def align_fPCA(f, time, num_comp=3, showplot=True, smoothdata=False, cores=-1):
"""
aligns a collection of functions while extracting principal components.
The functions are aligned to the principal components
:param f: numpy ndarray of shape (M,N) of N functions with M samples
:param time: vector of size M describing the sample points
:param num_comp: number of fPCA components
:param showplot: Shows plots of results using matplotlib (default = T)
:param smooth_data: Smooth the data using a box filter (default = F)
:param cores: number of cores for parallel (default = -1 (all))
:type sparam: double
:type smooth_data: bool
:type f: np.ndarray
:type time: np.ndarray
:rtype: tuple of numpy array
:return fn: aligned functions - numpy ndarray of shape (M,N) of N
functions with M samples
:return qn: aligned srvfs - similar structure to fn
:return q0: original srvf - similar structure to fn
:return mqn: srvf mean or median - vector of length M
:return gam: warping functions - similar structure to fn
:return q_pca: srsf principal directions
:return f_pca: functional principal directions
:return latent: latent values
:return coef: coefficients
:return U: eigenvectors
:return orig_var: Original Variance of Functions
:return amp_var: Amplitude Variance
:return phase_var: Phase Variance
"""
lam = 0.0
MaxItr = 50
coef = np.arange(-2., 3.)
Nstd = coef.shape[0]
M = f.shape[0]
N = f.shape[1]
if M > 500:
parallel = True
elif N > 100:
parallel = True
else:
parallel = False
eps = np.finfo(np.double).eps
f0 = f
if showplot:
plot.f_plot(time, f, title="Original Data")
# Compute SRSF function from data
f, g, g2 = uf.gradient_spline(time, f, smoothdata)
q = g / np.sqrt(abs(g) + eps)
print("Initializing...")
mnq = q.mean(axis=1)
a = mnq.repeat(N)
d1 = a.reshape(M, N)
d = (q - d1)**2
dqq = np.sqrt(d.sum(axis=0))
min_ind = dqq.argmin()
print("Aligning %d functions in SRVF space to %d fPCA components..." %
(N, num_comp))
itr = 0
mq = np.zeros((M, MaxItr + 1))
mq[:, itr] = q[:, min_ind]
fi = np.zeros((M, N, MaxItr + 1))
fi[:, :, 0] = f
qi = np.zeros((M, N, MaxItr + 1))
qi[:, :, 0] = q
gam = np.zeros((M, N, MaxItr + 1))
cost = np.zeros(MaxItr + 1)
while itr < MaxItr:
print("updating step: r=%d" % (itr + 1))
if itr == MaxItr:
print("maximal number of iterations is reached")
# PCA Step
a = mq[:, itr].repeat(N)
d1 = a.reshape(M, N)
qhat_cent = qi[:, :, itr] - d1
K = np.cov(qi[:, :, itr])
U, s, V = svd(K)
alpha_i = np.zeros((num_comp, N))
for ii in range(0, num_comp):
for jj in range(0, N):
alpha_i[ii, jj] = trapz(qhat_cent[:, jj] * U[:, ii], time)
U1 = U[:, 0:num_comp]
tmp = U1.dot(alpha_i)
qhat = d1 + tmp
# Matching Step
if parallel:
out = Parallel(n_jobs=cores)(
