def fitCoefficients(self,xName,T=[],xData=[]):
if (len(T)!=len(xData)):
raise (ValueError("Error: There has to be the same number of temperature and data points."))
if len(T)<self._minPoints:
raise (ValueError("Error: You should use at least "+str(self._minPoints)+" points."))
def fun(coefficients,xName,T,xData):
# Values for conductivity are very small,
# algorithms prefer larger values
if xName=='L':
calculated = numpy.array([self._PropsFit(coefficients,xName,T=Ti) for Ti in T])*1e6
data = numpy.array(xData)*1e6
# Fit logarithms for viscosity and saturation pressure
elif xName=='V' or xName=='Psat':
calculated = numpy.log([self._PropsFit(coefficients,xName,T=Ti) for Ti in T])
data = numpy.log(xData)
else:
calculated = numpy.array([self._PropsFit(coefficients,xName,T=Ti) for Ti in T])
data = numpy.array(xData)
res = numpy.sum((calculated-data)**2.)
return res
initValues = self.getCoefficients(xName)[:]
arguments = (xName,T,xData)
options = {'maxiter': 1e4, 'maxfev': 1e6}
res = minimize(fun, initValues, method='Powell', args=arguments, tol=1e-15, options=options)
if res.success:
return res.x
else:
print res
return False
def train(date=0, theta=0):
if date == 0:
filename = MERGEDTRAININGFILE
filename = DIR + r'\trainingset_3_8_5.merged.csv'
filename = ur'F:\AliRecommendHomeworkData\1000.csv'
else:
filename = TRAININGFILE % date
raw_data = load(filename)
#raw_data = expendX(raw_data) #加上除法特征
print 'data loaded,len=%d' % len(raw_data)
posi_dup = POSI_DUP
raw_data = np.array(raw_data)
if NEGA_RATE > 0 or posi_dup > 1:
posi = raw_data[raw_data[:, 2] == 1, :]
nega = raw_data[raw_data[:, 2] == 0, :]
np.random.shuffle(nega)
raw_data = nega[:NEGA_RATE * posi_dup * len(posi), :]
for i in range(posi_dup):
raw_data = np.append(raw_data, posi, axis=0)
#np.random.shuffle(raw_data)
x, y, online, result = getXY(raw_data)
print ur'扩充完毕'
print ur'正例:%d, 负例:%d' % (sum(y), sum(y == 0))
print ur'在线商品：%d, 在线商品中正例%d' % (sum(online), sum(y[online == 1]))
x = mapFeature(x)
print ur'正例扩充%d倍，训练集总大小：%d，维度：%d' % (posi_dup, len(x), x.shape[1])
if theta == 0:
theta = np.zeros(x.shape[1])
else:
theta = readTheta()
args = (x, y, pLambda)
res = minimize(costFunctionReg,
theta,
jac=gradFunctionReg,
args=args,
method='BFGS')
theta = res.x
p = predict(theta, x)
writeTheta(theta)
with open(MAINDIR + "\\thetas\\%d.txt" % date, 'w') as f:
f.write(','.join([str(item) for item in theta]))
accuracy = np.mean(p == y) * 100
print 'Train Accuracy:%f' % accuracy
print_analyse(sum(p[y == 1]), sum(p), sum(y))
pass
def train(date=0,theta=0):
if date == 0:
filename = MERGEDTRAININGFILE
filename = DIR + r'\trainingset_3_8_5.merged.csv'
filename = ur'F:\AliRecommendHomeworkData\1000.csv'
else:
filename = TRAININGFILE % date
raw_data = load(filename)
#raw_data = expendX(raw_data) #加上除法特征
print 'data loaded,len=%d' % len(raw_data)
posi_dup = POSI_DUP
raw_data = np.array(raw_data)
if NEGA_RATE > 0 or posi_dup > 1:
posi = raw_data[raw_data[:,2] == 1,:]
nega = raw_data[raw_data[:,2] == 0,:]
np.random.shuffle(nega)
raw_data = nega[:NEGA_RATE * posi_dup * len(posi),:]
for i in range(posi_dup):
raw_data = np.append(raw_data,posi,axis=0)
#np.random.shuffle(raw_data)
x,y,online,result = getXY(raw_data)
print ur'扩充完毕'
print ur'正例:%d, 负例:%d' % (sum(y),sum(y == 0))
print ur'在线商品：%d, 在线商品中正例%d' % (sum(online),sum(y[online == 1]))
x = mapFeature(x)
print ur'正例扩充%d倍，训练集总大小：%d，维度：%d' % (posi_dup,len(x),x.shape[1])
if theta == 0:
theta = np.zeros(x.shape[1])
else:
theta = readTheta()
args = (x,y,pLambda)
res = minimize(costFunctionReg,theta,jac=gradFunctionReg,args=args,method='BFGS')
theta = res.x
p = predict(theta,x)
writeTheta(theta)
with open(MAINDIR + "\\thetas\\%d.txt" % date,'w') as f:
f.write(','.join([str(item) for item in theta]))
accuracy = np.mean(p == y) * 100
print 'Train Accuracy:%f' % accuracy
print_analyse(sum(p[y == 1]),sum(p),sum(y))
pass
def train():
print ur'正在载入文件:', filename
raw_data = load(filename)
#raw_data = expendX(raw_data) #加上除法特征
print ur'数据载入成功,len=%d' % len(raw_data)
posi_dup = POSI_DUP
raw_data = np.array(raw_data)
if NEGA_RATE > 0 or posi_dup > 1:
posi = raw_data[raw_data[:, 2] == 1, :]
nega = raw_data[raw_data[:, 2] == 0, :]
np.random.shuffle(nega)
raw_data = nega[:NEGA_RATE * posi_dup * len(posi), :]
for i in range(posi_dup):
raw_data = np.append(raw_data, posi, axis=0)
np.random.shuffle(raw_data)
x, y, online, result = getXY(raw_data)
print ur'扩充完毕'
print ur'正例:%d, 负例:%d' % (sum(y), sum(y == 0))
print ur'在线商品：%d, 在线商品中正例%d' % (sum(online), sum(y[online == 1]))
x = mapFeature(x)
print ur'正例扩充%d倍，训练集总大小：%d，维度：%d' % (posi_dup, len(x), x.shape[1])
theta = np.zeros(x.shape[1])
args = (x, y, pLambda)
res = minimize(costFunctionReg,
theta,
jac=gradFunctionReg,
args=args,
method='BFGS')
