def _cal_δ(self, θ2):
"""Calculate δ (mean utility) via contraction mapping"""
v, D, X2 = self.v, self.D, self.X2
nmkts, nsiminds, nbrands = self.nmkts, self.nsiminds, self.nbrands
δ, ln_s_jt = self.δ, self.ln_s_jt # initial values
niter = 0
ε = 1e-13 # tight tolerance
μ = self.μ = _BLP.cal_mu(θ2, v.values, D.values, X2.values)
while True:
s = self._cal_s(δ, μ)
#_BLP.cal_s(δ, μ, s) # s gets updated
diff = ln_s_jt - np.log(s)
if np.isnan(diff).sum():
raise Exception('nan in diffs')
δ += diff
if (abs(diff).max() < ε) and (abs(diff).mean() < 1e-3):
break
niter += 1
print('contraction mapping finished in {} iterations'.format(niter))
return δ
def cal_δ(self, θ2):
"""Calculate δ (mean utility) via contraction mapping"""
v, D, X2 = self.v, self.D, self.X2
nmkt, nsimind, nbrand = self.nmkt, self.nsimind, self.nbrand
s, δ, ln_s_jt = self.s, self.δ_old, self.ln_s_jt
θ2_v, θ2_D = θ2[:, 0], θ2[:, 1:]
niter = 0
μ = _BLP.cal_mu(θ2_v, θ2_D, v, D, X2, nmkt, nsimind, nbrand)
while True:
exp_Xb = np.exp(δ.reshape(-1, 1) + μ)
_BLP.cal_s(exp_Xb, nmkt, nsimind, nbrand, s) # s gets updated
diff = ln_s_jt - np.log(s)
if np.isnan(diff).sum():
raise Exception('nan in diffs')
δ += diff
if (abs(diff).max() < self.etol) and (abs(diff).mean() < 1e-3):
break
niter += 1
print('contraction mapping finished in {} iterations'.format(niter))
return δ
def test_cal_mu(data):
BLP = pyBLP.BLP(data)
v, D, X2 = BLP.v, BLP.D, BLP.X2
θ20 = np.array([[0.3772, 3.0888, 0, 1.1859, 0],
[1.8480, 16.5980, -.6590, 0, 11.6245],
[-0.0035, -0.1925, 0, 0.0296, 0],
[0.0810, 1.4684, 0, -1.5143, 0]])
mu_python = BLP._cal_mu(θ20)
mu_cython = _BLP.cal_mu(θ20, v.values, D.values, X2.values)
assert np.allclose(mu_python, mu_cython)
def _cal_jacobian(self, θ2, δ):
"""calculate the Jacobian with the current value of δ"""
v, D, X2 = self.v, self.D, self.X2
nmkts, nsiminds, nbrands = self.nmkts, self.nsiminds, self.nbrands
ind_choice_prob = self.ind_choice_prob
μ = _BLP.cal_mu(θ2, v.values, D.values, X2.values)
_BLP.cal_ind_choice_prob(δ, μ, ind_choice_prob)
ind_choice_prob_vec = ind_choice_prob.transpose(0, 2, 1).reshape(-1, nsiminds)
nk = len(X2.coords['vars'])
nD = len(D.coords['vars'])
f1 = np.zeros((δ.flatten().shape[0], nk * (nD + 1)))
# cdid relates each observation to the market it is in
cdid = np.arange(nmkts).repeat(nbrands)
cdindex = np.arange(nbrands, nbrands * (nmkts + 1), nbrands) - 1
# compute ∂share/∂σ
for k in range(nk):
X2v = X2[..., k].values.reshape(-1, 1) @ np.ones((1, nsiminds))
X2v *= v[cdid, :, k].values
temp = (X2v * ind_choice_prob_vec).cumsum(axis=0)
sum1 = temp[cdindex, :]
sum1[1:, :] = sum1[1:, :] - sum1[:-1, :]
