def getP(self, Xmask, F, X_big):
size = F.shape[0]
Q = np.zeros((size, size))
P = np.zeros((size, size))
for i in range(size):
for j in range(size):
Q[i, j] = self.norm(F[i] - F[j])
P = (2 * Xmask * X_big - self.rho * Q) / (2 * Xmask + np.full(
(size, size), self.alpha))
return P
def test_creation():
a = np.array([1, 2, 3])
print(a)
b = np.array([[1, 2, 3], [2, 3, 4]])
print(b)
a = np.zeros((2, 3))
print(a)
b = np.ones((2, 3))
print(b)
c = np.full((2, 3), 7)
print(c)
d = np.empty((2, 3))
print(d)
def gaussian_random(structure,mode,weight,bias,lower,upper):
param = []
drelu_pos = []
for layer in range(len(structure) - 1):
param.append(np.random.normal(0, weight, (structure[layer],structure[layer+1])))
param.append(np.full(structure[layer + 1], bias))
for layer in range(len(structure) - 2):
if mode[layer] == 'drelu':
param.append(fixed_bound(structure[layer + 1], lower))
param.append(fixed_bound(structure[layer + 1], upper))
drelu_pos.append(layer)
return param, drelu_pos
def backpropagation(x, s, y, hidden_layers, wh, bh, w_out, b_out, alpha):
"""
Performs the backpropagation of a neural network.
:param x: The input data of form (N x D), where N is the number of observations an D is the dimensionality.
:param s: The score matrix of form (N x K), where N is the number of observations and K is the number of classes.
:param y: The ground truth labels for each observation.
:param hidden_layers: An array containing the values of each hidden layer as a vector.
:param wh: The weights of each hidden layer connection as array. Each weight is a matrix of (H_i-1 ... H_i),
where H_i-1 is the size of the previous hidden layer (or the input layer) and H_i is the size of the corresponding
hidden layer..
:param bh: The biases of each hidden layer as array. Each bias is a vector of the same length of the corresponding
hidden layer.
:param w_out: The weight of the output layer as matrix of form (H x K),
where H is the size of the last hidden layer and K is the number of classes.
:param b_out: The bias of the output layer as vector of length K, where K is the number of classes.
:param alpha: The factor by which negative inputs are scaled in ReLU activations. Set to 0 to avoid leaky ReLU.
:return: The backpropagation returns relevant gradients as a tuple containing the following values:
* An array containing the gradients for the connection weights of each hidden layer of the same form as `wh`.
* An array containing the gradients for the biases of each hidden layer of the same form as `bh`.
* An array containing the gradients for the connection weights of the output layer of the same form as `w_out`.
* An array containing the gradients for the biases of the output layer of the same form as `b_out`.
"""
dscores = cross_entropy_loss_gradient(s, y)
dw_out2 = hidden_layers[-1].T.dot(dscores)
db_out2 = np.sum(dscores, axis=0, keepdims=True)
dhiddens = {}
dwh2 = [np.full(w_i.shape, .0) for w_i in wh]
dbh2 = [np.empty(b_i.shape) for b_i in bh]
for h in range(len(hidden_layers) - 1, -1, -1):
if h == len(hidden_layers) - 1:
dhidden = dscores.dot(w_out.T)
else:
dhidden = dhiddens[h + 1].dot(wh[h + 1].T)
dhidden[hidden_layers[h] < 0] = alpha
dhiddens[h] = dhidden
if h == 0:
dwh2[h] = x.T.dot(dhidden)
else:
dwh2[h] = hidden_layers[h - 1].T.dot(dhidden)
dbh2[h] = np.sum(dhidden, axis=0, keepdims=True)
dw_out2 += lambda_ * w_out
return dwh2, dbh2, dw_out2, db_out2
