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dimensionality.py
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dimensionality.py
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"""
Copright © 2023 Howard Hughes Medical Institute, Authored by Carsen Stringer and Marius Pachitariu.
"""
import numpy as np
from scipy.interpolate import interp1d
from scipy.ndimage import gaussian_filter1d
from scipy.optimize import curve_fit
def fit_asymptote(x, y, xall, fitexp=False):
from sklearn.linear_model import LinearRegression
''' fit y = alpha + beta / sqrt(x)'''
xi = x.copy()**-0.5
if xi.ndim < 2:
xi = xi[:,np.newaxis]
xall = xall[:,np.newaxis]
reg = LinearRegression().fit(xi, y)
beta = reg.coef_
alpha = reg.intercept_
r2 = reg.score(xi, y)
if not fitexp:
ypred = alpha + np.dot(xall**-0.5, beta)
par = [alpha]
for b in beta:
par.append(b)
return par, r2, ypred
if xi.shape[1]==1:
par0 = [alpha, beta[0], 0.5]
f = asymp
else:
par0 = [alpha, beta[0], beta[1], 0.5, 0.5]
f = asymp2
par, mcov = curve_fit(f, x, y, par0)
if xi.shape[1]==1:
ypred = asymp(x, par[0], par[1], par[2])
else:
ypred = asymp2(x.T, par[0], par[1], par[2], par[3], par[4])
r2 = np.corrcoef(ypred, y)[0,1]
print(par, r2)
if xi.shape[1]==1:
ypred = asymp(xall, par[0], par[1], par[2])
else:
ypred = asymp2(xall.T, par[0], par[1], par[2], par[3], par[4])
return par, r2**2, ypred
def asymp(x, alpha, beta, t1):
y = alpha + beta / x**t1
return y
def asymp2(x, alpha, beta, gamma, t1, t2):
y = alpha + beta / x[0]**t1 + gamma / x[1]**t2
return y
def discrimination_threshold(P, x):
P = (P + 1-P[::-1])/2
par0 = np.array([5])
par, mcov = curve_fit(logistic, x, P, par0)
p75 = - np.log(1/0.75 - 1) * par[0]
return p75, logistic(x, par)
# psychometric function
def logistic(x, beta):
return 1. / (1 + np.exp( -x / beta ))
def get_powerlaw(ss, trange):
logss = np.log(np.abs(ss))
y = logss[trange][:,np.newaxis]
trange += 1
nt = trange.size
x = np.concatenate((-np.log(trange)[:,np.newaxis], np.ones((nt,1))), axis=1)
w = 1.0 / trange.astype(np.float32)[:,np.newaxis]
b = np.linalg.solve(x.T @ (x * w), (w * x).T @ y).flatten()
allrange = np.arange(0, ss.size).astype(int) + 1
x = np.concatenate((-np.log(allrange)[:,np.newaxis], np.ones((ss.size,1))), axis=1)
ypred = np.exp((x * b).sum(axis=1))
alpha = b[0]
return alpha,ypred
def shuff_cvPCA(X, nshuff=10):
''' X is 2 x stimuli x neurons '''
nc = min(1024, X.shape[1])
nr = X.shape[0]
ss=np.zeros((nshuff,nc))
for k in range(nshuff):
rperm = np.random.rand(X.shape[1])
iflip = rperm > 0.5
#X0 = np.float64(X.copy())
X0 = np.roll(X, k, axis=0)
for t in range(nr):
X0[t,iflip] = X[(t+1)%nr,iflip]
#X0[1,iflip] = X[0,iflip]
ss[k]=cvPCA(X0)
return ss
def repscvPCA(A,B, nshuff=10):
NC, NN = A.shape
ss = np.zeros((nshuff, NC))
for n in range(nshuff):
ss[n] = scvPCA(A,B)
return ss
def scvPCA(A, B):
""" A, B are neurons x stimuli, NC is # of eigenvalues to return """
NC, NN = A.shape
rperm = np.random.permutation(NN)
A1 = A[:,rperm[:NN//2]]
B1 = B[:,rperm[:NN//2]]
A2 = A[:,rperm[NN//2:]]
B2 = B[:,rperm[NN//2:]]
covAB = A1 @ B1.T
u,s,v = np.linalg.svd(covAB, full_matrices=False)
covAB2 = A2 @ B2.T
e_AB = np.sum(u * (covAB2 @ u), axis=0)
return e_AB
def cvPCA(X):
''' X is 2 x stimuli x neurons '''
from sklearn.decomposition import PCA
nr = X.shape[0]
pca = PCA(n_components=min(1024, X.shape[1])).fit(X[0])
#u = pca.components_.T
#sv = pca.singular_values_
#xproj = X[0].T @ (u / sv)
xproj = pca.components_.T
cproj0 = X[-2] @ xproj
cproj1 = X[-1] @ xproj
ss = (cproj0 * cproj1).sum(axis=0)
return ss
def SVCA(X):
from sklearn.decomposition import PCA
# compute power law
# SVCA
#X -= X.mean(axis=1)[:,np.newaxis]
NN,NT = X.shape
# split cells into test and train
norder = np.random.permutation(NN)
nhalf = int(norder.size/2)
ntrain = norder[:nhalf]
ntest = norder[nhalf:]
# split time into test and train
torder = np.random.permutation(NT)
thalf = int(torder.size/2)
ttrain = torder[:thalf]
ttest = torder[thalf:]
#if ntrain.size > ttrain.size:
# cov = X[np.ix_(ntrain, ttrain)].T @ X[np.ix_(ntest, ttrain)]
# u,sv,v = svdecon(cov, k=min(1024, nhalf-1))
# u = X[np.ix_(ntrain, ttrain)] @ u
# u /= (u**2).sum(axis=0)**0.5
# v = X[np.ix_(ntest, ttrain)] @ v
# v /= (v**2).sum(axis=0)**0.5
#else:
cov = X[np.ix_(ntrain, ttrain)] @ X[np.ix_(ntest, ttrain)].T
u = PCA(n_components=min(1024, nhalf-1), svd_solver='randomized').fit_transform(cov)
u /= (u**2).sum(axis=0)**0.5
v = cov.T @ u
v /= (v**2).sum(axis=0)**0.5
strain = u.T @ X[np.ix_(ntrain,ttest)]
stest = v.T @ X[np.ix_(ntest,ttest)]
# covariance k is uk.T * F * G.T * vk / npts
scov = (strain * stest).mean(axis=1)
varcov = (strain**2 + stest**2).mean(axis=1) / 2
return scov, varcov