Pseudorandom Number Generators 2. Here is robust code to fit a 2D gaussian. numpy.random.multivariate_normal¶ numpy.random.multivariate_normal(mean, cov [, size])¶ Draw random samples from a multivariate normal distribution. ... (5,5,5)) # zero-mean, unit-variance Gaussian random numbers in a 5x5x5 array Indexing arrays. ... noise - standard deviation of gaussian noise; ... corresponding to the data point. random. in a single step. About normal: For random we are taking .normal() numpy.random.normal(loc = 0.0, scale = 1.0, size = None) : creates an array of specified shape and fills it with random values which is actually a part of Normal(Gaussian)Distribution. Generator of 2D gaussian random fields. We will use the same function as argument for curve fit to t noisy data to it. 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. Matrix Multiplication in NumPy is a python library used for scientific computing. diag (numpy. NumPy has an extensive list of methods to generate random arrays and single numbers, or to randomly shuffle arrays. fft. The multivariate normal, multinormal or Gaussian distribution is a generalization of the one-dimensional normal distribution to higher dimensions. NumPy contains a fast and memory-efficient implementation of a list-like array data structure and it contains useful linear algebra and random number functions. Here we will use NumPy library to create matrix of random numbers, thus each time we run our program we will get a random matrix. Problem Statement: Whenever plotting Gaussian Distributions is mentioned, it is usually in regard to the Univariate Normal, and that is basically a 2D Gaussian Distribution method that samples from a range array over the X-axis, then applies the Gaussian function to it, and produces the Y-axis coordinates for the plot. gistfile1.py import numpy as np: def makeGaussian (size, fwhm = 3, center = None): """ Make a square gaussian kernel. We use cookies to ensure you have the best browsing experience on our website. samples, . Instead of specifying the full covariance matrix, popular It might seem intuitive that a cumulative sum is a single number obtained by aggregation. By using our site, you 2D array are also called as Matrices which can be represented as collection of rows and columns.. Generator of 2D gaussian random fields. numpy.random.normal¶ random.normal (loc = 0.0, scale = 1.0, size = None) ¶ Draw random samples from a normal (Gaussian) distribution. Covariance matrix of the distribution. Required for Gaussian noise and ignored for Poisson noise (the variance of the Poisson distribution is equal to its mean). For example, multiplying the DFT of an image by a two-dimensional Gaussian function is a common way to blur an image by decreasing the magnitude of its high-frequency components. ... + 1j * numpy. import numpy as np # Optionally you may set a random seed to make sequence of random numbers # repeatable between runs (or use a loop to run models with a repeatable # sequence of random numbers in each loop, for example to generate replicate # runs of a model with … The two-dimensional DFT is widely-used in image processing. Stack Overflow for Teams is a private, secure spot for you and The randint() method takes a size parameter where you can specify the shape of an array. seed (50) # Covariance matrix def covMat (x1, x2, covFunc, noise = 0): cov = covFunc (scipy. To create a 2 D Gaussian array using Numpy python module. random. approximations include: This geometrical property can be seen in two dimensions by plotting In this article, Let’s discuss how to generate a 2-D Gaussian array using NumPy. generate link and share the link here. The probability distribution of each variable follows a Normal distribution. Simply pass the python list to np.array() method as an argument and you are done. Problem Statement: Whenever plotting Gaussian Distributions is mentioned, it is usually in regard to the Univariate Normal, and that is basically a 2D Gaussian Distribution method that samples from a range array over the X-axis, then applies the Gaussian function to it, and produces the Y-axis coordinates for the plot. 10 means mk from a bivariate Gaussian distribution N((1,0)T,I) and labeled this class BLUE. import numpy as np def