delayed(uf.optimum_reparam)(qhat[:,
n], time, qi[:, n,
itr], "DP", lam)
for n in range(N))
gam_t = np.array(out)
gam[:, :, itr] = gam_t.transpose()
else:
gam[:, :, itr] = uf.optimum_reparam(qhat, time, qi[:, :, itr],
"DP", lam)
for k in range(0, N):
time0 = (time[-1] - time[0]) * gam[:, k, itr] + time[0]
fi[:, k, itr + 1] = np.interp(time0, time, fi[:, k, itr])
qi[:, k, itr + 1] = uf.f_to_srsf(fi[:, k, itr + 1], time)
qtemp = qi[:, :, itr + 1]
mq[:, itr + 1] = qtemp.mean(axis=1)
cost_temp = np.zeros(N)
for ii in range(0, N):
cost_temp[ii] = norm(qtemp[:, ii] - qhat[:, ii])**2
cost[itr + 1] = cost_temp.mean()
if abs(cost[itr + 1] - cost[itr]) < 1e-06:
break
itr += 1
if itr >= MaxItr:
itrf = MaxItr
else:
itrf = itr + 1
cost = cost[1:(itrf + 1)]
# Aligned data & stats
fn = fi[:, :, itrf]
qn = qi[:, :, itrf]
q0 = qi[:, :, 0]
mean_f0 = f0.mean(axis=1)
std_f0 = f0.std(axis=1)
mqn = mq[:, itrf]
gamf = gam[:, :, 0]
for k in range(1, itr):
gam_k = gam[:, :, k]
for l in range(0, N):
time0 = (time[-1] - time[0]) * gam_k[:, l] + time[0]
gamf[:, l] = np.interp(time0, time, gamf[:, l])
# Center Mean
gamI = uf.SqrtMeanInverse(gamf)
gamI_dev = np.gradient(gamI, 1 / float(M - 1))
time0 = (time[-1] - time[0]) * gamI + time[0]
mqn = np.interp(time0, time, mqn) * np.sqrt(gamI_dev)
for k in range(0, N):
qn[:, k] = np.interp(time0, time, qn[:, k]) * np.sqrt(gamI_dev)
fn[:, k] = np.interp(time0, time, fn[:, k])
gamf[:, k] = np.interp(time0, time, gamf[:, k])
mean_fn = fn.mean(axis=1)
std_fn = fn.std(axis=1)
# Get Final PCA
mididx = int(np.round(time.shape[0] / 2))
m_new = np.sign(fn[mididx, :]) * np.sqrt(np.abs(fn[mididx, :]))
mqn2 = np.append(mqn, m_new.mean())
qn2 = np.vstack((qn, m_new))
K = np.cov(qn2)
U, s, V = svd(K)
stdS = np.sqrt(s)
# compute the PCA in the q domain
q_pca = np.ndarray(shape=(M + 1, Nstd, num_comp), dtype=float)
for k in range(0, num_comp):
for l in range(0, Nstd):
q_pca[:, l, k] = mqn2 + coef[l] * stdS[k] * U[:, k]
# compute the correspondence in the f domain
f_pca = np.ndarray(shape=(M, Nstd, num_comp), dtype=float)
for k in range(0, num_comp):
for l in range(0, Nstd):
q_pca_tmp = q_pca[0:M, l, k] * np.abs(q_pca[0:M, l, k])
q_pca_tmp2 = np.sign(q_pca[M, l, k]) * (q_pca[M, l, k]**2)
f_pca[:, l, k] = uf.cumtrapzmid(time, q_pca_tmp, q_pca_tmp2,
np.floor(time.shape[0] / 2),
mididx)
N2 = qn.shape[1]
c = np.zeros((N2, num_comp))
for k in range(0, num_comp):
for l in range(0, N2):
c[l, k] = sum((np.append(qn[:, l], m_new[l]) - mqn2) * U[:, k])
if showplot:
CBcdict = {
'Bl': (0, 0, 0),
'Or': (.9, .6, 0),
'SB': (.35, .7, .9),
'bG': (0, .6, .5),
'Ye': (.95, .9, .25),
'Bu': (0, .45, .7),
'Ve': (.8, .4, 0),
'rP': (.8, .6, .7),
