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 _soft_l_value_demapper_af(rx_symbs, M, snr, bits_map):
num_bits = int(np.log2(M))
N = rx_symbs.shape[0]
k = bits_map.shape[1]
sig = af.np_to_af_array(rx_symbs)
bit_mtx = af.moddims(af.np_to_af_array(bits_map), 1, num_bits, k, 2)
tmp = af.sum(af.broadcast(lambda x,y: af.exp(-snr*af.abs(x-y)**2), bit_mtx, sig), dim=2)
lvl = af.log(tmp[:,:,:,1]) - af.log(tmp[:,:,:,0])
return np.array(lvl)
def log(x):
if isinstance(x, afnumpy.ndarray):
s = arrayfire.log(x.d_array)
return afnumpy.ndarray(x.shape,
dtype=pu.typemap(s.dtype()),
af_array=s)
else:
return numpy.log(x)
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 log_likelihoods(self,
*,
outputs: Outputs,
inputs: Inputs,
timeout: float = None,
iterations: int = None) -> CallResult[Sequence[float]]:
sk_inputs, columns_to_use = self._get_columns_to_fit(
inputs, self.hyperparams)
af_inputs = af.from_ndarray(sk_inputs.values)
weight_by_dist = self._weights == 'distance'
dist_type = self._get_dist_type(self.hyperparams['dist_type'])
probs = self._predict_proba(af_inputs, self._data, self._labels, \
self.hyperparams['n_neighbors'], dist_type, \
weight_by_dist)
return CallResult(af.log(probs).to_ndarray())
def black_scholes(S, X, R, V, T):
# S = Underlying stock price
# X = Strike Price
# R = Risk free rate of interest
# V = Volatility
# T = Time to maturity
d1 = af.log(S / X)
d1 = d1 + (R + (V * V) * 0.5) * T
d1 = d1 / (V * af.sqrt(T))
d2 = d1 - (V * af.sqrt(T))
cnd_d1 = cnd(d1)
cnd_d2 = cnd(d2)
C = S * cnd_d1 - (X * af.exp((-R) * T) * cnd_d2)
P = X * af.exp((-R) * T) * (1 - cnd_d2) - (S * (1 -cnd_d1))
return (C, P)
def black_scholes(S, X, R, V, T):
# S = Underlying stock price
# X = Strike Price
# R = Risk free rate of interest
# V = Volatility
# T = Time to maturity
d1 = af.log(S / X)
d1 = d1 + (R + (V * V) * 0.5) * T
d1 = d1 / (V * af.sqrt(T))
d2 = d1 - (V * af.sqrt(T))
cnd_d1 = cnd(d1)
cnd_d2 = cnd(d2)
C = S * cnd_d1 - (X * af.exp((-R) * T) * cnd_d2)
P = X * af.exp((-R) * T) * (1 - cnd_d2) - (S * (1 - cnd_d1))
return (C, P)
def simple_arith(verbose=False):
display_func = _util.display_func(verbose)
print_func = _util.print_func(verbose)
a = af.randu(3, 3)
b = af.constant(4, 3, 3)
display_func(a)
display_func(b)
c = a + b
d = a
d += b
display_func(c)
display_func(d)
display_func(a + 2)
display_func(3 + a)
c = a - b
d = a
d -= b
display_func(c)
display_func(d)
display_func(a - 2)
display_func(3 - a)
c = a * b
d = a
d *= b
display_func(c * 2)
display_func(3 * d)
display_func(a * 2)
display_func(3 * a)
c = a / b
d = a
d /= b
display_func(c / 2.0)
display_func(3.0 / d)
display_func(a / 2)
display_func(3 / a)
c = a % b
d = a
d %= b
display_func(c % 2.0)
display_func(3.0 % d)
display_func(a % 2)
display_func(3 % a)
c = a**b
d = a
d **= b
display_func(c**2.0)
display_func(3.0**d)
display_func(a**2)
display_func(3**a)
display_func(a < b)
display_func(a < 0.5)
display_func(0.5 < a)
display_func(a <= b)
