def cal_delta(self, theta):
"""Calculate delta (mean utility) from contraction mapping"""
_blp, theta, delta, v, D, x2, nmkt, nsimind, nbrand = self.set_aliases(
)
theta_v = theta[:, 0]
theta_D = theta[:, 1:]
niter = 0
exp_mu = np.exp(
_blp.cal_mu(theta_v, theta_D, v, D, x2, nmkt, nsimind, nbrand))
while True:
diff = self.ln_s_jt.copy()
exp_xb = np.exp(delta.reshape(-1, 1)) * exp_mu
diff -= np.log(_blp.cal_mktshr(exp_xb, nmkt, nsimind, nbrand))
if np.isnan(diff).sum():
print('nan in diffs')
break
delta += diff
if (abs(diff).max() < self.etol) and (abs(diff).mean() < 1e-3):
break
niter += 1
print('contraction mapping finished in {} iterations'.format(niter))
def cal_delta(self, theta):
"""Calculate delta (mean utility) from contraction mapping"""
_blp, theta, delta, v, D, x2, nmkt, nsimind, nbrand = self.set_aliases()
theta_v = theta[:, 0]
theta_D = theta[:, 1:]
niter = 0
exp_mu = np.exp(_blp.cal_mu(theta_v, theta_D,
v, D, x2,
nmkt, nsimind, nbrand))
while True:
diff = self.ln_s_jt.copy()
exp_xb = np.exp(delta.reshape(-1, 1)) * exp_mu
diff -= np.log(_blp.cal_mktshr(exp_xb, nmkt, nsimind, nbrand))
if np.isnan(diff).sum():
print('nan in diffs')
break
delta += diff
if (abs(diff).max() < self.etol) and (abs(diff).mean() < 1e-3):
break
niter += 1
print('contraction mapping finished in {} iterations'.format(niter))
def cal_jacobian(self, theta):
"""calculate the Jacobian"""
_blp, theta, delta, v, D, x2, nmkt, nsimind, nbrand = self.set_aliases(
)
mu = _blp.cal_mu(theta[:, 0], theta[:, 1:], v, D, x2, nmkt, nsimind,
nbrand)
exp_xb = np.exp(delta.reshape(-1, 1) + mu)
ind_choice_prob = _blp.cal_ind_choice_prob(exp_xb, nmkt, nsimind,
nbrand)
nk = self.x2.shape[1]
nD = theta.shape[1] - 1
f1 = np.zeros((delta.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 xrange(nk):
xv = x2[:, k].reshape(-1, 1).dot(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[0:-1, :]
f1[:, k] = (ind_choice_prob * (xv - sum1[cdid, :])).mean(axis=1)
for d in xrange(nD):
tmpD = D[cdid, nsimind * d:nsimind * (d + 1)]
temp1 = np.zeros((cdid.shape[0], nk))
for k in xrange(nk):
xd = x2[:, k].reshape(-1, 1).dot(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
rel = np.nonzero(theta.T.ravel())[0]
f = np.zeros((cdid.shape[0], rel.shape[0]))
n = 0
for i in xrange(cdindex.shape[0]):
temp = ind_choice_prob[n:cdindex[i] + 1, :]
H1 = temp.dot(temp.T)
H = (np.diag(temp.sum(axis=1)) - H1) / self.nsimind
f[n:cdindex[i] + 1, :] = -solve(H, f1[n:cdindex[i] + 1, rel])
n = cdindex[i] + 1
return (f)
def cal_jacobian(self, theta):
"""calculate the Jacobian"""
_blp, theta, delta, v, D, x2, nmkt, nsimind, nbrand = self.set_aliases()
mu = _blp.cal_mu(theta[:, 0], theta[:, 1:], v, D, x2, nmkt, nsimind, nbrand)
exp_xb = np.exp(delta.reshape(-1, 1) + mu)
ind_choice_prob = _blp.cal_ind_choice_prob(exp_xb, nmkt, nsimind, nbrand)
nk = self.x2.shape[1]
nD = theta.shape[1] - 1
f1 = np.zeros((delta.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 xrange(nk):
xv = x2[:, k].reshape(-1, 1).dot(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[0:-1, :]
f1[:, k] = (ind_choice_prob * (xv - sum1[cdid, :])).mean(axis=1)
for d in xrange(nD):
tmpD = D[cdid, nsimind * d:nsimind * (d + 1)]
temp1 = np.zeros((cdid.shape[0], nk))
for k in xrange(nk):
xd = x2[:, k].reshape(-1, 1).dot(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
rel = np.nonzero(theta.T.ravel())[0]
f = np.zeros((cdid.shape[0], rel.shape[0]))
n = 0
for i in xrange(cdindex.shape[0]):
temp = ind_choice_prob[n:cdindex[i] + 1, :]
H1 = temp.dot(temp.T)
H = (np.diag(temp.sum(axis=1)) - H1) / self.nsimind
f[n:cdindex[i] + 1, :] = - solve(H, f1[n:cdindex[i] + 1, rel])
n = cdindex[i] + 1
return(f)
def cal_jacobian(self, theta):
"""calculate the Jacobian"""
_blp, theta, delta, v, D, x2, nmkt, nsimind, nbrand = self.set_aliases()
# delta = log(scipy.io.loadmat(r'/home/joon/documents/coursework-phd/2008-fall/Hendricks - Industrial Organization/Problem Set 4/Data&Code/mvalold.mat')['mvalold'].reshape(-1, ))
mu = _blp.cal_mu(theta[:, 0], theta[:, 1:], v, D, x2, nmkt, nsimind, nbrand)
exp_xb = exp(delta.reshape(-1, 1) + mu)
ind_choice_prob = _blp.cal_ind_choice_prob(exp_xb, nmkt, nsimind, nbrand)
nk = self.x2.shape[1]
nD = theta.shape[1] - 1
f1 = zeros((delta.shape[0], nk * (nD + 1)))
# cdid relates each observation to the market it is in
cdid = arange(nmkt).repeat(nbrand)
cdindex = arange(nbrand, nbrand * (nmkt + 1), nbrand) - 1
# computing (partial share)/(partial sigma)
for k in xrange(nk):
xv = x2[:, k].reshape(-1, 1).dot(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[0:-1, :]
f1[:, k] = (ind_choice_prob * (xv - sum1[cdid, :])).mean(axis=1)
for d in xrange(nD):
tmpD = D[cdid, nsimind * d : nsimind * (d + 1)]
temp1 = zeros((cdid.shape[0], nk))
for k in xrange(nk):
xd = x2[:, k].reshape(-1, 1).dot(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
rel = nonzero(theta.T.ravel())[0]
f = zeros((cdid.shape[0], rel.shape[0]))
n = 0
for i in xrange(cdindex.shape[0]):
temp = ind_choice_prob[n : cdindex[i] + 1, :]
H1 = temp.dot(temp.T)
H = (diag(temp.sum(axis=1)) - H1) / self.nsimind
f[n : cdindex[i] + 1, :] = -solve(H, f1[n : cdindex[i] + 1, rel])
n = cdindex[i] + 1
return f