}
cl = sorted(CBcdict.keys())
# Align Plots
fig, ax = plot.f_plot(np.arange(0, M) / float(M - 1),
gamf,
title="Warping Functions")
ax.set_aspect('equal')
plot.f_plot(time, fn, title="Warped Data")
tmp = np.array([mean_f0, mean_f0 + std_f0, mean_f0 - std_f0])
tmp = tmp.transpose()
plot.f_plot(time, tmp, title=r"Original Data: Mean $\pm$ STD")
tmp = np.array([mean_fn, mean_fn + std_fn, mean_fn - std_fn])
tmp = tmp.transpose()
plot.f_plot(time, tmp, title=r"Warped Data: Mean $\pm$ STD")
# PCA Plots
fig, ax = plt.subplots(2, num_comp)
for k in range(0, num_comp):
axt = ax[0, k]
for l in range(0, Nstd):
axt.plot(time, q_pca[0:M, l, k], color=CBcdict[cl[l]])
axt.hold(True)
axt.set_title('q domain: PD %d' % (k + 1))
plot.rstyle(axt)
axt = ax[1, k]
for l in range(0, Nstd):
axt.plot(time, f_pca[:, l, k], color=CBcdict[cl[l]])
axt.hold(True)
axt.set_title('f domain: PD %d' % (k + 1))
plot.rstyle(axt)
fig.set_tight_layout(True)
cumm_coef = 100 * np.cumsum(s) / sum(s)
idx = np.arange(0, M + 1) + 1
plot.f_plot(idx, cumm_coef, "Coefficient Cumulative Percentage")
plt.xlabel("Percentage")
plt.ylabel("Index")
plt.show()
mean_f0 = f0.mean(axis=1)
std_f0 = f0.std(axis=1)
mean_fn = fn.mean(axis=1)
std_fn = fn.std(axis=1)
tmp = np.zeros(M)
tmp[1:] = cumtrapz(mqn * np.abs(mqn), time)
fmean = np.mean(f0[1, :]) + tmp
fgam = np.zeros((M, N))
for k in range(0, N):
time0 = (time[-1] - time[0]) * gamf[:, k] + time[0]
fgam[:, k] = np.interp(time0, time, fmean)
var_fgam = fgam.var(axis=1)
orig_var = trapz(std_f0**2, time)
amp_var = trapz(std_fn**2, time)
phase_var = trapz(var_fgam, time)
K = np.cov(fn)
U, s, V = svd(K)
align_fPCAresults = collections.namedtuple('align_fPCA', [
'fn', 'qn', 'q0', 'mqn', 'gam', 'q_pca', 'f_pca', 'latent', 'coef',
'U', 'orig_var', 'amp_var', 'phase_var', 'cost'
])
out = align_fPCAresults(fn, qn, q0, mqn, gamf, q_pca, f_pca, s, c, U,
orig_var, amp_var, phase_var, cost)
return out
def vertfPCA(fn, time, qn, no=1, showplot=True):
"""
This function calculates vertical functional principal component analysis
on aligned data
:param fn: numpy ndarray of shape (M,N) of N aligned functions with M
samples
:param time: vector of size N describing the sample points
:param qn: numpy ndarray of shape (M,N) of N aligned SRSF with M samples
:param no: number of components to extract (default = 1)
:param showplot: Shows plots of results using matplotlib (default = T)
:type showplot: bool
:type no: int
:rtype: tuple of numpy ndarray
:return q_pca: srsf principal directions
:return f_pca: functional principal directions
:return latent: latent values
:return coef: coefficients
:return U: eigenvectors
"""
coef = np.arange(-2., 3.)