display_func(a <= 0.5)
display_func(0.5 <= a)
display_func(a > b)
display_func(a > 0.5)
display_func(0.5 > a)
display_func(a >= b)
display_func(a >= 0.5)
display_func(0.5 >= a)
display_func(a != b)
display_func(a != 0.5)
display_func(0.5 != a)
display_func(a == b)
display_func(a == 0.5)
display_func(0.5 == a)
a = af.randu(3, 3, dtype=af.Dtype.u32)
b = af.constant(4, 3, 3, dtype=af.Dtype.u32)
display_func(a & b)
display_func(a & 2)
c = a
c &= 2
display_func(c)
display_func(a | b)
display_func(a | 2)
c = a
c |= 2
display_func(c)
display_func(a >> b)
display_func(a >> 2)
c = a
c >>= 2
display_func(c)
display_func(a << b)
display_func(a << 2)
c = a
c <<= 2
display_func(c)
display_func(-a)
display_func(+a)
display_func(~a)
display_func(a)
display_func(af.cast(a, af.Dtype.c32))
display_func(af.maxof(a, b))
display_func(af.minof(a, b))
display_func(af.rem(a, b))
a = af.randu(3, 3) - 0.5
b = af.randu(3, 3) - 0.5
display_func(af.abs(a))
display_func(af.arg(a))
display_func(af.sign(a))
display_func(af.round(a))
display_func(af.trunc(a))
display_func(af.floor(a))
display_func(af.ceil(a))
display_func(af.hypot(a, b))
display_func(af.sin(a))
display_func(af.cos(a))
display_func(af.tan(a))
display_func(af.asin(a))
display_func(af.acos(a))
display_func(af.atan(a))
display_func(af.atan2(a, b))
c = af.cplx(a)
d = af.cplx(a, b)
display_func(c)
display_func(d)
display_func(af.real(d))
display_func(af.imag(d))
display_func(af.conjg(d))
display_func(af.sinh(a))
display_func(af.cosh(a))
display_func(af.tanh(a))
display_func(af.asinh(a))
display_func(af.acosh(a))
display_func(af.atanh(a))
a = af.abs(a)
b = af.abs(b)
display_func(af.root(a, b))
display_func(af.pow(a, b))
display_func(af.pow2(a))
display_func(af.sigmoid(a))
display_func(af.exp(a))
display_func(af.expm1(a))
display_func(af.erf(a))
display_func(af.erfc(a))
display_func(af.log(a))
display_func(af.log1p(a))
display_func(af.log10(a))
display_func(af.log2(a))
display_func(af.sqrt(a))
display_func(af.cbrt(a))
a = af.round(5 * af.randu(3, 3) - 1)
b = af.round(5 * af.randu(3, 3) - 1)
display_func(af.factorial(a))
display_func(af.tgamma(a))
display_func(af.lgamma(a))
display_func(af.iszero(a))
display_func(af.isinf(a / b))
display_func(af.isnan(a / a))
a = af.randu(5, 1)
b = af.randu(1, 5)
c = af.broadcast(lambda x, y: x + y, a, b)
display_func(a)
display_func(b)
display_func(c)
@af.broadcast
def test_add(aa, bb):
return aa + bb
display_func(test_add(a, b))
def log(x):
if isinstance(x, afnumpy.ndarray):
s = arrayfire.log(x.d_array)
return afnumpy.ndarray(x.shape, dtype=pu.typemap(s.dtype()), af_array=s)
else:
return numpy.log(x)
def predict_log_prob(X, Weights):
return af.log(predict_prob(X, Weights))
