text: square () Examples. Critically though, the Numpy square root function also works on Numpy arrays. Usually in envs that is used to evaluate algorithm, obs_rms should be passed in. audiolab import Sndfile: def rms_flat (a): """ Return the root mean square of all the elements of *a*, flattened out. Thus, the units of a power spectrum are often referred to as quantity squared rms, where quantity is the unit of the time-domain signal. Return the mean of the values over the requested axis. sum ( (A-B)**2))가 됩니다. misc import psychopy. 25 mac - homebrew 로 python 2. When you use the NumPy sum function without specifying an axis, it will simply add together all of the values and produce a single scalar. float) so this won’t work if your data is a mix of int, float and string data types. The task is to calculate the Root Mean Square (RMS) of the given numbers. Remote office citigroup 4. Fourier transform provides the frequency components present in any periodic or non-periodic signal. histogram for more info. NumPy is a popular Python library for data science. Voice Engine. improntadipensiero. array( [ [ 0 ], [ 1 ], [ 0 ], [ 1 ], [ 1 ], [ 0 ] ] ) What do you want the neural network to do?. audiolab import numpy as np # data is a numpy array containing audio frames # find the maximum value of this signal sample_max = abs(max(data) # find the RMS of the first channel of the signal rms = np. A Tensor, floating point value, or a schedule that is a tf. • Numpy/MA/MV" • Genutil (developed at LLNL) "– Commonly used functions to compute correlation, covariance, auto-correlation, auto-covariance, lagged correlation, lagged covariance, mean absolute difference, root mean square, standard deviation, variance, geometric mean, median, percentiles, linear regression, etc. store - if True then writes each path (numpy. Numpy rms - cnlt. The RMS of a time history is a measure of the signal’s overall energy and is often used when extracting features from a signal for prognosis and trending of vibration data. and 3rd is the degree of freedom which is a correction to the standard deviation. A bit of a detour to explain how the FFT returns its results. The Kabsch algorithm uses linear and vector algebra to find the optimal rotation and translation of two sets of points in N-dimensional space as to minimize the RMSD between them. Moreover, it is the origin of many machine learning algorithms. The first-ever NumPy community survey is LIVE! See https://numpy. An array in numpy can be one dimension and two, three, or higher. Source code: Lib/statistics. If not provided or None, a freshly-allocated array is returned. feature_names) We are. pylab as pl import scipy import sys from matplotlib. Which means, we will establish a linear relationship between the input variables ( X) and single output variable ( Y ). SoundFile objects. Waveform class have a time dimension, in which case they are represented as numpy arrays with shape [n_components, T]. Returns the standard deviation, a measure of the spread of a distribution, of the array elements. However, as I checked, RMSE and RMS are two different concepts. pandas set index integer not float. What is r2 score? The r2 score varies between 0 and 100%. CoodingDessign is the biggest, most confided in online network for engineers to learn, share and their programming information, and assemble their vocations. ndarray], ** kwargs: Any) → None [source] ¶. "If you can't explain it simply, you don't understand it well enough. NumPy stands for Numerical Python. RMSD — AdKGromacsTutorial 2. Numpy root mean square deviation. The bar above the squared differences is the mean (similar to x̄). Load a ziBin file containing demodulator samples as saved by the ziControl User Interface into a numpy structured array. The same result can be achieved through a number of paths. Then I made functions. CalcRMSDRotationalMatrix()). Numpy arrays: reduction operations Reduction operation Operation that extracts a single scalar from a full array e. x = linspace (0,4*pi,10); y = sin (x); Use polyfit to fit a 7th-degree polynomial to the points. You test the model using the testing set. call(objects: List[parselmouth. View Kenny Lam's profile on LinkedIn, the world's largest professional community. fft_tools import correlate2d, fast_ffts from. to some artificial noisy data. csv') data['rms'] = data. wrap_at方法的具体用法？. This implementation of RMSprop uses plain momentum, not Nesterov momentum. The residue root mean square fluctuation RMSF is a measure of the flexibility of a residue. NET developers with extensive functionality including multi-dimensional