def mult(M1, M2):
assert (M1.m == M2.n)
c = M1.m
M = [[Interval(0) for _ in range(M2.m)] for _ in range(M1.n)]
for i in range(M1.n):
for j in range(M2.m):
for k in range(c):
p = Interval.mult(M1.matrix[i][k], M2.matrix[k][j])
M[i][j] = Interval.add(M[i][j], p)
return InterMatrix(M)
def ik(x, y):
s = In(0.0)
assert (len(x) == len(y)), "Not same length"
n = len(x)
for i in range(n):
diff = In.add(x[i], In.neg(y[i]))
sq = square.image(diff)
s = In.add(s, sq)
s = In.mult(In(-0.5), s)
return exp.image(s)
def test(n=50, noise=0.001, x=3, y=4):
X = [[np.random.rand() * 10, np.random.rand() * 10] for i in range(n)]
Y = [f(a) for a in X]
gp = InterGP(k, ik)
gp.fit(X, Y)
xx = [In(x), In(y)]
x = [In.fromNoise(x, noise), In.fromNoise(y, noise)]
a = gp.predict(xx)
b = gp.predict(x)
print("\nRESULTS:")
print(a)
print(b)
def predict(self, x):
interX = [[In(yy) for yy in y] for y in self.X]
K_star = self.generateMatrixCov([x], interX, True)
print("K star", K_star)
k_double_star = self.ik(x, x)
print("K double star", k_double_star)
interInvK = InterMatrix.createFromMatrix(self.inv_K)
interInvKf = InterMatrix.createFromMatrix(self.inv_K_f)
print("interInvKf", interInvKf)
mean = InterMatrix.mult(K_star, interInvKf)
K_star_T = K_star.transpose()
prod = InterMatrix.mult(interInvK, K_star_T)
prod = InterMatrix.mult(K_star, prod)
prod = prod.neg()
var = In.add(k_double_star, prod.matrix[0][0])
# var = k_double_star - K_star * self.inv_K * (K_star.T)
return (mean, var)
def image(self, inter):
xs = [inter.a, inter.b]
xs += [x for x in self.extrema if inter.contains(x)]
ys = [self.f(x) for x in xs]
m = min(ys)
M = max(ys)
return Interval(m, M)
def add(M1, M2):
assert (M1.n == M2.n)
assert (M1.m == M2.m)
M = [[0 for _ in range(M1.m)] for _ in range(M1.n)]
for i in range(M1.n):
for j in range(M1.m):
M[i][j] = Interval.add(M1.matrix[i][j], M2.matrix[i][j])
return InterMatrix(M)
def createFromMatrix(M):
n = np.shape(M)[0]
m = np.shape(M)[1]
iM = [[Interval(M[i, j]) for j in range(m)] for i in range(n)]
return InterMatrix(iM)
def neg(self):
N = [[Interval.neg(self.matrix[i][j])
for j in range(self.m)] for i in range(self.n)]
return InterMatrix(N)
def zeros(n, m):
M = [[Interval(0.0) for j in range(m)] for i in range(n)]
return InterMatrix(M)