def softmax_loss(x, y):
"""
Computes the loss and gradient for softmax classification.
Inputs:
- x: Input data, of shape (N, C) where x[i, j] is the score for the jth class
for the ith input.
- y: Vector of labels, of shape (N,) where y[i] is the label for x[i] and
0 <= y[i] < C
Returns a tuple of:
- loss: Scalar giving the loss
- dx: Gradient of the loss with respect to x
"""
#np.expand_dims(correct_class_scores, axis = 1)
#probs = np.exp(x - np.max(x, axis=1, keepdims=True))
#print "x.shape", x.shape
#Somehow Buggy. Max doesn't work.
probs = np.exp(x - np.max(x, axis=1))
#probs /= np.expand_dims(np.sum(probs, axis=1), axis = 1)
probs /= np.expand_dims(np.sum(probs, axis=1), axis=1)
N = x.shape[0]
loss = -np.sum(np.log(probs[np.arange(N), y])) / N
dx = probs.copy()
dx[np.arange(N), y] -= 1
dx /= N
return loss, dx
def softmax_loss(x, y):
"""
Computes the loss and gradient for softmax classification.
Inputs:
- x: Input data, of shape (N, C) where x[i, j] is the score for the jth class
for the ith input.
- y: Either of the followings:
- One hot encoding of labels, of shape (N, C)
- Label index of shape (N, ), each y[i] is the label of i^th example
(0 <= y[i] < C)
Returns a tuple of:
- loss: Scalar giving the loss
"""
N = x.shape[0]
C = x.shape[1]
if len(y.shape) == 1:
#convert it to one hot encoding
onehot_y = np.zeros([N, C])
np.onehot_encode(y, onehot_y)
else:
onehot_y = y
probs = x - np.max(x, axis=1, keepdims=True)
loss = -np.sum(probs * onehot_y) / N
loss += np.sum(np.log(np.sum(np.exp(probs), axis=1, keepdims=True))) / N
return loss
def pricepaths(S, tau, r, q, v, M, N):
dt = tau / M
g1 = (r - q - v / 2) * dt
g2 = math.sqrt(v * dt)
aux = math.log(S) + np.cumsum(
g1 + g2 * np.random.randn(M, N, dtype=np.float32), 0)
return np.exp(aux)
def forward(self, X):
"""Forward pass to obtain the action probabilities for each observation in `X`."""
a = np.dot(self.params['w1'], X.T)
h = np.maximum(0, a)
logits = np.dot(h.T, self.params['w2'].T)
p = 1.0 / (1.0 + np.exp(-logits))
return p
def softmax_loss(x, y):
"""
Computes the loss and gradient for softmax classification.
Inputs:
- x: Input data, of shape (N, C) where x[i, j] is the score for the jth class
for the ith input.
- y: Vector of labels, of shape (N,) where y[i] is the label for x[i] and
0 <= y[i] < C
Returns a tuple of:
- loss: Scalar giving the loss
- dx: Gradient of the loss with respect to x
"""
#np.expand_dims(correct_class_scores, axis = 1)
#probs = np.exp(x - np.max(x, axis=1, keepdims=True))
#print "x.shape", x.shape
#Somehow Buggy. Max doesn't work.
probs = np.exp(x - np.max(x, axis=1))
#probs /= np.expand_dims(np.sum(probs, axis=1), axis = 1)
probs /= np.expand_dims(np.sum(probs, axis=1), axis = 1)
N = x.shape[0]
loss = -np.sum(np.log(probs[np.arange(N), y])) / N
dx = probs.copy()
dx[np.arange(N), y] -= 1
dx /= N
return loss, dx
def softmax_loss(x, y):
"""
Computes the loss and gradient for softmax classification.
Inputs:
- x: Input data, of shape (N, C) where x[i, j] is the score for the jth class
for the ith input.
- y: Either of the followings:
- One hot encoding of labels, of shape (N, C)
- Label index of shape (N, ), each y[i] is the label of i^th example
(0 <= y[i] < C)
Returns a tuple of:
- loss: Scalar giving the loss
"""
N = x.shape[0]
C = x.shape[1]
if len(y.shape) == 1:
#convert it to one hot encoding
onehot_y = np.zeros([N, C])
np.onehot_encode(y, onehot_y)
else:
onehot_y = y
probs = x - np.max(x, axis=1, keepdims=True)
loss = -np.sum(probs * onehot_y) / N
loss += np.sum(np.log(np.sum(np.exp(probs), axis=1, keepdims=True))) / N
return loss
def _softmax_loss(self, X, y, *args):
N = X.shape[0]
scores = self._forward(X, *args)
scores = np.exp(scores - np.max(scores, axis=1, keepdims=True))
prob = scores / np.sum(scores, axis=1, keepdims=True)
loss = np.sum(-np.log(prob[np.arange(N), y])) / float(N)
return loss
def forward(self, X):
"""Forward pass to obtain the action probabilities for each observation in `X`."""
a = np.dot(self.params['w1'], X.T)
h = np.maximum(0, a)
logits = np.dot(h.T, self.params['w2'].T)
p = 1.0 / (1.0 + np.exp(-logits))
return p
def probs(scores):
"""
Calculates the probabilities out of a neural networks class scores.