arrays and matrices, linear algebra, FFT and many more via a compatible strong typed API. 56539 #MeV/c2 hbarc = 197. Numpy rms Numpy rms. A 1-D numpy array of the linear programming root-mean-square deviations from each of the conformations in target to the frame-th conformation in reference. This uses numpy. x = linspace (0,4*pi,10); y = sin (x); Use polyfit to fit a 7th-degree polynomial to the points. import matplotlib. Returns the average of the array elements. An adventure in Nuclear Physics! Using the SFO effective interaction to calculate 11Be within the psd-space gives the ground state configuration:. Linear regression is one of the most popular techniques for modelling a linear relationship between a dependent and one or more independent variables. Keras Optimizers Explained with Examples for Beginners. The problem is treated as a supervised link attribute inference problem on a user. This is a two-dimensional NumPy array that has 2 rows and 30 columns. Calculating the 2D RMSD between two trajectories is a bit more finicky; DistanceMatrix can only calculate the RMSD of a trajectory to itself. SoundFile objects. 本文整理汇总了Python中astropy. var (dataset) print (variance) See the output. csv からデータを読み込む。. NumPy was originally developed in the mid 2000s, and arose from an even older package called Numeric. cosine similarity = (a. And to begin with your Machine Learning Journey, join the Machine Learning - Basic Level Course. Every SoundFile has a specific sample rate, data format and a set number of channels. Whether this is the desired result or not depends on the array subclass, for example numpy matrices will silently produce an incorrect result. 25 mac - homebrew 로 python 2. When the other trajectory in pairwise RMSD is a different trajectory, the pairwise RMSD can be used to compare the similarity of the two conformational ensembles. import numpy import math import plotly. head() Out [58]: TV. DURATION is the length of the generated sample. 本文整理汇总了Python中astropy. linspace (1, 12, 50) plt. Calculate variance for each entry by subtracting the mean from the value of the entry. wav: numpy. To round all of the values in the data array, pass data as the argument to the np. wrap_at方法的具体用法？. CICE is a computer code developed through years of community collaborations, which solve a collection of mathematical equations that represent the physical processes that occur during sea ice evolution: growth, melting, and movement of sea ice, along with the snow and melt water carried with it. Python standard deviation example using numpy. Many speaker manufactures give you both values for a given speaker. wavelet to be applied to data. json, will retry with next repodata source. CoodingDessign is the biggest, most confided in online network for engineers to learn, share and their programming information, and assemble their vocations. In format of excel, text, etc. This is one example of the versatility of masked arrays. I want to take the Root Mean Square of each column one by one and subtract it from the original array. Each layer is capable of performing two things: - Process input to get output: output = layer. For the RMS, I think this is the clearest: from numpy import mean, sqrt, square, arange a = arange (10) # For example rms = sqrt (mean (square (a))) The code reads like you say it: "root-mean-square". About the Team. Numpy is used for data manipulation and tkinter for the GUI and 'scope display. NumPy also allows Python developers to quickly perform a wide variety of numerical computations. Least squares fitting with Numpy and Scipy nov 11, 2015 numerical-analysis optimization python numpy scipy. pylab as pl import scipy import sys from matplotlib. import numpy as np import soundfile as sf rms = [np. See the following output. g: score ['mean-pearson_r2_score'] > 0. bins (sequence) – The bin edges for the gamma histogram; see numpy. Next, we'll need to import NumPy, which is a popular library for numerical computing. After you import NumPy and Matplotlib, you define two constants: SAMPLE_RATE determines how many data points the signal uses to represent the sine wave per second. See numpy. An example of how to calculate a root mean square using python in the case of a linear regression model: import matplotlib. This uses numpy. The amplitude spectrum gives the amplitudes of the sinusoidal the signal is built up from, and the RMS (root-mean-square) amplitudes can easily be found by dividing these amplitudes with :math:\\sqrt{2}. A tuple including four items: obs a numpy. Numpy is known for its NumPy array data structure as well as its useful methods reshape, arange, and append. The MSE either assesses the quality of a predictor (i. In problems with many points, increasing the degree of the polynomial fit using polyfit does not always result in a better fit. Here is a quick and easy guide to calculate RMSE in Excel. The primary goals of current energy conversion (CEC) technology being developed today are to optimize energy output and minimize environmental impact. So that the noise will be flattened. 