makeGaussian(size, fwhm = 3, center=None): """ Make a square gaussian kernel. generated data-points: Diagonal covariance means that points are oriented along x or y-axis: Note that the covariance matrix must be positive semidefinite (a.k.a. size is the length of a side of the square: fwhm is full-width-half-maximum, which: can be thought of as an effective radius. """ numpy.random.multivariate_normal¶ random.multivariate_normal (mean, cov, size = None, check_valid = 'warn', tol = 1e-8) ¶ Draw random samples from a multivariate normal distribution. random. How to randomly place p elements in a 2D array? Μήτρα 2 × N, όχι συστοιχία 2D (μήτρα N × N). Populating the interactive namespace from numpy and matplotlib De ning a linear function to generate data. In other words, each entry out[i,j,...,:] is an N-dimensional real # Sets the standard deviation to one: This is 4 numpy generate random 2d array . And also passing axis = 0 to do all the tasks along rows. Please use ide.geeksforgeeks.org, In this we are specifically going to talk about 2D arrays. spatial. Returns-----image : 2D `~numpy.ndarray` Image containing random noise. Tag: python,numpy,scipy,gaussian. Classification,” 2nd ed., New York: Wiley, 2001. If no shape is specified, a single (N-D) sample is returned. The NumPy’s implementation discards one of the two generated Gaussians from the Box-Muller transform. value drawn from the distribution. Experience. whatever by Aryan Solanki on Nov 19 2020 Donate . brightness_4 Required for Gaussian noise and ignored for Poisson noise (the variance of the Poisson distribution is equal to its mean). T)) if noise: cov += numpy. seed int, optional. Given an input array, NumPy‘s cumsum() function calculates the cumulative sum of the values in the array. Tolerance when checking the singular values in covariance matrix. atleast_2d (x1). Covariance indicates the level to which two variables vary together. (average or “center”) and variance (standard deviation, or “width,” The probability density function of the normal distribution, first derived by De Moivre and 200 years later by both Gauss and Laplace independently , is often called the bell curve because of its characteristic shape (see the example below). Matrix with floating values element is the covariance of and . Compare the histograms of the two different denoised images. atleast_2d (x2). The following are 17 code examples for showing how to use numpy.random.multivariate_normal().These examples are extracted from open source projects. What is the NumPy cumsum() Function? The library uses Numpy+Scipy. positive-semidefinite for proper sampling. Strengthen your foundations with the Python Programming Foundation Course and learn the basics. Numpy.random.randn() function returns a sample (or samples) from the “standard normal” distribution. Functions used: numpy.meshgrid()– It is used to create a rectangular grid out of two given one-dimensional arrays representing the Cartesian indexing or Matrix indexing. I am currently predicting the parameters of a 2D XY gaussian distribution (mean_x, mean_y, std_x, std_y and corr), from which I subsequently sample to get the input at the next time-step. seed : int, optional A seed to initialize the `numpy.random.BitGenerator`. Parameters: X – 2d numpy array containing the initial inputs (one per row) of the model. Given a shape of, for example, (m,n,k), m*n*k samples are Cela génère directement une matrice 2d qui contient un 2d gaussien symétrique et mobile. simple numpy based 2d gaussian function Raw. In this article, Let’s discuss how to generate a 2-D Gaussian array using NumPy. standard deviation: Papoulis, A., “Probability, Random Variables, and Stochastic Recall that a random vector \\(X = (X_1, \\cdots, X_d)\\) has a multivariate normal (or Gaussian) distribution if every linear combination $$ \\sum_{i=1}^{d} a_iX_i, \\quad a_i\\in\\mathbb{R} $$ is normally distributed. numpy.random.normal¶ numpy.random.normal(loc=0.0, scale=1.0, size=None)¶ Draw random samples from a normal (Gaussian) distribution. There are different measures that we can use to do a descriptive analysis (distance, displacement, speed, velocity, angle distribution, indicator counts, confinement ratios etc) for random walks exhibited by a