:param scores: The score matrix of form (N x K), where N is the number of observations and K is the number of classes.
:return: The probabilities of the same form as the input scores.
"""
exp_scores = np.exp(scores)
return exp_scores / np.sum(exp_scores, axis=1, keepdims=True)
def softmax(x, y):
import numpy as np
y = y.astype(int)
probs = np.exp(x - np.max(x, axis=1, keepdims=True))
probs /= np.sum(probs, axis=1, keepdims=True)
N = x.shape[0]
loss = -np.sum(np.log(probs[np.arange(N), y])) / N
return loss
def forward(self, X):
a = np.dot(self.params['fc1'], X.T)
h = np.maximum(0, a)
logits = np.dot(h.T, self.params['policy_fc_last'].T)
ps = np.exp(logits - np.max(logits, axis=1, keepdims=True))
ps /= np.sum(ps, axis=1, keepdims=True)
vs = np.dot(h.T, self.params['vf_fc_last'].T) + self.params['vf_fc_last_bias']
return ps, vs
def softmax_crossentropy(x, y):
# x should be (batch, prob)
# y should be (batch, )
x_dev = x - np.max(x, axis=1, keepdims=True) # minpy doesn't support x.max()
sm = x_dev - np.log(np.sum(np.exp(x_dev), axis=1, keepdims=True))
ids = np.arange(0, y.shape[0])*x.shape[1] + y
ce = -np.sum(sm.reshape((sm.shape[0]*sm.shape[1],))[ids])/(1.0*y.shape[0]) # minpy doesn't support -1 in shape inference
return ce
def softmax_probability(p, channel):
N, C = p.shape
p -= np.max(p, axis=1).reshape((N, 1))
code = np.zeros((N, C))
np.onehot_encode(channel, code)
p = np.exp(p)
selected_p = p * code
total_p = np.sum(p, axis=1).reshape((N, 1))
return np.sum(selected_p / total_p, axis=1)
def grad(g):
import numpy as np
y = label.astype(int)
probs = np.exp(x - np.max(x, axis=1, keepdims=True))
probs /= np.sum(probs, axis=1, keepdims=True)
N = x.shape[0]
dx = probs.copy()
dx[np.arange(N), y] -= 1
dx /= N
return dx
def _loss_function(*args):
normal_loss = model.loss(model.forward(X, 'train'), Y)
noisy_output = model.forward(noisy_X, 'train')
noisy_output -= np.max(noisy_output, axis=1).reshape((K, 1))
noisy_output = np.exp(noisy_output)
model_p_noisy_X = noisy_output / np.sum(noisy_output, axis=1).reshape(
(K, 1))
kl = KL(1.0 / N_CLASSES, model_p_noisy_X)
noisy_loss = gamma * np.sum(kl) / float(K)
return gamma * normal_loss + (1 - gamma) * noisy_loss
def sigmoid(x):
"""
Computes the forward pass for a layer of sigmoid units.
Input:
- x: Inputs, of any shape
Returns a tuple of:
- out: Output, of the same shape as x
"""
return 1 / (1 + np.exp(-x))
def sigmoid(x):
"""
Computes the forward pass for a layer of sigmoid units.
Input:
- x: Inputs, of any shape
Returns a tuple of:
- out: Output, of the same shape as x
"""
return 1 / (1 + np.exp(-x))
def collectPhoton(self, x, y, z, react):
self.x = x
self.y = y
self.z = z / self.axialRatio #rescale of z coordinate
self.react = react
self.stepNum = len(x)
self.moleculeNum = x.size / len(x)
#print 'calculating fluorescence...'