2 documentation. safe_isnan(x)¶ numpy. rms on the difference between two arrays instead. 80% for training, and 20% for testing. Call a Praat command. The square root of complex number is also a complex number. Divide the gradient by the root of this average. Supporting Current Energy Conversion Projects through Numerical Modeling. sqrt () function can also be used to find the square root of complex numbers. target df = pd. Whether this is the desired result or not depends on the array subclass, for example numpy matrices will silently produce an incorrect result. ) – (float (ref) – optional) – Returns. nanmean() to use for the RMS difference calculation. NumPy (pronounced "numb pie") is one of the most important packages to grasp when you're starting to learn Python. audio_soundprocessing. Even if the energy seems to be within one bin, if the sampling is not synchronous with the signal, some spectral leakage may occur. The base class for any logger which is compatible with trainer. In the second video of the AC power series the basic mathematics behind calculating the root-mean-squared (RMS) value is being explained step-by-step. Calculate the test MSE on the observations in the fold. 1st is the NumPy array, containing the sample data. square () Examples. The unitcell dimensions of the system. In case you want to know how did the model predicted the values. Numpy rms - cnlt. array, power: bool = False, ref: float = 1. Built a linear regression model in CPU and GPU. Pls read the instructions carefullyy. 5 released 2021-01-05. csv file is same. 335-340), 1ame, i. 数値データであれば、pandas でなく、最初から numpy 配列として読み込んだほうがよいです。 loadtxt の引数は こちら など見ながらファイルに合わせて適宜変更してください。 # 最初の2000行をスキップして、data. Moreover, it is the origin of many machine learning algorithms. But there is no numpy. If it is ever adopted by SWIG developers, then it will be installed in a standard place where SWIG can find it. 時系列のサンプルデータとして、データ数 512 点、サンプリング間隔 dt=0. The formula is: Where: f = forecasts (expected values or unknown results), o = observed values (known results). , a mathematical function mapping a sample of data to an estimate of a parameter of the population from which the data is sampled). float64' object cannot be interpreted as an integer. The library is developed specifically to deal with Magnetic Resonance Imaging (MRI) radiofrequency (RF) coils. polyfit () function: import numpy as np #polynomial fit with degree = 3 model = np. next_states_val : numpy array of objects Each object is a numpy array that relates to one of the observations with size [batch_size * history size * size of punctual observation (which is 2D,1D or scalar)]. std(a, axis=None, dtype=None, out=None, ddof=0, keepdims=, *, where=) [source] ¶. Wikipedia defines r2 as. Urgently hiring. def rms_rfft(spectrum, n=None): """ Use Parseval's theorem to find the RMS value of an even-length signal from its rfft, without wasting time doing an inverse real FFT. Defaults to 1. Our Vision: To provide Free Online Training in the field of Artificial Intelligence for all. from numpy import mean, sqrt, square, arange a = arange (10) # For example rms = sqrt (mean (square (a))) The code reads like you say it: "root-mean-square". fft_tools import correlate2d, fast_ffts from. NumPy is a Python library used for working with arrays. I assume that you have basic knowledge of python programming and have used the basic libraries such as Numpy, Scipy, Pandas, Matplotlib and Sklearn. interpolate class WoodsSaxon: #grid setting rStart = 0. Use findpeaks from the Octave-Forge signal package through the oct2py bridge. 数値データであれば、pandas でなく、最初から numpy 配列として読み込んだほうがよいです。 loadtxt の引数は こちら など見ながらファイルに合わせて適宜変更してください。 # 最初の2000行をスキップして、data. abstract write (key: str, x: int, y: Union [int, numbers. event import psychopy. ndarray) in PSAnalysis. To round all of the values in the data array, pass data as the argument to the np. $60 -$75 an hour. I was recently challenged to make some MLPs with numpy and nothing else. 做个备份，对 numpy 不熟，每次都找函数找半天。 