population. It calculates the moments of the data to guess the initial parameters for an optimization routine. A NumPy array is similar to Python's list data structure. random. is used to create a rectangular grid out of two given one-dimensional arrays representing the Cartesian indexing or Matrix indexing. ifft2 (noise * amplitude). If both 'flux' and 'amplitude' are specified, then 'flux' will be ignored. The randint() method takes a size parameter where you can specify the shape of an array. its seed : int, optional A seed to initialize the `numpy.random.BitGenerator`. The following are 30 code examples for showing how to use numpy.atleast_2d().These examples are extracted from open source projects. We will create these following random matrix using the NumPy library. That is if the array is 1D then it will make it to 2D and so on. I'm very new to Python but I'm trying to produce a 2D Gaussian fit for some data. This will return 1D numpy array or a vector. In Python, numpy.random.randn() creates an array of specified shape and fills it with random specified value as per standard Gaussian / normal distribution. exponential of all the elements in the input array. - ‘GP_MCMC’, Gaussian process with prior in the hyper-parameters. You can create numpy array casting python list. Behavior when the covariance matrix is not positive semidefinite. 2D Array can be defined as array of an array. Sample Solution:- Python Code: Matrix with floating values “numpy generate random 2d array” Code Answer’s. acknowledge that you have read and understood our, GATE CS Original Papers and Official Keys, ISRO CS Original Papers and Official Keys, ISRO CS Syllabus for Scientist/Engineer Exam, Adding new column to existing DataFrame in Pandas, Python program to convert a list to string, How to get column names in Pandas dataframe, Reading and Writing to text files in Python, isupper(), islower(), lower(), upper() in Python and their applications, Python | Program to convert String to a List, Taking multiple inputs from user in Python, Different ways to create Pandas Dataframe, Change the position of MessageBox - Tkinter, Difference between "__eq__" VS "is" VS "==" in Python, Python - Ways to remove duplicates from list, Check whether given Key already exists in a Python Dictionary, Python | Get key from value in Dictionary, Python program to check if a string is palindrome or not, Write Interview The multivariate normal, multinormal or Gaussian distribution is a generalization of the one-dimensional normal distribution to higher dimensions. Returns-----image : 2D `~numpy.ndarray` Image containing random noise. multivariate_normal (meanI, cov, datapointsI). Mahotas – Edges using Difference of Gaussian for binary image, ML | Variational Bayesian Inference for Gaussian Mixture, Python - Inverse Gaussian Distribution in Statistics, Python - Normal Inverse Gaussian Distribution in Statistics, Python - Reciprocal Inverse Gaussian Distribution in Statistics, Generate five random numbers from the normal distribution using NumPy, Generate Random Numbers From The Uniform Distribution using NumPy, Generate a matrix product of two NumPy arrays, Python | Numpy numpy.ndarray.__truediv__(), Python | Numpy numpy.ndarray.__floordiv__(), Data Structures and Algorithms – Self Paced Course, Ad-Free Experience – GeeksforGeeks Premium. generalization of the one-dimensional normal distribution to higher python by Lucifer the Hacker on Nov 07 2020 Donate . We can also simulate and discuss directed/biased random walks where the direction of … Specifically, stellar fluxes linked to certain positions in a coordinate system/grid. Generator of 2D gaussian random fields. Generates 2D gaussian random maps. In case you want to create 2D numpy array or a matrix, simply pass python list of list to np.array() method. In this post, we discussed how to simulate a barebones random walk in 1D, 2D and 3D. simple numpy based 2d gaussian function Raw. eturns number spaces evenly w.r.t interval. Because #This source code is public domain #Author: Christian Schirm import numpy, scipy.spatial import matplotlib.pyplot as plt import imageio def covMat (x1, x2, covFunc, noise = 0): # Covariance matrix cov = covFunc (scipy. Example. 