Unable to obtain correct data type for curve_fit. ex: unhashable, array with sequence, etc

I am working with a script to analyze nmr relaxation rates using curve_fit, and am bringing both the input and output values in from external files. I was running into many error messages regarding these data types when I was actually trying to run curve_fit, such as the data being in an unhashable type, incorrectly converting an array to a sequence, data being different shapes, etc. I have modified my script to ensure they are the same data types (object string) and shape (36,), but am still unable to run it without getting error messages. I sense there is a very simple fix, and I am just missing something but I can't seem to figure out what, and any help would be greatly appreciated!

This is the current full script:

import math 
import numpy as np
from numpy import *
import scipy
import matplotlib.pyplot as plt
from scipy.optimize import curve_fit
import matplotlib.cm as cm
import nmrglue as ng
import sys
from mpl_toolkits.mplot3d import Axes3D
from pathlib import Path
import csv
import pandas as pd

def exp(x, a, b, c):
    d=1/b 
    return a+c*np.exp(-b*x) 

out=open((f'/Users/haileyrude/Dropbox/OkunoNMR/1/output.txt'), 'w')

List_area=[]
List_inten=[]

with open(str(f'Okuno Lab Python Work/Okuno Test 1/tau.list'), 'r') as d:
    reader = csv.reader(d)
    prepretauList = list(reader)
    pretauList = np.array(prepretauList)
    tauList = pretauList.astype(str)

dic,data = ng.pipe.read(str(Path(f'/Users/haileyrude/Dropbox/OkunoNMR/1/ft/test036.ft1')))#ZY

udic = ng.pipe.guess_udic(dic,data)
uc = ng.fileiobase.uc_from_udic(udic)
ppm_1H = uc.ppm_scale()
uc0 = ng.pipe.make_uc(dic,data,dim=0)
ub=uc0("6.5ppm")
lb=uc0("9.5ppm")

ppm = ppm_1H[lb:ub]
inten = data[lb:ub]
maxvalue=max(inten.real)
pt=np.where(data.real==maxvalue)
intensity=data[pt]
maxpt=uc0.ppm(pt[0])
    
display(uc0.ppm(pt[0]))
off=0
count=0
for i in range(1, len(tauList)+1, 1):
    
    off=off+500
    count=count+1
    try:
        dic,data = ng.pipe.read(str(Path(f'/Users/haileyrude/Dropbox/OkunoNMR/1/ft/test00{str(i)}.ft1')))#ZY
    except IOError:
        dic,data = ng.pipe.read(str(Path(f'/Users/haileyrude/Dropbox/OkunoNMR/1/ft/test0{str(i)}.ft1')))#ZY

    #print(dic,data)
    #define intergration area for the methyl, include some baseline
    ppm = ppm_1H[lb:ub]
    inten = data[lb:ub]
    intensity=data[pt]
    
    #intergrate
    area=inten.sum()
    List_area.append(float(area.real)) 
    List_inten.append(intensity.real)

    colors = cm.gist_heat(np.linspace(0, 1, len(tauList)+1))
    plt.xlim([6.5, 9.5])
    plt.plot(ppm, inten.real, color=colors[count]) 


prex=array(tauList, dtype="object")
arx=prex.astype(str)
x=prex.flatten()

prey=array(List_inten, dtype="object")
ary=prey.astype(str)
y=ary.flatten()

popt, pcov = curve_fit(exp, x, y)
#get the errors
errors=np.sqrt(pcov.diagonal())
print ('rate', popt[1], '+/-', errors[1] )   
print(out,'rate', popt[1], '+/-', errors[1]) 
    

#print 'Relax rate:', popt[1], '+/-', float(errors[1])


rate_fig = plt.figure(1)
plt.plot(tauList, List_inten, marker='o', markersize=10, linestyle='None')
plt.plot(xaxis, exp(xaxis, *popt), marker='None', linestyle='-', linewidth=2, color='r')
plt.show()

When I run this exact script I get the error message: "unhashable type: 'numpy.ndarray'", but again whenever I try others I just get similar error messages about incompatible data types for curve_fit.