self.Imax = 2 * self.power / (np.pi * self.radius**2
) # the center laser intensity (uW/um^2)
self.photonRate = self.Imax * self.Qfluor * self.react / self.ePhoton * self.Qdetect * self.sigma * 1e-12 #(us^-1)
self.singleTrace = np.random.poisson(
self.photonRate * self.dt) * np.exp(
-2 * (self.x**2 + self.y**2 + self.z**2) / self.radius**2)
self.trace = np.sum(self.singleTrace, axis=1)
self.singleTrace_nr = self.photonRate * self.dt * np.exp(
-2 * (self.x**2 + self.y**2 + self.z**2) / self.radius**2)
self.trace_nr = np.sum(self.singleTrace_nr, axis=1)
def softmax_crossentropy(x, y):
EPSI = 1e-6
batch_size, seq_len, prob_dim = x.shape
x = x.reshape((x.shape[0] * x.shape[1], x.shape[2]))
y = y.reshape((y.shape[0] * y.shape[1], ))
#print x.shape, y.shape
# x should be (batch, prob)
# y should be (batch, )
x_dev = x - np.max(x, axis=1,
keepdims=True) # minpy doesn't support x.max()
sm = x_dev - np.log(EPSI + np.sum(np.exp(x_dev), axis=1, keepdims=True))
ids = np.arange(0, y.shape[0]) * seq_len + y
ce = -np.sum(sm.reshape((sm.shape[0] * sm.shape[1], ))[ids]) / (
1.0 * y.shape[0]) # minpy doesn't support -1 in shape inference
return ce
def softmax_loss(x, y):
"""
Computes the loss and gradient for softmax classification.
Inputs:
- x: Input data, of shape (N, C) where x[i, j] is the score for the jth class
for the ith input.
- y: Vector of labels, of shape (N,) where y[i] is the label for x[i] and
0 <= y[i] < C
Returns a tuple of:
- loss: Scalar giving the loss
"""
#TODO: Missing Max Operator
probs = np.exp(x - np.expand_dims(np.max(x, axis=1), axis = 1))
probs = probs / np.expand_dims(np.sum(probs, axis=1), axis = 1)
N = x.shape[0]
loss = -np.sum(np.log(probs[np.arange(N), y])) / N
return loss
def softmax_loss(x, y):
"""
Computes the loss and gradient for softmax classification.
Inputs:
- x: Input data, of shape (N, C) where x[i, j] is the score for the jth class
for the ith input.
- y: Vector of labels, of shape (N,) where y[i] is the label for x[i] and
0 <= y[i] < C
Returns a tuple of:
- loss: Scalar giving the loss
"""
#TODO: Missing Max Operator
probs = np.exp(x - np.expand_dims(np.max(x, axis=1), axis=1))
probs = probs / np.expand_dims(np.sum(probs, axis=1), axis=1)
N = x.shape[0]
loss = -np.sum(np.log(probs[np.arange(N), y])) / N
return loss
def forward(X,y,*p): N, C, H, W = X.shape X = X.reshape((N,C*H*W)) print '>>',X.shape print '>>',p[0].shape first = np.dot( X, p[0] ) + p[1] second = np.dot( first, p[2] ) + p[3] exp = np.exp(second) pred = exp / np.sum(exp) N = X.shape[0] loss = -np.sum( pred[np.arange(N),y] ) return loss
def temporal_softmax_loss(x, y, mask, verbose=False):
"""
A temporal version of softmax loss for use in RNNs. We assume that we are
making predictions over a vocabulary of size V for each timestep of a
timeseries of length T, over a minibatch of size N. The input x gives scores
for all vocabulary elements at all timesteps, and y gives the indices of the
ground-truth element at each timestep. We use a cross-entropy loss at each
timestep, summing the loss over all timesteps and averaging across the
minibatch.
As an additional complication, we may want to ignore the model output at some
timesteps, since sequences of different length may have been combined into a
minibatch and padded with NULL tokens. The optional mask argument tells us
which elements should contribute to the loss.
Inputs:
- x: Input scores, of shape (N, T, V)
- y: Ground-truth indices, of shape (N, T) where each element is in the range
0 <= y[i, t] < V
- mask: Boolean array of shape (N, T) where mask[i, t] tells whether or not
the scores at x[i, t] should contribute to the loss.
Returns a tuple of:
- loss: Scalar giving loss
- dx: Gradient of loss with respect to scores x.
"""
N, T, V = x.shape
x_flat = x.reshape(N * T, V)
y_flat = y.reshape(N * T)
mask_flat = mask.reshape(N * T)
probs = np.exp(x_flat - np.max(x_flat, axis=1, keepdims=True))
probs = probs / np.sum(probs, axis=1, keepdims=True)
loss = -np.sum(mask_flat * np.log(probs[np.arange(N * T), y_flat])) / N
return loss
def temporal_softmax_loss(x, y, mask, verbose=False):
"""
A temporal version of softmax loss for use in RNNs. We assume that we are
making predictions over a vocabulary of size V for each timestep of a
timeseries of length T, over a minibatch of size N. The input x gives scores
for all vocabulary elements at all timesteps, and y gives the indices of the
ground-truth element at each timestep. We use a cross-entropy loss at each
timestep, summing the loss over all timesteps and averaging across the
minibatch.
