I have a tried curve_fit function for multiple variables. I have encountered a problem with "sigma has incorrect shape". I tried the following code. Could anyone explain why I get this error?
Here x and y are my independent variables and p,q,r are parameters I want to fit
xdata = [214.737191559, -5.64912101538e-36, 36.1372453686, 189.459700978, 233.562136902, 201.230228832, -5.59364882619e-36, -36.3232002416, -188.192199081, -212.837139143, -232.342545403, -200.699429716]
ydata = [-5.88273617837e-37, -211.536123799, -186.67108047, -35.9497006815, 200.282998159, 232.085860035, 213.44274878, 187.945919272, 35.7227474297, -6.00785257974e-37, -199.746844708, -230.856058666]
xdata = np.array(xdata)
ydata = np.array(ydata)
def func1(X,a,b,c):
x,y = X
n = 8
# % A = ydata
# % B = -xdata
# % C = xdata. - ydata
# % H = zdata
g = np.subtract(x,y)
I_0 = np.subtract(x,y) # x-y = C
I_1 = np.multiply(I_0,c) # c(x-y) = cC
I_2 = np.multiply(b,-x) #b(-x) = bB
I_3 = np.multiply(a,y) # aA
I3_0 = np.subtract(I_1,I_2) # cC-bB
I3_1 = np.subtract(I_3,I_1) # aA-cC
I3_2 = np.subtract(I_2,I_3) # bB-aA
I3_00 = np.multiply(I3_0,I3_1) # (cC-bB)(aA-cC)
I3_01 = np.multiply(I3_00,I3_2) # (cC-bB)(aA-cC)(bB-aA)
I3 = np.divide(I3_01,54) # (cC-bB)(aA-cC)(bB-aA)/54
I2_0 = np.power((I3_1),2) # (aA-cC)^2
I2_1 = np.power((I3_0),2) # (cC-bB)^2
I2_2 = np.power((I3_2),2) # (bB-aA)^2
I2_00 = np.add(I2_0,I2_1) # (aA-cC)^2 + (cC-bB)^2
I2_01 = np.add(I2_00,I2_2) # (aA-cC)^2 + (cC-bB)^2 + (bB-aA)^2
I2 = np.divide(I2_01,54) # ((aA-cC)^2 + (cC-bB)^2 + (bB-aA)^2)/54
th_0 = np.divide(I3,(np.power(I2,(3/2)))) # I3/(I2^(3/2))
th = np.arccos(np.clip((th_0),-1,1)) # arccos(I3/(I2^(3/2)))
ans_0 = np.divide(np.add((2*th),(np.pi)),6) # (2*th + pi)/6
ans_1 = np.divide(np.add((2*th),(3*np.pi)),6) # (2*th + 3*pi)/6
ans_2 = np.divide(np.add((2*th),(5*np.pi)),6) # (2*th + 5*pi)/6
ans_00 = np.multiply(np.cos(ans_0),2) # 2*cos((2*th + pi)/6)
ans_11 = np.multiply(np.cos(ans_1),2) # 2*cos((2*th + 3*pi)/6)
ans_22 = np.multiply(np.cos(ans_2),2) # 2*cos((2*th + 5*pi)/6)
ans_000 = np.power(np.absolute(ans_00),n) # (abs(2*cos((2*th + pi)/6)))^n
ans_111 = np.power(np.absolute(ans_11),n) # (abs(2*cos((2*th + 3*pi)/6)))^n
ans_222 = np.power(np.absolute(ans_22),n) # (abs(2*cos((2*th + 5*pi)/6)))^n
ans_0000 = np.add((np.power(np.absolute(ans_00),n)),(np.power(np.absolute(ans_11),n))) # (abs(2*cos((2*th + pi)/6)))^n + (abs(2*cos((2*th + 3*pi)/6)))^n
ans_1111 = np.add((ans_0000),(np.power(np.absolute(ans_22),n))) # (abs(2*cos((2*th + pi)/6)))^n + (abs(2*cos((2*th + 3*pi)/6)))^n + (abs(2*cos((2*th + 5*pi)/6)))^n
sna_0 = np.power(np.multiply(3,I2),(n/2)) # (3*I2)^(n/2) !!
sna_1 = 2*(np.power(190,n)) # 2*(sigma^n) !!
sna_00 = np.multiply(sna_0,ans_1111)
sna_11 = np.subtract(sna_00,sna_1)
return sna_11
a, b, c = 10., 4., 6.
z = func1((xdata,ydata), a, b, c) * 1 + np.random.random(12) / 100
# initial guesses for a,b,c:
a, b, c = 1, 1, 1
p0 = np.array([a, b, c])
# p0 = 8., 2., 7.
popt,pcov = (curve_fit(func1, (xdata,ydata),z, p0))
popt
When I run this I go the following error
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
<ipython-input-13-484bc542850b> in <module>()
6 p0 = np.array([a, b, c])
7 # p0 = 8., 2., 7.
