def calc_l_r_roots(self, n):
"""Returns the matrix square roots (and inverses) needed to calculate B.
Hermiticity of l[n] and r[n] is used to speed this up.
If an exception occurs here, it is probably because these matrices
are not longer Hermitian (enough).
"""
l_sqrt, evd = m.sqrtmh(self.l[n - 1], ret_evd=True)
l_sqrt_inv = m.invmh(l_sqrt, evd=evd)
r_sqrt, evd = m.sqrtmh(self.r[n], ret_evd=True)
r_sqrt_inv = m.invmh(r_sqrt, evd=evd)
return l_sqrt, r_sqrt, l_sqrt_inv, r_sqrt_inv
def calc_l_r_roots(self, n):
"""Returns the matrix square roots (and inverses) needed to calculate B.
Hermiticity of l[n] and r[n] is used to speed this up.
If an exception occurs here, it is probably because these matrices
are no longer Hermitian (enough).
If l[n] or r[n] are diagonal or the identity, further optimizations are
used.
"""
try:
l_sqrt = self.l[n - 1].sqrt()
except AttributeError:
l_sqrt, evd = mm.sqrtmh(self.l[n - 1], ret_evd=True)
try:
l_sqrt_inv = l_sqrt.inv()
except AttributeError:
l_sqrt_inv = mm.invmh(l_sqrt, evd=evd)
try:
r_sqrt = self.r[n].sqrt()
except AttributeError:
r_sqrt, evd = mm.sqrtmh(self.r[n], ret_evd=True)
try:
r_sqrt_inv = r_sqrt.inv()
except AttributeError:
r_sqrt_inv = mm.invmh(r_sqrt, evd=evd)
if self.sanity_checks:
if not sp.allclose(mm.mmul(l_sqrt, l_sqrt), self.l[n - 1]):
print "Sanity Fail in calc_l_r_roots: Bad l_sqrt_%u" % (n - 1)
if not sp.allclose(mm.mmul(r_sqrt, r_sqrt), self.r[n]):
print "Sanity Fail in calc_l_r_roots: Bad r_sqrt_%u" % (n)
if not sp.allclose(mm.mmul(l_sqrt, l_sqrt_inv), sp.eye(l_sqrt.shape[0])):
print "Sanity Fail in calc_l_r_roots: Bad l_sqrt_inv_%u" % (n - 1)
if not sp.allclose(mm.mmul(r_sqrt, r_sqrt_inv), sp.eye(r_sqrt.shape[0])):
print "Sanity Fail in calc_l_r_roots: Bad r_sqrt_inv_%u" % (n)
return l_sqrt, r_sqrt, l_sqrt_inv, r_sqrt_inv
def calc_l_r_roots(self):
try:
self.l_sqrt = self.l.sqrt()
self.l_sqrt_i = self.l_sqrt.inv()
except AttributeError:
self.l_sqrt, evd = m.sqrtmh(self.l, ret_evd=True)
self.l_sqrt_i = m.invmh(self.l_sqrt, evd=evd)
try:
self.r_sqrt = self.r.sqrt()
self.r_sqrt_i = self.r_sqrt.inv()
except AttributeError:
self.r_sqrt, evd = m.sqrtmh(self.r, ret_evd=True)
self.r_sqrt_i = m.invmh(self.r_sqrt, evd=evd)
if self.sanity_checks:
if not np.allclose(self.l_sqrt.dot(self.l_sqrt), self.l):
print "Sanity check failed: l_sqrt is bad!"
if not np.allclose(self.l_sqrt.dot(self.l_sqrt_i), np.eye(self.D)):
print "Sanity check failed: l_sqrt_i is bad!"
if not np.allclose(self.r_sqrt.dot(self.r_sqrt), self.r):
print "Sanity check failed: r_sqrt is bad!"
if (not np.allclose(self.r_sqrt.dot(self.r_sqrt_i), np.eye(self.D))):
print "Sanity check failed: r_sqrt_i is bad!"
