def cost(Weights, X, Y, lambda_param=1.0):
# Number of samples
m = Y.dims()[0]
dim0 = Weights.dims()[0]
dim1 = Weights.dims()[1] if len(Weights.dims()) > 1 else None
dim2 = Weights.dims()[2] if len(Weights.dims()) > 2 else None
dim3 = Weights.dims()[3] if len(Weights.dims()) > 3 else None
# Make the lambda corresponding to Weights(0) == 0
lambdat = af.constant(lambda_param, dim0, dim1, dim2, dim3)
# No regularization for bias weights
lambdat[0, :] = 0
# Get the prediction
H = predict_prob(X, Weights)
# Cost of misprediction
Jerr = -1 * af.sum(Y * af.log(H) + (1 - Y) * af.log(1 - H), dim=0)
# Regularization cost
Jreg = 0.5 * af.sum(lambdat * Weights * Weights, dim=0)
# Total cost
J = (Jerr + Jreg) / m
# Find the gradient of cost
D = (H - Y)
dJ = (af.matmulTN(X, D) + lambdat * Weights) / m
return J, dJ
def train(self, X, Y):
# Initialize parameters to 0
self.__weights = af.constant(0, X.dims()[1], Y.dims()[1])
# self.__weights = af.randu(X.dims()[1], Y.dims()[1])
for i in range(self.__maxiter):
P = self.predict_proba(X)
err = Y - P
mean_abs_err = af.mean(af.abs(err))
if mean_abs_err < self.__maxerr:
break
if self.__verbose and ((i + 1) % 25 == 0):
print("Iter: {}, Err: {}".format(i+1, mean_abs_err))
self.__weights = self.__weights + self.__alpha * af.matmulTN(X, err)
def _cost(self, Weights: af.Array, X: af.Array, Y: af.Array,
reg_constant: float, penalty: str) -> (af.Array, af.Array):
# Number of samples
m = Y.dims()[0]
dim0 = Weights.dims()[0]
dim1 = Weights.dims()[1] if len(Weights.dims()) > 1 else None
dim2 = Weights.dims()[2] if len(Weights.dims()) > 2 else None
dim3 = Weights.dims()[3] if len(Weights.dims()) > 3 else None
# Make the lambda corresponding to Weights(0) == 0
lambdat = af.constant(reg_constant, dim0, dim1, dim2, dim3)
# No regularization for bias weights
lambdat[0, :] = 0
# Get the prediction
H = self._predict_proba(X, Weights)
# Cost of misprediction
Jerr = -1 * af.sum(Y * af.log(H) + (1 - Y) * af.log(1 - H), dim=0)
# Regularization cost
penalty_norm = None
if penalty == 'l2':
penalty_norm = Weights * Weights
else:
penalty_norm = af.abs(Weights)
Jreg = 0.5 * af.sum(lambdat * penalty_norm, dim=0)
# Total cost
J = (Jerr + Jreg) / m
# Find the gradient of cost
D = (H - Y)
dJ = (af.matmulTN(X, D) + lambdat * Weights) / m
return J, dJ
def simple_lapack(verbose=False):
display_func = _util.display_func(verbose)
print_func = _util.print_func(verbose)
a = af.randu(5, 5)
l, u, p = af.lu(a)
display_func(l)
display_func(u)
display_func(p)
p = af.lu_inplace(a, "full")
display_func(a)
display_func(p)
a = af.randu(5, 3)
q, r, t = af.qr(a)
display_func(q)
display_func(r)
display_func(t)
af.qr_inplace(a)
display_func(a)
a = af.randu(5, 5)
a = af.matmulTN(a, a.copy()) + 10 * af.identity(5, 5)
R, info = af.cholesky(a)
display_func(R)
print_func(info)
af.cholesky_inplace(a)
display_func(a)
a = af.randu(5, 5)
ai = af.inverse(a)
display_func(a)
display_func(ai)
x0 = af.randu(5, 3)
b = af.matmul(a, x0)
x1 = af.solve(a, b)
display_func(x0)
display_func(x1)
p = af.lu_inplace(a)
x2 = af.solve_lu(a, p, b)
display_func(x2)
print_func(af.rank(a))
print_func(af.det(a))
print_func(af.norm(a, af.NORM.EUCLID))
print_func(af.norm(a, af.NORM.MATRIX_1))
print_func(af.norm(a, af.NORM.MATRIX_INF))
print_func(af.norm(a, af.NORM.MATRIX_L_PQ, 1, 1))
a = af.randu(10, 10)
display_func(a)
u, s, vt = af.svd(a)
display_func(af.matmul(af.matmul(u, af.diag(s, 0, False)), vt))
u, s, vt = af.svd_inplace(a)
display_func(af.matmul(af.matmul(u, af.diag(s, 0, False)), vt))
def simple_lapack(verbose=False):
display_func = _util.display_func(verbose)
print_func = _util.print_func(verbose)
a = af.randu(5,5)
l,u,p = af.lu(a)
display_func(l)
display_func(u)
display_func(p)
p = af.lu_inplace(a, "full")
display_func(a)
display_func(p)
a = af.randu(5,3)
q,r,t = af.qr(a)
display_func(q)
display_func(r)
display_func(t)
af.qr_inplace(a)
display_func(a)
a = af.randu(5, 5)
a = af.matmulTN(a, a) + 10 * af.identity(5,5)
R,info = af.cholesky(a)
display_func(R)
print_func(info)
af.cholesky_inplace(a)
display_func(a)
a = af.randu(5,5)
ai = af.inverse(a)
display_func(a)
display_func(ai)
x0 = af.randu(5, 3)
b = af.matmul(a, x0)
x1 = af.solve(a, b)
display_func(x0)
display_func(x1)
p = af.lu_inplace(a)
x2 = af.solve_lu(a, p, b)
display_func(x2)
print_func(af.rank(a))
print_func(af.det(a))
print_func(af.norm(a, af.NORM.EUCLID))
print_func(af.norm(a, af.NORM.MATRIX_1))
print_func(af.norm(a, af.NORM.MATRIX_INF))
print_func(af.norm(a, af.NORM.MATRIX_L_PQ, 1, 1))
af.display(p) a = af.randu(5, 3) q, r, t = af.qr(a) af.display(q) af.display(r) af.display(t) af.qr_inplace(a) af.display(a) a = af.randu(5, 5) a = af.matmulTN(a, a) + 10 * af.identity(5, 5) R, info = af.cholesky(a) af.display(R) print(info) af.cholesky_inplace(a) af.display(a) a = af.randu(5, 5) ai = af.inverse(a) af.display(a) af.display(ai) x0 = af.randu(5, 3)