Nstd = coef.shape[0]
# FPCA
mq_new = qn.mean(axis=1)
N = mq_new.shape[0]
mididx = np.round(time.shape[0] / 2)
m_new = np.sign(fn[mididx, :]) * np.sqrt(np.abs(fn[mididx, :]))
mqn = np.append(mq_new, m_new.mean())
qn2 = np.vstack((qn, m_new))
K = np.cov(qn2)
U, s, V = svd(K)
stdS = np.sqrt(s)
# compute the PCA in the q domain
q_pca = np.ndarray(shape=(N + 1, Nstd, no), dtype=float)
for k in range(0, no):
for l in range(0, Nstd):
q_pca[:, l, k] = mqn + coef[l] * stdS[k] * U[:, k]
# compute the correspondence in the f domain
f_pca = np.ndarray(shape=(N, Nstd, no), dtype=float)
for k in range(0, no):
for l in range(0, Nstd):
f_pca[:, l, k] = uf.cumtrapzmid(time, q_pca[0:N, l, k] * np.abs(q_pca[0:N, l, k]),
np.sign(q_pca[N, l, k]) * (q_pca[N, l, k] ** 2))
N2 = qn.shape[1]
c = np.zeros((N2, no))
for k in range(0, no):
for l in range(0, N2):
c[l, k] = sum((np.append(qn[:, l], m_new[l]) - mqn) * U[:, k])
vfpca_results = collections.namedtuple('vfpca', ['q_pca', 'f_pca', 'latent', 'coef', 'U'])
vfpca = vfpca_results(q_pca, f_pca, s, c, U)
if showplot:
CBcdict = {
'Bl': (0, 0, 0),
'Or': (.9, .6, 0),
'SB': (.35, .7, .9),
'bG': (0, .6, .5),
'Ye': (.95, .9, .25),
'Bu': (0, .45, .7),
'Ve': (.8, .4, 0),
'rP': (.8, .6, .7),
}
cl = sorted(CBcdict.keys())
fig, ax = plt.subplots(2, no)
for k in range(0, no):
axt = ax[0, k]
for l in range(0, Nstd):
axt.plot(time, q_pca[0:N, l, k], color=CBcdict[cl[l]])
axt.hold(True)
axt.set_title('q domain: PD %d' % (k + 1))
plot.rstyle(axt)
axt = ax[1, k]
for l in range(0, Nstd):
axt.plot(time, f_pca[:, l, k], color=CBcdict[cl[l]])
axt.hold(True)
axt.set_title('f domain: PD %d' % (k + 1))
plot.rstyle(axt)
fig.set_tight_layout(True)
cumm_coef = 100 * np.cumsum(s) / sum(s)
idx = np.arange(0, N + 1) + 1
plot.f_plot(idx, cumm_coef, "Coefficient Cumulative Percentage")
plt.xlabel("Percentage")
plt.ylabel("Index")
plt.show()
return vfpca
def align_fPCA(f, time, num_comp=3, showplot=True, smoothdata=False):
"""
aligns a collection of functions while extracting principal components.
The functions are aligned to the principal components
:param f: numpy ndarray of shape (M,N) of N functions with M samples
:param time: vector of size M describing the sample points
:param num_comp: number of fPCA components
:param showplot: Shows plots of results using matplotlib (default = T)
:param smooth_data: Smooth the data using a box filter (default = F)
:param sparam: Number of times to run box filter (default = 25)
:type sparam: double
:type smooth_data: bool
:type f: np.ndarray
:type time: np.ndarray
:rtype: tuple of numpy array
:return fn: aligned functions - numpy ndarray of shape (M,N) of N
functions with M samples
:return qn: aligned srvfs - similar structure to fn
:return q0: original srvf - similar structure to fn
:return mqn: srvf mean or median - vector of length M
:return gam: warping functions - similar structure to fn
:return q_pca: srsf principal directions
:return f_pca: functional principal directions
:return latent: latent values
:return coef: coefficients
:return U: eigenvectors
:return orig_var: Original Variance of Functions
:return amp_var: Amplitude Variance
:return phase_var: Phase Variance
"""
lam = 0.0
MaxItr = 50
coef = np.arange(-2., 3.)
