663683, -0.31427459, -0.28317047, -0.25206634, -0.22135512,
-0.18102468, -0.13108896, -0.07689042, -0.02318517, 0.02738243,
0.07818198, 0.14701599, 0.22918967, 0.31978884, 0.41431515,
0.48493772, 0.55000025, 0.63412425, 0.72775963, 0.82162403,
0.87984573, 0.92849841, 0.97470164, 1.02711062, 1.0820909 ,
1.12462382, 1.15583674, 1.18704967, 1.21796912, 1.25856295,
1.30880593, 1.36330716, 1.41729713, 1.46809564, 1.51919004,
1.58841181, 1.67102044, 1.76206092, 1.85696013, 1.92801041,
I am trying to store the numpy.ndarrays defined as x_c, y_c, and z_c for every iteration of the loop:
for z_value in np.arange(0, 5, 1):
ms.set_current_mesh(0)
planeoffset : float = z_value
ms.compute_planar_section(planeaxis = 'Z Axis', planeoffset = planeoffset)
m = ms.current_mesh()
matrix_name = m.vertex_matrix()
x_c = matrix_name[:,0]
y_c = matrix_name[:,1]
z_c = matrix_name[:,2]
I would like to be able to recall the three arrays at any z_value, preferably with reference to the z_value i.e x_c # z_value = 2 or similar.
Thanks for any help!
p.s very new to coding, so please go easy on me.
You have to store each array in an external variable, for example a dictionary
x_c={}
y_c={}
z_c={}
for z_value in np.arange(0, 5, 1):
ms.set_current_mesh(0)
planeoffset = float(z_value)
ms.compute_planar_section(planeaxis = 'Z Axis', planeoffset = planeoffset)
m = ms.current_mesh()
m.compact()
print(m.vertex_number(), "vertices in Planar Section Z =", planeoffset)
matrix_name = m.vertex_matrix()
x_c[planeoffset] = matrix_name[:,0]
y_c[planeoffset] = matrix_name[:,1]
z_c[planeoffset] = matrix_name[:,2]
Please, ensure you call m.compact() before accessing the vertex_matrix or you will get a MissingCompactnessException error. Please, note that it is not the same to store anything in x_c[2] or in x_c[2.0], so choose if your index has to be integers o floats and keep the same type (in this example, they are floats).
Later, you can recall values like this:
print("X Values with z=2.0")
print(x_c[2.0])
I am trying to solve a system with differential equations using odeint. I have 4 txt files (that look like the picture below). I read them and I save them in numpy arrays (length:8000) (maby not with the most effective way, but anyway...). I want to pass these 4 arrays as arguments in my odeint and solve the system. For example, at every time step the odeint takes (one from the 8000) to solve the system, I want it to use a different value from these arrays. Is there any way to do it automatically without getting lost in for loops? I tried to do it like this (see code below) but I get the error:
if g2>0: ValueError: The truth value of an array with more than one element is ambiguous. Use a.any() or a.all()
g2 supposed to be 1x1 size at every loop of odeint. So it has to be something with the way I use the 4 arrays (xdot,ydot,xdotdot,ydotdot).
I am new to python and I use python 2.7.12 on Ubuntu 16.04 LTS.
Thank you in advance.
import numpy as np
from scipy.integrate import odeint
import matplotlib.pyplot as plt
added_mass_x = 0.03 # kg
added_mass_y = 0.04
mb = 0.3 # kg
m1 = mb-added_mass_x
m2 = mb-added_mass_y
l1 = 0.07 # m
l2 = 0.05 # m
J = 0.00050797 # kgm^2
Sa = 0.0110 # m^2
Cd = 2.44
Cl = 3.41
Kd = 0.000655 # kgm^2
r = 1000 # kg/m^3
c1 = 0.5*r*Sa*Cd
c2 = 0.5*r*Sa*Cl
c3 = 0.5*mb*(l1**2)
c4 = Kd/J
c5 = (1/(2*J))*(l1**2)*mb*l2
c6 = (1/(3*J))*(l1**3)*mb
theta_0 = 10*(np.pi/180) # rad
theta_A = 20*(np.pi/180) # rad
f = 2 # Hz
###################################################################