代码里分几块： 1. Compute the standard deviation along the specified axis. Available for free under the MIT/X11 License. The Root Mean Square (RMS) value of a set of values is the square root of the arithmetic mean (average) of the squares of the original values. linuxfestnorthwest. float64 intermediate and return values are used for integer inputs. Returns the standard deviation, a measure of the spread of a distribution, of the array elements. This is a two-dimensional NumPy array that has 2 rows and 30 columns. 3 Processing. This is very straightforward. 296-309 or i. How to Calculate RMSE in Excel. size) res = rms (row_data) print (res) #5. data without wavelet of size \([n_y \times n_x. In the code below, we show how to calculate the standard deviation for a data set. fix_invalid(). Next, we'll need to import NumPy, which is a popular library for numerical computing. Numpy rms Numpy rms. Numpy excels when applied to matrix type calculations (see the next section) however, it can be used to read in tabulated datasets - remember though that a numpy array must be all of the same type (e. Requires a rather complicated and not very efficient setup to be called from Python code. With over 1 million apps deployed per month, Bitnami makes it incredibly easy to deploy apps with native installers, as virtual machines, docker containers or in the cloud. The root mean square is also known by its initials RMS (or rms), and as the quadratic mean. 時系列のサンプルデータとして、データ数 512 点、サンプリング間隔 dt=0. p = polyfit (x,y,7); Evaluate the polynomial on a finer grid and plot the results. std (num))) See the following output. linear_model import LinearRegression from sklearn. y_train = np. A Tensor, floating point value, or a schedule that is a tf. Nevertheless, It’s also possible to do operations on arrays of different. K-means was implemented in python using numpy. v) d V ∫ V d V. By the operation of ndarray, you can get and set (change) pixel values, trim images, concatenate images, etc. json, will retry with next repodata source. See the following output. This function does broadcast, but will not “up-cast” int dtype arguments unless accompanied by at least one float or complex dtype argument (see Raises below). ; Roberts, J. def getRootMeanSquaredFeatureValue (self): r """ **14. What problem does it solve? If you understand RMSE: (Root mean squared error), MSE: (Mean Squared Error) and RMS: (Root Mean Squared), then asking for a library to calculate it for you is unnecessary over-engineering. mean(array ** 2))) Generally we prefer to let users write their own helper functions rather than put everything they could conceivably need in NumPy itself. Numpy is known for its NumPy array data structure as well as its useful methods reshape, arange, and append. 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. mean (a) AVERAGE (a) Trimmed mean. 0 and higher, including Mono, and. Let's take another example:. The optional parameter fmt is a convenient way for defining basic formatting like color, marker and linestyle. wrap_at方法的具体用法？. The amplitude spectrum gives the amplitudes of the sinusoidal the signal is built up from, and the RMS (root-mean-square) amplitudes can easily be found by dividing these amplitudes with :math:\\sqrt{2}. json, will retry with next repodata source. With numpy, the std () function calculates the standard deviation for a given data set. I assume that you have basic knowledge of python programming and have used the basic libraries such as Numpy, Scipy, Pandas, Matplotlib and Sklearn. rgommers closed this on Dec 17, 2018. Numpy is used for data manipulation and tkinter for the GUI and 'scope display. sparse matrix. Numpy is the fundamental Python package for scientific computing. Explore Numpy Openings In Your Desired Locations Now!. New to Plotly? Plotly is a free and open-source graphing library for Python. The toolkits work on them. Here are the steps for same: Step 1) Install NumPy pip install numpy Step 2)Import the NumPy Module. 30+ days ago. Familiarity with data-processing packages such as NumPy and Pandas Experience with machine-learning tools such as PyTorch, Tensorflow, or Scikit-Learn. , a mathematical function mapping a sample of data to an estimate of a parameter of the population from which the data is sampled). You may have an amp rated at 50W continuous (or RMS), but when dimed. """ ellipse_fit tests for performing elliptical fits on height and slopes profiles inputs: reads the heights profiles from dabam database without detrending, output: some statisti. This is a two-dimensional NumPy array that has 2 rows and 30 columns. rms, K1, D1, K2, D2, R, T all are "return values". CoodingDessign is the biggest, most confided in online network for engineers