----> 8 popt,pcov = (curve_fit(func1, (xdata,ydata), p0))
9 popt
~/.conda/envs/ML/lib/python3.6/site-packages/scipy/optimize/minpack.py in curve_fit(f, xdata, ydata, p0, sigma, absolute_sigma, check_finite, bounds, method, jac, **kwargs)
749 # Remove full_output from kwargs, otherwise we're passing it in twice.
750 return_full = kwargs.pop('full_output', False)
--> 751 res = leastsq(func, p0, Dfun=jac, full_output=1, **kwargs)
752 popt, pcov, infodict, errmsg, ier = res
753 cost = np.sum(infodict['fvec'] ** 2)
~/.conda/envs/ML/lib/python3.6/site-packages/scipy/optimize/minpack.py in leastsq(func, x0, args, Dfun, full_output, col_deriv, ftol, xtol, gtol, maxfev, epsfcn, factor, diag)
381 if not isinstance(args, tuple):
382 args = (args,)
--> 383 shape, dtype = _check_func('leastsq', 'func', func, x0, args, n)
384 m = shape[0]
385 if n > m:
~/.conda/envs/ML/lib/python3.6/site-packages/scipy/optimize/minpack.py in _check_func(checker, argname, thefunc, x0, args, numinputs, output_shape)
25 def _check_func(checker, argname, thefunc, x0, args, numinputs,
26 output_shape=None):
---> 27 res = atleast_1d(thefunc(*((x0[:numinputs],) + args)))
28 if (output_shape is not None) and (shape(res) != output_shape):
29 if (output_shape[0] != 1):
~/.conda/envs/ML/lib/python3.6/site-packages/scipy/optimize/minpack.py in func_wrapped(params)
461 if transform is None:
462 def func_wrapped(params):
--> 463 return func(xdata, *params) - ydata
464 elif transform.ndim == 1:
465 def func_wrapped(params):
ValueError: operands could not be broadcast together with shapes (12,) (3,)
The error you are receiving ValueError: ``sigma`` has incorrect shape. is related to the incorrect call of curve_fit and the difference between what the function is expecting and what are you feeding it. Here is an example of a correct call:
p, q, r = 1, 1, 1
p0 = np.array([p, q, r])
cfit = curve_fit(func, xdata, ydata, p0)
print(cfit)
Unfortunately, that is not the only thing porblematic in your code. Your func1 will require from you some editing. You can refer to this post on how to use curve_fit.
Update:
I shortened your code and optimized some lines plus -as mentioned in the comments- you need an output variable so I generated some custom zdata that you can later replace with your data.
import numpy as np
from scipy.optimize import curve_fit
xdata = [214.737, -5.649e-36, 36.137, 189.459, 233.562, 201.230, -5.593e-36, -36.323, -188.192, -212.837, -232.342, -200.699]
ydata = [-5.882e-37, -211.536, -186.671, -35.949, 200.282, 232.085, 213.442, 187.945, 35.722, -6.007, -199.746, -230.856]
def func(X, p, q, r):
x = np.array(X[0])
y = np.array(X[1])
n = 8
a1 = (p * y) - (r * (x-y))
b1 = (q * -1 * x) - (p * y)
c1 = (r * (x - y)) - (q * -1 * x)
I3 = (a1 * b1 * c1) / 54
I2 = (a1**2 + b1**2 + c1**2) / 54
th = np.arccos( I3 / (I2**(3/2)) )
an1 = (np.abs(2 * np.cos((2 * th + 1 * np.pi) /6)))**n
an2 = (np.abs(2 * np.cos((2 * th + 3 * np.pi) /6)))**n
an3 = (np.abs(2 * np.cos((2 * th + 5 * np.pi) /6)))**n
res = ( (3 * I2)**(n/2) ) * (an1 + an2 + an3) - (2 * (189.32)**8)
return res
# init
p, q, r = 1, 1, 1
p0 = np.array([p, q, r])
# artificial zdata
zdata = func((xdata, ydata), p, q, r) + np.random.random(np.array(xdata).shape)
cfit = curve_fit(func, (xdata, ydata), zdata, p0)
# print output
print(cfit)
I still don't exactly get what you have inside of func which is causing a RuntimeWarning: due to invalid value encountered in arccos and that is why I edited the data you provided too.
