Python numpy.sqrt() Examples
The following are 30 code examples for showing how to use numpy.sqrt(). These examples are extracted from open source projects. You can vote up the ones you like or vote down the ones you don't like, and go to the original project or source file by following the links above each example.
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Example 1
Project: fenics-topopt Author: zfergus File: von_mises_stress.py License: MIT License | 6 votes |
def calculate_diff_stress(self, x, u, nu, side=1): """ Calculate the derivative of the Von Mises stress given the densities x, displacements u, and young modulus nu. Optionally, provide the side length (default: 1). """ rho = self.penalized_densities(x) EB = self.E(nu).dot(self.B(side)) EBu = sum([EB.dot(u[:, i][self.edofMat]) for i in range(u.shape[1])]) s11, s22, s12 = numpy.hsplit((EBu * rho / float(u.shape[1])).T, 3) drho = self.diff_penalized_densities(x) ds11, ds22, ds12 = numpy.hsplit( ((1 - rho) * drho * EBu / float(u.shape[1])).T, 3) vm_stress = numpy.sqrt(s11**2 - s11 * s22 + s22**2 + 3 * s12**2) if abs(vm_stress).sum() > 1e-8: dvm_stress = (0.5 * (1. / vm_stress) * (2 * s11 * ds11 - ds11 * s22 - s11 * ds22 + 2 * s22 * ds22 + 6 * s12 * ds12)) return dvm_stress return 0
Example 2
Project: Att-ChemdNER Author: lingluodlut File: initializations.py License: Apache License 2.0 | 6 votes |
def get_fans(shape, dim_ordering='th'): if len(shape) == 2: fan_in = shape[0] fan_out = shape[1] elif len(shape) == 4 or len(shape) == 5: # assuming convolution kernels (2D or 3D). # TH kernel shape: (depth, input_depth, ...) # TF kernel shape: (..., input_depth, depth) if dim_ordering == 'th': receptive_field_size = np.prod(shape[2:]) fan_in = shape[1] * receptive_field_size fan_out = shape[0] * receptive_field_size elif dim_ordering == 'tf': receptive_field_size = np.prod(shape[:2]) fan_in = shape[-2] * receptive_field_size fan_out = shape[-1] * receptive_field_size else: raise ValueError('Invalid dim_ordering: ' + dim_ordering) else: # no specific assumptions fan_in = np.sqrt(np.prod(shape)) fan_out = np.sqrt(np.prod(shape)) return fan_in, fan_out
Example 3
Project: xrft Author: xgcm File: xrft.py License: MIT License | 6 votes |
def _radial_wvnum(k, l, N, nfactor): """ Creates a radial wavenumber based on two horizontal wavenumbers along with the appropriate index map """ # compute target wavenumbers k = k.values l = l.values K = np.sqrt(k[np.newaxis,:]**2 + l[:,np.newaxis]**2) nbins = int(N/nfactor) if k.max() > l.max(): ki = np.linspace(0., l.max(), nbins) else: ki = np.linspace(0., k.max(), nbins) # compute bin index kidx = np.digitize(np.ravel(K), ki) # compute number of points for each wavenumber area = np.bincount(kidx) # compute the average radial wavenumber for each bin kr = (np.bincount(kidx, weights=K.ravel()) / np.ma.masked_where(area==0, area)) return ki, kr[1:-1]
Example 4
Project: FRIDA Author: LCAV File: point_cloud.py License: MIT License | 6 votes |
def classical_mds(self, D): ''' Classical multidimensional scaling Parameters ---------- D : square 2D ndarray Euclidean Distance Matrix (matrix containing squared distances between points ''' # Apply MDS algorithm for denoising n = D.shape[0] J = np.eye(n) - np.ones((n,n))/float(n) G = -0.5*np.dot(J, np.dot(D, J)) s, U = np.linalg.eig(G) # we need to sort the eigenvalues in decreasing order s = np.real(s) o = np.argsort(s) s = s[o[::-1]] U = U[:,o[::-1]] S = np.diag(s)[0:self.dim,:] self.X = np.dot(np.sqrt(S),U.T)