As an additional complication, we may want to ignore the model output at some
timesteps, since sequences of different length may have been combined into a
minibatch and padded with NULL tokens. The optional mask argument tells us
which elements should contribute to the loss.
Inputs:
- x: Input scores, of shape (N, T, V)
- y: Ground-truth indices, of shape (N, T) where each element is in the range
0 <= y[i, t] < V
- mask: Boolean array of shape (N, T) where mask[i, t] tells whether or not
the scores at x[i, t] should contribute to the loss.
Returns a tuple of:
- loss: Scalar giving loss
- dx: Gradient of loss with respect to scores x.
"""
N, T, V = x.shape
x_flat = x.reshape(N * T, V)
y_flat = y.reshape(N * T)
mask_flat = mask.reshape(N * T)
probs = np.exp(x_flat - np.max(x_flat, axis=1, keepdims=True))
probs = probs / np.sum(probs, axis=1, keepdims=True)
loss = -np.sum(mask_flat * np.log(probs[np.arange(N * T), y_flat])) / N
return loss
def test_ufunc():
x = np.array([-1.2, 1.2])
np.absolute(x)
np.absolute(1.2 + 1j)
x = np.linspace(start=-10, stop=10, num=101)
np.add(1.0, 4.0)
x1 = np.arange(9.0).reshape((3, 3))
x2 = np.arange(3.0)
np.add(x1, x2)
np.arccos([1, -1])
x = np.linspace(-1, 1, num=100)
np.arccosh([np.e, 10.0])
np.arccosh(1)
np.arcsin(0)
np.arcsinh(np.array([np.e, 10.0]))
np.arctan([0, 1])
np.pi / 4
x = np.linspace(-10, 10)
x = np.array([-1, +1, +1, -1])
y = np.array([-1, -1, +1, +1])
np.arctan2(y, x) * 180 / np.pi
np.arctan2([1., -1.], [0., 0.])
np.arctan2([0., 0., np.inf], [+0., -0., np.inf])
np.arctanh([0, -0.5])
np.bitwise_and(13, 17)
np.bitwise_and(14, 13)
# np.binary_repr(12) return str
np.bitwise_and([14, 3], 13)
np.bitwise_and([11, 7], [4, 25])
np.bitwise_and(np.array([2, 5, 255]), np.array([3, 14, 16]))
np.bitwise_and([True, True], [False, True])
np.bitwise_or(13, 16)
# np.binary_repr(29)
np.bitwise_or(32, 2)
np.bitwise_or([33, 4], 1)
np.bitwise_or([33, 4], [1, 2])
np.bitwise_or(np.array([2, 5, 255]), np.array([4, 4, 4]))
# np.array([2, 5, 255]) | np.array([4, 4, 4])
np.bitwise_or(np.array([2, 5, 255, 2147483647], dtype=np.int32),
np.array([4, 4, 4, 2147483647], dtype=np.int32))
np.bitwise_or([True, True], [False, True])
np.bitwise_xor(13, 17)
# np.binary_repr(28)
np.bitwise_xor(31, 5)
np.bitwise_xor([31, 3], 5)
np.bitwise_xor([31, 3], [5, 6])
np.bitwise_xor([True, True], [False, True])
a = np.array([-1.7, -1.5, -0.2, 0.2, 1.5, 1.7, 2.0])
np.ceil(a)
a = np.array([-1.7, -1.5, -0.2, 0.2, 1.5, 1.7, 2.0])
np.trunc(a)
np.cos(np.array([0, np.pi / 2, np.pi]))
np.cosh(0)
x = np.linspace(-4, 4, 1000)
rad = np.arange(12.) * np.pi / 6
np.degrees(rad)
out = np.zeros((rad.shape))
r = np.degrees(rad, out)
# np.all(r == out) return bool
np.rad2deg(np.pi / 2)
np.divide(2.0, 4.0)
x1 = np.arange(9.0).reshape((3, 3))
x2 = np.arange(3.0)
np.divide(2, 4)
np.divide(2, 4.)
np.equal([0, 1, 3], np.arange(3))
np.equal(1, np.ones(1))
x = np.linspace(-2 * np.pi, 2 * np.pi, 100)
np.exp2([2, 3])
np.expm1(1e-10)
np.exp(1e-10) - 1
np.fabs(-1)
np.fabs([-1.2, 1.2])
a = np.array([-1.7, -1.5, -0.2, 0.2, 1.5, 1.7, 2.0])
np.floor(a)
np.floor_divide(7, 3)
np.floor_divide([1., 2., 3., 4.], 2.5)
np.fmod([-3, -2, -1, 1, 2, 3], 2)
np.remainder([-3, -2, -1, 1, 2, 3], 2)
np.fmod([5, 3], [2, 2.])