t = np.linspace(0,100,8000) # s
###################################################################
# Save data from txt files into numpy arrays
xdot_list = []
ydot_list = []
xdotdot_list = []
ydotdot_list = []
with open('xdot.txt', 'r') as filehandle:
filecontents = filehandle.readlines()
for line in filecontents:
current_place = line[:-1]
xdot_list.append(current_place)
xdot = np.array(xdot_list, dtype=np.float32)
with open('ydot.txt', 'r') as filehandle:
filecontents = filehandle.readlines()
for line in filecontents:
current_place = line[:-1]
ydot_list.append(current_place)
ydot = np.array(ydot_list, dtype=np.float32)
with open('xdotdot.txt', 'r') as filehandle:
filecontents = filehandle.readlines()
for line in filecontents:
current_place = line[:-1]
xdotdot_list.append(current_place)
xdotdot = np.array(xdotdot_list, dtype=np.float32)
with open('ydotdot.txt', 'r') as filehandle:
filecontents = filehandle.readlines()
for line in filecontents:
current_place = line[:-1]
ydotdot_list.append(current_place)
ydotdot = np.array(ydotdot_list, dtype=np.float32)
def inverse(k,t,xdot,ydot,xdotdot,ydotdot):
vcx_i = k[0]
vcy_i = k[1]
psi_i = k[2]
wz_i = k[3]
theta_i = k[4]
theta_deg_i = k[5]
# Subsystem 4
vcx_i = xdot*np.cos(psi_i)-ydot*np.sin(psi_i)
vcy_i = ydot*np.cos(psi_i)+xdot*np.sin(psi_i)
psidot_i = wz_i
vcxdot_i = xdotdot*np.cos(psi_i)-xdot*np.sin(psi_i)*psidot_i-ydotdot*np.sin(psi_i)-ydot*np.cos(psi_i)*psidot_i
vcydot_i = ydotdot*np.cos(psi_i)-ydot*np.sin(psi_i)*psidot_i+xdotdot*np.sin(psi_i)+xdot*np.cos(psi_i)*psidot_i
g1 = -(m1/c3)*vcxdot_i+(m2/c3)*vcy_i*wz_i-(c1/c3)*vcx_i*np.sqrt((vcx_i**2)+(vcy_i**2))+(c2/c3)*vcy_i*np.sqrt((vcx_i**2)+(vcy_i**2))*np.arctan2(vcy_i,vcx_i)
g2 = (m2/c3)*vcydot_i+(m1/c3)*vcx_i*wz_i+(c1/c3)*vcy_i*np.sqrt((vcx_i**2)+(vcy_i**2))+(c2/c3)*vcx_i*np.sqrt((vcx_i**2)+(vcy_i**2))*np.arctan2(vcy_i,vcx_i)
A = 12*np.sin(2*np.pi*f*t+np.pi) # eksiswsi tail_frequency apo simulink
if A>=0.1:
wzdot_i = ((m1-m2)/J)*vcx_i*vcy_i-c4*wz_i**2*np.sign(wz_i)-c5*g2-c6*np.sqrt((g1**2)+(g2**2))
elif A<-0.1:
wzdot_i = ((m1-m2)/J)*vcx_i*vcy_i-c4*wz_i**2*np.sign(wz_i)-c5*g2+c6*np.sqrt((g1**2)+(g2**2))
else:
wzdot_i = ((m1-m2)/J)*vcx_i*vcy_i-c4*wz_i**2*np.sign(wz_i)-c5*g2
# Subsystem 5
if g2>0:
theta_i = np.arctan2(g1,g2)
elif g2<0 and g1>=0:
theta_i = np.arctan2(g1,g2)-np.pi
elif g2<0 and g1<0:
theta_i = np.arctan2(g1,g2)+np.pi
elif g2==0 and g1>0:
theta_i = -np.pi/2
elif g2==0 and g1<0:
theta_i = np.pi/2
elif g1==0 and g2==0:
theta_i = 0
theta_deg_i = (theta_i*180)/np.pi
return [vcxdot_i, vcydot_i, psidot_i, wzdot_i, theta_i, theta_deg_i]
# initial conditions
vcx_i_0 = 0.1257
vcy_i_0 = 0
psi_i_0 = 0
wz_i_0 = 0
theta_i_0 = 0
theta_deg_i_0 = 0
#theta_i_0 = 0.1745
#theta_deg_i_0 = 9.866
k0 = [vcx_i_0, vcy_i_0, psi_i_0, wz_i_0, theta_i_0, theta_deg_i_0]
# epilysi systimatos diaforikwn
k = odeint(inverse, k0, t, args=(xdot,ydot,xdotdot,ydotdot), tfirst=False)
# apothikeysi apotelesmatwn
vcx_i = k[:,0]
vcy_i = k[:,1]
psi_i = k[:,2]
wz_i = k[:,3]
theta_i = k[:,4]
theta_deg_i = k[:,5]
# Epanalipsi tu Subsystem 5 gia na mporun na plotaristun ta theta_i, theta_deg_i
theta_i = [inverse(k_i, t_i)[4] for t_i, k_i in zip(t, k)]
theta_deg_i = [inverse(k_i, t_i)[5] for t_i, k_i in zip(t, k)]
# Ypologismos mesis gwnias theta kai platus talantwsis
mesi_gwnia = sum(theta_i)/len(theta_i) # rad
platos = (max(theta_i)-min(theta_i))/2
UPDATE:
The most relevant solution I found so far is this:
Solving a system of odes (with changing constant!) using scipy.integrate.odeint?