Example 5
Project: FRIDA Author: LCAV File: point_cloud.py License: MIT License | 6 votes |
def trilateration(self, D): ''' Find the location of points based on their distance matrix using trilateration Parameters ---------- D : square 2D ndarray Euclidean Distance Matrix (matrix containing squared distances between points ''' dist = np.sqrt(D) # Simpler algorithm (no denoising) self.X = np.zeros((self.dim, self.m)) self.X[:,1] = np.array([0, dist[0,1]]) for i in xrange(2,m): self.X[:,i] = self.trilateration_single_point(self.X[1,1], dist[0,i], dist[1,i])
Example 6
Project: FRIDA Author: LCAV File: tools_fri_doa_plane.py License: MIT License | 6 votes |
def mtx_freq2visi(M, p_mic_x, p_mic_y): """ build the matrix that maps the Fourier series to the visibility :param M: the Fourier series expansion is limited from -M to M :param p_mic_x: a vector that constains microphones x coordinates :param p_mic_y: a vector that constains microphones y coordinates :return: """ num_mic = p_mic_x.size ms = np.reshape(np.arange(-M, M + 1, step=1), (1, -1), order='F') G = np.zeros((num_mic * (num_mic - 1), 2 * M + 1), dtype=complex, order='C') count_G = 0 for q in range(num_mic): p_x_outer = p_mic_x[q] p_y_outer = p_mic_y[q] for qp in range(num_mic): if not q == qp: p_x_qqp = p_x_outer - p_mic_x[qp] p_y_qqp = p_y_outer - p_mic_y[qp] norm_p_qqp = np.sqrt(p_x_qqp ** 2 + p_y_qqp ** 2) phi_qqp = np.arctan2(p_y_qqp, p_x_qqp) G[count_G, :] = (-1j) ** ms * sp.special.jv(ms, norm_p_qqp) * \ np.exp(1j * ms * phi_qqp) count_G += 1 return G
Example 7
Project: spectrum_painter Author: polygon File: spectrum_painter.py License: MIT License | 6 votes |
def convert_image(self, filename): pic = img.imread(filename) # Set FFT size to be double the image size so that the edge of the spectrum stays clear # preventing some bandfilter artifacts self.NFFT = 2*pic.shape[1] # Repeat image lines until each one comes often enough to reach the desired line time ffts = (np.flipud(np.repeat(pic[:, :, 0], self.repetitions, axis=0) / 16.)**2.) / 256. # Embed image in center bins of the FFT fftall = np.zeros((ffts.shape[0], self.NFFT)) startbin = int(self.NFFT/4) fftall[:, startbin:(startbin+pic.shape[1])] = ffts # Generate random phase vectors for the FFT bins, this is important to prevent high peaks in the output # The phases won't be visible in the spectrum phases = 2*np.pi*np.random.rand(*fftall.shape) rffts = fftall * np.exp(1j*phases) # Perform the FFT per image line, then concatenate them to form the final signal timedata = np.fft.ifft(np.fft.ifftshift(rffts, axes=1), axis=1) / np.sqrt(float(self.NFFT)) linear = timedata.flatten() linear = linear / np.max(np.abs(linear)) return linear
Example 8
Project: StructEngPy Author: zhuoju36 File: dynamic.py License: MIT License | 6 votes |
def solve_modal(model,k:int): """ Solve eigen mode of the MDOF system params: model: FEModel. k: number of modes to extract. """ K_,M_=model.K_,model.M_ if k>model.DOF: logger.info('Warning: the modal number to extract is larger than the system DOFs, only %d modes are available'%model.DOF) k=model.DOF omega2s,modes = sl.eigsh(K_,k,M_,sigma=0,which='LM') delta = modes/np.sum(modes,axis=0) model.is_solved=True model.mode_=delta model.omega_=np.sqrt(omega2s).reshape((k,1))
Example 9
Project: neural-fingerprinting Author: StephanZheng File: picklable_model.py License: BSD 3-Clause "New" or "Revised" License | 6 votes |