af.display(af.tanh(a)) af.display(af.asinh(a)) af.display(af.acosh(a)) af.display(af.atanh(a)) a = af.abs(a) b = af.abs(b) af.display(af.root(a, b)) af.display(af.pow(a, b)) af.display(af.pow2(a)) af.display(af.exp(a)) af.display(af.expm1(a)) af.display(af.erf(a)) af.display(af.erfc(a)) af.display(af.log(a)) af.display(af.log1p(a)) af.display(af.log10(a)) af.display(af.log2(a)) af.display(af.sqrt(a)) af.display(af.cbrt(a)) a = af.round(5 * af.randu(3, 3) - 1) b = af.round(5 * af.randu(3, 3) - 1) af.display(af.factorial(a)) af.display(af.tgamma(a)) af.display(af.lgamma(a)) af.display(af.iszero(a)) af.display(af.isinf(a / b)) af.display(af.isnan(a / a))
af.display(af.tanh(a)) af.display(af.asinh(a)) af.display(af.acosh(a)) af.display(af.atanh(a)) a = af.abs(a) b = af.abs(b) af.display(af.root(a, b)) af.display(af.pow(a, b)) af.display(af.pow2(a)) af.display(af.exp(a)) af.display(af.expm1(a)) af.display(af.erf(a)) af.display(af.erfc(a)) af.display(af.log(a)) af.display(af.log1p(a)) af.display(af.log10(a)) af.display(af.log2(a)) af.display(af.sqrt(a)) af.display(af.cbrt(a)) a = af.round(5 * af.randu(3,3) - 1) b = af.round(5 * af.randu(3,3) - 1) af.display(af.factorial(a)) af.display(af.tgamma(a)) af.display(af.lgamma(a)) af.display(af.iszero(a)) af.display(af.isinf(a/b)) af.display(af.isnan(a/a))
def gamma_rand_marsaglia_and_tsang_arrayfire(alpha: float,
lambda_: float,
n: int) \
-> af.array:
random_numbers = af.constant(0, n, dtype=Dtype.f32)
# Gamma(alpha, lambda) generator using Marsaglia and Tsang method
# Algorithm 4.33
if alpha >= 1.0:
d = alpha - 1 / 3
c = 1.0 / np.sqrt(9.0 * d)
number_generated = 0
number_generated_total = 0
while number_generated < n:
number_left = n - number_generated
z = af.randn(number_left, dtype=Dtype.f32)
y = (1.0 + c * z)
v = y * y * y
accept_index_1 = ((z >= -1.0 / c) & (v > 0.0))
z_accept_1 = z[accept_index_1]
# del z
v_accept_1 = v[accept_index_1]
# del v
u_accept_1 = af.randu(v_accept_1.elements(), dtype=Dtype.f32)
# del U
accept_index_2 = \
u_accept_1 < af.exp((0.5 * z_accept_1 * z_accept_1 + d - d * v_accept_1 + d * af.log(v_accept_1)))
x_accept = d * v_accept_1[accept_index_2] / lambda_
number_accept = x_accept.elements()
random_numbers[number_generated:np.minimum(n, number_generated + number_accept)] = \
x_accept[0:np.minimum(number_left, number_accept)]
number_generated += number_accept
number_generated_total += number_left
if GPUOptions.verbose:
print(f"Acceptance ratio = {n/number_generated_total}")
else:
random_numbers = gamma_rand_marsaglia_and_tsang_arrayfire(
alpha + 1, lambda_, n)
random_numbers *= af.randu(n, dtype=Dtype.f32)**(1.0 / alpha)
return random_numbers
def xlogy(x, y):
return x * af.log(y)
def predict_log_proba(self, X):
return af.log(self.predict_proba(X))
def simple_arith(verbose = False):
display_func = _util.display_func(verbose)
print_func = _util.print_func(verbose)
a = af.randu(3,3,dtype=af.Dtype.u32)
b = af.constant(4, 3, 3, dtype=af.Dtype.u32)
display_func(a)
display_func(b)
c = a + b
d = a
d += b
display_func(c)
display_func(d)
display_func(a + 2)
display_func(3 + a)
c = a - b
d = a
d -= b
display_func(c)
display_func(d)
display_func(a - 2)
display_func(3 - a)