Related
My idea is to plot a 3d divergence plot of a vector field,
where the marker at each point will be proportional to the divergence at that point.
The vector field i am using is (x^2 + y^2)i + (y^2 + z^2)j =(Z^2 +x^2)k
However , I am finding difficulty in setting the marker size as per the value of divergence.
def div(a1,b1,c1):
a,b,c= sp.symbols('a b c')
p = a**2 + b**2
q = b**2 + c**2
r = c**2 + a**2
div = sp.diff(p,a) + sp.diff(q,b) + sp.diff(r,c)
res_div = div.subs([(a,a1),(b,b1),(c,c1)])
return(abs(res_div))
a, b, c = np.meshgrid(np.arange(-2, 2, 0.8),
np.arange(-2, 2, 0.8),
np.arange(-2, 2, 0.8))
a = a.reshape(np.product(x.shape))
b = b.reshape(np.product(y.shape))
c = c.reshape(np.product(z.shape))
k = div(a,b,c)
ax.scatter(a,b,c , s= k ,c= "green")
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
<ipython-input-15-b669c8d62416> in <module>
72 c = c.reshape(np.product(z.shape))
73 k = div(a,b,c)
---> 74 ax.scatter(a,b,c , s= k ,c= "green")
C:\AnaConda\lib\site-packages\mpl_toolkits\mplot3d\axes3d.py in scatter(self, xs, ys, zs, zdir, s, c, depthshade, *args, **kwargs)
2357 xs, ys, zs, s, c = cbook.delete_masked_points(xs, ys, zs, s, c)
2358
-> 2359 patches = super().scatter(xs, ys, s=s, c=c, *args, **kwargs)
2360 art3d.patch_collection_2d_to_3d(patches, zs=zs, zdir=zdir,
2361 depthshade=depthshade)
C:\AnaConda\lib\site-packages\matplotlib\__init__.py in inner(ax, data, *args, **kwargs)
1599 def inner(ax, *args, data=None, **kwargs):
1600 if data is None:
-> 1601 return func(ax, *map(sanitize_sequence, args), **kwargs)
1602
1603 bound = new_sig.bind(ax, *args, **kwargs)
C:\AnaConda\lib\site-packages\matplotlib\axes\_axes.py in scatter(self, x, y, s, c, marker, cmap, norm, vmin, vmax, alpha, linewidths, verts, edgecolors, plotnonfinite, **kwargs)
4496 offsets=offsets,
4497 transOffset=kwargs.pop('transform', self.transData),
-> 4498 alpha=alpha
4499 )
4500 collection.set_transform(mtransforms.IdentityTransform())
C:\AnaConda\lib\site-packages\matplotlib\collections.py in __init__(self, paths, sizes, **kwargs)
883 Collection.__init__(self, **kwargs)
884 self.set_paths(paths)
--> 885 self.set_sizes(sizes)
886 self.stale = True
887
C:\AnaConda\lib\site-packages\matplotlib\collections.py in set_sizes(self, sizes, dpi)
855 self._sizes = np.asarray(sizes)
856 self._transforms = np.zeros((len(self._sizes), 3, 3))
--> 857 scale = np.sqrt(self._sizes) * dpi / 72.0 * self._factor
858 self._transforms[:, 0, 0] = scale
859 self._transforms[:, 1, 1] = scale
AttributeError: 'Abs' object has no attribute 'sqrt'
Ideally I want not only the size, but also the color of the marker to be Red or green , depending on divergence being negative , positive.
Finally able to get the desired result :
using below code block :
a,b,c = sp.symbols('a b c')
Pa = a**2 + b**2
Qb = b**2 + c**2
Rc = c**2 + a**2
divSp = sp.diff(Pa , a) + sp.diff(Qb , b) + sp.diff(Rc , c)
divnp = lambdify((a,b,c) , divSp ,"numpy")
col = np.where(divnp(x,y,z) > 0 , 'green' , 'red')
#colors=['red' if divnp(x,y,z) <=0 else 'green' if divnp(x,y,z) > 0]
for x1,y1,z1,d1,m in zip(x,y,z,abs(divnp(x,y,z)), col):
ax.scatter(x1, y1, z1,s = d1*70, c = m)
The marker size at each point is proprortional to divergence at that point , red indicates -ve & green +ve divergence
Black arrows show the vector field & red arrows the direction & magnitude of curl.