57. Duda, R. O., Hart, P. E., and Stork, D. G., “Pattern Using NumPy random function 2D array is generated. I have run numpy.random.seed with seed value ‘100’ for more than 1000 times and pseudo-random values are the same every time. First it is said to generate. By Jay Parmar. Today we will learn the basics of the Python Numpy module as well as understand some of the codes. The variables in the map are spatially correlated. Generate a generic 2D Gaussian-like array (★★☆) hint: np.meshgrid, np.exp. Random Numbers with NumPy Using this library, we can perform complex matrix operations like multiplication, dot product, multiplicative inverse, etc. Add some noise (e.g., 20% of noise) Try two different denoising methods for denoising the image: gaussian filtering and median filtering. The drawn samples, of shape size, if that was provided. The following is probably true, given that 0.6 is roughly twice the 1 @Octopus: Η δειγματοληψία ενός 2D gaussian σάς προσφέρει έναν πίνακα 2-πλειάδων, δηλ. Generate a 1-D array containing 5 random … - ‘sparseGP’, sparse Gaussian process. The library uses Numpy+Scipy. import numpy as np from numpy import pi, r_ import matplotlib.pyplot as plt from scipy import optimize # Generate data points with noise num_points = 150 Tx = np. #!/usr/bin/env python import matplotlib.pyplot as plt import numpy import csv cov = [[25, 20], [20, 25]] # diagonal covariance, points lie on x or y-axis meanI = [70, 40] datapointsI = 2000 meanII = [60, 20] datapointsII = 2000 dataI = numpy. (★★☆) hint: np.put, np.random.choice. @user824624 Sample with replacement or without? covariance matrix. We can generate uniform random numbers - for example, rand() / RAND_MAX in C/C++ can be used to generate a number between 0 and 1. In this post, we will be learning about different types of matrix multiplication in the numpy library. Numpy.random.randn() function returns a sample (or samples) from the “standard normal” distribution. Creation of Random Numpy array. squared) of the one-dimensional normal distribution. - ‘InputWarpedGP’, input warped Gaussian process - ‘RF’, random forest (scikit-learn). T, numpy. atleast_2d (x1). The variables in the map are spatially correlated. Add some noise (e.g., 20% of noise) Try two different denoising methods for denoising the image: gaussian filtering and median filtering. Normalization of Numpy array using Numpy using Sci-kit learn Module Here np.newaxis is used to increase the dimension of the array. © Copyright 2008-2009, The Scipy community. 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. As a result, only one Gaussian sample is returned, hence the return f … To create a 2 D Gaussian array using Numpy python module, numpy.meshgrid(*xi, copy=True, sparse=False, indexing=’xy’), numpy.linspace(start, stop, num = 50, endpoint = True, retstep = False, dtype = None), numpy.exp(array, out = None, where = True, casting = ‘same_kind’, order = ‘K’, dtype = None), edit The multivariate normal, multinormal or Gaussian distribution is a generalisation of the one-dimensional normal distribution to higher dimensions. random.choice only works on 1d vectors, and there don't appear to be any other tools for sampling built into numpy. Array is a linear data structure consisting of list of elements. numpy.random.multivariate_normal¶ numpy.random.multivariate_normal (mean, cov [, size, check_valid, tol]) ¶ Draw random samples from a multivariate normal distribution. In probability theory and statistics, the multivariate normal distribution, multivariate Gaussian distribution, or joint normal distribution is a generalization of the one-dimensional normal distribution to higher dimensions.One definition is that a random vector is said to be k-variate normally distributed if every linear combination of its k components has a univariate normal distribution. It produces a new array as a result. Further exercise (only if you are familiar with this stuff): A “wrapped border” appears in the upper left and top edges of the image. ones (len (cov)) * noise) return cov numpy. The multivariate normal, multinormal or Gaussian distribution is a These parameters are analogous to the mean Integers. analogous to the peak of the bell curve for the one-dimensional or This is because the padding is not done correctly, and