But since I have only values of my variables in arrays and not the equation of the variables that depend on time (e.g. xdot=f(t)), I tried to aply an interpolation between the values in my arrays, as shown here: ODEINT with multiple parameters (time-dependent)
I managed to make the code running without errors, but the total time increased dramatically and the results of the system solved are completely wrong. I tried any possible type of interpolation that I found here: https://docs.scipy.org/doc/scipy/reference/generated/scipy.interpolate.interp1d.html but still wring outcome. That means that my interpolation isn't the best possible, or my points in the arrays (8000 values) are too much to interpolate between them and solve the system correctly.
I have (in a larger project) data contained in numpy.array.
Based on user input I need to move a selected axis (dimAxisNr) to the first dimension of the array and slice one or more (including the first) dimension based on user input (such as Select2 and Select0 in the example).
Using this input I generate a DataSelect which contains the information needed to slice. But the output size of the sliced array is different from the one using inline indexing. So basically I need a way to generate the '37:40:2' and '0:2' from an input list.
import numpy as np
dimAxisNr = 1
Select2 = [37,39]
Select0 = [0,1]
plotData = np.random.random((102,72,145,2))
DataSetSize = np.shape(plotData)
DataSelect = [slice(0,item) for item in DataSetSize]
DataSelect[2] = np.array(Select2)
DataSelect[0] = np.array(Select0)
def shift(seq, n):
n = n % len(seq)
return seq[n:] + seq[:n]
#Sort and Slice the data
print(np.shape(plotData))
print(DataSelect)
plotData = np.transpose(plotData, np.roll(range(plotData.ndim),-dimAxisNr))
DataSelect = shift(DataSelect,dimAxisNr)
print(DataSelect)
print(np.shape(plotData))
plotData = plotData[DataSelect]
print(np.shape(plotData))
plotDataDirect = plotData[slice(0, 72, None), 37:40:2, slice(0, 2, None), 0:2]
print(np.shape(plotDataDirect))
I'm not sure I've understood your question at all...
But if the question is "How do I generate a slice based on a list of indices like [37,39,40,23] ?"
then I would answer : you don't have to, just use the list as is to select the right indices, like so :
a = np.random.rand(4,5)
print(a)
indices = [2,3,1]
print(a[0:2,indices])
Note that the sorting of the list matters: [2,3,1] yields a different result from [1,2,3]
Output :
>>> a
array([[ 0.47814802, 0.42069094, 0.96244966, 0.23886243, 0.86159478],
[ 0.09248812, 0.85569145, 0.63619014, 0.65814667, 0.45387509],
[ 0.25933109, 0.84525826, 0.31608609, 0.99326598, 0.40698516],
[ 0.20685221, 0.1415642 , 0.21723372, 0.62213483, 0.28025124]])
>>> a[0:2,[2,3,1]]
array([[ 0.96244966, 0.23886243, 0.42069094],
[ 0.63619014, 0.65814667, 0.85569145]])
I have found the answer to my question. I need to use numpy.ix_.
Here is the working code:
import numpy as np
dimAxisNr = 1
Select2 = [37,39]
Select0 = [0,1]
plotData = np.random.random((102,72,145,2))
DataSetSize = np.shape(plotData)
DataSelect = [np.arange(0,item) for item in DataSetSize]
DataSelect[2] = Select2
DataSelect[0] = Select0
#print(list(37:40:2))
def shift(seq, n):
n = n % len(seq)
return seq[n:] + seq[:n]
#Sort and Slice the data
print(np.shape(plotData))
print(DataSelect)
plotData = np.transpose(plotData, np.roll(range(plotData.ndim),-dimAxisNr))
DataSelect = shift(DataSelect,dimAxisNr)
plotDataSlice = plotData[np.ix_(*DataSelect)]
print(np.shape(plotDataSlice))
plotDataDirect = plotData[slice(0, 72, None), 37:40:2, slice(0, 2, None), 0:1]
print(np.shape(plotDataDirect))
I am setting up an optimization in OpenMDAO v0.13 using several components that are used many times. My assembly seems to be working just fine with the default driver, but when I run with an optimizer it does not solve. The optimizer simply runs with the inputs given and returns the answer using those inputs. I am not sure what the issue is, but I would appreciate any insights. I have included a simple code mimicking my structure that reproduces the error. I think the problem is in the connections, summer.fs does not update after initialization.