f1[:, k] = (ind_choice_prob_vec * (X2v - sum1[cdid, :])).mean(axis=1)
# compute ∂share/∂pi
for d in range(nD):
tmpD = D[cdid, :, d].values
temp1 = np.zeros((cdid.shape[0], nk))
for k in range(nk):
X2d = X2[..., k].values.reshape(-1, 1) @ np.ones((1, nsiminds)) * tmpD
temp = (X2d * ind_choice_prob_vec).cumsum(axis=0)
sum1 = temp[cdindex, :]
sum1[1:, :] = sum1[1:, :] - sum1[:-1, :]
temp1[:, k] = (ind_choice_prob_vec * (X2d - sum1[cdid, :])).mean(axis=1)
f1[:, nk * (d + 1):nk * (d + 2)] = temp1
# compute ∂δ/∂θ2
rel = np.nonzero(θ2.T.ravel())[0]
jacob = np.zeros((cdid.shape[0], rel.shape[0]))
n = 0
for i in range(cdindex.shape[0]):
temp = ind_choice_prob_vec[n:cdindex[i] + 1, :]
H1 = temp @ temp.T
H = (np.diag(temp.sum(axis=1)) - H1) / nsiminds
jacob[n:cdindex[i] + 1, :] = - solve(H, f1[n:cdindex[i] + 1, rel])
n = cdindex[i] + 1
return jacob
def cal_jacobian(self, θ2, δ):
"""calculate the Jacobian with the current value of δ"""
v, D, X2 = self.v, self.D, self.X2
nmkt, nsimind, nbrand = self.nmkt, self.nsimind, self.nbrand
μ = _BLP.cal_mu(
θ2[:, 0], θ2[:, 1:], v, D, X2, nmkt, nsimind, nbrand)
exp_Xb = np.exp(δ.reshape(-1, 1) + μ)
ind_choice_prob = _BLP.cal_ind_choice_prob(
exp_Xb, nmkt, nsimind, nbrand)
nk = X2.shape[1]
nD = θ2.shape[1] - 1
f1 = np.zeros((δ.shape[0], nk * (nD + 1)))
# cdid relates each observation to the market it is in
cdid = np.arange(nmkt).repeat(nbrand)
cdindex = np.arange(nbrand, nbrand * (nmkt + 1), nbrand) - 1
# compute (partial share) / (partial sigma)
for k in range(nk):
xv = X2[:, k].reshape(-1, 1) @ np.ones((1, nsimind))
xv *= v[cdid, nsimind * k:nsimind * (k + 1)]
temp = (xv * ind_choice_prob).cumsum(axis=0)
sum1 = temp[cdindex, :]
sum1[1:, :] = sum1[1:, :] - sum1[:-1, :]
f1[:, k] = (ind_choice_prob * (xv - sum1[cdid, :])).mean(axis=1)
# If no demogr comment out the next part
# computing (partial share)/(partial pi)
for d in range(nD):
tmpD = D[cdid, nsimind * d:nsimind * (d + 1)]
temp1 = np.zeros((cdid.shape[0], nk))
for k in range(nk):
xd = X2[:, k].reshape(-1, 1) @ np.ones((1, nsimind)) * tmpD
temp = (xd * ind_choice_prob).cumsum(axis=0)
sum1 = temp[cdindex, :]
sum1[1:, :] = sum1[1:, :] - sum1[0:-1, :]
temp1[:, k] = (ind_choice_prob * (xd-sum1[cdid, :])).mean(axis=1)
f1[:, nk * (d + 1):nk * (d + 2)] = temp1
# computing (partial delta)/(partial theta2)
rel = np.nonzero(θ2.T.ravel())[0]
jacob = np.zeros((cdid.shape[0], rel.shape[0]))
n = 0
for i in range(cdindex.shape[0]):
temp = ind_choice_prob[n:cdindex[i] + 1, :]
H1 = temp @ temp.T
H = (np.diag(temp.sum(axis=1)) - H1) / self.nsimind
jacob[n:cdindex[i] + 1, :] = - solve(H, f1[n:cdindex[i] + 1, rel])
n = cdindex[i] + 1
return jacob