theta = res.x
writeTheta(theta)
p = predict(theta, x)
accuracy = np.mean(p == y) * 100
print 'Train Accuracy:%f' % accuracy
print_analyse(sum(p[y == 1]), sum(p), sum(y))
test(theta)
pass
def fit(self, X, y):
# For loss function = l2
print("Yugal")
if self.lf == 'l2':
Xnew = numpy.vstack((X,numpy.ones(X.shape[0]))).T
self.params = numpy.linalg.pinv(Xnew).dot(y)
return None
# For loss function = huber
a = self.lfp
p1 = numpy.random.uniform(0.001,0.0008)
p2 = numpy.random.uniform(0.001,0.0008)
p = [p1,p2]
self.params = p
self.params = optimize.minimize(lambda x: self.huber_objfunc(X, y, x, a), self.params, method = 'BFGS',
jac = lambda x: self.huber_objfunc_derivative(X, y, x, a)).x
return None
def train():
print ur'正在载入文件:',filename
raw_data = load(filename)
#raw_data = expendX(raw_data) #加上除法特征
print ur'数据载入成功,len=%d' % len(raw_data)
posi_dup = POSI_DUP
raw_data = np.array(raw_data)
if NEGA_RATE > 0 or posi_dup > 1:
posi = raw_data[raw_data[:,2] == 1,:]
nega = raw_data[raw_data[:,2] == 0,:]
np.random.shuffle(nega)
raw_data = nega[:NEGA_RATE * posi_dup * len(posi),:]
for i in range(posi_dup):
raw_data = np.append(raw_data,posi,axis=0)
np.random.shuffle(raw_data)
x,y,online,result = getXY(raw_data)
print ur'扩充完毕'
print ur'正例:%d, 负例:%d' % (sum(y),sum(y == 0))
print ur'在线商品：%d, 在线商品中正例%d' % (sum(online),sum(y[online == 1]))
x = mapFeature(x)
print ur'正例扩充%d倍，训练集总大小：%d，维度：%d' % (posi_dup,len(x),x.shape[1])
theta = np.zeros(x.shape[1])
args = (x,y,pLambda)
res = minimize(costFunctionReg,theta,jac=gradFunctionReg,args=args,method='BFGS')
theta = res.x
writeTheta(theta)
p = predict(theta,x)
accuracy = np.mean(p == y) * 100
print 'Train Accuracy:%f' % accuracy
print_analyse(sum(p[y == 1]),sum(p),sum(y))
test(theta)
pass
def fitCoefficients(self, xName, T=[], xData=[]):
if (len(T) != len(xData)):
raise (ValueError(
"Error: There has to be the same number of temperature and data points."
))
if len(T) < self._minPoints:
raise (ValueError("Error: You should use at least " +
str(self._minPoints) + " points."))
def fun(coefficients, xName, T, xData):
# Values for conductivity are very small,
# algorithms prefer larger values
if xName == 'L':
calculated = numpy.array(
[self._PropsFit(coefficients, xName, T=Ti)
for Ti in T]) * 1e6
data = numpy.array(xData) * 1e6
# Fit logarithms for viscosity and saturation pressure
elif xName == 'V' or xName == 'Psat':
calculated = numpy.log(
[self._PropsFit(coefficients, xName, T=Ti) for Ti in T])
data = numpy.log(xData)
else:
calculated = numpy.array(
[self._PropsFit(coefficients, xName, T=Ti) for Ti in T])
data = numpy.array(xData)
res = numpy.sum((calculated - data)**2.)
return res
initValues = self.getCoefficients(xName)[:]
arguments = (xName, T, xData)
options = {'maxiter': 1e4, 'maxfev': 1e6}
res = minimize(fun,
initValues,
method='Powell',
args=arguments,
tol=1e-15,
options=options)
if res.success:
return res.x
else:
print res
return False
def fit_perspective_transform(X,A,guess): X_=np.zeros((len(X),3)) for i in range(len(X)): X_[i][0]=X[i][0] X_[i][1]=X[i][1] X_[i][2]=1.0 X=np.array(X_) A=np.array(A) def y(M): re=0 for n in range(X.shape[0]): u=M.dot(X[n]) u=[u[0]/u[2],u[1]/u[2]] re+=(u[0]-A[n][0])**2+(u[1]-A[n][1])**2 return re def y_multivar(i): return y(np.array([[i[0],i[1],i[2]],[i[3],i[4],i[5]],[i[6],i[7],i[8]]])) def p_y_p_Mij(M,i,j): delta=.001 delMij=np.zeros(M.shape) delMij[i,j]=delta return (y(M+delMij)-y(M))/delta def grad_y_by_M(M): re=np.zeros(M.shape) for i in range(M.shape[0]): for j in range(M.shape[1]): re[i,j]=p_y_p_Mij(M,i,j) return re M=minimize(y_multivar, [guess[0,0],guess[0,1],guess[0,2] ,guess[1,0],guess[1,1],guess[1,2], 0,0,1], args=())['x'] M=np.array([[M[0],M[1],M[2]],[M[3],M[4],M[5]],[M[6],M[7],M[8]]]) M/=M[2,2] return M
def getCoeffsIterative1D(x_in, z_in, eqnType, coeffs, DEBUG=False):
if x_in is None: raise ValueError("You did not provide data for the x-values.")
if z_in is None: raise ValueError("You did not provide data for the z-values.")
if eqnType is None: raise ValueError("You did not provide data for eqnType.")
if coeffs is None: raise ValueError("You did not provide data for the coefficients.")
if DEBUG is None: raise ValueError("You did not provide data for DEBUG.")
sErr = None
#fit = "Powell" # use Powell's algorithm
#fit = "BFGS" # use Broyden-Fletcher-Goldfarb-Shanno
#fit = "LMA" # use the Levenberg-Marquardt algorithm from curve_fit
fit = ["LMA","Powell","BFGS"] # First try LMA, use others as fall-back
# make sure that we use other routines for polynomials
if (eqnType==IncompressibleData.INCOMPRESSIBLE_POLYNOMIAL) or \
(eqnType==IncompressibleData.INCOMPRESSIBLE_EXPPOLYNOMIAL) :
raise ValueError("Please use the specific polynomial functions, they are much better.")
