inverse_st about deep_complex_networks

[obilaniu]

What would be incorrect with it?

Just for fun I tried creating a PSD matrix $V$ and then verifying that $VV^{-\frac{1}{2}}V^{-\frac{1}{2}} = I$, and it jolly well does:

>>> import numpy as np
>>> x = np.random.normal(size=(2,2))
>>> V = x.dot(x.T)
>>> V
array([[ 0.48580582, -1.27191924],
       [-1.27191924,  3.64642338]])
>>> Vrr, Vri, Vii = float(V[0,0]), float(V[0,1]), float(V[1,1])
>>> tau = Vrr + Vii
>>> delta = (Vrr * Vii) - (Vri ** 2)
>>> s = np.sqrt(delta)
>>> t = np.sqrt(tau + 2 * s)
>>> inverse_st = 1.0 / (s * t)
>>> Wrr = (Vii + s) * inverse_st
>>> Wii = (Vrr + s) * inverse_st
>>> Wri = -Vri * inverse_st
>>> W = np.array([[Wrr, Wri], [Wri, Wii]])
>>> W
array([[ 4.64616077,  1.46332366],
       [ 1.46332366,  1.00991855]])
>>> V.dot(W.dot(W))
array([[  1.00000000e+00,   3.02928156e-16],
       [ -4.25075250e-16,   1.00000000e+00]])

[gudovskiy]

@obilaniu Your solution is right. It is funny, but indeed 1/(st) = t / ( (Vrr + s)(Vii + s) - (Vri**2) ).