Python numpy.sqrt方法代碼示例

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import sqrt [as 別名]
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 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import sqrt [as 別名]
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 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import sqrt [as 別名]
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] 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import sqrt [as 別名]
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) 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import sqrt [as 別名]
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]) 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import sqrt [as 別名]
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 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import sqrt [as 別名]
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 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import sqrt [as 別名]
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)) 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import sqrt [as 別名]
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')) 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import sqrt [as 別名]
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 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import sqrt [as 別名]
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) 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import sqrt [as 別名]
def __init_weight(self, weight_init_std):
        """設定權重的初始值
        Parameters
        ----------
        weight_init_std : 指定權重的標準差（e.g. 0.01）
            指定'relu'或'he'的情況下設定“He的初始值”
            指定'sigmoid'或'xavier'的情況下設定“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的情況下推薦的初始值
            elif str(weight_init_std).lower() in ('sigmoid', 'xavier'):
                scale = np.sqrt(1.0 / all_size_list[idx - 1])  # 使用sigmoid的情況下推薦的初始值
            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]) 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import sqrt [as 別名]
def plot_n_image(X, n):
    """ plot first n images
    n has to be a square number
    """
    pic_size = int(np.sqrt(X.shape[1]))
    grid_size = int(np.sqrt(n))

    first_n_images = X[:n, :]

    fig, ax_array = plt.subplots(nrows=grid_size, ncols=grid_size,
                                    sharey=True, sharex=True, figsize=(8, 8))

    for r in range(grid_size):
        for c in range(grid_size):
            ax_array[r, c].imshow(first_n_images[grid_size * r + c].reshape((pic_size, pic_size)))
            plt.xticks(np.array([]))
            plt.yticks(np.array([])) 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import sqrt [as 別名]
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() 

# 需要導入模塊: import numpy [as 別名]
# 或者: from numpy import sqrt [as 別名]
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)