expLog = False
# Fitting the logarithm of z_in?
if (eqnType==IncompressibleData.INCOMPRESSIBLE_EXPONENTIAL or eqnType==IncompressibleData.INCOMPRESSIBLE_LOGEXPONENTIAL):
expLog = True
xData = np.array(x_in.flat)
if expLog: zData = np.log(np.clip(z_in.flat,1e-10,IncompressibleData.maxLin))
else: zData = np.array(z_in.flat)
# Remove np.nan elements
mask = np.isfinite(zData)
xData = xData[mask]
zData = zData[mask]
# The residual function
def fun(coefficients,xArray,yArray):
"""
This function takes the coefficient array and
x and y data. It evaluates the function and returns
the sum of the squared residuals if yArray is not
equal to None
"""
# No offset and no Tbase etc for 1D functions!
calculated = IncompressibleData.baseFunc(xArray, y=0.0, xbase=0.0, ybase=0.0, eqnType=eqnType, c=coefficients)
if expLog: calculated = np.log(calculated)
if yArray is None: return calculated
data = yArray
res = np.sum(np.square(calculated-data))
return res
# Loop through the list of algorithms with basic settings to keep track of our efforts
success = False
counter = 0
tolerance = 1e-16
while (not success):
algorithm = fit[counter]
#fit = "LMA" # use the Levenberg-Marquardt algorithm from curve_fit
if algorithm=="LMA":
def func(xVector, *coefficients):
return fun(np.array(coefficients), xVector, None)
#return self.baseFunction(xVector, 0.0, 0.0, 0.0, np.array(coefficients)) #np.array([self._PropsFit(coefficients,xName,T=Ti) for Ti in T])
try:
#print func(xData, coeffs_start)
# Do the actual fitting
popt, pcov = curve_fit(func, xData, zData, p0=coeffs, ftol=tolerance)
if np.any(popt!=coeffs):
success = True
if DEBUG: print("Fit succeeded with: {0}".format(algorithm))
sErr = zData - func(xData, popt)
#print "Fit succeeded for "+fit[counter]+": "
#print "data: {0}, func: {1}".format(yData[ 2],func(xData[ 2], popt))
#print "data: {0}, func: {1}".format(yData[ 6],func(xData[ 6], popt))
#print "data: {0}, func: {1}".format(yData[-1],func(xData[-1], popt))
#if DEBUG: print("Estimated covariance of parameters: {0}".format(pcov))
#ssErr = np.sqrt(np.diag(pcov)).sum()
#ssTot = ((zData-zData.mean())**2).sum()
#r2 = 1-(ssErr/ssTot )
#print("\n r2 FMA: ",r2.shape,r2,"\n")
return popt,sErr
else:
if DEBUG: print("Fit failed for {0}.".format(algorithm))
if DEBUG: sys.stdout.flush()
success = False
except RuntimeError as e:
if DEBUG: print("Exception using "+algorithm+": "+str(e))
if DEBUG: sys.stdout.flush()
success = False
#fit = "MIN" # use a home-made minimisation with Powell and Broyden-Fletcher-Goldfarb-Shanno
elif algorithm=="Powell" or algorithm=="BFGS":
arguments = (xData,zData)
#options = {'maxiter': 1e2, 'maxfev': 1e5}
try:
res = minimize(fun, coeffs, method=algorithm, args=arguments, tol=tolerance)
if res.success:
success = True
if DEBUG: print("Fit succeeded with: {0}".format(algorithm))
sErr = zData - fun(np.array(res.x), xData, None)
#if res.has_key('fvec'):
#ssErr = (res['fvec']**2).sum()
#ssTot = ((zData-zData.mean())**2).sum()
#r2 = 1-(ssErr/ssTot )
#print("\n r2 : ",r2.shape,r2,algorithm,"\n")
return res.x,sErr
else:
if DEBUG: print("Fit failed for {0}.".format(algorithm))
if DEBUG: sys.stdout.flush()
success = False
except RuntimeError as e:
if DEBUG: print("Exception using "+algorithm+": "+str(e))
if DEBUG: sys.stdout.flush()
success = False
# Something went wrong, probably a typo in the algorithm selector
else:
raise (ValueError("Error: You used an unknown fit method."))
if counter<len(fit)-1:
#print("Fit did not succeed with {0}, reducing tolerance to {1}.".format(algorithm,tol))
success = False
counter += 1
elif tolerance<1e-3:
tolerance *= 1e2
if DEBUG: print("Fit did not succeed, reducing tolerance to {0}.".format(tolerance))
success = False
counter = 0
else:
if DEBUG: print("--------------------------------------------------------------")
if DEBUG: print("Fit failed for {0}. ".format(fit))
if DEBUG: print("--------------------------------------------------------------")
return coeffs,1
def opt_hyper(gpr, hyperparams,
Ifilter=None, maxiter=1000,
gradcheck=False,
bounds=None, callback=None,
# optimizer=OPT.fmin_tnc,
gradient_tolerance=1e-8,
messages=True, *args, **kw_args):
"""
Optimize hyperparemters of :py:class:`pygp.gp.basic_gp.GP` ``gpr`` starting from given hyperparameters ``hyperparams``.
**Parameters:**
gpr : :py:class:`pygp.gp.basic_gp`
GP regression class
hyperparams : {'covar':logtheta, ...}
Dictionary filled with starting hyperparameters
for optimization. logtheta are the CF hyperparameters.
Ifilter : [boolean]
Index vector, indicating which hyperparameters shall
be optimized. For instance::
logtheta = [1,2,3]
Ifilter = [0,1,0]
means that only the second entry (which equals 2 in
this example) of logtheta will be optimized
and the others remain untouched.