Divergence plot
enter image description here
between the codes there are the following codes:
def regTreeEval(model, inDat):
if model is not None:
return float(model)
def modelTreeEval(model, inDat):
n = shape(inDat)[1]
X = mat(ones((1, n+1)))
X[:, 1: n+1] = inDat
# print X, model
xmodel = X*model
if xmodel is not None:
return float(X * model)
<pre><code>def modelErr(dataSet):
ws, X, Y = linearSolve(dataSet)
yHat = X * ws
# print corrcoef(yHat, Y, rowvar=0)
return sum(power(Y - yHat, 2))
def linearSolve(dataSet):
m,n = shape(dataSet)
X = mat(ones((m,n)))
Y = mat(ones((m,1)))
X[:,1:n] = dataSet[:,0:n-1]
Y = dataSet[:,-1]
xTx = X.T*X
if linalg.det(xTx) ==0.0:
raiseNameError("This matrix is singular, cannot do inverse")
ws = X.T*X.I*(X.T*Y)
return ws,X,Y` def modelErr(dataSet):
ws, X, Y = linearSolve(dataSet)
yHat = X * ws
# print corrcoef(yHat, Y, rowvar=0)
return sum(power(Y - yHat, 2))
def linearSolve(dataSet):
m,n = shape(dataSet)
X = mat(ones((m,n)))
Y = mat(ones((m,1)))
X[:,1:n] = dataSet[:,0:n-1]
Y = dataSet[:,-1]
xTx = X.T*X
if linalg.det(xTx) ==0.0:
raiseNameError("This matrix is singular, cannot do inverse")
ws = X.T*X.I*(X.T*Y)
return ws,X,Y
<pre><code>def modelTreeEval(model,inDat):
n=shape(inDat)[1]
X=mat(ones((1,n+1)))
X[:,1:n+1] = inDat
print('X',X,'\n','model',model)
return float(X*model)
---------------------------------------------------------------------------
<pre><code>
TypeError Traceback (most recent call last)
<ipython-input-50-c482daea3463> in <module>()
116 myDat = loadDataSet('F:/data4.txt')
117 myMat = mat(myDat)
--> 118 myTree = createTree(myMat, modelLeaf, modelErr)
119 print(myTree)
120
<ipython-input-42-60c716a5beb4> in createTree(dataSet, leafType, errType, ops)
12 """
13 #
---> 14 feat,val = chooseBestSplit(dataSet,leafType,errType,ops)
15 #
16 '''
<ipython-input-41-4305f5a748bb> in chooseBestSplit(dataSet, leafType, errType, ops)
76 s = set(dataSet[:,-1].T.tolist()[0])
77 if len(s) ==1:
---> 78 return None,leafType(dataSet)
79 m,n = shape(dataSet)
80 #
<ipython-input-43-6a297b0e048d> in modelLeaf(dataSet)
9 ###
10 """
---> 11 ws,X,Y = linearSolve(dataSet)
12 return ws
13
<ipython-input-43-6a297b0e048d> in linearSolve(dataSet)
42 X = mat(ones((m,n)))
43 Y = mat(ones((m,1)))
---> 44 X[:,1:n] = dataSet[:,0:n-1]
45 Y = dataSet[:,-1]
46 xTx = X.T*X
TypeError: float() argument must be a string or a number, not 'map'
Hello Stackoverflow community,
I am trying to fit data to a Faddeeva function (optimize.special.wofz) using pyhton's optimize.leastsq() or optimize.curve_fit(). The fit parameters are the following two: z1 and z2. They are complex, whereas the independent variable (time) and the output of the function (meas_data) are purely real numbers. This is my first attempt to fit the data:
import numpy as np
from scipy import optimize
from scipy import special
meas_data = np.loadtxt('directory')
time = np.loadtxt('directory')
def test(params, time):
z1 = params[0]
z2 = params[1]
a = z1*np.sqrt(time)
b = z2*np.sqrt(time)
a = np.complex(0, a)
b = np.complex(0, b)
c = special.wofz(a)
d = special.wofz(b)
return np.real(c*d)
def test_error(params, time, t_error):
return test(params, time) - t_error
initial_guess = (300+200j, 300-200j)
params_fit, cov_x, infodict, mesg, ier = optimize.leastsq(test_error, initial_guess, args = (time, meas_data), full_output = True)
My second attempt looks like :
import numpy as np
from scipy import optimize
from scipy import special
meas_data = np.loadtxt('directory')
time = np.loadtxt('directory')
def test(time, z1, z2):
a = z1*np.sqrt(time)
b = z2*np.sqrt(time)
a = np.complex(0, a)
b = np.complex(0, b)
c = special.wofz(a)
d = special.wofz(b)
return np.real(c*d)
popt, pcov = optimize.curve_fit(test, time, meas_data)