does not take the kernel size into account (so the convolution “flows out of bounds of the image”). The covariance matrix Transform this random Gaussian vector so that it lines up with the mean and covariance provided by the user. import numpy as np import scipy.ndimage.filters as fi def gkern2(kernlen=21, nsig=3): """Returns a 2D Gaussian kernel array.""" univariate normal distribution. The following are 30 code examples for showing how to use scipy.signal.gaussian().These examples are extracted from open source projects. “spread”). The probability density function of the normal distribution, first derived by De Moivre and 200 years later by both Gauss and Laplace independently , is often called the bell curve because of its characteristic shape (see the example below). numpy.random.multivariate_normal¶ numpy.random.multivariate_normal(mean, cov [, size])¶ Draw random samples from a multivariate normal distribution. generated, and packed in an m-by-n-by-k arrangement. About normal: For random we are taking .normal() numpy.random.normal(loc = 0.0, scale = 1.0, size = None) : creates an array of specified shape and fills it with random values which is actually a part of Normal(Gaussian)Distribution. print column in 2d numpy array . spatial. Create a binary image (of 0s and 1s) with several objects (circles, ellipses, squares, or random shapes). The multivariate normal, multinormal or Gaussian distribution is a generalization of the one-dimensional normal distribution to higher dimensions. location where samples are most likely to be generated. We first generate X, a 2D array, then use the Numpy methods to compare statistics against the parameters used. numpy.random.multivariate_normal¶ numpy.random.multivariate_normal(mean, cov [, size])¶ Draw random samples from a multivariate normal distribution. Such a distribution is specified by its mean and 58. The random module from numpy offers a wide range ways to generate random numbers sampled from a known distribution with a fixed set of parameters. 0.96000544 0.84936582 0.69256932 0.52045012 0.36044779 0.2300663  0.13533528][0.12992261 0.2208649  0.34603184 0.49963495 0.66487032 0.81539581 0.92161045 0.96000544 0.92161045 0.81539581 0.66487032 0.49963495 0.34603184 0.2208649  0.12992261][0.11494916 0.19541045 0.30615203 0.44205254 0.58824471 0.72142229 0.81539581 0.84936582 0.81539581 0.72142229 0.58824471 0.44205254 0.30615203 0.19541045 0.11494916][0.09372907 0.15933686 0.24963508 0.36044779 0.47965227 0.58824471 0.66487032 0.69256932 0.66487032 0.58824471 0.47965227 0.36044779 0.24963508 0.15933686 0.09372907][0.07043526 0.11973803 0.1875951  0.27086833 0.36044779 0.44205254 0.49963495 0.52045012 0.49963495 0.44205254 0.36044779 0.27086833 0.1875951  0.11973803 0.07043526][0.0487813  0.08292689 0.12992261 0.1875951  0.24963508 0.30615203 0.34603184 0.36044779 0.34603184 0.30615203 0.24963508 0.1875951 0.12992261 0.08292689 0.0487813 ][0.03113609 0.0529305  0.08292689 0.11973803 0.15933686 0.19541045 0.2208649  0.2300663  0.2208649  0.19541045 0.15933686 0.11973803 0.08292689 0.0529305  0.03113609][0.01831564 0.03113609 0.0487813  0.07043526 0.09372907 0.11494916 0.12992261 0.13533528 0.12992261 0.11494916 0.09372907 0.07043526 0.0487813  0.03113609 0.01831564]]. - ‘warperdGP’, warped Gaussian process. Je dois noter que j'ai trouvé ce code dans les archives de la liste de diffusion scipy et que je l'ai modifié un peu. NumPy: Generate a generic 2D Gaussian-like array Last update on February 26 2020 08:09:24 (UTC/GMT +8 hours) NumPy: Array Object Exercise-79 with Solution. It must be symmetric and This is Distribution is also known as Bell Curve because of its characteristics shape. Write a NumPy program to generate a generic 2D Gaussian-like array. Writing code in comment? If `None`, then fresh, unpredictable entropy will be pulled from the OS. Random seed 2d array. Processes,” 3rd ed., New York: McGraw-Hill, 1991. Attention geek! In Python, numpy.random.randn() creates an array of specified shape and fills it with random specified value as per standard Gaussian / normal distribution. #This source code is public domain #Author: Christian Schirm import numpy, scipy.spatial import matplotlib.pyplot as plt import imageio numpy. In probability theory