a = np.arange(-3, 3).reshape(3, 2)
np.fmod(a, [2, 2])
np.greater([4, 2], [2, 2])
a = np.array([4, 2])
b = np.array([2, 2])
a > b
np.greater_equal([4, 2, 1], [2, 2, 2])
np.hypot(3 * np.ones((3, 3)), 4 * np.ones((3, 3)))
np.hypot(3 * np.ones((3, 3)), [4])
np.bitwise_not is np.invert
np.invert(np.array([13], dtype=np.uint8))
# np.binary_repr(242, width=8)
np.invert(np.array([13], dtype=np.uint16))
np.invert(np.array([13], dtype=np.int8))
# np.binary_repr(-14, width=8)
np.invert(np.array([True, False]))
# np.isfinite(1)
# np.isfinite(0)
# np.isfinite(np.nan)
# np.isfinite(np.inf)
# np.isfinite(np.NINF)
x = np.array([-np.inf, 0., np.inf])
y = np.array([2, 2, 2])
np.isfinite(x, y)
# np.isinf(np.inf)
# np.isinf(np.nan)
# np.isinf(np.NINF)
# np.isinf([np.inf, -np.inf, 1.0, np.nan])
x = np.array([-np.inf, 0., np.inf])
y = np.array([2, 2, 2])
# np.isinf(x, y)
# np.isnan(np.nan)
# np.isnan(np.inf)
# np.binary_repr(5)
np.left_shift(5, 2)
# np.binary_repr(20)
np.left_shift(5, [1, 2, 3])
np.less([1, 2], [2, 2])
np.less_equal([4, 2, 1], [2, 2, 2])
x = np.array([0, 1, 2, 2**4])
xi = np.array([0 + 1.j, 1, 2 + 0.j, 4.j])
np.log2(xi)
prob1 = np.log(1e-50)
prob2 = np.log(2.5e-50)
prob12 = np.logaddexp(prob1, prob2)
prob12
np.exp(prob12)
prob1 = np.log2(1e-50)
prob2 = np.log2(2.5e-50)
prob12 = np.logaddexp2(prob1, prob2)
prob1, prob2, prob12
2**prob12
np.log1p(1e-99)
np.log(1 + 1e-99)
# np.logical_and(True, False)
# np.logical_and([True, False], [False, False])
x = np.arange(5)
# np.logical_and(x>1, x<4)
# np.logical_not(3)
# np.logical_not([True, False, 0, 1])
x = np.arange(5)
# np.logical_not(x<3)
# np.logical_or(True, False)
# np.logical_or([True, False], [False, False])
x = np.arange(5)
# np.logical_or(x < 1, x > 3)
# np.logical_xor(True, False)
# np.logical_xor([True, True, False, False], [True, False, True, False])
x = np.arange(5)
# np.logical_xor(x < 1, x > 3)
# np.logical_xor(0, np.eye(2))
np.maximum([2, 3, 4], [1, 5, 2])
# np.maximum([np.nan, 0, np.nan], [0, np.nan, np.nan])
# np.maximum(np.Inf, 1)
np.minimum([2, 3, 4], [1, 5, 2])
# np.minimum([np.nan, 0, np.nan],[0, np.nan, np.nan])
# np.minimum(-np.Inf, 1)
np.fmax([2, 3, 4], [1, 5, 2])
np.fmax(np.eye(2), [0.5, 2])
# np.fmax([np.nan, 0, np.nan],[0, np.nan, np.nan])
np.fmin([2, 3, 4], [1, 5, 2])
np.fmin(np.eye(2), [0.5, 2])
# np.fmin([np.nan, 0, np.nan],[0, np.nan, np.nan])
np.modf([0, 3.5])
np.modf(-0.5)
np.multiply(2.0, 4.0)
x1 = np.arange(9.0).reshape((3, 3))
x2 = np.arange(3.0)
np.multiply(x1, x2)
np.negative([1., -1.])
np.not_equal([1., 2.], [1., 3.])
np.not_equal([1, 2], [[1, 3], [1, 4]])
x1 = range(6)
np.power(x1, 3)
x2 = [1.0, 2.0, 3.0, 3.0, 2.0, 1.0]
np.power(x1, x2)
x2 = np.array([[1, 2, 3, 3, 2, 1], [1, 2, 3, 3, 2, 1]])
np.power(x1, x2)
deg = np.arange(12.) * 30.
