def mlogit_warp_grad(alpha, nu, q, y, max_itr=8000, tol=1e-4,
deltaO=0.008, deltag=0.008, display=0):
"""
calculates optimal warping for functional multinomial logistic regression
:param alpha: scalar
:param nu: numpy ndarray of shape (M,N) of M functions with N samples
:param q: numpy ndarray of shape (M,N) of M functions with N samples
:param y: numpy ndarray of shape (1,N) of M functions with N samples
responses
:param max_itr: maximum number of iterations (Default=8000)
:param tol: stopping tolerance (Default=1e-10)
:param deltaO: gradient step size for rotation (Default=0.008)
:param deltag: gradient step size for warping (Default=0.008)
:param display: display iterations (Default=0)
:rtype: tuple of numpy array
:return gam_old: warping function
"""
alpha = alpha/norm(alpha)
q, scale = cf.scale_curve(q) # q/norm(q)
for ii in range(0, nu.shape[2]):
nu[:, :, ii], scale = cf.scale_curve(nu[:, :, ii]) # nu/norm(nu)
gam_old, O_old = mw.ocmlogit_warp(np.ascontiguousarray(alpha),
np.ascontiguousarray(nu),
np.ascontiguousarray(q),
np.ascontiguousarray(y, dtype=np.int32),
max_itr, tol, deltaO, deltag, display)
return (gam_old, O_old)
def preproc_open_curve(beta, T=100):
n, M, k = beta.shape
q = np.zeros((n, T, k))
beta2 = np.zeros((n, T, k))
for i in range(0, k):
beta1 = beta[:, :, i]
beta1, scale = cf.scale_curve(beta1)
beta1 = cf.resamplecurve(beta1, T)
centroid1 = cf.calculatecentroid(beta1)
beta1 = beta1 - np.tile(centroid1, [T, 1]).T
beta2[:, :, i] = beta1
q[:, :, i] = cf.curve_to_q(beta1)
return (q, beta2)
def curve_principal_directions(betamean, mu, K, mode='O', no=3, N=5):
"""
Computes principal direction of variation specified by no. N is
Number of shapes away from mean. Creates 2*N+1 shape sequence
:param betamean: numpy ndarray of shape (n, M) describing the mean curve
:param mu: numpy ndarray of shape (n, M) describing the mean srvf
:param K: numpy ndarray of shape (M, M) describing the covariance
:param mode: Open ('O') or closed curve ('C') (default 'O')
:param no: number of direction (default 3)
:param N: number of shapes (2*N+1) (default 5)
:rtype: tuple of numpy array
:return pd: principal directions
"""
n, T = betamean.shape
modes = ['O', 'C']
mode = [i for i, x in enumerate(modes) if x == mode]
if len(mode) == 0:
mode = 0
else:
mode = mode[0]
U, s, V = svd(K)
qarray = empty((no, 2*N+1), dtype=object)
qarray1 = empty(N, dtype=object)
qarray2 = empty(N, dtype=object)
pd = empty((no, 2*N+1), dtype=object)
pd1 = empty(N, dtype=object)
pd2 = empty(N, dtype=object)
for m in range(0, no):
princDir = vstack((U[0:T, m], U[T:2*T, m]))
v = sqrt(s[m]) * princDir
q1 = mu
epsilon = 2./N
# Forward direction from mean
for i in range(0, N):
normv = sqrt(cf.innerprod_q2(v, v))
if normv < 1e-4:
q2 = mu
else:
q2 = cos(epsilon*normv)*q1 + sin(epsilon*normv)*v/normv
if mode == 1:
q2 = cf.project_curve(q2)
qarray1[i] = q2
p = cf.q_to_curve(q2)
centroid1 = -1*cf.calculatecentroid(p)
beta_scaled, scale = cf.scale_curve(p + tile(centroid1, [T, 1]).T)
pd1[i] = beta_scaled
# Parallel translate tangent vector
basis2 = cf.find_basis_normal(q2)
v = cf.parallel_translate(v, q1, q2, basis2, mode)
q1 = q2
# Backward direction from mean
v = -sqrt(s[m])*princDir
q1 = mu
for i in range(0, N):
normv = sqrt(cf.innerprod_q2(v, v))