def test_numeric():
# 'newaxis', 'ndarray', 'flatiter', 'nditer', 'nested_iters', 'ufunc',
# 'arange', 'array', 'zeros', 'count_nonzero', 'empty', 'broadcast',
# 'dtype', 'fromstring', 'fromfile', 'frombuffer', 'int_asbuffer',
# 'where', 'argwhere', 'copyto', 'concatenate', 'fastCopyAndTranspose',
# 'lexsort', 'set_numeric_ops', 'can_cast', 'promote_types',
# 'min_scalar_type', 'result_type', 'asarray', 'asanyarray',
# 'ascontiguousarray', 'asfortranarray', 'isfortran', 'empty_like',
# 'zeros_like', 'ones_like', 'correlate', 'convolve', 'inner', 'dot',
# 'einsum', 'outer', 'vdot', 'alterdot', 'restoredot', 'roll',
# 'rollaxis', 'moveaxis', 'cross', 'tensordot', 'array2string',
# 'get_printoptions', 'set_printoptions', 'array_repr', 'array_str',
# 'set_string_function', 'little_endian', 'require', 'fromiter',
# 'array_equal', 'array_equiv', 'indices', 'fromfunction', 'isclose', 'load',
# 'loads', 'isscalar', 'binary_repr', 'base_repr', 'ones', 'identity',
# 'allclose', 'compare_chararrays', 'putmask', 'seterr', 'geterr',
# 'setbufsize', 'getbufsize', 'seterrcall', 'geterrcall', 'errstate',
# 'flatnonzero', 'Inf', 'inf', 'infty', 'Infinity', 'nan', 'NaN', 'False_',
# 'True_', 'bitwise_not', 'full', 'full_like', 'matmul'
x = np.arange(6)
x = x.reshape((2, 3))
np.zeros_like(x)
y = np.arange(3, dtype=np.float)
np.zeros_like(y)
np.ones(5)
np.ones((5, ), dtype=np.int)
np.ones((2, 1))
s = (2, 2)
np.ones(s)
x = np.arange(6)
x = x.reshape((2, 3))
np.ones_like(x)
y = np.arange(3, dtype=np.float)
np.ones_like(y)
np.full((2, 2), np.inf)
x = np.arange(6, dtype=np.int)
np.full_like(x, 1)
np.full_like(x, 0.1)
np.full_like(y, 0.1)
np.count_nonzero(np.eye(4))
np.count_nonzero([[0, 1, 7, 0, 0], [3, 0, 0, 2, 19]])
np.count_nonzero([[0, 1, 7, 0, 0], [3, 0, 0, 2, 19]], axis=0)
np.count_nonzero([[0, 1, 7, 0, 0], [3, 0, 0, 2, 19]], axis=1)
a = [1, 2]
np.asarray(a)
a = np.array([1, 2])
np.asarray(a) is a
a = np.array([1, 2], dtype=np.float32)
np.asarray(a, dtype=np.float32) is a
np.asarray(a, dtype=np.float64) is a
np.asarray(a) is a
np.asanyarray(a) is a
a = [1, 2]
np.asanyarray(a)
np.asanyarray(a) is a
x = np.arange(6).reshape(2, 3)
np.ascontiguousarray(x, dtype=np.float32)
x = np.arange(6).reshape(2, 3)
y = np.asfortranarray(x)
x = np.arange(6).reshape(2, 3)
y = np.require(x, dtype=np.float32, requirements=['A', 'O', 'W', 'F'])
a = np.array([[1, 2, 3], [4, 5, 6]], order='C')
np.isfortran(a)
b = np.array([[1, 2, 3], [4, 5, 6]], order='FORTRAN')
np.isfortran(b)
a = np.array([[1, 2, 3], [4, 5, 6]], order='C')
np.isfortran(a)
b = a.T
np.isfortran(b)
np.isfortran(np.array([1, 2], order='FORTRAN'))
x = np.arange(6).reshape(2, 3)
np.argwhere(x > 1)
x = np.arange(-2, 3)
np.flatnonzero(x)
np.correlate([1, 2, 3], [0, 1, 0.5])
np.correlate([1, 2, 3], [0, 1, 0.5], "same")
np.correlate([1, 2, 3], [0, 1, 0.5], "full")
np.correlate([1 + 1j, 2, 3 - 1j], [0, 1, 0.5j], 'full')
np.correlate([0, 1, 0.5j], [1 + 1j, 2, 3 - 1j], 'full')
np.convolve([1, 2, 3], [0, 1, 0.5])
np.convolve([1, 2, 3], [0, 1, 0.5], 'same')
np.convolve([1, 2, 3], [0, 1, 0.5], 'valid')
rl = np.outer(np.ones((5, )), np.linspace(-2, 2, 5))
# im = np.outer(1j*np.linspace(2, -2, 5), np.ones((5,)))
# grid = rl + im
x = np.array(['a', 'b', 'c'], dtype=object)
np.outer(x, [1, 2, 3])
a = np.arange(60.).reshape(3, 4, 5)
b = np.arange(24.).reshape(4, 3, 2)
c = np.tensordot(a, b, axes=([1, 0], [0, 1]))