For both cases, I get a similar error message:
for the first attempt:
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
<ipython-input-13-9286b2981692> in <module>()
22
23 initial_guess = (300+200j, 300-200j)
---> 24 params_fit, cov_x, infodict, mesg, ier = optimize.leastsq(test_error, initial_guess, args = (time, msd), full_output = True)
/Users/tthalheim/anaconda/lib/python3.5/site-packages/scipy/optimize/minpack.py in leastsq(func, x0, args, Dfun, full_output, col_deriv, ftol, xtol, gtol, maxfev, epsfcn, factor, diag)
375 if not isinstance(args, tuple):
376 args = (args,)
--> 377 shape, dtype = _check_func('leastsq', 'func', func, x0, args, n)
378 m = shape[0]
379 if n > m:
/Users/tthalheim/anaconda/lib/python3.5/site-packages/scipy/optimize/minpack.py in _check_func(checker, argname, thefunc, x0, args, numinputs, output_shape)
24 def _check_func(checker, argname, thefunc, x0, args, numinputs,
25 output_shape=None):
---> 26 res = atleast_1d(thefunc(*((x0[:numinputs],) + args)))
27 if (output_shape is not None) and (shape(res) != output_shape):
28 if (output_shape[0] != 1):
<ipython-input-13-9286b2981692> in test_error(params, time, t_error)
19
20 def test_error(params, time, t_error):
---> 21 return test(params, time) - t_error
22
23 initial_guess = (z1, z2)
<ipython-input-13-9286b2981692> in test(params, time)
10 b = z2*np.sqrt(time)
11
---> 12 a = np.complex(0, a)
13 b = np.complex(0, b)
14
TypeError: only length-1 arrays can be converted to Python scalars
and for the second attempt:
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
<ipython-input-8-8f631a7ede54> in <module>()
16 return np.real(c*d)
17
---> 18 popt, pcov = optimize.curve_fit(test, time, msd)
/Users/tthalheim/anaconda/lib/python3.5/site-packages/scipy/optimize/minpack.py in curve_fit(f, xdata, ydata, p0, sigma, absolute_sigma, check_finite, bounds, method, jac, **kwargs)
674 # Remove full_output from kwargs, otherwise we're passing it in twice.
675 return_full = kwargs.pop('full_output', False)
--> 676 res = leastsq(func, p0, Dfun=jac, full_output=1, **kwargs)
677 popt, pcov, infodict, errmsg, ier = res
678 cost = np.sum(infodict['fvec'] ** 2)
/Users/tthalheim/anaconda/lib/python3.5/site-packages/scipy/optimize/minpack.py in leastsq(func, x0, args, Dfun, full_output, col_deriv, ftol, xtol, gtol, maxfev, epsfcn, factor, diag)
375 if not isinstance(args, tuple):
376 args = (args,)
--> 377 shape, dtype = _check_func('leastsq', 'func', func, x0, args, n)
378 m = shape[0]
379 if n > m:
/Users/tthalheim/anaconda/lib/python3.5/site-packages/scipy/optimize/minpack.py in _check_func(checker, argname, thefunc, x0, args, numinputs, output_shape)
24 def _check_func(checker, argname, thefunc, x0, args, numinputs,
25 output_shape=None):
---> 26 res = atleast_1d(thefunc(*((x0[:numinputs],) + args)))
27 if (output_shape is not None) and (shape(res) != output_shape):
28 if (output_shape[0] != 1):
/Users/tthalheim/anaconda/lib/python3.5/site-packages/scipy/optimize/minpack.py in func_wrapped(params)
453 if weights is None:
454 def func_wrapped(params):
--> 455 return func(xdata, *params) - ydata
456 else:
457 def func_wrapped(params):
<ipython-input-8-8f631a7ede54> in test(time, z1, z2)
7 b = z2*np.sqrt(time)
8
----> 9 a = np.complex(0, a)
10 b = np.complex(0, b)
11
TypeError: only length-1 arrays can be converted to Python scalars
The data I am using for fitting are times in the range of 10e-6 to 10e-2 and measurement data in the range of 10e-19 to 10e-16. Both test functions used for calculating individual numbers given that the z1 and z2 are known work. I think that it has something to do with python's fitting routines which maybe not can handle complex values during their calculation?