if normv < 1e-4:
q2 = mu
else:
q2 = cos(epsilon*normv)*q1+sin(epsilon*normv)*v/normv
if mode == 1:
q2 = cf.project_curve(q2)
qarray2[i] = q2
p = cf.q_to_curve(q2)
centroid1 = -1*cf.calculatecentroid(p)
beta_scaled, scale = cf.scale_curve(p + tile(centroid1, [T, 1]).T)
pd2[i] = beta_scaled
# Parallel translate tangent vector
basis2 = cf.find_basis_normal(q2)
v = cf.parallel_translate(v, q1, q2, basis2, mode)
q1 = q2
for i in range(0, N):
qarray[m, i] = qarray2[(N-1)-i]
pd[m, i] = pd2[(N-1)-i]
qarray[m, N] = mu
centroid1 = -1*cf.calculatecentroid(betamean)
beta_scaled, scale = cf.scale_curve(betamean +
tile(centroid1, [T, 1]).T)
pd[m, N] = beta_scaled
for i in range(N+1, 2*N+1):
qarray[m, i] = qarray1[i-(N+1)]
pd[m, i] = pd1[i-(N+1)]
return(pd)
def curve_principal_directions(betamean, mu, K, mode='O', no=3, N=5):
"""
Computes principal direction of variation specified by no. N is
Number of shapes away from mean. Creates 2*N+1 shape sequence
:param betamean: numpy ndarray of shape (n, M) describing the mean curve
:param mu: numpy ndarray of shape (n, M) describing the mean srvf
:param K: numpy ndarray of shape (M, M) describing the covariance
:param mode: Open ('O') or closed curve ('C') (default 'O')
:param no: number of direction (default 3)
:param N: number of shapes (2*N+1) (default 5)
:rtype: tuple of numpy array
:return pd: principal directions
"""
n, T = betamean.shape
modes = ['O', 'C']
mode = [i for i, x in enumerate(modes) if x == mode]
if len(mode) == 0:
mode = 0
else:
mode = mode[0]
U, s, V = svd(K)
qarray = empty((no, 2*N+1), dtype=object)
qarray1 = empty(N, dtype=object)
qarray2 = empty(N, dtype=object)
pd = empty((no, 2*N+1), dtype=object)
pd1 = empty(N, dtype=object)
pd2 = empty(N, dtype=object)
for m in range(0, no):
princDir = vstack((U[0:T, m], U[T:2*T, m]))
v = sqrt(s[m]) * princDir
q1 = mu
epsilon = 2./N
# Forward direction from mean
for i in range(0, N):
normv = sqrt(cf.innerprod_q2(v, v))
if normv < 1e-4:
q2 = mu
else:
q2 = cos(epsilon*normv)*q1 + sin(epsilon*normv)*v/normv
if mode == 1:
q2 = cf.project_curve(q2)
qarray1[i] = q2
p = cf.q_to_curve(q2)
centroid1 = -1*cf.calculatecentroid(p)
beta_scaled, scale = cf.scale_curve(p + tile(centroid1, [T, 1]).T)
pd1[i] = beta_scaled
# Parallel translate tangent vector
basis2 = cf.find_basis_normal(q2)
v = cf.parallel_translate(v, q1, q2, basis2, mode)
q1 = q2
# Backward direction from mean
v = -sqrt(s[m])*princDir
q1 = mu
for i in range(0, N):
normv = sqrt(cf.innerprod_q2(v, v))
if normv < 1e-4:
q2 = mu
else:
q2 = cos(epsilon*normv)*q1+sin(epsilon*normv)*v/normv
if mode == 1:
q2 = cf.project_curve(q2)
qarray2[i] = q2
p = cf.q_to_curve(q2)
centroid1 = -1*cf.calculatecentroid(p)
beta_scaled, scale = cf.scale_curve(p + tile(centroid1, [T, 1]).T)
pd2[i] = beta_scaled
# Parallel translate tangent vector
basis2 = cf.find_basis_normal(q2)
v = cf.parallel_translate(v, q1, q2, basis2, mode)
q1 = q2
for i in range(0, N):
qarray[m, i] = qarray2[(N-1)-i]
pd[m, i] = pd2[(N-1)-i]
qarray[m, N] = mu
centroid1 = -1*cf.calculatecentroid(betamean)
beta_scaled, scale = cf.scale_curve(betamean +
tile(centroid1, [T, 1]).T)
pd[m, N] = beta_scaled
for i in range(N+1, 2*N+1):
qarray[m, i] = qarray1[i-(N+1)]
pd[m, i] = pd1[i-(N+1)]
return(pd)