bounds : [[min,max]]
Array with min and max value that can be attained for any hyperparameter
maxiter: int
maximum number of function evaluations
gradcheck: boolean
check gradients comparing the analytical gradients to their approximations
** argument passed onto LML**
priors : [:py:class:`pygp.priors`]
non-default prior, otherwise assume
first index amplitude, last noise, rest:lengthscales
"""
# optimizer: :py:class:`scipy.optimize`
# which scipy optimizer to use? (standard lbfgsb)
global __last_lml__
__last_lml__ = 0
# i=0
# mill = {0:'-',1:'\\',2:"|",4:'-',3:'/'}
# def callback(x):
# i = (i+1)%5
# import sys;
# sys.stdout.flush()
# sys.stdout.write("optimizing...{}\r".format(mill[i]))
def f(x):
x_ = X0
x_[Ifilter_x] = x
global __last_lml__
__last_lml__ = gpr.LML(param_list_to_dict(x_, param_struct, skeys), *args, **kw_args)
# LG.debug("L("+str(x_)+")=="+str(rv))
if SP.isnan(__last_lml__):
return 1E6
return __last_lml__
def df(x):
x_ = X0
x_[Ifilter_x] = x
rv = gpr.LMLgrad(param_list_to_dict(x_, param_struct, skeys), *args, **kw_args)
rv = param_dict_to_list(rv, skeys)
# LG.debug("dL("+str(x_)+")=="+str(rv))
if not SP.isfinite(rv).all(): # SP.isnan(rv).any():
In = ~SP.isfinite(rv)#SP.isnan(rv)
rv[In] = 1E6
return rv[Ifilter_x]
# 0. store parameter structure
skeys = SP.sort(hyperparams.keys())
param_struct = dict([(name, hyperparams[name].shape) for name in skeys])
# 1. convert the dictionaries to parameter lists
X0 = param_dict_to_list(hyperparams, skeys)
if Ifilter is not None:
Ifilter_x = SP.array(param_dict_to_list(Ifilter, skeys), dtype='bool')
else:
Ifilter_x = slice(None)#SP.ones(len(X0), dtype='bool')
# 2. bounds
if bounds is not None:
# go through all hyperparams and build bound array (flattened)
_b = []
for key in skeys:
if key in bounds.keys():
_b.extend(bounds[key])
else:
_b.extend([(-SP.inf, +SP.inf)] * hyperparams[key].size)
bounds = SP.array(_b)
bounds = bounds[Ifilter_x]
pass
# 2. set starting point of optimization, truncate the non-used dimensions
x = X0.copy()[Ifilter_x]
LG.debug("startparameters for opt:" + str(x))
if gradcheck:
checkgrad(f, df, x, hyper_names=None)
LG.info("check_grad (pre) (Enter to continue):" + str(OPT.check_grad(f, df, x)))
raw_input()
# #
LG.debug("start optimization")
# general optimizer interface
# note: x is a subset of X, indexing the parameters that are optimized over
# Ifilter_x pickes the subest of X, yielding x
try:
#=======================================================================
# TNC:
# opt_RV, opt_lml = optimizer(f, x, fprime=df, maxfun=int(maxiter), pgtol=gradient_tolerance, messages=messages, bounds=bounds)[:2]
#=======================================================================
#=======================================================================
# L BFGS:
# opt_RV, opt_lml = OPT.fmin_l_bfgs_b(f, x, fprime=df, maxfun=int(maxiter), approx_grad=False, iprint=0, bounds=bounds, factr=10.0 , pgtol=gradient_tolerance)[:2]
#=======================================================================
#=======================================================================
# L_BFGS_B minimize
iprint = -1
if messages:
iprint = 1
res = minimize(f, x, method="L-BFGS-B", jac=df,
bounds=bounds, callback=callback,
tol=gradient_tolerance,
options=dict(maxiter=maxiter,
iprint=iprint))
opt_RV, opt_lml = res.x, res.fun
#=======================================================================
opt_x = opt_RV
except LinAlgError as error:
print error
opt_x = X0
opt_lml = __last_lml__
# opt_RV = OPT.fmin_bfgs(f, x, fprime=df, maxiter=int(maxiter), disp=1)
# opt_x = opt_RV
# relate back to X
Xopt = X0.copy()
Xopt[Ifilter_x] = opt_x
# convert into dictionary
opt_hyperparams = param_list_to_dict(Xopt, param_struct, skeys)
# get the log marginal likelihood at the optimum:
# opt_lml = gpr.LML(opt_hyperparams,**kw_args)
if gradcheck:
checkgrad(f, df, Xopt, hyper_names=None)
LG.info("check_grad (post) (Enter to continue):" + str(OPT.check_grad(f, df, opt_x)))
pdb.set_trace()
# # raw_input()
# LG.debug("old parameters:")
# LG.debug(str(hyperparams))
# LG.debug("optimized parameters:")
# LG.debug(str(opt_hyperparams))
# LG.debug("grad:"+str(df(opt_x)))
return [opt_hyperparams, opt_lml]
def optimize(self):
frequency_grape = self.D0 + self.AN #-C_known[0]
#---------- 作成したいSTATE ----------#
n_goal = len(self.target_list)
n_tslot = int(np.round(self.pulse_time / self.t_div))
permin = -self.permax
rate_hem = 2 #触らない
freq_cut = 10 #触らない
class_pulse = pulsegen.create_pulse_gen(pulse_type='RNDFOURIER',
dyn=None,
pulse_params=None)
class_pulse.num_tslots = n_tslot
#class_pulse.num_ctrl = 1
init_pulse_prescale = class_pulse.gen_pulse()
init_pulse = init_pulse_prescale * self.permax / max(
init_pulse_prescale)
#init_pulse = 1/pulse_time/2.0*(sin(2*pi*(AN)*linspace(t_div,pulse_time,n_tslot)))
t_hem = self.pulse_time * rate_hem
n_hem = int(round(t_hem / self.t_div))
f_list = linspace(0, 1.0 / self.t_div, n_tslot + n_hem * 2)
Φ1_j = np.zeros(n_tslot)
Φ2_j = np.zeros(n_tslot)
"""
Create and return a pulse generator object matching the given type.
The pulse generators each produce a different type of pulse,
see the gen_pulse function description for details.
These are the random pulse options:
RND - Independent random value in each timeslot
RNDFOURIER - Fourier series with random coefficients
RNDWAVES - Summation of random waves
RNDWALK1 - Random change in amplitude each timeslot
RNDWALK2 - Random change in amp gradient each timeslot
These are the other non-periodic options:
LIN - Linear, i.e. contant gradient over the time
ZERO - special case of the LIN pulse, where the gradient is 0
These are the periodic options
SINE - Sine wave
SQUARE - Square wave
SAW - Saw tooth wave
TRIANGLE - Triangular wave
If a Dynamics object is passed in then this is used in instantiate
the PulseGen, meaning that some timeslot and amplitude properties
are copied over.