c.shape
# A slower but equivalent way of computing the same...
d = np.zeros((5, 2))
a = np.array(range(1, 9))
A = np.array(('a', 'b', 'c', 'd'), dtype=object)
x = np.arange(10)
np.roll(x, 2)
x2 = np.reshape(x, (2, 5))
np.roll(x2, 1)
np.roll(x2, 1, axis=0)
np.roll(x2, 1, axis=1)
a = np.ones((3, 4, 5, 6))
np.rollaxis(a, 3, 1).shape
np.rollaxis(a, 2).shape
np.rollaxis(a, 1, 4).shape
x = np.zeros((3, 4, 5))
np.moveaxis(x, 0, -1).shape
np.moveaxis(x, -1, 0).shape
np.transpose(x).shape
np.moveaxis(x, [0, 1], [-1, -2]).shape
np.moveaxis(x, [0, 1, 2], [-1, -2, -3]).shape
x = [1, 2, 3]
y = [4, 5, 6]
np.cross(x, y)
x = [1, 2]
y = [4, 5, 6]
np.cross(x, y)
x = [1, 2, 0]
y = [4, 5, 6]
np.cross(x, y)
x = [1, 2]
y = [4, 5]
np.cross(x, y)
x = np.array([[1, 2, 3], [4, 5, 6]])
y = np.array([[4, 5, 6], [1, 2, 3]])
np.cross(x, y)
np.cross(x, y, axisc=0)
x = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
y = np.array([[7, 8, 9], [4, 5, 6], [1, 2, 3]])
np.cross(x, y)
np.cross(x, y, axisa=0, axisb=0)
# np.array_repr(np.array([1,2]))
# np.array_repr(np.ma.array([0.]))
# np.array_repr(np.array([], np.int32))
x = np.array([1e-6, 4e-7, 2, 3])
# np.array_repr(x, precision=6, suppress_small=True)
# np.array_str(np.arange(3))
a = np.arange(10)
x = np.arange(4)
np.set_string_function(lambda x: 'random', repr=False)
grid = np.indices((2, 3))
grid.shape
grid[0] # row indices
grid[1] # column indices
x = np.arange(20).reshape(5, 4)
row, col = np.indices((2, 3))
x[row, col]
np.fromfunction(lambda i, j: i == j, (3, 3), dtype=int)
np.fromfunction(lambda i, j: i + j, (3, 3), dtype=int)
np.isscalar(3.1)
np.isscalar([3.1])
np.isscalar(False)
# np.binary_repr(3)
# np.binary_repr(-3)
# np.binary_repr(3, width=4)
# np.binary_repr(-3, width=3)
# np.binary_repr(-3, width=5)
# np.base_repr(5)
# np.base_repr(6, 5)
# np.base_repr(7, base=5, padding=3)
# np.base_repr(10, base=16)
# np.base_repr(32, base=16)
np.identity(3)
np.allclose([1e10, 1e-7], [1.00001e10, 1e-8])
np.allclose([1e10, 1e-8], [1.00001e10, 1e-9])
np.allclose([1e10, 1e-8], [1.0001e10, 1e-9])
# np.allclose([1.0, np.nan], [1.0, np.nan])
# np.allclose([1.0, np.nan], [1.0, np.nan], equal_nan=True)
np.isclose([1e10, 1e-7], [1.00001e10, 1e-8])
np.isclose([1e10, 1e-8], [1.00001e10, 1e-9])
np.isclose([1e10, 1e-8], [1.0001e10, 1e-9])
# np.isclose([1.0, np.nan], [1.0, np.nan])
# np.isclose([1.0, np.nan], [1.0, np.nan], equal_nan=True)
np.array_equal([1, 2], [1, 2])
np.array_equal(np.array([1, 2]), np.array([1, 2]))
np.array_equal([1, 2], [1, 2, 3])
np.array_equal([1, 2], [1, 4])
np.array_equiv([1, 2], [1, 2])
np.array_equiv([1, 2], [1, 3])
np.array_equiv([1, 2], [[1, 2], [1, 2]])
np.array_equiv([1, 2], [[1, 2, 1, 2], [1, 2, 1, 2]])
np.array_equiv([1, 2], [[1, 2], [1, 3]])
def test_numeric():
