def log(self, x, y):
xty = utils.transposem(x) @ y
u = utils.logm(xty)
return (u - utils.transposem(u)) / 2.0
def dist(self, x, y, keepdims=False):
x_sqrt_inv = tf.linalg.inv(tf.linalg.sqrtm(x))
log = utils.logm(x_sqrt_inv @ y @ x_sqrt_inv)
return tf.linalg.norm(log, axis=[-2, -1], ord="fro", keepdims=keepdims)
def log(self, x, y):
x_sqrt = tf.linalg.sqrtm(x)
x_sqrt_inv = tf.linalg.inv(x_sqrt)
return x_sqrt @ utils.logm(x_sqrt_inv @ y @ x_sqrt_inv) @ x_sqrt
def pairmean(self, x, y):
return tf.linalg.expm((utils.logm(x) + utils.logm(y)) / 2.0)
def geodesic(self, x, u, t):
return tf.linalg.expm(utils.logm(x) + t * self._diff_log(x, u))
def log(self, x, y):
return self._diff_exp(utils.logm(x), utils.logm(y) - utils.logm(x))
def exp(self, x, u):
return tf.linalg.expm(utils.logm(x) + self._diff_log(x, u))
def dist(self, x, y, keepdims=False):
diff = utils.logm(y) - utils.logm(x)
return tf.linalg.norm(diff,
axis=[-2, -1],
ord="fro",
keepdims=keepdims)