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TypeError: Can not understand

I am fitting a very simple curve having three points. with leastsq method, following all the rules. But still I am getting error. I cannot understand. Can anyone help. Thank you so much
import numpy as np
import matplotlib.pyplot as plt
from scipy.optimize import leastsq
x = np.array([2.0,30.2,15.0])
y = np.array([45.0,56.2,30.0])
print(x)
print(y)
# model
def t(x,a,b,c):
return a*x**2 + b*x + c
#residual fucntion
def residual_t(x,y,a,b,c):
return y-t(x,a,b,c)
#initial parameters
g0 = np.array([0.0,0.0,0.0])
#leastsq method
coeffs, cov = leastsq(residual_t, g0, args=(x,y))
plt.plot(x,t(x,*coeffs),'r')
plt.plot(x,y,'b')
plt.show()
#finding out Rsquared and Radj squared value
absError = residual_t(y,x,*coeffs)
se = np.square(absError) # squared errors
Rsquared = 1.0 - (np.var(absError) / np.var(y))
n = len(x)
k = len(coeffs)
Radj_sq = (1-((1-Rsquared)/(n-1)))/(n-k-1)
print (f'Rsquared value: {Rsquared} adjusted R saquared value: {Radj_sq}')
TypeError: residual_t() missing 2 required positional arguments: 'b' and 'c'
Why??
coeffs is already a array containing best it values of a, b,c. coeffs is also showing undefined and residual_t is also showing problem. Could you please help me to understand.

With a copy-n-paste of your code (including the *coeffs change), I get
1135:~/mypy$ python3 stack58206395.py
[ 2. 30.2 15. ]
[45. 56.2 30. ]
Traceback (most recent call last):
File "stack58206395.py", line 24, in <module>
coeffs, cov = leastsq(residual_t, g0, args=(x,y))
File "/usr/local/lib/python3.6/dist-packages/scipy/optimize/minpack.py", line 383, in leastsq
shape, dtype = _check_func('leastsq', 'func', func, x0, args, n)
File "/usr/local/lib/python3.6/dist-packages/scipy/optimize/minpack.py", line 26, in _check_func
res = atleast_1d(thefunc(*((x0[:numinputs],) + args)))
TypeError: residual_t() missing 2 required positional arguments: 'b' and 'c'
That is the error is in the use of residual_t within the leastsq call.
If I add
residual_t(g0, x, y)
right after the g0 definition I get the same error:
1136:~/mypy$ python3 stack58206395.py
[ 2. 30.2 15. ]
[45. 56.2 30. ]
Traceback (most recent call last):
File "stack58206395.py", line 23, in <module>
residual_t(g0, x, y)
TypeError: residual_t() missing 2 required positional arguments: 'b' and 'c'
So you need to define residual_t to work with a call like this. I'm not going to take a guess as to what you really want, so I'll leave the fix up to you.
Just remember that residual_t will be called with the x0, spliced with the args tuple. This is typical usage for scipy.optimize functions. Review the docs if necessary.
edit
Defining the function as:
def residual_t(abc, x, y):
a,b,c = abc
return y-t(x,a,b,c)
runs without error.

scipy.optimize.shgo ValueError: The truth value of an array with more than one element is ambiguous. Use a.any() or a.all()