Nstd = coef.shape[0]
M = f.shape[0]
N = f.shape[1]
if M > 500:
parallel = True
elif N > 100:
parallel = True
else:
parallel = False
eps = np.finfo(np.double).eps
f0 = f
if showplot:
plot.f_plot(time, f, title="Original Data")
# Compute SRSF function from data
f, g, g2 = uf.gradient_spline(time, f, smoothdata)
q = g / np.sqrt(abs(g) + eps)
print ("Initializing...")
mnq = q.mean(axis=1)
a = mnq.repeat(N)
d1 = a.reshape(M, N)
d = (q - d1) ** 2
dqq = np.sqrt(d.sum(axis=0))
min_ind = dqq.argmin()
print("Aligning %d functions in SRVF space to %d fPCA components..."
% (N, num_comp))
itr = 0
mq = np.zeros((M, MaxItr + 1))
mq[:, itr] = q[:, min_ind]
fi = np.zeros((M, N, MaxItr + 1))
fi[:, :, 0] = f
qi = np.zeros((M, N, MaxItr + 1))
qi[:, :, 0] = q
gam = np.zeros((M, N, MaxItr + 1))
cost = np.zeros(MaxItr + 1)
while itr < MaxItr:
print("updating step: r=%d" % (itr + 1))
if itr == MaxItr:
print("maximal number of iterations is reached")
# PCA Step
a = mq[:, itr].repeat(N)
d1 = a.reshape(M, N)
qhat_cent = qi[:, :, itr] - d1
K = np.cov(qi[:, :, itr])
U, s, V = svd(K)
alpha_i = np.zeros((num_comp, N))
for ii in range(0, num_comp):
for jj in range(0, N):
alpha_i[ii, jj] = trapz(qhat_cent[:, jj] * U[:, ii], time)
U1 = U[:, 0:num_comp]
tmp = U1.dot(alpha_i)
qhat = d1 + tmp
# Matching Step
if parallel:
out = Parallel(n_jobs=-1)(
delayed(uf.optimum_reparam)(qhat[:, n], time, qi[:, n, itr],
lam) for n in range(N))
gam_t = np.array(out)
gam[:, :, itr] = gam_t.transpose()
else:
gam[:, :, itr] = uf.optimum_reparam(qhat, time, qi[:, :, itr], lam)
for k in range(0, N):
time0 = (time[-1] - time[0]) * gam[:, k, itr] + time[0]
fi[:, k, itr + 1] = np.interp(time0, time, fi[:, k, itr])
qi[:, k, itr + 1] = uf.f_to_srsf(fi[:, k, itr + 1], time)
qtemp = qi[:, :, itr + 1]
mq[:, itr + 1] = qtemp.mean(axis=1)
cost_temp = np.zeros(N)
for ii in range(0, N):
cost_temp[ii] = norm(qtemp[:, ii] - qhat[:, ii]) ** 2
cost[itr + 1] = cost_temp.mean()
if abs(cost[itr + 1] - cost[itr]) < 1e-06:
break
itr += 1
if itr >= MaxItr:
itrf = MaxItr
else:
itrf = itr+1
cost = cost[1:(itrf+1)]
# Aligned data & stats
fn = fi[:, :, itrf]
qn = qi[:, :, itrf]
q0 = qi[:, :, 0]
mean_f0 = f0.mean(axis=1)
std_f0 = f0.std(axis=1)
mqn = mq[:, itrf]
gamf = gam[:, :, 0]
for k in range(1, itr):
gam_k = gam[:, :, k]
for l in range(0, N):
time0 = (time[-1] - time[0]) * gam_k[:, l] + time[0]
gamf[:, l] = np.interp(time0, time, gamf[:, l])
# Center Mean
gamI = uf.SqrtMeanInverse(gamf)
gamI_dev = np.gradient(gamI, 1 / float(M - 1))
time0 = (time[-1] - time[0]) * gamI + time[0]
mqn = np.interp(time0, time, mqn) * np.sqrt(gamI_dev)
for k in range(0, N):
qn[:, k] = np.interp(time0, time, qn[:, k]) * np.sqrt(gamI_dev)