and statistics, the multivariate normal distribution, multivariate Gaussian distribution, or joint normal distribution is a generalization of the one-dimensional normal distribution to higher dimensions.One definition is that a random vector is said to be k-variate normally distributed if every linear combination of its k components has a univariate normal distribution. each sample is N-dimensional, the output shape is (m,n,k,N). Write a NumPy program to create a 5x5 array with random values and find the minimum and maximum values. What is the equivalent of enumerate for numpy arrays? Here we will use NumPy library to create matrix of random numbers, thus each time we run our program we will get a random matrix. nonnegative-definite). Δεν βλέπω πώς είναι ανεπαρκές. NumPy, an acronym for Numerical Python, is a package to perform scientific computing in Python efficiently.It includes random number generation capabilities, functions for basic linear algebra and much more. ... That is if the array is 1D then it will make it to 2D and so on. Contribute to bsciolla/gaussian-random-fields development by creating an account on GitHub. close, link Otherwise, the behavior of this method is If 'flux' is specified, but not 'amplitude' then the 2D Gaussian amplitudes will be calculated and placed in the output table. For consistency, we will simplify refer to to SciPy, although some of the online documentation makes reference to NumPy. 55. The random.randn() function creates an array of specified shape and fills it with random values as per standard normal distribution. Step 3: Use the Methods defined here Method 1: Using the Numpy Python Library. The element is the variance of (i.e. Model parameters not defined in param_ranges will be set to the default value. The probability distribution of each variable follows a Normal distribution. NumPy (Numerical Python) is the core module for numerical computation in Python. Generating 1d Gaussian random numbers. It is important to emphasize the difference between the cumulative sum and the sum:. Generate Random Array. To begin with, your interview preparations Enhance your Data Structures concepts with the Python DS Course. size is the length of a side of the square: fwhm is full-width-half-maximum, which: can be thought of as an effective radius. """ undefined and backwards compatibility is not guaranteed. the shape is (N,). From the multivariate normal distribution, we draw N-dimensional If not, The random.randn() function creates an array of specified shape and fills it with random values as per standard normal distribution. Draw random samples from a multivariate normal distribution. If `None`, then fresh, unpredictable entropy will be pulled from the OS. This is Distribution is also known as Bell Curve because of its characteristics shape. How to generate 2-D Gaussian array using NumPy? With the same seed, the same 2D array with the same random numbers will be generated. The ravel() method returns the contiguous flattened array. distance_matrix (numpy. The mean is a coordinate in N-dimensional space, which represents the distance_matrix (numpy. check_valid : { ‘warn’, ‘raise’, ‘ignore’ }, optional. 56. To create a 2 D Gaussian array using Numpy python module Functions used: numpy.meshgrid() – It is used to create a rectangular grid out of two given one-dimensional arrays representing the Cartesian indexing or Matrix indexing. The correlations are due to a scale-free spectrum P(k) ~ 1/|k|^(alpha/2). This example serves simply to illustrate the syntax and format of NumPy's two-dimensional FFT implementation. 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. dimensions. However not all of the positions in my grid have corresponding flux values. The probability density function of the normal distribution, first derived by De Moivre and 200 years later by both Gauss and Laplace independently , is often called the bell curve because of its characteristic shape (see the example below). (★★☆) hint: np.ndenumerate, np.ndindex. NumPy: Create a 5x5 array with random values and find the minimum and maximum values Last update on February 26 2020 08:09:27 (UTC/GMT +8 hours) NumPy: Random Exercise-4 with Solution. numpy.random.normal¶ numpy.random.normal (loc=0.0, scale=1.0, size=None) ¶ Draw random samples from a normal (Gaussian) distribution. Random Numbers with Python 3. normal (size = (size, size)) # To real space: gfield = numpy. Compare the histograms of the two different denoised images. The multivariate normal, multinormal or Gaussian distribution is a generalization of the one-dimensional normal distribution to higher dimensions. You may simply gaussian-filter a simple 2D dirac function, the result is then the filter function that was being used:. gistfile1.py import numpy as np: def makeGaussian (size, fwhm = 3, center = None): """ Make a square gaussian kernel. A large portion of NumPy is actually written in the C programming language. We will create these following random matrix using the NumPy library. The correlations are due to a scale-free spectrum P(k) ~ 1/|k|^(alpha/2). Creating numpy array from python list or nested lists. This tutorial is divided into 3 parts; they are: 1. In NumPy we work with arrays, and you can use the two methods from the above examples to make random arrays. The probability density function of the normal distribution, first derived by De Moivre and 200 years later by both Gauss and Laplace independently , is often called the bell curve because of its characteristic shape (see the example below). numpy.random.normal¶ numpy.random.normal(loc=0.0, scale=1.0, size=None)¶ Draw random samples from a normal (Gaussian) distribution. I am trying to build in Python the scatter plot in part 2 of Elements of Statistical Learning. Python 2D Gaussian Fit with NaN Values in Data Tag: python , numpy , scipy , gaussian I'm very new to Python but I'm trying to produce a 2D Gaussian fit for some data. Create a binary image (of 0s and 1s) with several objects (circles, ellipses, squares, or random shapes). (The same array objects are accessible within the NumPy package, which is a subset of SciPy. code, 2D Gaussian array:[[0.36787944 0.44822088 0.51979489 0.57375342 0.60279818 0.602798180.57375342 0.51979489 0.44822088 0.36787944][0.44822088 0.54610814 0.63331324 0.69905581 0.73444367 0.734443670.69905581 0.63331324 0.54610814 0.44822088][0.51979489 0.63331324 0.73444367 0.81068432 0.85172308 0.851723080.81068432 0.73444367 0.63331324 0.51979489][0.57375342 0.69905581 0.81068432 0.89483932 0.9401382  0.94013820.89483932 0.81068432 0.69905581 0.57375342][0.60279818 0.73444367 0.85172308 0.9401382  0.98773022 0.987730220.9401382  0.85172308 0.73444367 0.60279818][0.60279818 0.73444367 0.85172308 0.9401382  0.98773022 0.987730220.9401382  0.85172308 0.73444367 0.60279818][0.57375342 0.69905581 0.81068432 0.89483932 0.9401382  0.94013820.89483932 0.81068432 0.69905581 0.57375342][0.51979489 0.63331324 0.73444367 0.81068432 0.85172308 0.851723080.81068432 0.73444367 0.63331324 0.51979489][0.44822088 0.54610814 0.63331324 0.69905581 0.73444367 0.734443670.69905581 0.63331324 0.54610814 0.44822088][0.36787944 0.44822088 0.51979489 0.57375342 0.60279818 0.602798180.57375342 0.51979489 0.44822088 0.36787944]], 2D Gaussian array:[[0.01831564 0.03113609 0.0487813  0.07043526 0.09372907 0.11494916 0.12992261 0.13533528 0.12992261 0.11494916 0.09372907 0.07043526 0.0487813  0.03113609 0.01831564][0.03113609 0.0529305  0.08292689 0.11973803 0.15933686 0.19541045 0.2208649  0.2300663  0.2208649  0.19541045 0.15933686 0.11973803 0.08292689 0.0529305  0.03113609][0.0487813  0.08292689 0.12992261 0.1875951  0.24963508 0.30615203 0.34603184 0.36044779 0.34603184 0.30615203 0.24963508 0.1875951 0.12992261 0.08292689 0.0487813 ][0.07043526 0.11973803 0.1875951  0.27086833 0.36044779 0.44205254 0.49963495 0.52045012 0.49963495 0.44205254 0.36044779 0.27086833 0.1875951  0.11973803 0.07043526][0.09372907 0.15933686 0.24963508 0.36044779 0.47965227 0.58824471 0.66487032 0.69256932 0.66487032 0.58824471 0.47965227 0.36044779 0.24963508 0.15933686 0.09372907][0.11494916 0.19541045 0.30615203 0.44205254 0.58824471 0.72142229 0.81539581 0.84936582 0.81539581 0.72142229 0.58824471 0.44205254 0.30615203 0.19541045 0.11494916][0.12992261 0.2208649  0.34603184 0.49963495 0.66487032 0.81539581 0.92161045 0.96000544 0.92161045 0.81539581 0.66487032 0.49963495 0.34603184 0.2208649  0.12992261][0.13533528 0.2300663  0.36044779 0.52045012 0.69256932 0.84936582 0.96000544 1.