I would be very happy, if someone could help me fixing this problem.
The third comment by PRMoureu on my question fixed the problem.
EDIT: The data set is the MNIST data set from the Homework of Week 4 of Andrew Ng's Machine Learning Course
I've checked the question on scipy optimize but I still couldn't figure out what is wrong with my code. I am trying to optimize theta for the oneVsAll question on the Andrew Ng coursera course.
Here is the relevant code
def sigmoid(x):
a = []
for item in x:
a.append(1/(1+math.exp(-item)))
return a
def hypothesis(x, theta):
return np.array(sigmoid(np.dot(x, theta)))
def costFunction(theta, x, y, lamba_):
m = X.shape[0]
part1 = np.dot(y.T, np.log(hypothesis(x, theta)).reshape(m,1))
part2 = np.dot((np.ones((m,1)) - y).T, np.log( 1 - hypothesis(x, theta)).reshape(m,1))
summ = (part1 + part2)
return -summ[0]/m
def gradientVect(theta, x, y, lambda_):
n = X.shape[1]
m = X.shape[0]
gradient = []
theta = theta.reshape(n,1)
beta = hypothesis(x, theta) - y
reg = theta[1:] * lambda_/m
grad = np.dot(X.T, beta) * 1./m
grad[1:] = grad[1:] * reg
return grad.flatten()
from scipy import optimize
def optimizeTheta(x, y, nLabels, lambda_):
for i in np.arange(0, nLabels):
theta = np.zeros((n,1))
res = optimize.minimize(costFunction, theta, args=(x, (y == i)*1, lambda_), method=None,
jac=gradientVect, options={'maxiter':50})
print(res)
return result
but running
optimizeTheta(X, y, 10, 0) # X shape = 401, 500
Gives me the following error:
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
<ipython-input-247-e0e6e4c1eddd> in <module>()
3 n = X.shape[1]
4
----> 5 optimizeTheta(X, y, 10, 0)
<ipython-input-246-0a15e9f4769a> in optimizeTheta(x, y, nLabels, lambda_)
54 theta = np.zeros((n,1))
55 res = optimize.minimize(costFunction, x0 = theta, args=(x, (y == i)*1, lambda_), method=None,
---> 56 jac=gradientVect, options={'maxiter':50})
57 print(res)
58 return result
//anaconda/lib/python3.5/site-packages/scipy/optimize/_minimize.py in minimize(fun, x0, args, method, jac, hess, hessp, bounds, constraints, tol, callback, options)
439 return _minimize_cg(fun, x0, args, jac, callback, **options)
440 elif meth == 'bfgs':
--> 441 return _minimize_bfgs(fun, x0, args, jac, callback, **options)
442 elif meth == 'newton-cg':
443 return _minimize_newtoncg(fun, x0, args, jac, hess, hessp, callback,
//anaconda/lib/python3.5/site-packages/scipy/optimize/optimize.py in _minimize_bfgs(fun, x0, args, jac, callback, gtol, norm, eps, maxiter, disp, return_all, **unknown_options)
859 gnorm = vecnorm(gfk, ord=norm)
860 while (gnorm > gtol) and (k < maxiter):
--> 861 pk = -numpy.dot(Hk, gfk)
862 try:
863 alpha_k, fc, gc, old_fval, old_old_fval, gfkp1 = \
ValueError: shapes (401,401) and (2005000,) not aligned: 401 (dim 1) != 2005000 (dim 0)
And I can't figure out why the shapes are not aligned.
Thanks!
So I realized what was wrong with my question.