fn[:, k] = np.interp(time0, time, fn[:, k])
gamf[:, k] = np.interp(time0, time, gamf[:, k])
mean_fn = fn.mean(axis=1)
std_fn = fn.std(axis=1)
# Get Final PCA
mididx = np.round(time.shape[0] / 2)
m_new = np.sign(fn[mididx, :]) * np.sqrt(np.abs(fn[mididx, :]))
mqn2 = np.append(mqn, m_new.mean())
qn2 = np.vstack((qn, m_new))
K = np.cov(qn2)
U, s, V = svd(K)
stdS = np.sqrt(s)
# compute the PCA in the q domain
q_pca = np.ndarray(shape=(M + 1, Nstd, num_comp), dtype=float)
for k in range(0, num_comp):
for l in range(0, Nstd):
q_pca[:, l, k] = mqn2 + coef[l] * stdS[k] * U[:, k]
# compute the correspondence in the f domain
f_pca = np.ndarray(shape=(M, Nstd, num_comp), dtype=float)
for k in range(0, num_comp):
for l in range(0, Nstd):
q_pca_tmp = q_pca[0:M, l, k] * np.abs(q_pca[0:M, l, k])
q_pca_tmp2 = np.sign(q_pca[M, l, k]) * (q_pca[M, l, k] ** 2)
f_pca[:, l, k] = uf.cumtrapzmid(time, q_pca_tmp, q_pca_tmp2)
N2 = qn.shape[1]
c = np.zeros((N2, num_comp))
for k in range(0, num_comp):
for l in range(0, N2):
c[l, k] = sum((np.append(qn[:, l], m_new[l]) - mqn2) * U[:, k])
if showplot:
CBcdict = {
'Bl': (0, 0, 0),
'Or': (.9, .6, 0),
'SB': (.35, .7, .9),
'bG': (0, .6, .5),
'Ye': (.95, .9, .25),
'Bu': (0, .45, .7),
'Ve': (.8, .4, 0),
'rP': (.8, .6, .7),
}
cl = sorted(CBcdict.keys())
# Align Plots
fig, ax = plot.f_plot(np.arange(0, M) / float(M - 1), gamf,
title="Warping Functions")
ax.set_aspect('equal')
plot.f_plot(time, fn, title="Warped Data")
tmp = np.array([mean_f0, mean_f0 + std_f0, mean_f0 - std_f0])
tmp = tmp.transpose()
plot.f_plot(time, tmp, title="Original Data: Mean $\pm$ STD")
tmp = np.array([mean_fn, mean_fn + std_fn, mean_fn - std_fn])
tmp = tmp.transpose()
plot.f_plot(time, tmp, title="Warped Data: Mean $\pm$ STD")
# PCA Plots
fig, ax = plt.subplots(2, num_comp)
for k in range(0, num_comp):
axt = ax[0, k]
for l in range(0, Nstd):
axt.plot(time, q_pca[0:M, l, k], color=CBcdict[cl[l]])
axt.hold(True)
axt.set_title('q domain: PD %d' % (k + 1))
plot.rstyle(axt)
axt = ax[1, k]
for l in range(0, Nstd):
axt.plot(time, f_pca[:, l, k], color=CBcdict[cl[l]])
axt.hold(True)
axt.set_title('f domain: PD %d' % (k + 1))
plot.rstyle(axt)
fig.set_tight_layout(True)
cumm_coef = 100 * np.cumsum(s) / sum(s)
idx = np.arange(0, M + 1) + 1
plot.f_plot(idx, cumm_coef, "Coefficient Cumulative Percentage")
plt.xlabel("Percentage")
plt.ylabel("Index")
plt.show()
mean_f0 = f0.mean(axis=1)
std_f0 = f0.std(axis=1)
mean_fn = fn.mean(axis=1)
std_fn = fn.std(axis=1)
tmp = np.zeros(M)
tmp[1:] = cumtrapz(mqn * np.abs(mqn), time)
fmean = np.mean(f0[1, :]) + tmp
fgam = np.zeros((M, N))
for k in range(0, N):
time0 = (time[-1] - time[0]) * gamf[:, k] + time[0]