Additionally, while trying to understand the root of my problem I ran this cell:

print(x)
print(len(x))
print(x.shape)
print(x.dtype)

print(y)
print(len(y))
print(y.shape)
print(y.dtype)

and received this output:

x = ['0.001000' '0.001500' '0.002000' '0.002500' '0.003000' '0.004000'
 '0.005000' '0.007500' '0.010000' '0.012500' '0.015000' '0.017500'
 '0.020000' '0.022500' '0.025000' '0.027500' '0.030000' '0.035000'
 '0.050000' '0.075000' '0.100000' '0.125000' '0.150000' '0.175000'
 '0.250000' '0.500000' '0.750000' '1.000000' '1.250000' '1.500000'
 '1.750000' '2.000000' '2.500000' '3.000000' '3.500000' '5.000000']

len(x) = 36

x.shape = (36,)

x dtype = object

y = ['-157341216.0' '-156514192.0' '-156109792.0' '-155292736.0'
 '-155541808.0' '-154359088.0' '-153406112.0' '-152017536.0'
 '-150163360.0' '-148821312.0' '-147121408.0' '-145200544.0'
 '-143513360.0' '-142319280.0' '-140684704.0' '-139887536.0'
 '-138132720.0' '-135468448.0' '-127346128.0' '-114155104.0'
 '-101980152.0' '-90303376.0' '-78995040.0' '-68271560.0' '-38386176.0'
 '38851676.0' '89095032.0' '121053536.0' '142517744.0' '155447904.0'
 '163979280.0' '168583824.0' '174455648.0' '176974160.0' '177651056.0'
 '178662960.0']

len(y) = 36

y.shape = (36,)

y dtype = <U12

Again, I imagine there is a very simple solution, but I unfortunately can't seem to find it.

The main problem is probably the type of your data.

import numpy as np
import matplotlib.pyplot as plt
from scipy import optimize

You must cast it into numeric type (float):

x = ['0.001000', '0.001500', '0.002000', '0.002500', '0.003000', '0.004000', '0.005000', '0.007500', '0.010000', '0.012500', '0.015000', '0.017500', '0.020000', '0.022500', '0.025000', '0.027500', '0.030000', '0.035000', '0.050000', '0.075000', '0.100000', '0.125000', '0.150000', '0.175000', '0.250000', '0.500000', '0.750000', '1.000000', '1.250000', '1.500000', '1.750000', '2.000000', '2.500000', '3.000000', '3.500000', '5.000000']
y = ['-157341216.0', '-156514192.0', '-156109792.0', '-155292736.0', '-155541808.0', '-154359088.0', '-153406112.0', '-152017536.0', '-150163360.0', '-148821312.0', '-147121408.0', '-145200544.0', '-143513360.0', '-142319280.0', '-140684704.0', '-139887536.0', '-138132720.0', '-135468448.0', '-127346128.0', '-114155104.0', '-101980152.0', '-90303376.0', '-78995040.0', '-68271560.0', '-38386176.0', '38851676.0', '89095032.0', '121053536.0', '142517744.0', '155447904.0', '163979280.0', '168583824.0', '174455648.0', '176974160.0', '177651056.0', '178662960.0']

x = np.array(x, dtype="float64")
y = np.array(y, dtype="float64")

Then rewrite your model as follow:

def model(x, a, b, c):
    return a - c * np.exp(- b * x) 

And you will able to fit it as this:

popt, pcov = optimize.curve_fit(model, x, y)
# (array([1.78891661e+08, 1.75535824e+00, 3.35100511e+08]),
#  array([[ 1.15003627e+11, -1.55092365e+03,  1.04426615e+11],
#         [-1.55092365e+03,  4.71871162e-05, -1.02346030e+03],
#         [ 1.04426615e+11, -1.02346030e+03,  1.27053653e+11]]))

Which fits the dataset pretty well: