def train(arduino_serial, is_right_side):
training_values = collect_points(arduino_serial, is_right_side)
[M1, M2, M3, M4] = populate_matrices(training_values)
# find inverses using singular value decomposition
M1inv = linalg.pinv2(M1)
M2inv = linalg.pinv2(M2)
M3inv = linalg.pinv2(M3)
M4inv = linalg.pinv2(M4)
print M1inv.shape
print x.shape
# find coefficients
xCoeff1 = M1inv * x
xCoeff2 = M2inv * x
xCoeff3 = M3inv * x
xCoeff4 = M4inv * x
print xCoeff1
yCoeff1 = M1inv * y
yCoeff2 = M2inv * y
yCoeff3 = M3inv * y
yCoeff4 = M4inv * y
print yCoeff1
return [xCoeff1, xCoeff2, xCoeff3, xCoeff4, yCoeff1, yCoeff2, yCoeff3, yCoeff4]
def _nipals_twoblocks_inner_loop(X, Y, mode="A", max_iter=500, tol=1e-06,
norm_y_weights=False):
"""Inner loop of the iterative NIPALS algorithm.
Provides an alternative to the svd(X'Y); returns the first left and right
singular vectors of X'Y. See PLS for the meaning of the parameters. It is
similar to the Power method for determining the eigenvectors and
eigenvalues of a X'Y.
"""
y_score = Y[:, [0]]
x_weights_old = 0
ite = 1
X_pinv = Y_pinv = None
eps = np.finfo(X.dtype).eps
# Inner loop of the Wold algo.
while True:
# 1.1 Update u: the X weights
if mode == "B":
if X_pinv is None:
# We use slower pinv2 (same as np.linalg.pinv) for stability
# reasons
X_pinv = pinv2(X, check_finite=False)
x_weights = np.dot(X_pinv, y_score)
else: # mode A
# Mode A regress each X column on y_score
x_weights = np.dot(X.T, y_score) / np.dot(y_score.T, y_score)
# If y_score only has zeros x_weights will only have zeros. In
# this case add an epsilon to converge to a more acceptable
# solution
if np.dot(x_weights.T, x_weights) < eps:
x_weights += eps
# 1.2 Normalize u
x_weights /= np.sqrt(np.dot(x_weights.T, x_weights)) + eps
# 1.3 Update x_score: the X latent scores
x_score = np.dot(X, x_weights)
# 2.1 Update y_weights
if mode == "B":
if Y_pinv is None:
Y_pinv = pinv2(Y, check_finite=False) # compute once pinv(Y)
y_weights = np.dot(Y_pinv, x_score)
else:
# Mode A regress each Y column on x_score
y_weights = np.dot(Y.T, x_score) / np.dot(x_score.T, x_score)
# 2.2 Normalize y_weights
if norm_y_weights:
y_weights /= np.sqrt(np.dot(y_weights.T, y_weights)) + eps
# 2.3 Update y_score: the Y latent scores
y_score = np.dot(Y, y_weights) / (np.dot(y_weights.T, y_weights) + eps)
# y_score = np.dot(Y, y_weights) / np.dot(y_score.T, y_score) ## BUG
x_weights_diff = x_weights - x_weights_old
if np.dot(x_weights_diff.T, x_weights_diff) < tol or Y.shape[1] == 1:
break
if ite == max_iter:
warnings.warn('Maximum number of iterations reached',
ConvergenceWarning)
break
x_weights_old = x_weights
ite += 1
return x_weights, y_weights, ite
def add_fit(self,X):
n_samples = X.shape[0]
# old
first = safe_sparse_dot(self.hidden_activations_.T, self.hidden_activations_)
M = pinv2(first+1*np.identity(first.shape[0]))
beta = self.coef_output_
# new
H = self._get_hidden_activations(X)
# update
first = pinv2(1*np.identity(n_samples)+safe_sparse_dot(safe_sparse_dot(H,M),H.T))
second = safe_sparse_dot(safe_sparse_dot(safe_sparse_dot(safe_sparse_dot(M,H.T),first),H),M)
M = M - second
self.coef_output_ = beta + safe_sparse_dot(safe_sparse_dot(M,H.T),(X - safe_sparse_dot(H,beta)))
def _compute_eloreta_inv(G, W, n_orient, n_nzero, lambda2, force_equal):
"""Invert weights and compute M."""
W_inv = np.empty_like(W)
n_src = W_inv.shape[0]
if n_orient == 1 or force_equal:
W_inv[:] = 1. / W
else:
for ii in range(n_src):
# Here we use a single-precision-suitable `rcond` (given our
# 3x3 matrix size) because the inv could be saved in single
# precision.
W_inv[ii] = linalg.pinv2(W[ii], rcond=1e-7)
# Weight the gain matrix
W_inv_Gt = np.empty_like(G).T
for ii in range(n_src):
sl = slice(n_orient * ii, n_orient * (ii + 1))
W_inv_Gt[sl, :] = np.dot(W_inv[ii], G[:, sl].T)
# Compute the inverse, normalizing by the trace
G_W_inv_Gt = np.dot(G, W_inv_Gt)
G_W_inv_Gt *= n_nzero / np.trace(G_W_inv_Gt)
u, s, v = linalg.svd(G_W_inv_Gt)
s = s / (s ** 2 + lambda2)
M = np.dot(v.T[:, :n_nzero] * s[:n_nzero], u.T[:n_nzero])
return M, W_inv
def fit(self, X, y):
if self.activation is None:
# Useful to quantify the impact of the non-linearity
self._activate = lambda x: x
else:
self._activate = self.activations[self.activation]
rng = check_random_state(self.random_state)
# one-of-K coding for output values
self.classes_ = unique_labels(y)
Y = label_binarize(y, self.classes_)
# set hidden layer parameters randomly
n_features = X.shape[1]
if self.rank is None:
if self.density == 1:
self.weights_ = rng.randn(n_features, self.n_hidden)
else:
self.weights_ = sparse_random_matrix(
self.n_hidden, n_features, density=self.density,
random_state=rng).T
else:
# Low rank weight matrix
self.weights_u_ = rng.randn(n_features, self.rank)
self.weights_v_ = rng.randn(self.rank, self.n_hidden)
self.biases_ = rng.randn(self.n_hidden)
# map the input data through the hidden layer
H = self.transform(X)
# fit the linear model on the hidden layer activation
self.beta_ = np.dot(pinv2(H), Y)
return self
def calculate_arm_q_dot(self, cmd):
# ctr_mod decides to control translational or rotational velecity
if cmd.ctrl_mod:
eef_vel = np.array(
[0., 0., 0., cmd.eef_vel[5], -cmd.eef_vel[3], cmd.eef_vel[4]])
else:
eef_vel = np.array(
[cmd.eef_vel[2], -cmd.eef_vel[0], cmd.eef_vel[1], 0., 0., 0.])
# print('EEF Cmd: {} '.format(eef_vel))
# get position jacobian of eef
jac_pos = self.sim.data.get_body_jacp(self.eef_link)
jac_pos = jac_pos.reshape(3, self.sim.model.nv)
jac_pos = jac_pos[:, 0:7]
# get position jacobian of eef
jac_rot = self.sim.data.get_body_jacr(self.eef_link)
jac_rot = jac_rot.reshape(3, self.sim.model.nv)
jac_rot = jac_rot[:, 0:7]
jac_full = np.concatenate((jac_pos, jac_rot))
# calculate pseudo-inverse of jacobian
jac_inv = pinv2(jac_full)
q_dot = np.dot(jac_inv, eef_vel)
return q_dot
def fit(self, X=None, y=None):
"""
The Gaussian Process model fitting method.
Parameters
----------
X : double array_like
An array with shape (n_samples, n_features) with the input at which
observations were made.
y : array_like, shape (n_samples, 3)
An array with shape (n_eval, 3) with the observations of the output to be predicted.
of shape (n_samples, 3) with the Best Linear Unbiased Prediction at x.
Returns
-------
gp : self
A fitted Gaussian Process model object awaiting data to perform
predictions.
"""
if X:
K_list = self.calc_scalar_kernel_matrices(X)
else:
K_list = self.calc_scalar_kernel_matrices()
# add diagonal noise to each scalar kernel matrix
K_list = [K + self.nugget * sp.ones(K.shape[0]) for K in K_list]
Kglob = None
# outer_iv = [sp.outer(iv, iv.T) for iv in self.ivs] # NO, wrong
for K, ivs, iv_corr in zip(K_list, self.ivs, self.iv_corr):
# make the outer product tensor of shape (N_ls, N_ls, 3, 3) and multiply it with the scalar kernel
K3D = iv_corr * K[:, :, None, None] * rotmat_multi(ivs, ivs)
# reshape tensor onto a 2D array tiled with 3x3 matrix blocks
if Kglob is None:
Kglob = K3D
else:
Kglob += K3D
Kglob = my_tensor_reshape(Kglob)
# # all channels merged into one covariance matrix
# # K^{glob}_{ij} = \sum_{k = 1}^{N_{IVs}} w_k D_{k, ij} |v_k^i\rangle \langle v_k^j |
try:
inv = LA.pinv2(Kglob)
except LA.LinAlgError as err:
print("pinv2 failed: %s. Switching to pinvh" % err)
try:
inv = LA.pinvh(Kglob)
except LA.LinAlgError as err:
print("pinvh failed: %s. Switching to pinv2" % err)
inv = None
# alpha is the vector of regression coefficients of GaussianProcess
alpha = sp.dot(inv, self.y.ravel())
if not self.low_memory:
self.inverse = inv
self.Kglob = Kglob
self.alpha = sp.array(alpha)
def fit(self, X, y, activation='relu'):
"""Fits the training data to the model based on an activation function.
Parameters:
-----------
X : array-like
The input data to be fit by the model.
y : array-like
The targets of the data. This is the target matrix T
activation: string
The selected activation function. Options are:
'relu', 'sigmoid', 'tanh'
Returns:
--------
Beta : array
The learned weights.
"""
# convert X and y to arrays
X = np.array(X)
y = np.array(y)
# set the activation function for the whole ELM object
self.activation = activation
# compute the output weight vectors (beta)
# This is retrieved using the Moore-Penrose generalized inverse
self.beta = np.dot(pinv2(self.hidden_nodes(X)), y)
return self.beta
def compute_transcription_factor_activity(
self, allow_self_interactions_for_duplicate_prior_columns=True):
activity, self.prior, non_zero_tfs = process_expression_into_activity(
self.expression_matrix, self.prior)
self.fix_self_interacting(
non_zero_tfs,
allow_duplicates=allow_self_interactions_for_duplicate_prior_columns
)
# Set the activity of non-zero tfs to the pseudoinverse of the prior matrix times the expression
if len(non_zero_tfs) > 0:
utils.Debug.vprint(
"Calculating TFA for {nz} TFs from prior targets".format(
nz=len(non_zero_tfs)),
level=1)
activity.loc[non_zero_tfs, :] = np.matrix(
linalg.pinv2(self.prior[non_zero_tfs])) * np.matrix(
self.expression_matrix_halftau)
else:
utils.Debug.vprint(
"No prior information for TFs exists. Using expression for TFA exclusively.",
level=0)
activity_nas = activity.isna().any(axis=1)
if activity_nas.sum() > 0:
lose_tfs = activity_nas.index[activity_nas].tolist()
utils.Debug.vprint("Dropping TFs with NaN values: {drop}".format(
drop=" ".join(lose_tfs)))
activity = activity.dropna(axis=0)
return activity
def test_simple_rows(self):
a = array([[1, 2], [3, 4], [5, 6]], dtype=float)
a_pinv = pinv(a)
a_pinv2 = pinv2(a)
a_pinv3 = pinv3(a)
assert_array_almost_equal(a_pinv,a_pinv2)
assert_array_almost_equal(a_pinv,a_pinv3)
def test_pinv_array(self):
from scipy.linalg import pinv2
tests = []
tests.append(rand(1, 1, 1))
tests.append(rand(3, 1, 1))
tests.append(rand(1, 2, 2))
tests.append(rand(3, 2, 2))
tests.append(rand(1, 3, 3))
tests.append(rand(3, 3, 3))
A = rand(1, 3, 3)
A[0, 0, :] = A[0, 1, :]
tests.append(A)
tests.append(rand(1, 1, 1) + 1.0j * rand(1, 1, 1))
tests.append(rand(3, 1, 1) + 1.0j * rand(3, 1, 1))
tests.append(rand(1, 2, 2) + 1.0j * rand(1, 2, 2))
tests.append(rand(3, 2, 2) + 1.0j * rand(3, 2, 2))
tests.append(rand(1, 3, 3) + 1.0j * rand(1, 3, 3))
tests.append(rand(3, 3, 3) + 1.0j * rand(3, 3, 3))
A = rand(1, 3, 3) + 1.0j * rand(1, 3, 3)
A[0, 0, :] = A[0, 1, :]
tests.append(A)
for test in tests:
pinv_test = zeros_like(test)
for i in range(pinv_test.shape[0]):
pinv_test[i] = pinv2(test[i])
pinv_array(test)
assert_array_almost_equal(test, pinv_test, decimal=4)
def _compute_eloreta_inv(G, W, n_orient, n_nzero, lambda2, force_equal):
"""Invert weights and compute M."""
W_inv = np.empty_like(W)
n_src = W_inv.shape[0]
if n_orient == 1 or force_equal:
W_inv[:] = 1. / W
else:
for ii in range(n_src):
# Here we use a single-precision-suitable `rcond` (given our
# 3x3 matrix size) because the inv could be saved in single
# precision.
W_inv[ii] = linalg.pinv2(W[ii], rcond=1e-7)
# Weight the gain matrix
W_inv_Gt = np.empty_like(G).T
for ii in range(n_src):
sl = slice(n_orient * ii, n_orient * (ii + 1))
W_inv_Gt[sl, :] = np.dot(W_inv[ii], G[:, sl].T)
# Compute the inverse, normalizing by the trace
G_W_inv_Gt = np.dot(G, W_inv_Gt)
G_W_inv_Gt *= n_nzero / np.trace(G_W_inv_Gt)
u, s, v = linalg.svd(G_W_inv_Gt)
s = s / (s**2 + lambda2)
M = np.dot(v.T[:, :n_nzero] * s[:n_nzero], u.T[:n_nzero])
return M, W_inv
def _evaluateNet(self):
wtRatio=1./3.
inputs=self.dataset.getField('input')
targets=self.dataset.getField('target')
training_start=int(wtRatio*len(inputs))
washout_inputs=inputs[:training_start]
training_inputs=inputs[training_start:]
training_targets=targets[training_start:]
phis=[]
self.model.network.reset()
self.model.washout(washout_inputs)
phis.append(self.model.washout(training_inputs))
PHI=concatenate(phis).T
PHI_INV=pinv2(PHI)
TARGET=concatenate(training_targets).T
W=dot(TARGET,PHI_INV)
self.model.setOutputWeightMatrix(W)
self.model.activate(washout_inputs)
outputs=self.model.activate(training_inputs)
OUTPUT=concatenate(outputs)
TARGET=TARGET.T
fitness=self.evalfunc(OUTPUT,TARGET)
return fitness
def fit(self, X, y):
if self.activation is None:
# Useful to quantify the impact of the non-linearity
self._activate = lambda x: x
else:
self._activate = self.activations[self.activation]
rng = check_random_state(self.random_state)
# one-of-K coding for output values
self.classes_ = unique_labels(y)
Y = label_binarize(y, self.classes_)
# set hidden layer parameters randomly
n_features = X.shape[1]
if self.rank is None:
if self.density == 1:
self.weights_ = rng.randn(n_features, self.n_hidden)
else:
self.weights_ = sparse_random_matrix(self.n_hidden,
n_features,
density=self.density,
random_state=rng).T
else:
# Low rank weight matrix
self.weights_u_ = rng.randn(n_features, self.rank)
self.weights_v_ = rng.randn(self.rank, self.n_hidden)
self.biases_ = rng.randn(self.n_hidden)
# map the input data through the hidden layer
H = self.transform(X)
# fit the linear model on the hidden layer activation
self.beta_ = np.dot(pinv2(H), Y)
return self
def test_simple_cols(self):
a = array([[1, 2, 3], [4, 5, 6]], dtype=float)
a_pinv = pinv(a)
a_pinv2 = pinv2(a)
a_pinv3 = pinv3(a)
assert_array_almost_equal(a_pinv,a_pinv2)
assert_array_almost_equal(a_pinv,a_pinv3)
def unwhiten(X, comp):
"""
Inverse process of whitening.
_comp_ is assumed to be column wise.
"""
uw = la.pinv2(comp)
return np.dot(X, uw)
def _pseudo_inverse_dense(L, rhoss, method='direct'):
"""
Internal function for computing the pseudo inverse of an Liouvillian using
dense matrix methods. See pseudo_inverse for details.
"""
if method == 'direct':
rho_vec = np.transpose(mat2vec(rhoss.full()))
tr_mat = tensor([identity(n) for n in L.dims[0][0]])
tr_vec = np.transpose(mat2vec(tr_mat.full()))
N = np.prod(L.dims[0][0])
I = np.identity(N * N)
P = np.kron(np.transpose(rho_vec), tr_vec)
Q = I - P
LIQ = np.linalg.solve(L.full(), Q)
R = np.dot(Q, LIQ)
return Qobj(R, dims=L.dims)
elif method == 'numpy':
return Qobj(np.linalg.pinv(L.full()), dims=L.dims)
elif method == 'scipy':
return Qobj(la.pinv(L.full()), dims=L.dims)
elif method == 'scipy2':
return Qobj(la.pinv2(L.full()), dims=L.dims)
else:
raise ValueError("Unsupported method '%s'. Use 'direct' or 'numpy'" %
method)
def baseline(y, deg=None, max_it=None, tol=None):
"""
Computes the baseline of a given data.
Iteratively performs a polynomial fitting in the data to detect its
baseline. At every iteration, the fitting weights on the regions with
peaks are reduced to identify the baseline only.
Parameters
----------
y : ndarray
Data to detect the baseline.
deg : int
Degree of the polynomial that will estimate the data baseline. A low
degree may fail to detect all the baseline present, while a high
degree may make the data too oscillatory, especially at the edges.
max_it : int
Maximum number of iterations to perform.
tol : float
Tolerance to use when comparing the difference between the current
fit coefficients and the ones from the last iteration. The iteration
procedure will stop when the difference between them is lower than
*tol*.
Returns
-------
baseline : ndarray
Array with the baseline amplitude for every original point in *y*
"""
# for not repeating ourselves in `envelope`
if deg is None:
deg = 3
if max_it is None:
max_it = 100
if tol is None:
tol = 1e-3
order = deg + 1
coeffs = np.ones(order)
# try to avoid numerical issues
cond = math.pow(y.max(), 1. / order)
x = np.linspace(0., cond, y.size)
base = y.copy()
vander = np.vander(x, order)
vander_pinv = la.pinv2(vander)
for _ in range(max_it):
coeffs_new = np.dot(vander_pinv, y)
if la.norm(coeffs_new - coeffs) / la.norm(coeffs) < tol:
break
coeffs = coeffs_new
base = np.dot(vander, coeffs)
y = np.minimum(y, base)
return base
def compute_G(self, D): """ Computes matrix G given the selected model @param D Prototypes matrix [n_prototypes, n_features]. @return Matrix G [n_prototypes, n_prototypes]. """ # Computing matrix G according with selected model if (self.model == "SBM"): # Computing similarity matrix and inverting G = psimilarity(A=D, kernel=self.kernel, gamma=self.gamma,\ norm=self.norm, icov_mtx=self.icov_mtx) G = pinv2(G) #G = np.linalg.pinv(G) elif (self.model == "AAKR"): # Using identity matrix as inverse similarity matrix G = np.eye(D.shape[0]) # Return G return G
def test_simple_complex(self):
a = (array([[1, 2, 3], [4, 5, 6], [7, 8, 10]], dtype=float) +
1j * array([[10, 8, 7], [6, 5, 4], [3, 2, 1]], dtype=float))
a_pinv = pinv(a)
assert_array_almost_equal(dot(a, a_pinv), np.eye(3))
a_pinv = pinv2(a)
assert_array_almost_equal(dot(a, a_pinv), np.eye(3))
def test_simple_complex(self):
a = (array([[1, 2, 3], [4, 5, 6], [7, 8, 10]], dtype=float)
+ 1j * array([[10, 8, 7], [6, 5, 4], [3, 2, 1]], dtype=float))
a_pinv = pinv(a)
assert_array_almost_equal(dot(a, a_pinv), np.eye(3))
a_pinv = pinv2(a)
assert_array_almost_equal(dot(a, a_pinv), np.eye(3))
def test_pinv_array(self):
from scipy.linalg import pinv2
tests = []
tests.append(np.random.rand(1, 1, 1))
tests.append(np.random.rand(3, 1, 1))
tests.append(np.random.rand(1, 2, 2))
tests.append(np.random.rand(3, 2, 2))
tests.append(np.random.rand(1, 3, 3))
tests.append(np.random.rand(3, 3, 3))
A = np.random.rand(1, 3, 3)
A[0, 0, :] = A[0, 1, :]
tests.append(A)
tests.append(np.random.rand(1, 1, 1) + 1.0j*np.random.rand(1, 1, 1))
tests.append(np.random.rand(3, 1, 1) + 1.0j*np.random.rand(3, 1, 1))
tests.append(np.random.rand(1, 2, 2) + 1.0j*np.random.rand(1, 2, 2))
tests.append(np.random.rand(3, 2, 2) + 1.0j*np.random.rand(3, 2, 2))
tests.append(np.random.rand(1, 3, 3) + 1.0j*np.random.rand(1, 3, 3))
tests.append(np.random.rand(3, 3, 3) + 1.0j*np.random.rand(3, 3, 3))
A = np.random.rand(1, 3, 3) + 1.0j*np.random.rand(1, 3, 3)
A[0, 0, :] = A[0, 1, :]
tests.append(A)
for test in tests:
pinv_test = np.zeros_like(test)
for i in range(pinv_test.shape[0]):
pinv_test[i] = pinv2(test[i])
pinv_array(test)
assert_array_almost_equal(test, pinv_test, decimal=4)
def train(self, trajs, silent=False):
trans_obs = [
self._transform_observations(traj.obs[:]) for traj in trajs
]
X = np.concatenate([obs[:-1, :] for obs in trans_obs]).T
Y = np.concatenate([obs[1:, :] for obs in trans_obs]).T
U = np.concatenate([traj.ctrls[:-1, :] for traj in trajs]).T
n = X.shape[0] # state dimension
m = U.shape[0] # control dimension
XU = np.concatenate((X, U), axis=0) # stack X and U together
if self.method == "lstsq": # Least Squares Solution
AB = np.dot(Y, sla.pinv2(XU))
A = AB[:n, :n]
B = AB[:n, n:]
elif self.method == "lasso": # Call lasso regression on coefficients
print("Call Lasso")
clf = Lasso(alpha=self.lasso_alpha)
clf.fit(XU.T, Y.T)
AB = clf.coef_
A = AB[:n, :n]
B = AB[:n, n:]
elif self.method == "stable": # Compute stable A, and B
print("Compute Stable Koopman")
# call function
A, _, _, _, B, _ = stabilize_discrete(X, U, Y)
self.A, self.B = A, B
def _pseudo_inverse_dense(L, rhoss, method='direct', **pseudo_args):
"""
Internal function for computing the pseudo inverse of an Liouvillian using
dense matrix methods. See pseudo_inverse for details.
"""
if method == 'direct':
rho_vec = np.transpose(mat2vec(rhoss.full()))
tr_mat = tensor([identity(n) for n in L.dims[0][0]])
tr_vec = np.transpose(mat2vec(tr_mat.full()))
N = np.prod(L.dims[0][0])
I = np.identity(N * N)
P = np.kron(np.transpose(rho_vec), tr_vec)
Q = I - P
LIQ = np.linalg.solve(L.full(), Q)
R = np.dot(Q, LIQ)
return Qobj(R, dims=L.dims)
elif method == 'numpy':
return Qobj(np.linalg.pinv(L.full()), dims=L.dims)
elif method == 'scipy':
return Qobj(la.pinv(L.full()), dims=L.dims)
elif method == 'scipy2':
return Qobj(la.pinv2(L.full()), dims=L.dims)
else:
raise ValueError("Unsupported method '%s'. Use 'direct' or 'numpy'" %
method)
def solve_dXdE(Espan, nsteps, Xini, Jlam, dVdElam, S):
'''
Parameters
Espan: df, 1st and 2nd columns are integration interval, enzyme in rows
nsteps: int, # of integration steps
Xini: array, ini values of X
Jlam: lambdified function, Jacobian matrix
dVdElam: lambdified function, dVdE
S: df, stoichiometric matrix, metabolite in rows, reaction in columns
Returns
Eout: df, enzyme expression range, enzyme in rows, columns are the same with Xout
Xout: df, metabolite concentration range, metabolite in rows, columns are the same with Eout (initial input metabolite not included)
'''
import numpy as np
import pandas as pd
from scipy.linalg import eigvals, pinv2
from constants import eigThreshold
# prepare initial X, E
Espan = np.matrix(Espan)
dE = (Espan[:, 1] - Espan[:, 0]) / nsteps
X = np.matrix(Xini[:, np.newaxis])
E = Espan[:, 0]
# prepare initial Xout, Eout
Xout = pd.DataFrame(index=S.index, columns=range(nsteps + 1))
Eout = pd.DataFrame(index=S.columns, columns=range(nsteps + 1))
Xout.iloc[:, 0] = X
Eout.iloc[:, 0] = E
for i in range(1, nsteps + 1):
XE = np.array(np.concatenate((X, E)))
# update Jacobian matrix and screen
J = np.matrix(Jlam(*XE)).astype(np.float)
if np.any(eigvals(J).real >= eigThreshold): break
# update X, E and screen
dVdE = np.matrix(dVdElam(*XE)).astype(np.float)
dX = -pinv2(J) * np.matrix(S) * dVdE * np.matrix(dE)
X = X + dX
E = E + dE
if X.min() <= 0: break
# update Xout, Eout
Xout.iloc[:, i] = X
Eout.iloc[:, i] = E
return Eout, Xout
def calculate_control_speed(V, Baxis_mat, config, F_matrix, wheels_angles, M0e, Tb0, dt): J = get_jacobian(Baxis_mat, config[3:8], F_matrix, M0e, Tb0) control_speeds = sc.pinv2(J, pinv_cutt_off_threshold) @ V config, wheels_angles = NextState(config, wheels_angles, control_speeds.reshape((9,1)), dt, 0, F_matrix) # test if any joint exceeds limits violations = testJointsLimits(config) # if any joint is found to be exceeding limit, the associated jacobian column will be zeroed out and the twist will be recalculated recalculate_twist = True if any(violations) else False for i in range(3,len(violations)): if violations[i] == True: J[0:6, i + 1] = np.zeros((6,)) if recalculate_twist: control_speeds = sc.pinv2(J, pinv_cutt_off_threshold) @ V # this is to balance the effect of multiplying the Chassis jacobian by the factor control_speeds[0:4] = control_speeds[0:4]*(wheels_influence_factor) return control_speeds
def test_simple(self):
a = array([[1, 2, 3], [4, 5, 6.], [7, 8, 10]])
a_pinv = pinv(a)
assert_array_almost_equal(dot(a, a_pinv),
[[1, 0, 0], [0, 1, 0], [0, 0, 1]])
a_pinv = pinv2(a)
assert_array_almost_equal(dot(a, a_pinv),
[[1, 0, 0], [0, 1, 0], [0, 0, 1]])
def neurons(x,y,nb_neurons):
n=x.shape[1]
# random generation of the neurons parameters
w=st.norm.rvs(size=(n, nb_neurons))
b=st.norm.rvs(size=(1,nb_neurons))
h=H(w,b,x) # activation matrix computation
beta_chapeau=dot(la.pinv2(h),y) # Penrose-Moore inversion
return w,b,beta_chapeau
def test_check_finite(self):
a = array([[1,2,3],[4,5,6.],[7,8,10]])
a_pinv = pinv(a, check_finite=False)
assert_array_almost_equal(dot(a,a_pinv),[[1,0,0],[0,1,0],[0,0,1]])
a_pinv = pinv2(a, check_finite=False)
assert_array_almost_equal(dot(a,a_pinv),[[1,0,0],[0,1,0],[0,0,1]])
a_pinv = pinv3(a, check_finite=False)
assert_array_almost_equal(dot(a,a_pinv),[[1,0,0],[0,1,0],[0,0,1]])
def _fit_regression(self, y):
""" Fit regression using pseudo-inverse or supplied regressor"""
if self.regressor is None:
self.coefs_ = safe_sparse_dot(pinv2(self.hidden_activations_), y)
else:
self.regressor.fit(self.hidden_activations_, y)
self.fitted_ = True
def test_check_finite(self):
a = array([[1, 2, 3], [4, 5, 6.], [7, 8, 10]])
a_pinv = pinv(a, check_finite=False)
assert_array_almost_equal(dot(a, a_pinv),
[[1, 0, 0], [0, 1, 0], [0, 0, 1]])
a_pinv = pinv2(a, check_finite=False)
assert_array_almost_equal(dot(a, a_pinv),
[[1, 0, 0], [0, 1, 0], [0, 0, 1]])
def test_simple_real(self):
a = array([[1, 2, 3], [4, 5, 6], [7, 8, 10]], dtype=float)
a_pinv = pinv(a)
assert_array_almost_equal(dot(a,a_pinv), np.eye(3))
a_pinv = pinv2(a)
assert_array_almost_equal(dot(a,a_pinv), np.eye(3))
a_pinv = pinv3(a)
assert_array_almost_equal(dot(a,a_pinv), np.eye(3))
def test_pinvh_nonpositive():
a = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]], dtype=np.float64)
a = np.dot(a, a.T)
u, s, vt = np.linalg.svd(a)
s[0] *= -1
a = np.dot(u * s, vt) # a is now symmetric non-positive and singular
a_pinv = pinv2(a)
a_pinvh = pinvh(a)
assert_almost_equal(a_pinv, a_pinvh)
def fit(self,X,y):
self.hl = HiddenLayer(self.k, kernel=self.kernel, p=self.p, compute_widths=self.compute_widths,
set_centers=self.set_centers, verbose=self.verbose)
# Computes hidden layer actiovations.
self.hidden_ = self.hl.fit_transform(X)
# Computes output layer weights.
if self.verbose: print("Solving output weights.")
self.w_ = np.dot(linalg.pinv2(self.hidden_),y)
return self
def __init__(self, cov, lllim, dlogl, nobj):
self.cov = cov # enforce_posdef(cov)
self.nspec = len(cov)
self.lllim = lllim
self.loglllim = np.log10(self.lllim)
self.dlogl = dlogl
self.nobj = nobj
self.precision, self.cov_rank = pinv2(self.cov, return_rank=True, rcond=1.0e-3)
def test_nonpositive(self):
a = array([[1, 2, 3], [4, 5, 6], [7, 8, 9]], dtype=float)
a = np.dot(a, a.T)
u, s, vt = np.linalg.svd(a)
s[0] *= -1
a = np.dot(u * s, vt) # a is now symmetric non-positive and singular
a_pinv = pinv2(a)
a_pinvh = pinvh(a)
assert_array_almost_equal(a_pinv, a_pinvh)
def zero_freq_noise(liouvillian, jump_liouvillian, sys_dim, stationary_state, dv_pops, Gamma_L, Gamma_R):
J_1 = cs.differentiate_jump_matrix(jump_liouvillian)
Q = np.eye(sys_dim**2) - np.outer(stationary_state, dv_pops)
R0 = np.dot(Q, np.dot(la.pinv2(-liouvillian), Q)) #analytic_R0(Gamma_L, Gamma_R) #
noise = - cs.trace_density_vector(np.dot(cs.differentiate_jump_matrix(J_1), stationary_state), dv_pops) \
- 2. * cs.trace_density_vector(np.dot(np.dot(np.dot(J_1, R0), J_1), stationary_state), dv_pops)
return noise
def __init__(self, obs_ens, observation, obs_err_cov):
"""Prepare the update."""
Y = mean0(obs_ens)
obs_cov = obs_err_cov*(N-1) + Y.T@Y
obs_pert = randn(N, len(observation)) @ sqrt(obs_err_cov)
innovations = observation - (obs_ens + obs_pert)
# (pre-) Kalman gain * Innovations
self.KGdY = innovations @ sla.pinv2(obs_cov) @ Y.T
def fastica(X,
nSources=None,
algorithm="parallel fp",
decorrelation="mdum",
nonlinearity="logcosh",
alpha=1.0,
maxIterations=500,
tolerance=1e-05,
Winit=None,
scaled=True):
algorithm_funcs = {'parallel fp': ica_par_fp, 'deflation': ica_def}
orthog_funcs = {'mdum': decorrelation_mdum, 'witer': decorrelation_witer}
if nonlinearity == 'logcosh':
g = lc
gprime = lcp
elif nonlinearity == 'exp':
g = gauss
gprime = gaussp
elif nonlinearity == 'skew':
g = skew
gprime = skewp
else:
g = cube
gprime = cubep
nmix, nsamp = X.shape
if nSources is None:
nSources = nmix
if Winit is None:
Winit = randn(nSources, nSources)
# preprocessing (centering/whitening/pca)
rowmeansX, X = rowcenter(X)
Kw, Kd = whiteningmatrix(X, nSources)
X = dot(Kw, X)
#kwargs = {'tolerance': tolerance, 'g': g, 'gprime': gprime, 'orthog': orthog_funcs[decorrelation], 'alpha': alpha,
# 'maxIterations': maxIterations, 'Winit': Winit}
func = algorithm_funcs[algorithm]
# run ICA
W = func(X) #, **kwargs)
# consruct the sources - means are not restored
S = dot(W, X)
# mixing matrix
A = pinv2(dot(W, Kw))
if scaled == True:
S = S / S.std(axis=-1)[:, newaxis]
A = A * S.std(axis=-1)[newaxis, :]
return A, W, S
def compute_transcription_factor_activity(
self, allow_self_interactions_for_duplicate_prior_columns=True):
# Find TFs that have non-zero columns in the priors matrix
non_zero_tfs = pd.Index(
self.prior.columns[(self.prior != 0).any(axis=0)])
# Delete tfs that have neither prior information nor expression
delete_tfs = self.prior.columns.difference(
self.expression_matrix.index).difference(non_zero_tfs)
# Raise warnings
if len(delete_tfs) > 0:
message = "{num} TFs are removed from activity (no expression or prior exists)".format(
num=len(delete_tfs))
utils.Debug.vprint(message, level=0)
self.prior = self.prior.drop(delete_tfs, axis=1)
# Create activity dataframe with values set by default to the transcription factor's expression
# Create an empty dataframe [K x G]
activity = pd.DataFrame(0.0,
index=self.prior.columns,
columns=self.expression_matrix.columns)
# Populate with expression values as a default
add_default_activity = self.prior.columns.intersection(
self.expression_matrix.index)
activity.loc[add_default_activity, :] = self.expression_matrix.loc[
add_default_activity, :]
# Find all non-zero TFs that are duplicates of any other non-zero tfs
is_duplicated = self.prior[non_zero_tfs].transpose().duplicated(
keep=False)
# Find non-zero TFs that are also present in target gene list
self_interacting_tfs = non_zero_tfs.intersection(self.prior.index)
if is_duplicated.sum() > 0:
duplicates = is_duplicated[is_duplicated].index.tolist()
# If this flag is set to true, don't count duplicates as self-interacting when setting the diag to zero
if allow_self_interactions_for_duplicate_prior_columns:
self_interacting_tfs = self_interacting_tfs.difference(
duplicates)
# Set the diagonal of the matrix subset of self-interacting tfs to zero
subset = self.prior.loc[self_interacting_tfs,
self_interacting_tfs].values
np.fill_diagonal(subset, 0)
self.prior.at[self_interacting_tfs, self_interacting_tfs] = subset
# Set the activity of non-zero tfs to the pseudoinverse of the prior matrix times the expression
if len(non_zero_tfs) > 0:
activity.loc[non_zero_tfs, :] = np.matrix(
linalg.pinv2(self.prior[non_zero_tfs])) * np.matrix(
self.expression_matrix_halftau)
return activity
def fit(self, X, y):
self.X = X
self.y = y
self.n, self.p = self.X.shape
self.R = self.R_ij(self.X)
#print self.R
self.RI = pinv2(self.R)
# self.RI = inv(self.R)
#print self.RI
self.b = self.get_b()
def _compute_cov(self):
'''Compute covariance
'''
somefixed = (self.par_fix is not None) and any(isfinite(self.par_fix))
H = np.asmatrix(self._hessian(self._fitfun, self.par, self.data))
self.H = H
try:
if somefixed:
allfixed = all(isfinite(self.par_fix))
if allfixed:
self.par_cov[:, :] = 0
else:
pcov = -pinv2(H[self.i_notfixed, :][..., self.i_notfixed])
for row, ix in enumerate(list(self.i_notfixed)):
self.par_cov[ix, self.i_notfixed] = pcov[row, :]
else:
self.par_cov = -pinv2(H)
except:
self.par_cov[:, :] = nan
def _calcBatchUpdate(self, fitnesses):
invSigma = inv(self.sigma)
samples = self.allSamples[-self.batchSize:]
phi = zeros((self.batchSize, self.numParams+1))
phi[:, :self.xdim] = self._logDerivsX(samples, self.x, invSigma)
phi[:, self.xdim:-1] = self._logDerivsFactorSigma(samples, self.x, invSigma, self.factorSigma)
phi[:, -1] = 1
update = dot(pinv2(phi), fitnesses)[:-1]
return update
def fit(self):
self.R = self.R_ij(self.X)
if np.linalg.matrix_rank(self.R) < self.R.shape[1]:
wait = 1.
try:
self.RI = pinv2(self.R)
except:
wait = 1.
self.b = self.get_b()
def __init__(self, obs_ens, observations, obs_err_cov):
"""Prepare the update."""
Y, _ = center(obs_ens, rescale=True)
obs_cov = obs_err_cov * (N - 1) + Y.T @ Y
obs_pert = rnd.randn(N, len(observations)) @ sqrt(obs_err_cov)
innovations = observations - (obs_ens + obs_pert)
# (pre-) Kalman gain * Innovations
# Also called the X5 matrix by Evensen'2003.
self.KGdY = innovations @ sla.pinv2(obs_cov) @ Y.T
def fit(self):
self.R = self.R_ij(self.X)
if np.linalg.matrix_rank(self.R) < self.R.shape[1]:
wait = 1.
try:
self.RI = pinv2(self.R)
except:
wait = 1.
self.b = self.get_b()
def __slowSolve__(x, m):
n = len(x)
p = m + 1
r = np.zeros(p)
nx = np.min((p, n))
x = np.correlate(x, x, 'full')
r[:nx] = x[n - 1:n+m]
a = np.dot(sla.pinv2(sla.toeplitz(r[:-1])), -r[1:])
gain = np.sqrt(r[0] + np.sum(a * r[1:]))
return a, gain
def _fit_regression(self, y):
"""
fit regression using internal linear regression
or supplied regressor
"""
if (self.regressor is None):
self.coefs_ = safe_sparse_dot(pinv2(self.hidden_activations_), y)
else:
self.regressor.fit(self.hidden_activations_, y)
self.fitted_ = True
def fit2(self, X, y):
"""
Fit the model using X, y as training data.