to learn, share and their programming information, and assemble their vocations. After you import NumPy and Matplotlib, you define two constants: SAMPLE_RATE determines how many data points the signal uses to represent the sine wave per second. It also has functions for working in domain of linear algebra, fourier transform, and matrices. The same result can be achieved through a number of paths. For the ground state, the percentage of the s-orbit is 71% and that of the d-orbital is 24%. Numpy arrays: reduction operations Reduction operation Operation that extracts a single scalar from a full array e. Legal Notice. py from AMATH 301 at University of Washington, Seattle. i0(x) [source] ¶ Modified Bessel function of the first kind, order 0. shape[0]) corresponds to rows, while the second (camera. mean(a, axis=None, dtype=None, out=None, keepdims=False) [source] ¶. requests are coming from a nginx tcp forwarder Is there a phrase for expressing something is 'very red'?. The mean, not including the extremes — for very noisy data. Numpy rms Numpy rms. pylab as pl import scipy import sys from matplotlib. targetdir named “filename( trajectory )XXX*infix*_psa”, where “XXX” is a number between 000 and 999; the extension of each. It includes building blocks such as KWS (keyword spotting), DOA (Direction Of Arrival). edited Sep 10 '14 at 15:58. parse_awg_waveform (wave_uint[, channels, …]) Converts a received waveform from the AWG waveform node into floating point and separates its contents into the respective waves (2 waveform waves and 1 marker wave), depending. sparse matrix. After you import NumPy and Matplotlib, you define two constants: SAMPLE_RATE determines how many data points the signal uses to represent the sine wave per second. The sub-module numpy. This function does broadcast, but will not “up-cast” int dtype arguments unless accompanied by at least one float or complex dtype argument (see Raises below). Compare Search ( Please select at least 2 keywords ) Most Searched Keywords. You can import numpy with the following statement:. In this application, we are plotting the two dimensional (2D) and three-dimensional (3D) graph by fetching the RMS (in X, Y, Z axis) values from the sensor wirelessly. CICE is a computer code developed through years of community collaborations, which solve a collection of mathematical equations that represent the physical processes that occur during sea ice evolution: growth, melting, and movement of sea ice, along with the snow and melt water carried with it. On the other hand, MATLAB uses "length" to denote the number of elements n in a vector. With numpy, the std () function calculates the standard deviation for a given data set. RMS Geospatial Development team designs and engineers the geographic information-management platform that underlies the company’s spectrum of applications. dBm to watts conversion calculator How to convert watts to dBm. Numpy is used for data manipulation and tkinter for the GUI and 'scope display. import pandas as pd import numpy as np window_size = 3 rms = lambda d: np. Compute the standard deviation along the specified axis. Computing the “signal to noise” ratio of an audio file is pretty simple if it’s already a wav file – if not, I suggest you convert it to one first. # Get x values of the sine wave. linalg implements basic linear algebra, such as solving linear systems, singular value decomposition, etc. 3 and higher (with builds for. Numpy excels when applied to matrix type calculations (see the next section) however, it can be used to read in tabulated datasets - remember though that a numpy array must be all of the same type (e. So, we can assume the equation. 重采样 多重采样 numpy数组 python numpy python-numpy 一个数组 数据采样 采样位数 采样点数 音频重采样 python numpy Python NumPy Python numpy Python&NumPy ADC采样 numpy NumPy Numpy numpy Numpy Python 重采样 库 hi3518 重采样 alsa重采样 ffplay 重采样 histc 重采样 pcm. 30+ days ago. Numpy rms Numpy rms. float64 intermediate and return values are used for integer inputs. It also has functions for working in domain of linear algebra, fourier transform, and matrices. cosine similarity = (a. i file is currently located in the numpy/docs/swig sub-directory under the numpy installation directory. Pls read the instructions carefullyy. What is RMSE? Also known as MSE or RMS. matplotlib. NET is the most complete. The 2D numpy array is stored in C-order (row-major). Calculating the 2D RMSD between two trajectories is a bit more finicky; DistanceMatrix can only calculate the RMSD of a trajectory to itself. This uses numpy. The rms of a discontinuous triangle waveform is