The problem was the sigmoid function returning a list and not an integer and therefore it messed up the matrixes multiplications afterwards. The new sigmoid function is
def sigmoid(z):
return(1 / (1 + np.exp(-z)))
OK so here's my code for a multi-classification task using one-vs-all logistic regression with some regularization. I've been struggling with this for the past 2 days, I don't know why it doesn't work.
import pandas as pd
import numpy as np
import scipy.optimize as sp
Data = pd.read_csv(Location,
sep=';',
dtype = np.float64,
header = None)
X = Data.ix[:,0:1]
y = Data.ix[:,2:]
y.columns = [0]
def sigmoid(z) :
g = 1.0/(1.0+np.exp(-z))
return g
def lrCostFunction(theta, X, y, lambd):
m , n = X.shape
J=-(y.T.dot(np.log(sigmoid(X.dot(theta))))+(1-y).T.dot(np.log(1-sigmoid(X.dot(theta)))))/m
J = J + (theta.T.dot(theta)- np.power(theta[0,0],2))*(lambd)/(2*m);
return J.ix[0,0]
def Gradient(theta, X, y, lambd):
m , n = X.shape
grad = X.T.dot(sigmoid(X.dot(theta))-y)/m
grad.ix[1:(n-1),:] = grad.ix[1:(n-1),:] + lambd*theta.ix[1:(n-1),:]/m;
return grad.values.flatten().tolist()
def oneVsAll(X, y, num_labels, lambd):
m , n = X.shape
all_theta = pd.DataFrame(data = [[0 for col in range(n+1)] for row in range(num_labels)])
ones = pd.DataFrame(data = [1 for i in range(X.shape[0])])
X = pd.concat([ones,X], axis = 1)
for c in range(0,num_labels-1) :
initial_theta = pd.DataFrame(data = [0 for i in range(n+1)])
theta = sp.minimize(fun = lrCostFunction,
x0 = initial_theta,
args = (X,y,lambd),
method = 'TNC',
jac = Gradient)
all_theta.ix[c,:] = theta
return all_theta
oneVsAll(X, y, 4, 0.1)
And it says :
---------------------------------------------------------------------------
IndexError Traceback (most recent call last)
<ipython-input-27-b18648b06674> in <module>()
1 theta = pd.DataFrame(data = [0 for i in range(X.shape[1])])
----> 2 oneVsAll(X, y, 4, 0.1)
<ipython-input-26-ba0f7093d1f6> in oneVsAll(X, y, num_labels, lambd)
10 args = (X,y,lambd),
11 method = 'TNC',
---> 12 jac = Gradient)
13 all_theta.ix[c,:] = theta
14 return all_theta
/Users/jean-marcmarty/anaconda/lib/python2.7/site-packages/scipy/optimize/_minimize.pyc in minimize(fun, x0, args, method, jac, hess, hessp, bounds, constraints, tol, callback, options)
381 elif meth == 'tnc':
382 return _minimize_tnc(fun, x0, args, jac, bounds, callback=callback,
--> 383 **options)
384 elif meth == 'cobyla':
385 return _minimize_cobyla(fun, x0, args, constraints, **options)
/Users/jean-marcmarty/anaconda/lib/python2.7/site-packages/scipy/optimize/tnc.pyc in _minimize_tnc(fun, x0, args, jac, bounds, eps, scale, offset, mesg_num, maxCGit, maxiter, eta, stepmx, accuracy, minfev, ftol, xtol, gtol, rescale, disp, callback, **unknown_options)
396 offset, messages, maxCGit, maxfun,
397 eta, stepmx, accuracy, fmin, ftol,
--> 398 xtol, pgtol, rescale, callback)
399
400 funv, jacv = func_and_grad(x)
/Users/jean-marcmarty/anaconda/lib/python2.7/site-packages/scipy/optimize/tnc.pyc in func_and_grad(x)
358 else:
359 def func_and_grad(x):
--> 360 f = fun(x, *args)
361 g = jac(x, *args)
362 return f, g
<ipython-input-24-5f31e87e00da> in lrCostFunction(theta, X, y, lambd)
2 m , n = X.shape
3 J=-(y.T.dot(np.log(sigmoid(X.dot(theta))))+(1-y).T.dot(np.log(1-sigmoid(X.dot(theta)))))/m
----> 4 J = J + (theta.T.dot(theta)- np.power(theta[0,0],2))*(lambd)/(2*m);
5 return J.ix[0,0]
IndexError: too many indices
I don't know anything about the math, but the error is coming from this code:
theta[0,0]
Theta is a 1d array, so you'd need to index at as theta[0], unless there was some reason you were expecting it to be 2d?