I am trying to fit a function y(x,T,p) to get the coefficients a,b,c,d,e,f. The data for y,x,T,p are known. With a global optimizer I want to find a good starting point. shgo seems to be the only one that accept constraints.
import numpy as np
import matplotlib.pyplot as plt
from scipy.optimize import shgo
# test data
x = np.array([0.1,0.2,0.3,1])
T = np.array([300,300,300,300])
p = np.array([67.2,67.2,67.2,67.2])
y = np.array([30,50,55,67.2])
# function
def func(pars,x,T,p):
a,b,c,d,e,f = pars
return x*p+x*(1-x)*(a+b*T+c*T**2+d*x+e*x*T+f*x*T**2)*p
# residual
def resid(pars):
return ((func(pars,x,T,p) - y) ** 2).sum()
# constraint: derivation is positive in every data point
def der(pars):
a,b,c,d,e,f = pars
return -p*((3*f*T**2+3*e*T+3*d)*x**2+((2*c-2*f)*T**2+(2*b-2*e)*T-2*d+2*a)*x-c*T**2-b*T-a-1)
con1 = ({'type':'ineq', 'fun':der})
# minimizer shgo
bounds = [(-1,1),(-1,1),(-1,1),(-1,1),(-1,1),(-1,1)]
res = shgo(resid, bounds, constraints=con1)
print("a = %f , b = %f, c = %f, d = %f, e = %f, f = %f" % (res[0], res[1], res[2], res[3], res[4], res[5]))
# plotting
x0 = np.linspace(0, 1, 100)
fig, ax = plt.subplots()
fig.dpi = 80
ax.plot(x,y,'ro',label='data')
for i,txt in enumerate(T):
ax.annotate(txt,(x[i],y[i]))
ax.plot(x0, func(res.x, x0, 300,67.2), '-', label='fit1')
plt.xlabel('x')
plt.ylabel('y')
plt.legend()
plt.show()
With this I am getting ValueError: The truth value of an array with more than one element is ambiguous. Use a.any() or a.all()
I do not know what that Error means and other threads with the same Error does not realy help me to understand. When I use a local minimizer (scipy.optimize.minimize with the method cobyla) the error does not appear.
Can someone help me to understand my problem or even help to fix it?
Thanks
EDIT:
Traceback (most recent call last):
File "C:\Users\...\Python\Python36\site-packages\scipy\optimize\_shgo_lib\triangulation.py", line 759, in __getitem__
return self.cache[x]
KeyError: (0, 0, 0, 0, 0, 0)
During handling of the above exception, another exception occurred:
Traceback (most recent call last):
File "C:/Users/.../test.py", line 70, in <module>
res = shgo(resid, bounds, constraints=con1)
File "C:\Users\...\Python\Python36\site-packages\scipy\optimize\_shgo.py", line 423, in shgo
shc.construct_complex()
File "C:\Users\...\Python\Python36\site-packages\scipy\optimize\_shgo.py", line 726, in construct_complex
self.iterate()
File "C:\Users\...\Python\Python36\site-packages\scipy\optimize\_shgo.py", line 869, in iterate
self.iterate_complex()
File "C:\Users\...\Python\Python36\site-packages\scipy\optimize\_shgo.py", line 890, in iterate_hypercube
self.g_args)
File "C:\Users\...\Python\Python36\site-packages\scipy\optimize\_shgo_lib\triangulation.py", line 121, in __init__
self.n_cube(dim, symmetry=symmetry)
File "C:\Users\...\Python\Python36\site-packages\scipy\optimize\_shgo_lib\triangulation.py", line 172, in n_cube
self.C0.add_vertex(self.V[origintuple])
File "C:\Users\...\Python\Python36\site-packages\scipy\optimize\_shgo_lib\triangulation.py", line 767, in __getitem__
index=self.index)
File "C:\Users\...\Python\Python36\site-packages\scipy\optimize\_shgo_lib\triangulation.py", line 681, in __init__
if g(self.x_a, *args) < 0.0:
ValueError: The truth value of an array with more than one element is ambiguous. Use a.any() or a.all()

The problem is, that der returns an array instead of a scalar value. Changing
con1 = ({'type':'ineq', 'fun':der})
to
con_list = [{'type':'ineq', 'fun': lambda x: der(x)[i_out]} for i_out in range(T.shape[0])]
removes the error. This transforms each output of der into its own inequality constraint.

Also, since your constraints are all written so that der(x)>=0, one can simply keep the definition of oyur constraint with vector output and then fetch the minimum of the outputs, i.e., take a scalar value constraint x -> \min (der(x)).

Result from function call is not an array of floats

Following my previous two posts (post1, post 2), I have now reached the point where I use scipy to find a curve fit. However, the code I have produces an error.
A sample of the .csv file I'm working with is located in post1. I tried to copy and substitute examples from the Internet, but it doesn't seem to be working.
Here's what I have (the .py file)
import pandas as pd
import numpy as np
from scipy import optimize
df = pd.read_csv("~/Truncated raw data hcl.csv", usecols=['time' , '1mnaoh trial 1']).dropna()
data1 = df
array1 = np.asarray(data1)
x , y = np.split(array1,[-1],axis=1)
def func(x, a , b , c , d , e):
return a + (b - a)/((1 + c*np.exp(-d*x))**(1/e))
popt, pcov = optimize.curve_fit(func, x , y , p0=[23.2, 30.1 , 1 , 1 , 1])
popt
From the limited research I've done, it might be a problem with the x and y arrays. The title states the error that is written. It is a minpack.error.
Edit: the error returned
ValueError: object too deep for desired array
Traceback (most recent call last):
File "~/test2.py", line 15, in <module>
popt, pcov = optimize.curve_fit(func, x , y , p0=[23.2, 30.1 , 1 , 1 , 1])
File "~/'virtualenvname'/lib/python3.7/site-packages/scipy/optimize/minpack.py", line 744, in curve_fit
res = leastsq(func, p0, Dfun=jac, full_output=1, **kwargs)
File "~/'virtualenvname'/lib/python3.7/site-packages/scipy/optimize/minpack.py", line 394, in leastsq
gtol, maxfev, epsfcn, factor, diag)
minpack.error: Result from function call is not a proper array of floats.
Thank you.