"""
def callback(self, pulse, f_list, t_hem, n_hem, n_tslot, freq_cut,
permin):
#print("========== Before FFT ==========") 描画する時はコメントアウトしない
"""
plt.plot(pulse)
plt.grid(b="on")
plt.show()
"""
pulse_hem_fft = hstack((zeros(n_hem), pulse, zeros(n_hem)))
t_list = linspace(self.t_div, self.pulse_time + t_hem * 2,
n_tslot + n_hem * 2)
FFT = np.fft.fft(pulse_hem_fft) / (n_tslot + n_hem * 2)
FFT_cut = hstack(
(FFT[0:int((n_tslot + n_hem * 2) /
(1 / self.t_div / freq_cut))],
zeros(
len(FFT) - int((n_tslot + n_hem * 2) /
(1 / self.t_div / freq_cut))))) * 2
pulse_hem = np.fft.fft(FFT_cut)[::-1].real
pulse = pulse_hem[n_hem:len(pulse_hem) - n_hem]
"""描画したいときはコメントアウトしない
plt.plot(f_list,FFT)
plt.plot(f_list,FFT_cut)
plt.xlim(0,freq_cut)
plt.grid(b="on")
plt.show()
pulse = np.clip(pulse,permin,self.permax)
print("========== After FFT ==========")
plt.plot(pulse)
plt.grid(b="on")
plt.show()
"""
return pulse
#=============================================== GRAPE!!! ===============================================#
number_C_known = len(self.C_known)
number_H = len(self.C_inhomo)
II_C_known = Qobj(qeye(2**number_C_known),
dims=[
list(2 * ones(number_C_known)),
list(2 * ones(number_C_known))
])
HhfCz_inhomo = 0
if number_C_known == 0:
for i in range(number_H):
HhfCz_inhomo = HhfCz_inhomo - self.C_inhomo[i] * tensor(
ket2dm(basis(number_H, i)), Sz, III, sigz)
else:
for i in range(number_H):
HhfCz_inhomo = HhfCz_inhomo - self.C_inhomo[i] * tensor(
ket2dm(basis(number_H, i)), Sz, III, II_C_known, sigz)
if number_H == 0:
II_inhomo = Qobj([[1]])
else:
II_inhomo = qeye(number_H)
H0 = defH0(self.D0, self.QN, self.AN, self.C_known, self.Bz)
Hdrift = matrix((tensor(II_inhomo, H0, II) + HhfCz_inhomo).full())
Hdrive1 = matrix(
tensor(II_inhomo, Hxdrive(1, 0, 0, 0, self.theta), III, II_C_known,
II).full())
Hdrive2 = matrix(
tensor(II_inhomo, Hxdrive(0, 1, 0, 0, self.theta), III, II_C_known,
II).full())
Hdetuning = matrix(tensor(II_inhomo, Szz, III, II_C_known, II).full())
U0 = matrix(tensor(II_inhomo, III, III, II_C_known, II).full())
for i in range(n_goal):
if number_H == 0:
self.state_init[i] = matrix(
tensor(II_inhomo, self.state_init[i], II / 2.0).full())
self.state_goal[i] = matrix(
tensor(II_inhomo, self.state_goal[i], II / 2.0).full())
else:
self.state_init[i] = matrix(
tensor(II_inhomo / number_H, self.state_init[i],
II / 2.0).full())
self.state_goal[i] = matrix(
tensor(II_inhomo / number_H, self.state_goal[i],
II / 2.0).full())
"""
weighting_value_targ = []
for i in range(n_goal):
weighting_value_targ = weighting_value_targ+[weighting_value[target_list[i]]]
"""
bounds = [(permin, self.permax)] * n_tslot
pulse = init_pulse
state_init = self.state_init
t_div = self.t_div
state_goal = self.state_goal
weighting_value = self.weighting_value
def grape_fid_err(pulse):
U_b = U0
fid_sum = []
for i in range(n_goal):
for j in range(n_tslot):
U_b = matrix(
sclin.expm(-2 * pi * 1j *
(Hdrift - (frequency_grape) * Hdetuning +
pulse[j] * Hdrive1) * self.t_div)) * U_b
state_final = U_b * state_init[i] * conj(U_b.T)
state_final_qobj = Qobj(state_final)
state_goal_qobj = Qobj(state_goal[i])
fid_sum = fid_sum + [
fidelity(state_final_qobj, state_goal_qobj) *
weighting_value[i]
]
fid_ave = sum(fid_sum) / sum(weighting_value)
#print("fid = "+str(fid_ave)) 描画する時はコメントアウトしない
return 1 - fid_ave
def grape_fid_err_grad(pulse):
U_rho_j = []
U_lamda_j = []
fid_err_grad_ave = []
U_rho = U0
U_lamda = U0
for j in range(n_tslot):
U_rho = matrix(
sclin.expm(-2 * pi * 1j *
(Hdrift - (frequency_grape) * Hdetuning +
pulse[j] * Hdrive1) * t_div)) * U_rho
U_lamda = conj(
matrix(
sclin.expm(-2 * pi * 1j *
(Hdrift - (frequency_grape) * Hdetuning +
pulse[n_tslot - j - 1] * Hdrive1) *
t_div)).T) * U_lamda
U_rho_j = U_rho_j + [U_rho]
U_lamda_j = U_lamda_j + [U_lamda]
for j in range(n_tslot):
fid_err_grad_j_sum = []
for k in range(n_goal):
lamda = (U_lamda_j[n_tslot - j -
2]) * state_goal[k] * conj(
U_lamda_j[n_tslot - j - 2].T)
state_j = U_rho_j[j] * state_init[k] * conj(U_rho_j[j].T)
fid_err_grad_j = np.real(
1j * 2 * pi * t_div *
trace(lamda * (Hdrive1 * state_j - state_j * Hdrive1)))
fid_err_grad_j_sum = fid_err_grad_j_sum + [
fid_err_grad_j * weighting_value[k]
]
fid_err_grad_ave = fid_err_grad_ave + [
sum(fid_err_grad_j_sum) / sum(weighting_value)
]
return array(fid_err_grad_ave)
for i in range(2):
pulse = callback(self, pulse, f_list, t_hem, n_hem, n_tslot,
freq_cut, permin)
result = sp_min.minimize(grape_fid_err,pulse,method="L-BFGS-B",jac=grape_fid_err_grad,bounds=bounds,\
options={'disp': None, 'maxcor': 10, 'ftol': 2.220446049250313e-09, 'gtol': 1e-05, 'eps': 1e-9, 'maxfun': 15000, 'maxiter': 1500, 'iprint': -1, 'maxls': 20})#,tol=1e-2)
pulse = result.x
Ω1_j = pulse #ラビ周波数の配列
Ω2_j = np.zeros(n_tslot)
return Φ1_j, Ω1_j
"""
def getCoeffsIterative1D(x_in, z_in, eqnType, coeffs, DEBUG=False):
if x_in is None:
raise ValueError("You did not provide data for the x-values.")
if z_in is None:
raise ValueError("You did not provide data for the z-values.")
if eqnType is None:
raise ValueError("You did not provide data for eqnType.")
if coeffs is None:
raise ValueError("You did not provide data for the coefficients.")
if DEBUG is None:
raise ValueError("You did not provide data for DEBUG.")
sErr = None
#fit = "Powell" # use Powell's algorithm
#fit = "BFGS" # use Broyden-Fletcher-Goldfarb-Shanno
#fit = "LMA" # use the Levenberg-Marquardt algorithm from curve_fit
fit = ["LMA", "Powell",
"BFGS"] # First try LMA, use others as fall-back
# make sure that we use other routines for polynomials
if (eqnType==IncompressibleData.INCOMPRESSIBLE_POLYNOMIAL) or \
(eqnType==IncompressibleData.INCOMPRESSIBLE_EXPPOLYNOMIAL) :
raise ValueError(
"Please use the specific polynomial functions, they are much better."