def set_input_shape(self, input_shape): batch_size, dim = input_shape self.input_shape = [batch_size, dim] self.output_shape = [batch_size, self.num_hid] if self.init_mode == "norm": init = tf.random_normal([dim, self.num_hid], dtype=tf.float32) init = init / tf.sqrt(1e-7 + tf.reduce_sum(tf.square(init), axis=0, keep_dims=True)) init = init * self.init_scale elif self.init_mode == "uniform_unit_scaling": scale = np.sqrt(3. / dim) init = tf.random_uniform([dim, self.num_hid], dtype=tf.float32, minval=-scale, maxval=scale) else: raise ValueError(self.init_mode) self.W = PV(init) if self.use_bias: self.b = PV((np.zeros((self.num_hid,)) + self.init_b).astype('float32'))
Example 10
Project: deep-learning-note Author: wdxtub File: layers.py License: MIT License | 6 votes |
def __forward(self, x, train_flg): if self.running_mean is None: N, D = x.shape self.running_mean = np.zeros(D) self.running_var = np.zeros(D) if train_flg: mu = x.mean(axis=0) xc = x - mu var = np.mean(xc ** 2, axis=0) std = np.sqrt(var + 10e-7) xn = xc / std self.batch_size = x.shape[0] self.xc = xc self.xn = xn self.std = std self.running_mean = self.momentum * self.running_mean + (1 - self.momentum) * mu self.running_var = self.momentum * self.running_var + (1 - self.momentum) * var else: xc = x - self.running_mean xn = xc / ((np.sqrt(self.running_var + 10e-7))) out = self.gamma * xn + self.beta return out
Example 11
Project: deep-learning-note Author: wdxtub File: optimizer.py License: MIT License | 6 votes |
def update(self, params, grads): if self.m is None: self.m, self.v = {}, {} for key, val in params.items(): self.m[key] = np.zeros_like(val) self.v[key] = np.zeros_like(val) self.iter += 1 lr_t = self.lr * np.sqrt(1.0 - self.beta2 ** self.iter) / (1.0 - self.beta1 ** self.iter) for key in params.keys(): # self.m[key] = self.beta1*self.m[key] + (1-self.beta1)*grads[key] # self.v[key] = self.beta2*self.v[key] + (1-self.beta2)*(grads[key]**2) self.m[key] += (1 - self.beta1) * (grads[key] - self.m[key]) self.v[key] += (1 - self.beta2) * (grads[key] ** 2 - self.v[key]) params[key] -= lr_t * self.m[key] / (np.sqrt(self.v[key]) + 1e-7) # unbias_m += (1 - self.beta1) * (grads[key] - self.m[key]) # correct bias # unbisa_b += (1 - self.beta2) * (grads[key]*grads[key] - self.v[key]) # correct bias # params[key] += self.lr * unbias_m / (np.sqrt(unbisa_b) + 1e-7)
Example 12
Project: deep-learning-note Author: wdxtub File: multi_layer_net_extend.py License: MIT License | 6 votes |
def __init_weight(self, weight_init_std): """设定权重的初始值 Parameters ---------- weight_init_std : 指定权重的标准差(e.g. 0.01) 指定'relu'或'he'的情况下设定“He的初始值” 指定'sigmoid'或'xavier'的情况下设定“Xavier的初始值” """ all_size_list = [self.input_size] + self.hidden_size_list + [self.output_size] for idx in range(1, len(all_size_list)): scale = weight_init_std if str(weight_init_std).lower() in ('relu', 'he'): scale = np.sqrt(2.0 / all_size_list[idx - 1]) # 使用ReLU的情况下推荐的初始值 elif str(weight_init_std).lower() in ('sigmoid', 'xavier'): scale = np.sqrt(1.0 / all_size_list[idx - 1]) # 使用sigmoid的情况下推荐的初始值 self.params['W' + str(idx)] = scale * np.random.randn(all_size_list[idx - 1], all_size_list[idx]) self.params['b' + str(idx)] = np.zeros(all_size_list[idx])
Example 13
Project: deep-learning-note Author: wdxtub File: simulate_sin.py License: MIT License | 6 votes |
def run_eval(sess, test_X, test_y): ds = tf.data.Dataset.from_tensor_slices((test_X, test_y)) ds = ds.batch(1) X, y = ds.make_one_shot_iterator().get_next() with tf.variable_scope("model", reuse=True): prediction, _, _ = lstm_model(X, [0.0], False) predictions = [] labels = [] for i in range(TESTING_EXAMPLES): p, l = sess.run([prediction, y]) predictions.append(p) labels.append(l) predictions = np.array(predictions).squeeze() labels = np.array(labels).squeeze() rmse = np.sqrt(((predictions-labels) ** 2).mean(axis=0)) print("Mean Square Error is: %f" % rmse) plt.figure() plt.plot(predictions, label='predictions') plt.plot(labels, label='real_sin') plt.legend() plt.show()
Example 14
Project: neuropythy Author: noahbenson File: util.py License: GNU Affero General Public License v3.0 | 6 votes |
def point_on_segment(ac, b, atol=1e-8): ''' point_on_segment((a,b), c) yields True if point x is on segment (a,b) and False otherwise. Note that this differs from point_in_segment in that a point that if c is equal to a or b it is considered 'on' but not 'in' the segment. The option atol can be given and is used only to test for difference from 0; by default it is 1e-8. ''' (a,c) = ac abc = [np.asarray(u) for u in (a,b,c)] if any(len(u.shape) > 1 for u in abc): (a,b,c) = [np.reshape(u,(len(u),-1)) for u in abc] else: (a,b,c) = abc vab = b - a vbc = c - b vac = c - a dab = np.sqrt(np.sum(vab**2, axis=0)) dbc = np.sqrt(np.sum(vbc**2, axis=0)) dac = np.sqrt(np.sum(vac**2, axis=0)) return np.isclose(dab + dbc - dac, 0, atol=atol)
Example 15
Project: svviz Author: svviz File: kde.py License: MIT License | 5 votes |
def _compute_covariance(self): self.factor = self.scotts_factor() # Cache covariance and inverse covariance of the data if not hasattr(self, '_data_inv_cov'): self._data_covariance = atleast_2d(np.cov(self.dataset, rowvar=1, bias=False)) self._data_inv_cov = linalg.inv(self._data_covariance) self.covariance = self._data_covariance * self.factor**2 self.inv_cov = self._data_inv_cov / self.factor**2 self._norm_factor = sqrt(linalg.det(2*pi*self.covariance)) * self.n
Example 16
Project: libTLDA Author: wmkouw File: suba.py License: MIT License | 5 votes |
def zca_whiten(self, X): """ Perform ZCA whitening (aka Mahalanobis whitening). Parameters ---------- X : array (M samples x D features) data matrix. Returns ------- X : array (M samples x D features) whitened data. """ # Covariance matrix Sigma = np.cov(X.T) # Singular value decomposition U, S, V = svd(Sigma) # Whitening constant to prevent division by zero epsilon = 1e-5 # ZCA whitening matrix W = np.dot(U, np.dot(np.diag(1.0 / np.sqrt(S + epsilon)), V)) # Apply whitening matrix return np.dot(X, W)
Example 17
Project: Financial-NLP Author: Coldog2333 File: NLP.py License: Apache License 2.0 | 5 votes |
def unitvec(vector, ax=1): v=vector*vector if len(vector.shape)==1: sqrtv=np.sqrt(np.sum(v)) elif len(vector.shape)==2: sqrtv=np.sqrt([np.sum(v, axis=ax)]) else: raise Exception('It\'s too large.') if ax==1: result=np.divide(vector,sqrtv.T) elif ax==0: result=np.divide(vector,sqrtv) return result
Example 18
Project: fenics-topopt Author: zfergus File: filter.py License: MIT License | 5 votes |
def __init__(self, nelx, nely, rmin): """ Filter: Build (and assemble) the index+data vectors for the coo matrix format. """ nfilter = int(nelx * nely * ((2 * (np.ceil(rmin) - 1) + 1)**2)) iH = np.zeros(nfilter) jH = np.zeros(nfilter) sH = np.zeros(nfilter) cc = 0 for i in range(nelx): for j in range(nely): row = i * nely + j kk1 = int(np.maximum(i - (np.ceil(rmin) - 1), 0)) kk2 = int(np.minimum(i + np.ceil(rmin), nelx)) ll1 = int(np.maximum(j - (np.ceil(rmin) - 1), 0)) ll2 = int(np.minimum(j + np.ceil(rmin), nely)) for k in range(kk1, kk2): for l in range(ll1, ll2): col = k * nely + l fac = rmin - np.sqrt( ((i - k) * (i - k) + (j - l) * (j - l))) iH[cc] = row jH[cc] = col sH[cc] = np.maximum(0.0, fac) cc = cc + 1 # Finalize assembly and convert to csc format self.H = scipy.sparse.coo_matrix((sH, (iH, jH)), shape=(nelx * nely, nelx * nely)).tocsc() self.Hs = self.H.sum(1)
Example 19
Project: fenics-topopt Author: zfergus File: von_mises_stress.py License: MIT License | 5 votes |
def calculate_stress(self, x, u, nu, side=1): """ Calculate the Von Mises stress given the densities x, displacements u, and young modulus nu. """ s11, s22, s12 = self.calculate_principle_stresses(x, u, nu, side) vm_stress = numpy.sqrt(s11**2 - s11 * s22 + s22**2 + 3 * s12**2) return vm_stress
Example 20
Project: fenics-topopt Author: zfergus File: filter.py License: MIT License | 5 votes |
def __init__(self, nelx, nely, rmin): """ Filter: Build (and assemble) the index+data vectors for the coo matrix format. """ nfilter = int(nelx * nely * ((2 * (np.ceil(rmin) - 1) + 1)**2)) iH = np.zeros(nfilter) jH = np.zeros(nfilter) sH = np.zeros(nfilter) cc = 0 for i in range(nelx): for j in range(nely): row = i * nely + j kk1 = int(np.maximum(i - (np.ceil(rmin) - 1), 0)) kk2 = int(np.minimum(i + np.ceil(rmin), nelx)) ll1 = int(np.maximum(j - (np.ceil(rmin) - 1), 0)) ll2 = int(np.minimum(j + np.ceil(rmin), nely)) for k in range(kk1, kk2): for l in range(ll1, ll2): col = k * nely + l fac = rmin - np.sqrt( ((i - k) * (i - k) + (j - l) * (j - l))) iH[cc] = row jH[cc] = col sH[cc] = np.maximum(0.0, fac) cc = cc + 1 # Finalize assembly and convert to csc format self.H = scipy.sparse.coo_matrix((sH, (iH, jH)), shape=(nelx * nely, nelx * nely)).tocsc() self.Hs = self.H.sum(1)
Example 21
Project: fenics-topopt Author: zfergus File: von_mises_stress.py License: MIT License | 5 votes |
def calculate_stress(self, x, u, nu, side=1): """ Calculate the Von Mises stress given the densities x, displacements u, and young modulus nu. """ s11, s22, s12 = self.calculate_principle_stresses(x, u, nu, side) vm_stress = numpy.sqrt(s11**2 - s11 * s22 + s22**2 + 3 * s12**2) return vm_stress
Example 22
Project: keras_mixnets Author: titu1994 File: custom_objects.py License: MIT License | 5 votes |
def __call__(self, shape, dtype=None): dtype = dtype or K.floatx() kernel_height, kernel_width, _, out_filters = shape fan_out = int(kernel_height * kernel_width * out_filters) return tf.random_normal( shape, mean=0.0, stddev=np.sqrt(2.0 / fan_out), dtype=dtype) # Obtained from https://github.com/tensorflow/tpu/blob/master/models/official/efficientnet/efficientnet_model.py
Example 23
Project: keras_mixnets Author: titu1994 File: custom_objects.py License: MIT License | 5 votes |
def __call__(self, shape, dtype=None): dtype = dtype or K.floatx() init_range = 1.0 / np.sqrt(shape[1]) return tf.random_uniform(shape, -init_range, init_range, dtype=dtype) # Obtained from https://github.com/tensorflow/tpu/blob/master/models/official/efficientnet/efficientnet_model.py
Example 24
Project: Att-ChemdNER Author: lingluodlut File: utils.py License: Apache License 2.0 | 5 votes |
def shared(shape, name): #{{{ """ Create a shared object of a numpy array. """ init=initializations.get('glorot_uniform'); if len(shape) == 1: value = np.zeros(shape) # bias are initialized with zeros return theano.shared(value=value.astype(theano.config.floatX), name=name) else: drange = np.sqrt(6. / (np.sum(shape))) value = drange * np.random.uniform(low=-1.0, high=1.0, size=shape) return init(shape=shape,name=name); #}}}