this multiplied by the square root of mark-space ratio, which as the ratio is 0. In this NumPy Mean tutorial, we shall calculate mean of elements in a array, as a whole, or along an axis, or multiple axes, using numpy. The notation for L 1 norm of a vector x is ‖ x ‖ 1. float32 internally). arange (0, 10, 0. """ ellipse_fit tests for performing elliptical fits on height and slopes profiles inputs: reads the heights profiles from dabam database without detrending, output: some statisti. docx from AMATH 301 at University of Washington, Seattle. We will see how to do this in code and what effect it has on image appearance below, but here is the effect on the intensity histogram: import numpy as np import scipy. 0 features ulab (pronounced: micro lab), a Python package for quickly manipulating arrays of numbers. Welcome to Intellipaat Community. :param x: the time series to calculate the feature of:type x: numpy. Sergii Boiko. Y_predict = X_b. This is a two-dimensional NumPy array that has 2 rows and 30 columns. 13 cannot be used on Windows XP or earlier. csv file is same. The MSE either assesses the quality of a predictor (i. i file is currently located in the numpy/docs/swig sub-directory under the numpy installation directory. I did it a few times for processing EEG signals as well. In Part 1 of our series on writing efficient code with NumPy we cover why loops are slow in Python, and how to replace them with vectorized code. To begin with, your interview preparations Enhance your Data Structures concepts with the Python DS Course. A projection is formed by drawing a set of parallel rays through the 2D object of interest, assigning the integral of the object's contrast along each ray to a single pixel in the projection. Choose one of the folds to be the holdout set. pad for valid values. The learning rate. Numpy rms Numpy rms. #!/usr/bin/env python # # Hi There! # # You may be wondering what this giant blob of binary data here is, you might # even be worried that we're up to something nefarious (good for you for being # paranoid!). Call the integrate () method on an FeMesh object. 000001 else : #Update the structure by moving all the atoms in #this model (not just the ones used for the alignment) super_imposer. This function does broadcast, but will not “up-cast” int dtype arguments unless accompanied by at least one float or complex dtype argument (see Raises below). This site hosts packages and documentation uploaded by authors of packages on the Python Package Index. Calculate the root mean square. This is one example of the versatility of masked arrays. We will see how to do this in code and what effect it has on image appearance below, but here is the effect on the intensity histogram: import numpy as np import scipy. S= NX 1 i=0 y i Again, could be done with a for loop: S = 0 for i in range(N): S = S + y[i] But is computationally faster with numpy reduction methods S = np. The centered version additionally maintains a moving average of the gradients, and uses that average to estimate the variance. plot (polyline, model (polyline. normalisation. 0 print ('mse: ', mse) Another solution is to use the python module sklearn:. Computing the RMS value from audio samples is faster as it doesn't require a STFT calculation. blocks ('myfile. We show a bunch of examples for DeepChem by the doctest style. call(objects: List[parselmouth. To begin with, your interview preparations Enhance your Data Structures concepts with the Python DS Course. I defined a Goertzel class that saved the norm and coefficients, then had a filter () method to apply the filter. Compute area root-mean-square difference between two quantities. Net? nginx deny all requests to a virtual host. In mathematics, the root mean square (abbreviated RMS or rms) is a statistical measure of the magnitude of a varying quantity. class Layer: """ A building block. We wish to maximize this. def func (x, a, b): return a + b * b * x # Term b*b will create bimodality. The root mean square can be then calculated in python: (4) m s e = 1 m ∑ i = 1 m ( θ T. 本文整理汇总了Python中astropy. Numpy rms Numpy rms. A 2D array (masked numpy) of values, for a total of ncol * nrow entries. sum ( (Y_predict-Y)**2 ) / 1000. In bioinformatics, the root-mean-square deviation of atomic positions is the measure of the average distance between the atoms of superimposed proteins. MDAnalysis provides a DistanceMatrix class for easy calculation of the pairwise RMSD of a trajectory to itself. read_csv("Bike. As the figure above shows, the unweighted fit is seen to be thrown off by the noisy region. 