)
expLog = False
# Fitting the logarithm of z_in?
if (eqnType == IncompressibleData.INCOMPRESSIBLE_EXPONENTIAL or eqnType
== IncompressibleData.INCOMPRESSIBLE_LOGEXPONENTIAL):
expLog = True
xData = np.array(x_in.flat)
if expLog:
zData = np.log(np.clip(z_in.flat, 1e-10,
IncompressibleData.maxLin))
else:
zData = np.array(z_in.flat)
# Remove np.nan elements
mask = np.isfinite(zData)
xData = xData[mask]
zData = zData[mask]
# The residual function
def fun(coefficients, xArray, yArray):
"""
This function takes the coefficient array and
x and y data. It evaluates the function and returns
the sum of the squared residuals if yArray is not
equal to None
"""
# No offset and no Tbase etc for 1D functions!
calculated = IncompressibleData.baseFunc(xArray,
y=0.0,
xbase=0.0,
ybase=0.0,
eqnType=eqnType,
c=coefficients)
if expLog: calculated = np.log(calculated)
if yArray is None: return calculated
data = yArray
res = np.sum(np.square(calculated - data))
return res
# Loop through the list of algorithms with basic settings to keep track of our efforts
success = False
counter = 0
tolerance = 1e-16
while (not success):
algorithm = fit[counter]
#fit = "LMA" # use the Levenberg-Marquardt algorithm from curve_fit
if algorithm == "LMA":
def func(xVector, *coefficients):
return fun(np.array(coefficients), xVector, None)
#return self.baseFunction(xVector, 0.0, 0.0, 0.0, np.array(coefficients)) #np.array([self._PropsFit(coefficients,xName,T=Ti) for Ti in T])
try:
#print func(xData, coeffs_start)
# Do the actual fitting
popt, pcov = curve_fit(func,
xData,
zData,
p0=coeffs,
ftol=tolerance)
if np.any(popt != coeffs):
success = True
if DEBUG:
print("Fit succeeded with: {0}".format(algorithm))
sErr = zData - func(xData, popt)
#print "Fit succeeded for "+fit[counter]+": "
#print "data: {0}, func: {1}".format(yData[ 2],func(xData[ 2], popt))
#print "data: {0}, func: {1}".format(yData[ 6],func(xData[ 6], popt))
#print "data: {0}, func: {1}".format(yData[-1],func(xData[-1], popt))
#if DEBUG: print("Estimated covariance of parameters: {0}".format(pcov))
#ssErr = np.sqrt(np.diag(pcov)).sum()
#ssTot = ((zData-zData.mean())**2).sum()
#r2 = 1-(ssErr/ssTot )
#print("\n r2 FMA: ",r2.shape,r2,"\n")
return popt, sErr
else:
if DEBUG:
print("Fit failed for {0}.".format(algorithm))
if DEBUG: sys.stdout.flush()
success = False
except RuntimeError as e:
if DEBUG:
print("Exception using " + algorithm + ": " + str(e))
if DEBUG: sys.stdout.flush()
success = False
#fit = "MIN" # use a home-made minimisation with Powell and Broyden-Fletcher-Goldfarb-Shanno
elif algorithm == "Powell" or algorithm == "BFGS":
arguments = (xData, zData)
#options = {'maxiter': 1e2, 'maxfev': 1e5}
try:
res = minimize(fun,
coeffs,
method=algorithm,
args=arguments,
tol=tolerance)
if res.success:
success = True
if DEBUG:
print("Fit succeeded with: {0}".format(algorithm))
sErr = zData - fun(np.array(res.x), xData, None)
#if res.has_key('fvec'):
#ssErr = (res['fvec']**2).sum()
#ssTot = ((zData-zData.mean())**2).sum()
#r2 = 1-(ssErr/ssTot )
#print("\n r2 : ",r2.shape,r2,algorithm,"\n")
return res.x, sErr
else:
if DEBUG:
print("Fit failed for {0}.".format(algorithm))
if DEBUG: sys.stdout.flush()
success = False
except RuntimeError as e:
if DEBUG:
print("Exception using " + algorithm + ": " + str(e))
if DEBUG: sys.stdout.flush()
success = False
# Something went wrong, probably a typo in the algorithm selector
else:
raise (ValueError("Error: You used an unknown fit method."))
if counter < len(fit) - 1:
#print("Fit did not succeed with {0}, reducing tolerance to {1}.".format(algorithm,tol))
success = False
counter += 1
elif tolerance < 1e-3:
tolerance *= 1e2
if DEBUG:
print("Fit did not succeed, reducing tolerance to {0}.".
format(tolerance))
success = False
counter = 0
else:
if DEBUG:
print(
"--------------------------------------------------------------"
)
if DEBUG: print("Fit failed for {0}. ".format(fit))
if DEBUG:
print(
"--------------------------------------------------------------"
)
return coeffs, 1
m= X.shape[0]
theta = np.matrix(np.zeros(X.shape[1]))
## using multiple one vs all logistic regression models to build a multi class classifier. There are 10 different numbers contained in the images 0 - 9,
## thus 10 classes and 10 logistic regression classifiers
thetaList = []
yList = np.unique(Y)
for i in yList:
## We train the data by looping each multi variate variable, and set y to 1 for the variable we wish to train, and zero from the rest.