Using Woodbury formula
Parameters
----------
X : {array-like, sparse matrix} of shape [n_samples, n_features]
Training vectors, where n_samples is the number of samples
and n_features is the number of features.
y : array-like of shape [n_samples, n_outputs]
Target values (class labels in classification, real numbers in
regression)
Returns
-------
self : object
Returns an instance of self.
"""
# fit random hidden layer and compute the hidden layer activations
#self.H = self.hidden_layer.fit_transform(X)
H = self._create_random_layer().fit_transform(X)
y = as_float_array(y, copy=True)
if self.beta is None:
# Then, this is the first time the model is fitted
assert len(X) >= self.n_hidden, ValueError(
"The first time the model is fitted, X must have "
"at least equal number of samples than n_hidden value!")
# TODO: handle cases of singular matrices (maybe with a try clause)
self.P = pinv2(safe_sparse_dot(H.T, H))
self.beta = multiple_safe_sparse_dot(self.P, H.T, y)
else:
M = np.eye(len(H)) + multiple_safe_sparse_dot(H, self.P, H.T)
self.P -= multiple_safe_sparse_dot(self.P, H.T, pinv2(M), H,
self.P)
e = y - safe_sparse_dot(H, self.beta)
self.beta += multiple_safe_sparse_dot(self.P, H.T, e)
return self
def baseline(y, deg=3, max_it=100, tol=1e-3):
"""Computes the baseline of a given data.
Iteratively performs a polynomial fitting in the data to detect its
baseline. At every iteration, the fitting weights on the regions with
peaks are reduced to identify the baseline only.
Parameters
----------
y : ndarray
Data to detect the baseline.
deg : int
Degree of the polynomial that will estimate the data baseline. A low
degree may fail to detect all the baseline present, while a high
degree may make the data too oscillatory, especially at the edges.
max_it : int
Maximum number of iterations to perform.
tol : float
Tolerance to use when comparing the difference between the current
fit coefficient and the ones from the last iteration. The iteration
procedure will stop when the difference between them is lower than
*tol*.
Returns
-------
ndarray
Array with the baseline amplitude for every original point in *y*
Information:
This function is stolen from https://bitbucket.org/lucashnegri/peakutils
Documentation: https://pythonhosted.org/PeakUtils/reference.html
(MIT License)
"""
order = deg + 1
coeffs = np.ones(order)
# try to avoid numerical issues
cond = math.pow(y.max(), 1. / order)
x = np.linspace(0., cond, y.size)
base = y.copy()
vander = np.vander(x, order)
vander_pinv = LA.pinv2(vander)
for _ in range(max_it):
coeffs_new = np.dot(vander_pinv, y)
if LA.norm(coeffs_new - coeffs) / LA.norm(coeffs) < tol:
break
coeffs = coeffs_new
base = np.dot(vander, coeffs)
y = np.minimum(y, base)
return base
def derivativeSquareOfGeodesicOnSPD(x,y):
if len(x.shape)!=1:
sq = sqrtm(x)
invsq = pinv2(sq)
F = np.dot(np.dot(invsq, y), invsq)
return 2*np.dot(np.dot(sq,logm(F),sq))
else:
sq = x**0.5
invsq = 1.0 / sq
F = invsq * y * invsq
return 2*sq*np.log(F)*sq
def geodesicDistanceOnSPD(x, y):
if len(x.shape)!=1:
sq = sqrtm(x)
invsq = pinv2(sq)
F = np.dot(np.dot(invsq, y), invsq)
return np.linalg.norm(logm(F))
else:
sq = x**0.5
invsq = 1.0 / sq
F = invsq * y * invsq
return np.linalg.norm(np.log(F))
def calcMeanOnSPD(p, q):
if len(p.shape)!=1:
sq = sqrtm(p)
invsq = pinv2(sq)
F = sqrtm(np.dot(np.dot(sq, q), sq))
return np.dot(np.dot(invsq,F),invsq)
else:
sq = p**0.5
invsq = 1.0 / sq
F = (sq * q * sq) **0.5
return invsq * F * invsq
def _compute_cov(self):
"""Compute covariance
"""
somefixed = (self.par_fix is not None) and any(isfinite(self.par_fix))
# H1 = numpy.asmatrix(self.dist.hessian_nnlf(self.par, self.data))
H = numpy.asmatrix(self.dist.hessian_nlogps(self.par, self.data))
self.H = H
try:
if somefixed:
allfixed = all(isfinite(self.par_fix))
if allfixed:
self.par_cov[:, :] = 0
else:
pcov = -pinv2(H[self.i_notfixed, :][..., self.i_notfixed])
for row, ix in enumerate(list(self.i_notfixed)):
self.par_cov[ix, self.i_notfixed] = pcov[row, :]
else:
self.par_cov = -pinv2(H)
except:
self.par_cov[:, :] = nan
def laplacian_psinv(self):
l_l = []
#laplacian matrix
for n in xrange(self.number_table):
if(self.graphList[n] != None):
if(self.graphList[n].laplacian_psinv == None):
if(self.graphList[n].laplacian_psinv == None):
#get the graph laplacian
l = self.graphList[n].graph.laplacian(weights=self.graphList[n].graph.es["weight"], normalized=False)
#pseudoinverse
self.graphList[n].laplacian_psinv = lpsinv = linalg.pinv2(l)
def _fit_3step(self, X, Y):
self.hl = HiddenLayer(self.h)
self.hl.fit(X)
D = self.hl.transform(X)
# compute w
print(D.shape)
print(Y.shape)
self.w_ = np.dot(linalg.pinv2(D), Y)
return self
def _fit_regression(self, y):
"""
fit regression using pseudo-inverse
or supplied regressor
"""
if (self.regressor is None):
self.coefs_ = safe_sparse_dot(pinv2(self.hidden_activations_), y)
else:
self.regressor.fit(self.hidden_activations_, y)
self.fitted_ = True