np.radians(deg)
out = np.zeros((deg.shape))
ret = np.radians(deg, out)
ret is out
np.deg2rad(180)
np.reciprocal(2.)
np.reciprocal([1, 2., 3.33])
np.remainder([4, 7], [2, 3])
np.remainder(np.arange(7), 5)
# np.binary_repr(10)
np.right_shift(10, 1)
# np.binary_repr(5)
np.right_shift(10, [1, 2, 3])
a = np.array([-1.7, -1.5, -0.2, 0.2, 1.5, 1.7, 2.0])
np.rint(a)
np.sign([-5., 4.5])
np.sign(0)
# np.sign(5-2j)
# np.signbit(-1.2)
np.signbit(np.array([1, -2.3, 2.1]))
np.copysign(1.3, -1)
np.copysign([-1, 0, 1], -1.1)
np.copysign([-1, 0, 1], np.arange(3) - 1)
np.sin(np.pi / 2.)
np.sin(np.array((0., 30., 45., 60., 90.)) * np.pi / 180.)
x = np.linspace(-np.pi, np.pi, 201)
np.sinh(0)
# np.sinh(np.pi*1j/2)
np.sqrt([1, 4, 9])
np.sqrt([4, -1, -3 + 4J])
np.cbrt([1, 8, 27])
np.square([-1j, 1])
np.subtract(1.0, 4.0)
x1 = np.arange(9.0).reshape((3, 3))
x2 = np.arange(3.0)
np.subtract(x1, x2)
np.tan(np.array([-pi, pi / 2, pi]))
np.tanh((0, np.pi * 1j, np.pi * 1j / 2))
x = np.arange(5)
np.true_divide(x, 4)
x = np.arange(9)
y1, y2 = np.frexp(x)
y1 * 2**y2
np.ldexp(5, np.arange(4))
x = np.arange(6)
np.ldexp(*np.frexp(x))
def sigmoid(x):
return 1 / (1 + np.exp(-x))
def sigmoid(x):
return 1.0/(1.0 + mp.exp(-x))
def U(beta):
return mp.sum(mp.log(1 + mp.exp(mp.dot(X, beta))))-mp.dot(y.T,(mp.dot(X,beta)))+(0.5/alpha)*mp.sum(beta**2)
def logsumexp(X, axis=1):
max_X = np.max(X)
return max_X + np.log(np.sum(np.exp(X - max_X), axis=axis, keepdims=True))
def logsumexp(X, axis=1):
max_X = np.max(X)
return max_X + np.log(np.sum(np.exp(X - max_X), axis=axis, keepdims=True))
def sigmoid(X):
return 1 / (1 + np.exp(-X))
def logsoftmax(x, valid_idx):
x[np.array(valid_idx)] += 1e6
x_max = np.max(x)
return x - x_max - np.log(np.sum(np.exp(x - x_max)))
def forward(self, inputs, *args):
return 1 / (1 + np.exp(-inputs))
def logsumexp(X, axis, keepdims=False):
max_X = np.max(X)
return max_X + np.log(np.sum(np.exp(X - max_X), axis=axis, keepdims=keepdims))
def sigmoid(x):
return 1/(1+np.exp(-x))
def test_ufunc():
x = np.array([-1.2, 1.2])
np.absolute(x)
np.absolute(1.2 + 1j)
x = np.linspace(start=-10, stop=10, num=101)
np.add(1.0, 4.0)
x1 = np.arange(9.0).reshape((3, 3))
x2 = np.arange(3.0)
np.add(x1, x2)
np.arccos([1, -1])
x = np.linspace(-1, 1, num=100)
np.arccosh([np.e, 10.0])
np.arccosh(1)
np.arcsin(0)
np.arcsinh(np.array([np.e, 10.0]))
np.arctan([0, 1])
np.pi/4
x = np.linspace(-10, 10)
x = np.array([-1, +1, +1, -1])
y = np.array([-1, -1, +1, +1])
np.arctan2(y, x) * 180 / np.pi
np.arctan2([1., -1.], [0., 0.])