유클리드 거리는 두 점 사이의 거리를 구할 때 많이 사용하는 방법으로 2차원 뿐만 아니라 다차원상의 두 점 간의 거리 계산에도 사용이 됩니다. average() function computes the weighted average of elements in an array according to their respective weight given in another array. Voice Engine. Pls read the instructions carefullyy. The same formula can be written with the following, slightly different, notation (Barnston, 1992): Where: Σ = summation (“add up”) (z f. Summation: It is just a Greek Symbol to tell you to add up a whole list. power(data[:0], 2)), 0. In “An introduction to Statistical Learning,” the authors. Extensions to gradient descent like AdaGrad and RMSProp update the algorithm to use a separate step size for. (6) for any positive constant. sqrt ( (d ** 2 ). Show this page source. If we simply want to set the NaNs to a number (say, 0) for processing in some later routine, we can do it easily with np. Explore how to implement real-life use cases. All these metrics are a single line of python code at most 2 inches long. import pandas as pd import numpy as np window_size = 3 rms = lambda d: np. Keras RMSProp Optimizer (Root Mean Square Propagation) 3. This module provides functions for calculating mathematical statistics of numeric ( Real -valued) data. The values of each item in this NumPy array correspond to the coefficient on that specific feature in the data set. NumPyとは、Pythonの学術計算ライブラリになります！ ndarrayというNumPyの配列を使用し、 高速に少ないコード量 で様々な数値計算が行えます。 NumPyの四則演算や様々な数学計算はこちらの記事にも紹介されていますので参考にしてください！. About the Team. rms_current object1, selection1, object2, selection2 e. The live streaming on 2D and 3D has various uses but for the basic start, we have used. 2 documentation. data y = boston. NET initiative and is the result of merging dnAnalytics with Math. 2002 mitsubishi eclipse gt parts 1. csv からデータを読み込む。. Must be an numpy. The bar above the squared differences is the mean (similar to x̄). Essentially, the NumPy sum function is adding up all of the values contained within np_array_2x3. Python numpy. safe_isinf(x)¶ numpy. One thing you may not have considered is that when taking a spectrum, not all the energy is in one "bin" or element of the spectrum array. fft import rfft, irfft: from numpy import argmax, sqrt, mean, absolute, arange, log10: import numpy as np: try: import soundfile as sf: except ImportError: from scikits. 0 Desktop is written in Python and includes the Numpy extension for numerical analysis. Within the C code (backend for python functions), arrays are stored in 1D, C-order and are usually named p_map_v in the code. 1st is the NumPy array, containing the sample data. event import psychopy. Critically though, the Numpy square root function also works on Numpy arrays. 8% THD (the author regularly sees 5% THD on mains). rms_flat(a)¶ Return the root mean square of all the elements of a, flattened out. This will give the variance. Consider the following data giving the absorbance over a path length of 55 mm of UV light at 280 nm, A, by a protein as a function of the concentration, [ P]: We expect the absorbance to be linearly related to the protein concentration: A = m [ P. To know about RMS Prop, we need to know about R prop. The long term goal is to use this as the basis for other instruments like a tachometer, rms voltmeter, wattmeter, tachometer, lock in amplifier, capacitance and inductance meters, etc. NumPy already has a very large API to maintain. Consider the following data giving the absorbance over a path length of 55 mm of UV light at 280 nm, A, by a protein as a function of the concentration, [ P]: We expect the absorbance to be linearly related to the protein concentration: A = m [ P. csv からデータを読み込む。. ndarray' object has no attribute 'diff'. pyplot as plt import numpy as np from scipy. The MSE either assesses the quality of a predictor (i. sizes if NumPy can transform these arrays so that they all have. There is no requirement that the two trajectories be the same length. RMS (root mean squared error) calculation is missing from numpy package #15940. If it is ever adopted by SWIG developers, then it will be installed in a standard place where SWIG can find it. metrics as metrics import matplotlib. When the other trajectory in pairwise RMSD is a different trajectory, the pairwise RMSD can be used to compare the similarity of the two conformational ensembles. blocks ('myfile. eval_measures. norm = numpy. It gives a sense for the typical size of the numbers. import numpy as np import soundfile as sf rms = [np. nanmean() to use for the RMS difference calculation. rms_flat(a)¶ Return the root mean square of all the elements of a, flattened out. NumPy was created in 2005 by Travis