c = a * b
d = a
d *= b
display_func(c * 2)
display_func(3 * d)
display_func(a * 2)
display_func(3 * a)
c = a / b
d = a
d /= b
display_func(c / 2.0)
display_func(3.0 / d)
display_func(a / 2)
display_func(3 / a)
c = a % b
d = a
d %= b
display_func(c % 2.0)
display_func(3.0 % d)
display_func(a % 2)
display_func(3 % a)
c = a ** b
d = a
d **= b
display_func(c ** 2.0)
display_func(3.0 ** d)
display_func(a ** 2)
display_func(3 ** a)
display_func(a < b)
display_func(a < 0.5)
display_func(0.5 < a)
display_func(a <= b)
display_func(a <= 0.5)
display_func(0.5 <= a)
display_func(a > b)
display_func(a > 0.5)
display_func(0.5 > a)
display_func(a >= b)
display_func(a >= 0.5)
display_func(0.5 >= a)
display_func(a != b)
display_func(a != 0.5)
display_func(0.5 != a)
display_func(a == b)
display_func(a == 0.5)
display_func(0.5 == a)
display_func(a & b)
display_func(a & 2)
c = a
c &= 2
display_func(c)
display_func(a | b)
display_func(a | 2)
c = a
c |= 2
display_func(c)
display_func(a >> b)
display_func(a >> 2)
c = a
c >>= 2
display_func(c)
display_func(a << b)
display_func(a << 2)
c = a
c <<= 2
display_func(c)
display_func(-a)
display_func(+a)
display_func(~a)
display_func(a)
display_func(af.cast(a, af.Dtype.c32))
display_func(af.maxof(a,b))
display_func(af.minof(a,b))
display_func(af.rem(a,b))
a = af.randu(3,3) - 0.5
b = af.randu(3,3) - 0.5
display_func(af.abs(a))
display_func(af.arg(a))
display_func(af.sign(a))
display_func(af.round(a))
display_func(af.trunc(a))
display_func(af.floor(a))
display_func(af.ceil(a))
display_func(af.hypot(a, b))
display_func(af.sin(a))
display_func(af.cos(a))
display_func(af.tan(a))
display_func(af.asin(a))
display_func(af.acos(a))
display_func(af.atan(a))
display_func(af.atan2(a, b))
c = af.cplx(a)
d = af.cplx(a,b)
display_func(c)
display_func(d)
display_func(af.real(d))
display_func(af.imag(d))
display_func(af.conjg(d))
display_func(af.sinh(a))
display_func(af.cosh(a))
display_func(af.tanh(a))
display_func(af.asinh(a))
display_func(af.acosh(a))
display_func(af.atanh(a))
a = af.abs(a)
b = af.abs(b)
display_func(af.root(a, b))
display_func(af.pow(a, b))
display_func(af.pow2(a))
display_func(af.exp(a))
display_func(af.expm1(a))
display_func(af.erf(a))
display_func(af.erfc(a))
display_func(af.log(a))
display_func(af.log1p(a))
display_func(af.log10(a))
display_func(af.log2(a))
display_func(af.sqrt(a))
display_func(af.cbrt(a))
a = af.round(5 * af.randu(3,3) - 1)
b = af.round(5 * af.randu(3,3) - 1)
display_func(af.factorial(a))
display_func(af.tgamma(a))
display_func(af.lgamma(a))
display_func(af.iszero(a))
display_func(af.isinf(a/b))
display_func(af.isnan(a/a))
a = af.randu(5, 1)
b = af.randu(1, 5)
c = af.broadcast(lambda x,y: x+y, a, b)
display_func(a)
display_func(b)
display_func(c)
@af.broadcast
def test_add(aa, bb):
return aa + bb
display_func(test_add(a, b))
def _predict_log_proba(self, X: af.Array, Weights: af.Array) -> af.Array:
return af.log(self._predict_proba(X, Weights))