np.arctan2([0., 0., np.inf], [+0., -0., np.inf])
np.arctanh([0, -0.5])
np.bitwise_and(13, 17)
np.bitwise_and(14, 13)
# np.binary_repr(12) return str
np.bitwise_and([14,3], 13)
np.bitwise_and([11,7], [4,25])
np.bitwise_and(np.array([2,5,255]), np.array([3,14,16]))
np.bitwise_and([True, True], [False, True])
np.bitwise_or(13, 16)
# np.binary_repr(29)
np.bitwise_or(32, 2)
np.bitwise_or([33, 4], 1)
np.bitwise_or([33, 4], [1, 2])
np.bitwise_or(np.array([2, 5, 255]), np.array([4, 4, 4]))
# np.array([2, 5, 255]) | np.array([4, 4, 4])
np.bitwise_or(np.array([2, 5, 255, 2147483647], dtype=np.int32),
np.array([4, 4, 4, 2147483647], dtype=np.int32))
np.bitwise_or([True, True], [False, True])
np.bitwise_xor(13, 17)
# np.binary_repr(28)
np.bitwise_xor(31, 5)
np.bitwise_xor([31,3], 5)
np.bitwise_xor([31,3], [5,6])
np.bitwise_xor([True, True], [False, True])
a = np.array([-1.7, -1.5, -0.2, 0.2, 1.5, 1.7, 2.0])
np.ceil(a)
a = np.array([-1.7, -1.5, -0.2, 0.2, 1.5, 1.7, 2.0])
np.trunc(a)
np.cos(np.array([0, np.pi/2, np.pi]))
np.cosh(0)
x = np.linspace(-4, 4, 1000)
rad = np.arange(12.)*np.pi/6
np.degrees(rad)
out = np.zeros((rad.shape))
r = np.degrees(rad, out)
# np.all(r == out) return bool
np.rad2deg(np.pi/2)
np.divide(2.0, 4.0)
x1 = np.arange(9.0).reshape((3, 3))
x2 = np.arange(3.0)
np.divide(2, 4)
np.divide(2, 4.)
np.equal([0, 1, 3], np.arange(3))
np.equal(1, np.ones(1))
x = np.linspace(-2*np.pi, 2*np.pi, 100)
np.exp2([2, 3])
np.expm1(1e-10)
np.exp(1e-10) - 1
np.fabs(-1)
np.fabs([-1.2, 1.2])
a = np.array([-1.7, -1.5, -0.2, 0.2, 1.5, 1.7, 2.0])
np.floor(a)
np.floor_divide(7,3)
np.floor_divide([1., 2., 3., 4.], 2.5)
np.fmod([-3, -2, -1, 1, 2, 3], 2)
np.remainder([-3, -2, -1, 1, 2, 3], 2)
np.fmod([5, 3], [2, 2.])
a = np.arange(-3, 3).reshape(3, 2)
np.fmod(a, [2,2])
np.greater([4,2],[2,2])
a = np.array([4,2])
b = np.array([2,2])
a > b
np.greater_equal([4, 2, 1], [2, 2, 2])
np.hypot(3*np.ones((3, 3)), 4*np.ones((3, 3)))
np.hypot(3*np.ones((3, 3)), [4])
np.bitwise_not is np.invert
np.invert(np.array([13], dtype=np.uint8))
# np.binary_repr(242, width=8)
np.invert(np.array([13], dtype=np.uint16))
np.invert(np.array([13], dtype=np.int8))
# np.binary_repr(-14, width=8)
np.invert(np.array([True, False]))
# np.isfinite(1)
# np.isfinite(0)
# np.isfinite(np.nan)
# np.isfinite(np.inf)
# np.isfinite(np.NINF)
x = np.array([-np.inf, 0., np.inf])
y = np.array([2, 2, 2])
np.isfinite(x, y)
# np.isinf(np.inf)
# np.isinf(np.nan)
# np.isinf(np.NINF)
# np.isinf([np.inf, -np.inf, 1.0, np.nan])
x = np.array([-np.inf, 0., np.inf])
y = np.array([2, 2, 2])
# np.isinf(x, y)
# np.isnan(np.nan)
# np.isnan(np.inf)
# np.binary_repr(5)
np.left_shift(5, 2)
# np.binary_repr(20)
np.left_shift(5, [1,2,3])
np.less([1, 2], [2, 2])
np.less_equal([4, 2, 1], [2, 2, 2])
x = np.array([0, 1, 2, 2**4])
xi = np.array([0+1.j, 1, 2+0.j, 4.j])
np.log2(xi)
prob1 = np.log(1e-50)
prob2 = np.log(2.5e-50)
prob12 = np.logaddexp(prob1, prob2)
prob12
np.exp(prob12)
prob1 = np.log2(1e-50)
prob2 = np.log2(2.5e-50)
prob12 = np.logaddexp2(prob1, prob2)
prob1, prob2, prob12
2**prob12