After the split, the shape of x and y is (..., 1). This means that each element of them itself are arrays of length one. You want to flatten the array first, i.e. via x = np.flatten(x).
But I think you don't need the split at all. You can just do the following
array1 = np.asarray(data1).T
x , y = array1
You want x and y to be the first and second columns of array1. So an easy way to achieve this is to transpose the array first. You could also access them via [:,0] and [:,1].

Use optimize.minimize from scipy with 2 variables and interpolated function

I didn't find a way to perform optimize.minimize from scipy with a multidimensional function. In nearly all examples an analytical function is optimized while my function is interpolated. The test data set looks like this:
x = np.array([2000,2500,3000,3500])
y = np.array([10,15,25,50])
z = np.array([10,12,17,19,13,13,16,20,17,60,25,25,8,35,15,20])
data = np.array([x,y,z])
While the function is like F(x,y) = z
What I want to know is what happens at f(2200,12) and what is the global maximum in the range of x (2000:3500) and y (10:50). The interpolation works fine. But finding the global maximum doesn't work so far.
The interpolation
self.F2 = interp2d(xx, -yy, z, kind, bounds_error=False)
yields
<scipy.interpolate.interpolate.interp2d object at 0x0000000002C3BBE0>
I tried to optimize via:
x0 = [(2000,3500),(10,50)]
res = scipy.optimize.minimize(self.F2, x0, method='Nelder-Mead')
An exception is thrown:
TypeError: __call__() missing 1 required positional argument: 'y'
I think that the optimizer can't handle the object from the interpolation. In the examples the people used lambda to get values from their function. What do I have to do in my case?
Best,
Alex

First, to find global maximum (instead of minimum) you need to interpolate your function with opposite sign:
F2 = interp2d(x, y, -z)
Second, the callable in minimize takes a tuple of arguments, and interp2d object needs input coordinates to be given as separate positional arguments. Therefore, we cannot use interp2d object in minimize directly; we need a wrapper that will unpack a tuple of arguments from minimize and feed it to interp2d:
f = lambda x: F2(*x)
And third, to use minimize you need to specify an initial guess for minimum (and bounds, in your case). Any reasonable point will do:
x0 = (2200, 12)
bounds = [(2000,3500),(10,50)]
print minimize(f, x0, method='SLSQP', bounds=bounds)
This yields:
status: 0
success: True
njev: 43
nfev: 243
fun: array([-59.99999488])
x: array([ 2500.00002708, 24.99999931])
message: 'Optimization terminated successfully.'
jac: array([ 0.07000017, 1. , 0. ])
nit: 43

One more possible solution (hope you get the idea):
One more function is created (f), and the minimized values are sent as arguments to this function.
from scipy.optimize import minimize
x = data.Height.values
y = data.Weight.values
def f(params):
w0, w1 = params
return mse(w0, w1, x, y)
optimum = minimize(f, (0,0), method = 'L-BFGS-B', bounds = ((-100, 100), (-5,5)) )
w0 = optimum.x[0]
w1 = optimum.x[1]
Also tried implementation with lambda function, but had no luck.

input/output error in scipy.optimize.fsolve

I seem to be getting an error when I use the root-finder in scipy. I was wondering if anyone could point out what I'm doing wrong.
The function I'm finding the root of is just an easy example, and not particularly important.
If I run this code with scipy 0.9.0:
import numpy as np
from scipy.optimize import fsolve
tmpFunc = lambda xIn: (xIn[0]-4)**2 + (xIn[1]-5)**2 + (xIn[2]-7)**3
x0 = [3,4,5]
xFinal = fsolve(tmpFunc, x0 )
print xFinal
I get the following error message:
Traceback (most recent call last):
File "tmpStack.py", line 7, in <module>
xFinal = fsolve(tmpFunc, x0 )
File "/usr/lib/python2.7/dist-packages/scipy/optimize/minpack.py", line 115, in fsolve
_check_func('fsolve', 'func', func, x0, args, n, (n,))
File "/usr/lib/python2.7/dist-packages/scipy/optimize/minpack.py", line 26, in _check_func
raise TypeError(msg)
TypeError: fsolve: there is a mismatch between the input and output shape of the 'func' argument '<lambda>'.

Well it looks like I was trying to use this routine incorrectly. This routine requires the same number of equations and variables vs. the one equation with three variables I gave it. So if the input to the function to be minimized is a 3-D array the output should be a 3-D array. This code works:
import numpy as np
from scipy.optimize import fsolve
tmpFunc = lambda xIn: np.array( [(xIn[0]-4)**2 + xIn[1], (xIn[1]-5)**2 - xIn[2]) \
, (xIn[2]-7)**3 + xIn[0] ] )
x0 = [3,4,5]
xFinal = fsolve(tmpFunc, x0 )
print xFinal
Which represents solving three equations simultaneously.