# 'newaxis', 'ndarray', 'flatiter', 'nditer', 'nested_iters', 'ufunc',
# 'arange', 'array', 'zeros', 'count_nonzero', 'empty', 'broadcast',
# 'dtype', 'fromstring', 'fromfile', 'frombuffer', 'int_asbuffer',
# 'where', 'argwhere', 'copyto', 'concatenate', 'fastCopyAndTranspose',
# 'lexsort', 'set_numeric_ops', 'can_cast', 'promote_types',
# 'min_scalar_type', 'result_type', 'asarray', 'asanyarray',
# 'ascontiguousarray', 'asfortranarray', 'isfortran', 'empty_like',
# 'zeros_like', 'ones_like', 'correlate', 'convolve', 'inner', 'dot',
# 'einsum', 'outer', 'vdot', 'alterdot', 'restoredot', 'roll',
# 'rollaxis', 'moveaxis', 'cross', 'tensordot', 'array2string',
# 'get_printoptions', 'set_printoptions', 'array_repr', 'array_str',
# 'set_string_function', 'little_endian', 'require', 'fromiter',
# 'array_equal', 'array_equiv', 'indices', 'fromfunction', 'isclose', 'load',
# 'loads', 'isscalar', 'binary_repr', 'base_repr', 'ones', 'identity',
# 'allclose', 'compare_chararrays', 'putmask', 'seterr', 'geterr',
# 'setbufsize', 'getbufsize', 'seterrcall', 'geterrcall', 'errstate',
# 'flatnonzero', 'Inf', 'inf', 'infty', 'Infinity', 'nan', 'NaN', 'False_',
# 'True_', 'bitwise_not', 'full', 'full_like', 'matmul'
x = np.arange(6)
x = x.reshape((2, 3))
np.zeros_like(x)
y = np.arange(3, dtype=np.float)
np.zeros_like(y)
np.ones(5)
np.ones((5,), dtype=np.int)
np.ones((2, 1))
s = (2,2)
np.ones(s)
x = np.arange(6)
x = x.reshape((2, 3))
np.ones_like(x)
y = np.arange(3, dtype=np.float)
np.ones_like(y)
np.full((2, 2), np.inf)
x = np.arange(6, dtype=np.int)
np.full_like(x, 1)
np.full_like(x, 0.1)
np.full_like(y, 0.1)
np.count_nonzero(np.eye(4))
np.count_nonzero([[0,1,7,0,0],[3,0,0,2,19]])
np.count_nonzero([[0,1,7,0,0],[3,0,0,2,19]], axis=0)
np.count_nonzero([[0,1,7,0,0],[3,0,0,2,19]], axis=1)
a = [1, 2]
np.asarray(a)
a = np.array([1, 2])
np.asarray(a) is a
a = np.array([1, 2], dtype=np.float32)
np.asarray(a, dtype=np.float32) is a
np.asarray(a, dtype=np.float64) is a
np.asarray(a) is a
np.asanyarray(a) is a
a = [1, 2]
np.asanyarray(a)
np.asanyarray(a) is a
x = np.arange(6).reshape(2,3)
np.ascontiguousarray(x, dtype=np.float32)
x = np.arange(6).reshape(2,3)
y = np.asfortranarray(x)
x = np.arange(6).reshape(2,3)
y = np.require(x, dtype=np.float32, requirements=['A', 'O', 'W', 'F'])
a = np.array([[1, 2, 3], [4, 5, 6]], order='C')
np.isfortran(a)
b = np.array([[1, 2, 3], [4, 5, 6]], order='FORTRAN')
np.isfortran(b)
a = np.array([[1, 2, 3], [4, 5, 6]], order='C')
np.isfortran(a)
b = a.T
np.isfortran(b)
np.isfortran(np.array([1, 2], order='FORTRAN'))
x = np.arange(6).reshape(2,3)
np.argwhere(x>1)
x = np.arange(-2, 3)
np.flatnonzero(x)
np.correlate([1, 2, 3], [0, 1, 0.5])
np.correlate([1, 2, 3], [0, 1, 0.5], "same")
np.correlate([1, 2, 3], [0, 1, 0.5], "full")
np.correlate([1+1j, 2, 3-1j], [0, 1, 0.5j], 'full')
np.correlate([0, 1, 0.5j], [1+1j, 2, 3-1j], 'full')
np.convolve([1, 2, 3], [0, 1, 0.5])
np.convolve([1,2,3],[0,1,0.5], 'same')
np.convolve([1,2,3],[0,1,0.5], 'valid')
rl = np.outer(np.ones((5,)), np.linspace(-2, 2, 5))
# im = np.outer(1j*np.linspace(2, -2, 5), np.ones((5,)))
# grid = rl + im
x = np.array(['a', 'b', 'c'], dtype=object)
np.outer(x, [1, 2, 3])
a = np.arange(60.).reshape(3,4,5)
b = np.arange(24.).reshape(4,3,2)
c = np.tensordot(a,b, axes=([1,0],[0,1]))