## Once trained, we then evaluate the probability that a training example belongs to a particular output based on the sigmoid function
yhat = np.zeros(Y.shape[0])
yhat[np.where(Y == i)[0]] = 1
m = X.shape[0]
thetaOut = minimize(fun = logisticCost, x0 = np.asarray(theta)[0], args = (m,X,yhat,True,1), method = 'SLSQP' ,options = {'maxiter':500})['x']
hyp = sigmoid(X,thetaOut)
## see the distribution of probabilities of the training examples belonging to Y set i
#plt.plot(np.array(hyp)[0])
thetaList.append(thetaOut)
## Thus we are learning what for example a "4" looks like, by training the regression parameters on the pixels of different images of 4s where we set y = 1, and others were we set y = 0 when clssifying a 4, that will yield
## the highest probability from the sigmoid hypothesis. i.e. this combination of pixels when applied to the regression parameters for a 4 will predict a 4. This could then work for anything
## really, just training a set of regression parameters so that when applied to a group of pixels it will be a able to tell with a certain confidence if we have
## the image that was trained on or not.
testHyp = sigmoid(X,np.matrix(thetaList))
prediction = [np.where(np.array(testHyp[x,:] == testHyp[x,:].max())[0])[0][0]+1 for x in range(testHyp.shape[0])]
## Precision of predictions based on learned parameters per digit
fig = plt.figure()
plt.scatter(data1.exam1[data1.yesNo == 1 ], data1.exam2[data1.yesNo == 1 ], marker = '+', color = 'black', label = 'admitted')
plt.scatter(data1.exam1[data1.yesNo == 0 ], data1.exam2[data1.yesNo == 0 ], marker = 'o', color = 'yellow', label = 'not admitted')
legend = plt.legend(loc = 'upper right')
## Hypothesis for logistic regression uses sigmoid funtion, so hypothesis is either 1 or zero for binary logistic regression
X = np.concatenate((np.matrix(np.ones(data1.shape[0])).T,data1.iloc[:,:2].as_matrix()),axis =1)
m= X.shape[0]
Y = np.array(data1.iloc[:,2])
theta = np.matrix(np.zeros(X.shape[1]))
sigVals = sigmoid(X, theta)
## now try to find minimum with a built in minimizer
theta = minimize(fun = logisticCost, x0 = np.asarray(theta)[0], args = (m,X,Y), method = 'SLSQP' )
## thus we use the sigmoid function using a particular training set and the calculated thetas to get a
# 1 or a zero i.e. a yes or a no
## plot the decision boundary, y = 1: theta0 + theta1X1 + theta2X2 >= 0, => X2 = (-theta0 - theta1X1)/ theta2
plt.plot(np.array(data1.exam1), (np.array(X[:,:2].dot(-theta.x[:2]))[0])/theta.x[2])
#### Regularized logistic regression
data2 = pd.read_csv('C:\\Users\\Nicholas.R_adm\\Documents\\workspace\\Python\\Home Scripts\\ML exercises\\ex2\\ex2Data2.txt',header=None )
data2.columns = ['test1','test2','yesNo']
fig = plt.figure()
plt.scatter(data2.test1[data2.yesNo == 1 ], data2.test2[data2.yesNo == 1 ], marker = '+', color = 'black', label = 'admitted')
Y = data['y'].flatten().astype('float64')
Ytest = data['ytest'].flatten().astype('float64')
Yval = data['yval'].flatten().astype('float64')
m= X.shape[0]
imgplot = plt.plot(X,Y, 'x')
X = np.concatenate((np.matrix(np.ones(X.shape[0])).T,np.matrix(X).T),axis =1).astype('float64')
Xval = np.concatenate((np.matrix(np.ones(Xval.shape[0])).T,np.matrix(Xval).T),axis =1).astype('float64')
theta = np.matrix([1,1])
regLinCost(theta,X,np.matrix(Y).T,m,lamb = 1)
thetaSolve = minimize(fun = regLinCost, x0 = np.array(theta)[0], args = (X,np.matrix(Y).T,m,0), method = 'TNC', jac = True ,options = {'maxiter':100000})['x']
plt.plot(X[:,1],X.dot(np.matrix(thetaSolve).T))
''' NOTE: when calculating the trsining or cross validation error, ALWAYS set lamb to 0! '''
train = np.zeros(X.shape[0])
cv = np.zeros(Xval.shape[0])
for i in range(1,X.shape[0]):
thetaSolve = minimize(fun = regLinCost, x0 = np.array(theta)[0], args = (X[:i],np.matrix(Y[:i]).T,m,0), method = 'TNC', jac = True ,options = {'maxiter':100000})['x']
train[i] = regLinCost(thetaSolve,X[:i],np.matrix(Y[:i]).T,m,lamb = 0)[0]
cv[i] = regLinCost(thetaSolve,Xval,np.matrix(Yval).T,m,lamb = 0)[0]
## This reflects high bias, as increasing the number of observations imcreases the amount of training error (the lower line). The model is too simple to fit all of the data, and as we increase,
## the number of training examples we get no further decrease in the cross validation error. THus more training examples will not improve performance, but a more complicated model might.
def fitCoefficients(self,xName,T=[],xData=[]):
if (len(T)!=len(xData)):
raise (ValueError("Error: There has to be the same number of temperature and data points."))
if len(T)<self._minPoints:
raise (ValueError("Error: You should use at least "+str(self._minPoints)+" points."))
def fun(coefficients,xName,T,xData):
# Values for conductivity are very small,
# algorithms prefer larger values
if xName=='L':
calculated = numpy.array([self._PropsFit(coefficients,xName,T=Ti) for Ti in T])
data = numpy.array(xData)
# Fit logarithms for viscosity and saturation pressure
elif xName=='V' or xName=='Psat':
calculated = numpy.log(numpy.array([self._PropsFit(coefficients,xName,T=Ti) for Ti in T]))
data = numpy.log(numpy.array(xData))
else:
calculated = numpy.array([self._PropsFit(coefficients,xName,T=Ti) for Ti in T])
data = numpy.array(xData)
res = numpy.sum((calculated-data)**2.)
return res
initValues = self.getCoefficients(xName)[:]
# Fit logarithms for viscosity and saturation pressure
if xName=='V' or xName=='Psat':
#fit = "MIN" # use a home-made minimisation with Powell and Broyden-Fletcher-Goldfarb-Shanno
#fit = "LMA" # use the Levenberg-Marquardt algorithm from curve_fit
#fit = "POL" # use a polynomial in an exponential function
fit = ["LMA","MIN"] # First try LMA, use MIN as a fall-back solver
success = False
counter = -1
while (not success):
counter += 1
if fit[counter]=="LMA":
xData = numpy.array(xData)
fit_log = True
def func(T, *coefficients):
result = numpy.array([self._PropsFit(coefficients,xName,T=Ti) for Ti in T])
if fit_log:
return numpy.log(result)
else:
return result
if fit_log:
xData = numpy.log(xData)
try:
# Do the actual fitting
popt, pcov = curve_fit(func, T, xData, p0=initValues, maxfev=1000)
#print popt
#print pcov
success = True
return popt
except RuntimeError as e:
print "Exception: "+str(e)
print "Using: "+str(fit[counter+1])+" as a fall-back."
success = False
elif fit[counter]=="MIN":
print "Fitting exponential with "+str(len(initValues))+" coefficients."
