from math import sqrt,log
import numpy as np
from matplotlib import pyplot
import rft1d


def here_cca_single_node(y, x):
	N          = y.shape[0]
	X,Y        = np.matrix(x.T).T, np.matrix(y)
	Z          = np.matrix(np.ones(N)).T
	Rz         = np.eye(N) - Z*np.linalg.inv(Z.T*Z)*Z.T
	XStar      = Rz * X
	YStar      = Rz * Y
	p,r        = 1.0, 1.0   #nContrasts, nNuisanceFactors
	m          = N - p - r
	H          = YStar.T * XStar  *  np.linalg.inv( XStar.T * XStar  )  * XStar.T * YStar / p
	W          = YStar.T  * (np.eye(nResponses)  -  XStar*np.linalg.inv(XStar.T*XStar)*XStar.T) * YStar  / m
	#estimate maximum canonical correlation:
	F          = np.linalg.inv(W)*H
	ff         = np.linalg.eigvals(  F  )
	fmax       = float( np.real(ff.max()) )
	r2max      = fmax * p  / (m + fmax*p)
	rmax       = sqrt(r2max)
	### compute test statistic:
	p,m        = float(N), float(y.shape[1])
	x2         = -(p-1-0.5*(m+2)) * log(  (1-rmax**2) )
	return x2


def here_cca(y, x):
	Q  = y.shape[1]
	z  = [here_cca_single_node(y[:,q,:], x)   for q in range(Q)]
	return np.array(z)




#(0) Set parameters:
np.random.seed(123456789)
nResponses  = 20  #20 or more for convergence
nNodes      = 101
nComponents = 2
nIterations = 100  #1000 or more for convergence
FWHM        = 15.0
W0          = np.eye(nComponents)
### derived parameters:
df          = nComponents
x           = np.linspace(0, 1, nResponses) #independent variable



#(1) Generate Gaussian 1D fields, compute test stat, store field maximum:
X2          = []
generator   = rft1d.random.GeneratorMulti1D(nResponses, nNodes, nComponents, FWHM, W0)
for i in range(nIterations):
	y       = generator.generate_sample()
	chi2    = here_cca(y, x)
	X2.append( chi2.max()  )
X2          = np.asarray(X2)


#(2) Compute survival function (SF) for the field maximumimum:
heights     = np.linspace(7, 15, 21)
sf          = np.array(  [ (X2>h).mean()  for h in heights]  )
sfE         = rft1d.chi2.sf(heights, df, nNodes, FWHM)  #theoretical
sf0D        = rft1d.chi2.sf0d(heights, df) #theoretical (0D)


#(3) Plot results:
pyplot.close('all')
name        = 'Times New Roman'
ax          = pyplot.axes()
ax.plot(heights, sf,   'o',  label='Simulated')
ax.plot(heights, sfE,  '-',  label='Theoretical')
ax.plot(heights, sf0D, 'r-', label='Theoretical (0D)')
ax.set_xlabel(r'$u$', size=20, usetex=True)
ax.set_ylabel(r'$P (\chi^2_\mathrm{max} > u)$', size=20, usetex=True)
leg = ax.legend()
pyplot.setp( leg.get_texts(), name=name)
ax.set_title("CCA validation (1D)", size=20, name=name)
# pyplot.show()