RIM-create-gaussians

gaussians1.py

n = 50  # Size of spectrum
N = 5000  # Number of spectra
def gaussian(x, mu, sig):
    return 1*np.exp(-np.power(x - mu, 2.) / (2 * np.power(sig, 2.)))

def conv_mat(n):
    """
    Create convolution matrix that is an identity matrix with noise
    """
    conv_mat = np.eye(n)+np.random.normal(0, 0.05, (n,n))
    return conv_mat

def create_convolved(N):
    '''
    Create convolved Gaussian that are 28x28
    Args:
     n - number of Gausians
    Return:
     gaussians - List of convolved Gaussians
    '''
    a = 0.01  # Powerlaw slope
    gaussians_initial = []  # List of initial Gaussians
    powerlaw_conv = []  # List of Powerlaws used in convolution
    gaussians_final = []  # List of final Gaussians after convolution
    noise = []  # List of noises added
    for i in range(N):
        # Create original 1D Gaussian (32 points)
        x = np.linspace(-1,1,n)
        gaus_orig = gaussian(x, np.random.uniform(0,.01), np.random.uniform(0,0.1))
        gaussians_initial.append(gaus_orig)
        # Convolve with additional Gaussian
        conv_mat_ = conv_mat(n)
        gaus_conv = conv_mat_@gaus_orig
        # Add noise
        noise_ = np.random.normal(0,0.1, n)
        gaus_noise = gaus_conv + noise_
        gaussians_final.append(gaus_noise)
        powerlaw_conv.append(conv_mat_)
        noise.append(noise_)

    return gaussians_initial,gaussians_final,powerlaw_conv,noise

# Create N instances
gaussians_initial, gaussians_final,powerlaw_conv,noise = create_convolved(N)