TypeError: fmin_() missing 1 required positional argument: 'pp'

name 'np' is not defined

import numpy as np
import pandas as pd
import seaborn as sn

from math import pi
from math import sqrt
from math import cos

from scipy.stats import norm
from scipy.optimize import fmin

from Fit_Alpha import attraction_function
from Fit_Alpha import perception_probability

from Compute_confidence import alpha_all_participants

#Basic parameters
a=1
bs = [1.5,1.5,1,1];
nstim = len(bs)
number_orientations=4
gammas = [60,70.53,75,60]
gamma_rad =[] 
for i in gammas:
    gamma_rad.append(i*pi/180)

# To compute f_vectors and p_vectors
array_orientations= np.zeros((nstim,number_orientations))
array_orientations[:,0]=a

for i in range(nstim):
    b = bs[i]
    gam = gamma_rad[i]
    c = sqrt((a**2)+(b**2)-(2*a*b*cos(gam)))
    d = sqrt((a**2)+(b**2)+(2*a*b*cos(gam)))
    array_orientations[i,1]=b
    array_orientations[i,2]=c
    array_orientations[i,3]=d  

#Get the probabilities to see each vector for each participant's alpha and store this into an array.

probs_all_participants= np.zeros((len(alpha_all_participants),nstim,number_orientations))

index= 0

for alpha in alpha_all_participants:
    
    f_vectors = np.zeros((nstim,4))
    p_vectors = np.zeros((nstim,4))
                   
    for i in range(nstim):
               for j in range(number_orientations):                   
                   f_vectors[i,j]=attraction_function(array_orientations[i,j],a,alpha)
                   
    for i in range(nstim):
               for j in range(number_orientations):
                   p_vectors[i,j]= perception_probability(f_vectors[i,j],
                                                          f_vectors[i,0],
                                                          f_vectors[i,1],
                                                          f_vectors[i,2],
                                                          f_vectors[i,3])

    probs_all_participants[index]=p_vectors
    index+=1

simul_nb= 1000

#Initial guess of the mus for the b, c and d vectors
initguess_oblique = [0.000, -2.747, -1.985, -4.679]
initguess_centrect= [0.000, -2.820, -2.822, -6.586]
initguess_rhombic= [0.000, 0.000, -1.185, -9.313]
initguess_hexa= [0.000, 0.000,  0.000, -7.996]

#Fit the mus from the probabilities (depending on the alpha value of each participant).
def mu2pr(mu_list):
  '''Gives the probabilities estimated from the found mu'''
  my_mu_lst= [0.0]+ mu_list
  mu_nb=len(my_mu_lst)
  prob_lst= np.zeros((1,4))
  max_inds=[]
 
  for i in range(simul_nb):
    simul_mat= np.array(my_mu_lst)+np.random.randn(mu_nb)
    max_inds.append(np.argmax(simul_mat))
  
  for probindex in range(mu_nb-1):
    prob_lst[0,probindex]= max_inds.count(probindex)/ simul_nb

  return prob_lst

def minimize(real_prob,pp):
    ''' We try to get the minimize the difference between the computed 
    probabilities and the probabilities we get from the estimated mus (mu2pr)'''
    mu2pr(pp)
    errfunc= sum(((real_prob - mu2pr(pp)) **2))
    return errfunc

mus_all_participants= np.zeros((len(alpha_all_participants),nstim,number_orientations))

for index in range(len(probs_all_participants)):
    
     prob_oblique= probs_all_participants[index,0]
     prob_centrect= probs_all_participants[index,1]
     prob_rhombic= probs_all_participants[index,2]
     prob_hexa= probs_all_participants[index,3]

     p1ob= fmin(minimize,initguess_oblique,args=prob_oblique)
     oblique_mus= [0.0]+ p1ob
 
     p1cent= fmin(minimize,initguess_centrect,args=prob_centrect)
     centrect_mus= [0.0]+ p1cent
 
     p1rho= fmin(minimize,initguess_rhombic,args=prob_rhombic)
     rhombic_mus= [0.0]+ p1rho
 
     p1hex= fmin(minimize,initguess_hexa,args=prob_hexa)
     hexa_mus= [0.0]+ p1hex