from openmdao.main.api import Assembly, Component
from openmdao.lib.datatypes.api import Float, Array, List
from openmdao.lib.drivers.api import DOEdriver, SLSQPdriver, COBYLAdriver, CaseIteratorDriver
from pyopt_driver.pyopt_driver import pyOptDriver
import numpy as np
class component1(Component):
x = Float(iotype='in')
y = Float(iotype='in')
term1 = Float(iotype='out')
a = Float(iotype='in', default_value=1)
def execute(self):
x = self.x
a = self.a
term1 = a*x**2
self.term1 = term1
print "In comp1", self.name, self.a, self.x, self.term1
def list_deriv_vars(self):
return ('x',), ('term1',)
def provideJ(self):
x = self.x
a = self.a
dterm1_dx = 2.*a*x
J = np.array([[dterm1_dx]])
print 'In comp1, J = %s' % J
return J
class component2(Component):
x = Float(iotype='in')
y = Float(iotype='in')
term1 = Float(iotype='in')
f = Float(iotype='out')
def execute(self):
y = self.y
x = self.x
term1 = self.term1
f = term1 + x + y**2
self.f = f
print "In comp2", self.name, self.x, self.y, self.term1, self.f
class summer(Component):
total = Float(iotype='out', desc='sum of all f values')
def __init__(self, size):
super(summer, self).__init__()
self.size = size
self.add('fs', Array(np.ones(size), iotype='in', desc='f values from all cases'))
def execute(self):
self.total = sum(self.fs)
print 'In summer, fs = %s and total = %s' % (self.fs, self.total)
class assembly(Assembly):
x = Float(iotype='in')
y = Float(iotype='in')
total = Float(iotype='out')
def __init__(self, size):
super(assembly, self).__init__()
self.size = size
self.add('a_vals', Array(np.zeros(size), iotype='in', dtype='float'))
self.add('fs', Array(np.zeros(size), iotype='out', dtype='float'))
print 'in init a_vals = %s' % self.a_vals
def configure(self):
# self.add('driver', SLSQPdriver())
self.add('driver', pyOptDriver())
self.driver.optimizer = 'SNOPT'
# self.driver.pyopt_diff = True
#create this first, so we can connect to it
self.add('summer', summer(size=len(self.a_vals)))
self.connect('summer.total', 'total')
print 'in configure a_vals = %s' % self.a_vals
# create instances of components
for i in range(0, self.size):
c1 = self.add('comp1_%d'%i, component1())
c1.missing_deriv_policy = 'assume_zero'
c2 = self.add('comp2_%d'%i, component2())
self.connect('a_vals[%d]' % i, 'comp1_%d.a' % i)
self.connect('x', ['comp1_%d.x'%i, 'comp2_%d.x'%i])
self.connect('y', ['comp1_%d.y'%i, 'comp2_%d.y'%i])
self.connect('comp1_%d.term1'%i, 'comp2_%d.term1'%i)
self.connect('comp2_%d.f'%i, 'summer.fs[%d]'%i)
self.driver.workflow.add(['comp1_%d'%i, 'comp2_%d'%i])
self.connect('summer.fs[:]', 'fs[:]')
self.driver.workflow.add(['summer'])
# set up main driver (optimizer)
self.driver.iprint = 1
self.driver.maxiter = 100
self.driver.accuracy = 1.0e-6
self.driver.add_parameter('x', low=-5., high=5.)
self.driver.add_parameter('y', low=-5., high=5.)
self.driver.add_objective('summer.total')
if __name__ == "__main__":
""" the result should be -1 at (x, y) = (-0.5, 0) """
import time
from openmdao.main.api import set_as_top
a_vals = np.array([1., 1., 1., 1.])
test = set_as_top(assembly(size=len(a_vals)))
test.a_vals = a_vals
print test.a_vals
test.x = 2.
test.y = 2.
tt = time.time()
test.run()
print "Elapsed time: ", time.time()-tt, "seconds"
print 'result = ', test.summer.total
print '(x, y) = (%s, %s)' % (test.x, test.y)
print test.fs
I played around with your model, and found that the following line caused problems:
#self.connect('summer.fs[:]', 'fs[:]')
When I commented it out, I got the optimization to move.
I am not sure what is happening there, but the graph transformations sometimes have some issues with component input nodes that are promoted as outputs on the assembly boundary. If you still want those values to be available on the assembly, you could try promoting the outputs from the comp2_n components instead.