arguments = (xName,T,numpy.exp(xData))
#options = {'maxiter': 1e2, 'maxfev': 1e5}
if xName=='V':
method = "Powell"
elif xName=='Psat':
method = "BFGS"
tolStart = 1e-13
tol = tolStart
res = minimize(fun, initValues, method=method, args=arguments, tol=tol)
while ((not res.success) and tol<1e-2):
tol *= 1e2
print "Fit did not succeed, reducing tolerance to "+str(tol)
res = minimize(fun, initValues, method=method, args=arguments, tol=tol)
# Include these lines for an additional fit with new guess values.
#if res.success and tol>tolStart:
# print "Refitting with new guesses and original tolerance of "+str(tolStart)
# res = minimize(fun, res.x, method=method, args=arguments, tol=tolStart)
if res.success:
success = True
return res.x
else:
print "Fit failed: "
print res
success = False
elif fit[counter]=="POL":
print "Fitting exponential polynomial with "+str(len(initValues))+" coefficients."
z = numpy.polyfit(T, numpy.log(xData)[:], len(initValues)-1)
return z[::-1]
else:
raise (ValueError("Error: You used an unknown fit method."))
else: # just a polynomial
print "Fitting polynomial with "+str(len(initValues))+" coefficients."
z = numpy.polyfit(T, xData, len(initValues)-1)
return z[::-1]
def fitCoefficients(self, xName, T=[], xData=[]):
if (len(T) != len(xData)):
raise (ValueError(
"Error: There has to be the same number of temperature and data points."
))
if len(T) < self._minPoints:
raise (ValueError("Error: You should use at least " +
str(self._minPoints) + " points."))
def fun(coefficients, xName, T, xData):
# Values for conductivity are very small,
# algorithms prefer larger values
if xName == 'L':
calculated = numpy.array(
[self._PropsFit(coefficients, xName, T=Ti) for Ti in T])
data = numpy.array(xData)
# Fit logarithms for viscosity and saturation pressure
elif xName == 'V' or xName == 'Psat':
calculated = numpy.log(
numpy.array([
self._PropsFit(coefficients, xName, T=Ti) for Ti in T
]))
data = numpy.log(numpy.array(xData))
else:
calculated = numpy.array(
[self._PropsFit(coefficients, xName, T=Ti) for Ti in T])
data = numpy.array(xData)
res = numpy.sum((calculated - data)**2.)
return res
initValues = self.getCoefficients(xName)[:]
# Fit logarithms for viscosity and saturation pressure
if xName == 'V' or xName == 'Psat':
#fit = "MIN" # use a home-made minimisation with Powell and Broyden-Fletcher-Goldfarb-Shanno
#fit = "LMA" # use the Levenberg-Marquardt algorithm from curve_fit
#fit = "POL" # use a polynomial in an exponential function
fit = ["LMA",
"MIN"] # First try LMA, use MIN as a fall-back solver
if self._expPoly:
fit = ["POL"] # Overwrite preferences for polynomial
success = False
counter = -1
while (not success):
counter += 1
if fit[counter] == "LMA":
xData = numpy.array(xData)
fit_log = True
def func(T, *coefficients):
result = numpy.array([
self._PropsFit(coefficients, xName, T=Ti)
for Ti in T
])
if fit_log:
return numpy.log(result)
else:
return result
if fit_log:
xData = numpy.log(xData)
try:
# Do the actual fitting
popt, pcov = curve_fit(func,
T,
xData,
p0=initValues,
maxfev=1000)
#print popt
#print pcov
success = True
return popt
except RuntimeError as e:
print("Exception: " + str(e))
print("Using: " + str(fit[counter + 1]) +
" as a fall-back.")
success = False
elif fit[counter] == "MIN":
print("Fitting exponential with " + str(len(initValues)) +
" coefficients.")
arguments = (xName, T, numpy.exp(xData))
#options = {'maxiter': 1e2, 'maxfev': 1e5}
if xName == 'V':
method = "Powell"
elif xName == 'Psat':
method = "BFGS"
tolStart = 1e-13
tol = tolStart
res = minimize(fun,
initValues,
method=method,
args=arguments,
tol=tol)
while ((not res.success) and tol < 1e-2):
tol *= 1e2
print("Fit did not succeed, reducing tolerance to " +
str(tol))
res = minimize(fun,
initValues,
method=method,
args=arguments,
tol=tol)
# Include these lines for an additional fit with new guess values.
#if res.success and tol>tolStart:
# print "Refitting with new guesses and original tolerance of "+str(tolStart)
# res = minimize(fun, res.x, method=method, args=arguments, tol=tolStart)
if res.success:
success = True
return res.x
else:
print("Fit failed: ")
print(res)
success = False
elif fit[counter] == "POL":
print("Fitting exponential polynomial with " +
str(len(initValues)) + " coefficients.")
z = numpy.polyfit(T - self._Tbase,
numpy.log(xData)[:],
len(initValues) - 1)
return z[::-1]
else:
raise (
ValueError("Error: You used an unknown fit method."))
else: # just a polynomial
print("Fitting polynomial with " + str(len(initValues)) +
" coefficients.")
z = numpy.polyfit(T - self._Tbase, xData, len(initValues) - 1)
return z[::-1]
''' solve '''
layerNum = len(weights2)
layerdim = []
for i in range(len(weights2)):
layerdim.append(weights2[i].shape)
inputWeights = np.concatenate((weights2[0].flatten(), weights2[1].flatten()))
''' need to provide gradients to solver to improve performance, as solver uses finite differences,
but if you can calculate the jacobian instead then will be much more efficiant.
Setting jacobian = True tells the solver that the "fun" will return the objective function along with
the gradients'''
weightsOut = minimize(fun = NNlogisticCost, x0 = inputWeights, args = (m,X,YhatMat,True,1, layerNum, layerdim), method = 'TNC', jac = True ,options = {'maxiter':100000})['x']
weights = []
if (layerNum is not None) & (layerdim is not None):
strt = 0
for i in range(layerNum):
weights.append(weightsOut[strt:strt+np.array(layerdim[i]).prod()].reshape(layerdim[i]))
strt += np.array(layerdim[i]).prod()
nLayer = X
for i in range(len(weights)):
nLayer = sigmoid(nLayer,np.matrix(weights[i]))
if i != len(weights)-1:
nLayer = np.concatenate((np.matrix(np.ones(nLayer.shape[0])).T,nLayer), axis = 1)
##which output has the highest probability per training example. We add 1 as the examples are from 1 -> 10, where 10 represents a 0.