fgam[:, k] = np.interp(time0, time, fmean)
var_fgam = fgam.var(axis=1)
orig_var = trapz(std_f0 ** 2, time)
amp_var = trapz(std_fn ** 2, time)
phase_var = trapz(var_fgam, time)
K = np.cov(fn)
U, s, V = svd(K)
align_fPCAresults = collections.namedtuple('align_fPCA', ['fn', 'qn',
'q0', 'mqn', 'gam', 'q_pca',
'f_pca', 'latent', 'coef',
'U', 'orig_var', 'amp_var',
'phase_var', 'cost'])
out = align_fPCAresults(fn, qn, q0, mqn, gamf, q_pca, f_pca, s, c,
U, orig_var, amp_var, phase_var, cost)
return out
def horizfPCA(gam, time, no, showplot=True):
"""
This function calculates horizontal functional principal component analysis on aligned data
:param gam: numpy ndarray of shape (M,N) of N warping functions
:param time: vector of size M describing the sample points
:param no: number of components to extract (default = 1)
:param showplot: Shows plots of results using matplotlib (default = T)
:type showplot: bool
:type no: int
:rtype: tuple of numpy ndarray
:return q_pca: srsf principal directions
:return f_pca: functional principal directions
:return latent: latent values
:return coef: coefficients
:return U: eigenvectors
"""
# Calculate Shooting Vectors
mu, gam_mu, psi, vec = uf.SqrtMean(gam)
tau = np.arange(1, 6)
TT = time.shape[0]
# TFPCA
K = np.cov(vec)
U, s, V = svd(K)
vm = vec.mean(axis=1)
gam_pca = np.ndarray(shape=(tau.shape[0], mu.shape[0] + 1, no), dtype=float)
psi_pca = np.ndarray(shape=(tau.shape[0], mu.shape[0], no), dtype=float)
for j in range(0, no):
for k in tau:
v = (k - 3) * np.sqrt(s[j]) * U[:, j]
vn = norm(v) / np.sqrt(TT)
if vn < 0.0001:
psi_pca[k-1, :, j] = mu
else:
psi_pca[k-1, :, j] = np.cos(vn) * mu + np.sin(vn) * v / vn
tmp = np.zeros(TT)
tmp[1:TT] = np.cumsum(psi_pca[k-1, :, j] * psi_pca[k-1, :, j])
gam_pca[k-1, :, j] = (tmp - tmp[0]) / (tmp[-1] - tmp[0])
hfpca_results = collections.namedtuple('hfpca', ['gam_pca', 'psi_pca', 'latent', 'U', 'gam_mu'])
hfpca = hfpca_results(gam_pca, psi_pca, s, U, gam_mu)
if showplot:
CBcdict = {
'Bl': (0, 0, 0),
'Or': (.9, .6, 0),
'SB': (.35, .7, .9),
'bG': (0, .6, .5),
'Ye': (.95, .9, .25),
'Bu': (0, .45, .7),
'Ve': (.8, .4, 0),
'rP': (.8, .6, .7),
}
fig, ax = plt.subplots(1, no)
for k in range(0, no):
axt = ax[k]
axt.set_color_cycle(CBcdict[c] for c in sorted(CBcdict.keys()))
tmp = gam_pca[:, :, k]
axt.plot(np.linspace(0, 1, TT), tmp.transpose())
axt.set_title('PD %d' % (k + 1))
axt.set_aspect('equal')
plot.rstyle(axt)
fig.set_tight_layout(True)
cumm_coef = 100 * np.cumsum(s) / sum(s)
idx = np.arange(0, TT-1) + 1
plot.f_plot(idx, cumm_coef, "Coefficient Cumulative Percentage")
plt.xlabel("Percentage")
plt.ylabel("Index")
plt.show()
return hfpca