c.shape
# A slower but equivalent way of computing the same...
d = np.zeros((5,2))
a = np.array(range(1, 9))
A = np.array(('a', 'b', 'c', 'd'), dtype=object)
x = np.arange(10)
np.roll(x, 2)
x2 = np.reshape(x, (2,5))
np.roll(x2, 1)
np.roll(x2, 1, axis=0)
np.roll(x2, 1, axis=1)
a = np.ones((3,4,5,6))
np.rollaxis(a, 3, 1).shape
np.rollaxis(a, 2).shape
np.rollaxis(a, 1, 4).shape
x = np.zeros((3, 4, 5))
np.moveaxis(x, 0, -1).shape
np.moveaxis(x, -1, 0).shape
np.transpose(x).shape
np.moveaxis(x, [0, 1], [-1, -2]).shape
np.moveaxis(x, [0, 1, 2], [-1, -2, -3]).shape
x = [1, 2, 3]
y = [4, 5, 6]
np.cross(x, y)
x = [1, 2]
y = [4, 5, 6]
np.cross(x, y)
x = [1, 2, 0]
y = [4, 5, 6]
np.cross(x, y)
x = [1,2]
y = [4,5]
np.cross(x, y)
x = np.array([[1,2,3], [4,5,6]])
y = np.array([[4,5,6], [1,2,3]])
np.cross(x, y)
np.cross(x, y, axisc=0)
x = np.array([[1,2,3], [4,5,6], [7, 8, 9]])
y = np.array([[7, 8, 9], [4,5,6], [1,2,3]])
np.cross(x, y)
np.cross(x, y, axisa=0, axisb=0)
# np.array_repr(np.array([1,2]))
# np.array_repr(np.ma.array([0.]))
# np.array_repr(np.array([], np.int32))
x = np.array([1e-6, 4e-7, 2, 3])
# np.array_repr(x, precision=6, suppress_small=True)
# np.array_str(np.arange(3))
a = np.arange(10)
x = np.arange(4)
np.set_string_function(lambda x:'random', repr=False)
grid = np.indices((2, 3))
grid.shape
grid[0] # row indices
grid[1] # column indices
x = np.arange(20).reshape(5, 4)
row, col = np.indices((2, 3))
x[row, col]
np.fromfunction(lambda i, j: i == j, (3, 3), dtype=int)
np.fromfunction(lambda i, j: i + j, (3, 3), dtype=int)
np.isscalar(3.1)
np.isscalar([3.1])
np.isscalar(False)
# np.binary_repr(3)
# np.binary_repr(-3)
# np.binary_repr(3, width=4)
# np.binary_repr(-3, width=3)
# np.binary_repr(-3, width=5)
# np.base_repr(5)
# np.base_repr(6, 5)
# np.base_repr(7, base=5, padding=3)
# np.base_repr(10, base=16)
# np.base_repr(32, base=16)
np.identity(3)
np.allclose([1e10,1e-7], [1.00001e10,1e-8])
np.allclose([1e10,1e-8], [1.00001e10,1e-9])
np.allclose([1e10,1e-8], [1.0001e10,1e-9])
# np.allclose([1.0, np.nan], [1.0, np.nan])
# np.allclose([1.0, np.nan], [1.0, np.nan], equal_nan=True)
np.isclose([1e10,1e-7], [1.00001e10,1e-8])
np.isclose([1e10,1e-8], [1.00001e10,1e-9])
np.isclose([1e10,1e-8], [1.0001e10,1e-9])
# np.isclose([1.0, np.nan], [1.0, np.nan])
# np.isclose([1.0, np.nan], [1.0, np.nan], equal_nan=True)
np.array_equal([1, 2], [1, 2])
np.array_equal(np.array([1, 2]), np.array([1, 2]))
np.array_equal([1, 2], [1, 2, 3])
np.array_equal([1, 2], [1, 4])
np.array_equiv([1, 2], [1, 2])
np.array_equiv([1, 2], [1, 3])
np.array_equiv([1, 2], [[1, 2], [1, 2]])
np.array_equiv([1, 2], [[1, 2, 1, 2], [1, 2, 1, 2]])
np.array_equiv([1, 2], [[1, 2], [1, 3]])
def fixed_bound(structure, value):
return np.full(structure, value)
def prepare_nodes_array(count, initialization=0):
# weight, bias, metabolism
return np.full((count, 3))