Example 25
Project: Att-ChemdNER Author: lingluodlut File: initializations.py License: Apache License 2.0 | 5 votes |
def lecun_uniform(shape, name=None, dim_ordering='th'): ''' Reference: LeCun 98, Efficient Backprop http://yann.lecun.com/exdb/publis/pdf/lecun-98b.pdf ''' fan_in, fan_out = get_fans(shape, dim_ordering=dim_ordering) scale = np.sqrt(3. / fan_in) return uniform(shape, scale, name=name)
Example 26
Project: Att-ChemdNER Author: lingluodlut File: initializations.py License: Apache License 2.0 | 5 votes |
def glorot_normal(shape, name=None, dim_ordering='th'): ''' Reference: Glorot & Bengio, AISTATS 2010 ''' fan_in, fan_out = get_fans(shape, dim_ordering=dim_ordering) s = np.sqrt(2. / (fan_in + fan_out)) return normal(shape, s, name=name)
Example 27
Project: Att-ChemdNER Author: lingluodlut File: initializations.py License: Apache License 2.0 | 5 votes |
def glorot_uniform(shape, name=None, dim_ordering='th'): fan_in, fan_out = get_fans(shape, dim_ordering=dim_ordering) s = np.sqrt(6. / (fan_in + fan_out)) return uniform(shape, s, name=name)
Example 28
Project: Att-ChemdNER Author: lingluodlut File: initializations.py License: Apache License 2.0 | 5 votes |
def he_uniform(shape, name=None, dim_ordering='th'): fan_in, fan_out = get_fans(shape, dim_ordering=dim_ordering) s = np.sqrt(6. / fan_in) return uniform(shape, s, name=name)
Example 29
Project: xrft Author: xgcm File: xrft.py License: MIT License | 5 votes |
def isotropize(ps, fftdim, nfactor=4): """ Isotropize a 2D power spectrum or cross spectrum by taking an azimuthal average. .. math:: \text{iso}_{ps} = k_r N^{-1} \sum_{N} |\mathbb{F}(da')|^2 where :math:`N` is the number of azimuthal bins. Parameters ---------- ps : `xarray.DataArray` The power spectrum or cross spectrum to be isotropized. fftdim : list The fft dimensions overwhich the isotropization must be performed. nfactor : int, optional Ratio of number of bins to take the azimuthal averaging with the data size. Default is 4. """ # compute radial wavenumber bins k = ps[fftdim[1]] l = ps[fftdim[0]] N = [k.size, l.size] ki, kr = _radial_wvnum(k, l, min(N), nfactor) # average azimuthally ps = ps.assign_coords(freq_r=np.sqrt(k**2+l**2)) iso_ps = (ps.groupby_bins('freq_r', bins=ki, labels=kr).mean() .rename({'freq_r_bins': 'freq_r'}) ) return iso_ps * iso_ps.freq_r
Example 30
Project: xrft Author: xgcm File: test_xrft.py License: MIT License | 5 votes |
def test_isotropize(N=512): """Test the isotropization of a power spectrum.""" # generate synthetic 2D spectrum, isotropize and check values dL, amp, s = 1., 1e1, -3. dims = ['x','y'] fftdim = ['freq_x', 'freq_y'] spacing_tol = 1e-3 nfactor = 4 def _test_iso(theta): ps = xrft.power_spectrum(theta, spacing_tol, dim=dims) ps = np.sqrt(ps.freq_x**2+ps.freq_y**2) ps_iso = xrft.isotropize(ps, fftdim, nfactor=nfactor) assert len(ps_iso.dims)==1 assert ps_iso.dims[0]=='freq_r' npt.assert_allclose(ps_iso, ps_iso.freq_r**2, atol=0.02) # np data theta = synthetic_field_xr(N, dL, amp, s) _test_iso(theta) # np with other dim theta = synthetic_field_xr(N, dL, amp, s, other_dim_sizes=[10], dim_order=True) _test_iso(theta) # da chunked, order 1 theta = synthetic_field_xr(N, dL, amp, s, chunks={'y': None, 'x': None, 'd0': 2}, other_dim_sizes=[10], dim_order=True) _test_iso(theta) # da chunked, order 2 theta = synthetic_field_xr(N, dL, amp, s, chunks={'y': None, 'x': None, 'd0': 2}, other_dim_sizes=[10], dim_order=False) _test_iso(theta)