np.log1p(1e-99)
np.log(1 + 1e-99)
# np.logical_and(True, False)
# np.logical_and([True, False], [False, False])
x = np.arange(5)
# np.logical_and(x>1, x<4)
# np.logical_not(3)
# np.logical_not([True, False, 0, 1])
x = np.arange(5)
# np.logical_not(x<3)
# np.logical_or(True, False)
# np.logical_or([True, False], [False, False])
x = np.arange(5)
# np.logical_or(x < 1, x > 3)
# np.logical_xor(True, False)
# np.logical_xor([True, True, False, False], [True, False, True, False])
x = np.arange(5)
# np.logical_xor(x < 1, x > 3)
# np.logical_xor(0, np.eye(2))
np.maximum([2, 3, 4], [1, 5, 2])
# np.maximum([np.nan, 0, np.nan], [0, np.nan, np.nan])
# np.maximum(np.Inf, 1)
np.minimum([2, 3, 4], [1, 5, 2])
# np.minimum([np.nan, 0, np.nan],[0, np.nan, np.nan])
# np.minimum(-np.Inf, 1)
np.fmax([2, 3, 4], [1, 5, 2])
np.fmax(np.eye(2), [0.5, 2])
# np.fmax([np.nan, 0, np.nan],[0, np.nan, np.nan])
np.fmin([2, 3, 4], [1, 5, 2])
np.fmin(np.eye(2), [0.5, 2])
# np.fmin([np.nan, 0, np.nan],[0, np.nan, np.nan])
np.modf([0, 3.5])
np.modf(-0.5)
np.multiply(2.0, 4.0)
x1 = np.arange(9.0).reshape((3, 3))
x2 = np.arange(3.0)
np.multiply(x1, x2)
np.negative([1.,-1.])
np.not_equal([1.,2.], [1., 3.])
np.not_equal([1, 2], [[1, 3],[1, 4]])
x1 = range(6)
np.power(x1, 3)
x2 = [1.0, 2.0, 3.0, 3.0, 2.0, 1.0]
np.power(x1, x2)
x2 = np.array([[1, 2, 3, 3, 2, 1], [1, 2, 3, 3, 2, 1]])
np.power(x1, x2)
deg = np.arange(12.) * 30.
np.radians(deg)
out = np.zeros((deg.shape))
ret = np.radians(deg, out)
ret is out
np.deg2rad(180)
np.reciprocal(2.)
np.reciprocal([1, 2., 3.33])
np.remainder([4, 7], [2, 3])
np.remainder(np.arange(7), 5)
# np.binary_repr(10)
np.right_shift(10, 1)
# np.binary_repr(5)
np.right_shift(10, [1,2,3])
a = np.array([-1.7, -1.5, -0.2, 0.2, 1.5, 1.7, 2.0])
np.rint(a)
np.sign([-5., 4.5])
np.sign(0)
# np.sign(5-2j)
# np.signbit(-1.2)
np.signbit(np.array([1, -2.3, 2.1]))
np.copysign(1.3, -1)
np.copysign([-1, 0, 1], -1.1)
np.copysign([-1, 0, 1], np.arange(3)-1)
np.sin(np.pi/2.)
np.sin(np.array((0., 30., 45., 60., 90.)) * np.pi / 180. )
x = np.linspace(-np.pi, np.pi, 201)
np.sinh(0)
# np.sinh(np.pi*1j/2)
np.sqrt([1,4,9])
np.sqrt([4, -1, -3+4J])
np.cbrt([1,8,27])
np.square([-1j, 1])
np.subtract(1.0, 4.0)
x1 = np.arange(9.0).reshape((3, 3))
x2 = np.arange(3.0)
np.subtract(x1, x2)
np.tan(np.array([-pi,pi/2,pi]))
np.tanh((0, np.pi*1j, np.pi*1j/2))
x = np.arange(5)
np.true_divide(x, 4)
x = np.arange(9)
y1, y2 = np.frexp(x)
y1 * 2**y2
np.ldexp(5, np.arange(4))
x = np.arange(6)
np.ldexp(*np.frexp(x))
def sigmoid(x):
return 1 / (1 - np.exp(-1 * x))
def nonlinearity(self, x):
return 1 / (1 + np.exp(-x))
def dU(beta):
return mp.dot(X.T, (mp.exp(mp.dot(X,beta))/(1+mp.exp(mp.dot(X,beta))) - y)) + beta/alpha
def forward(self, inputs, *args):
return 1 / (1 + np.exp(-inputs))
def predict(w, x):
a = np.exp(np.dot(x, w))
a_sum = np.sum(a, axis=1, keepdims=True)
prob = a / a_sum
return prob
def check_fn(x):
y = x + 1
print(mp.exp(y))
return mp.sum(2 * y)
def predict(w, x):
a = np.exp(np.dot(x, w))
a_sum = np.sum(a, axis=1, keepdims=True)
prob = a / a_sum
return prob