Oliphant. std () to calculate standard deviation. std (a, axis=None, dtype=None, out=None, ddof=0, keepdims=) [source] ¶. Defaults to 0. In Part 1 of our series on writing efficient code with NumPy we cover why loops are slow in Python, and how to replace them with vectorized code. The root mean square is also known by its initials RMS (or rms), and as the quadratic mean. Finally, apply numpy. numpy square () int array. Compute root-mean-square (RMS) value for each frame, either from the audio samples y or from a spectrogram S. interpolate import. open(biasfile) # copy the image data into a. If you haven't already, download Python and Pip. By Ayoosh Kathuria. Random forest is an ensemble machine learning algorithm. 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. The RMSE value of our is coming out to be approximately 73 which is not bad. layers import Dense, LSTM, Embedding, RepeatVector from keras. This example uses norm(x)/sqrt(n) to obtain the root-mean-square (RMS) value of an n-element vector x. If not given, it will initialize a new one. CICE is a computer code developed through years of community collaborations, which solve a collection of mathematical equations that represent the physical processes that occur during sea ice evolution: growth, melting, and movement of sea ice, along with the snow and melt water carried with it. wrap_at方法的具体用法？. pyplot as plt # Chose a model that will create bimodality. size) data = pd. View real-time and historical performance metrics in an intuitive dashboard and easily drill down into details to uncover the root cause of performance problems. MaskedArray The array for which to calculate the background RMS value. around() function. i0(x) [source] ¶ Modified Bessel function of the first kind, order 0. A limitation of gradient descent is that it uses the same step size (learning rate) for each input variable. Numpy rms Numpy rms. The Numpy module of python is the toolkit. Let's take another example:. is the root mean square (rms) amplitude of the sinusoidal component at frequency k. shape[1]) corresponds to columns, with the origin (camera[0, 0]) at the top-left corner. You will slowly get a hang on how when you deal with PyTorch tensors, you just keep on making sure your raw data is in numpy form to make sure everything's good. Data is parsed from the logs, but what is done with that info, and which info is analyzed is up to the user. Returns: d: numpy. We also dig deep into how broadcasting works, along with a few practical examples. ndarray) in PSAnalysis. dot (V, W) and B can be rotated. We will see how to do this in code and what effect it has on image appearance below, but here is the effect on the intensity histogram: import numpy as np import scipy. A straight-line best fit is just a special case of a polynomial least-squares fit (with deg=1 ). blocks ('myfile. 0 print ('mse: ', mse) Another solution is to use the python module sklearn:. json): done Solving environment: failed with current_repodata. A simple histogram can be a great first step in understanding a dataset. The output volume. If we simply want to set the NaNs to a number (say, 0) for processing in some later routine, we can do it easily with np. ] parD = [1. 0 released 2020-12-31. Returns the standard deviation, a measure of the spread of a distribution, of the array elements. the RMS (root mean squared) value of a signal is a way of expressing its average (mean) power. We want to think of ŷᵢ as an underlying physical quantity, such as the exact distance from Mars to the Sun at a particular point in time. To calculate the norm, you need to take the sum of the absolute vector values. ndarray], ** kwargs: Any) → None [source] ¶. from numpy import mean, sqrt, square, arange a = arange (10) # For example rms = sqrt (mean (square (a))) The code reads like you say it: "root-mean-square". Download Windows installer (32-bit) Download Windows installer (64-bit) Python 3. NET initiative and is the result of merging dnAnalytics with Math. And RMSD can. The average is taken over the flattened array by default, otherwise over the specified axis. This algorithm allows to make a double sided detection, which means it will detect both local maxima and minima in a single run. scatter (x, y) plt. The usage is extended into the physical sciences and related technologies in the same context. A limitation of gradient descent is that it uses the same step size (learning rate) for each input variable. It goes hand-in-hand with numpy where the combination of array operations and C compiling can speed your code up by several orders of magnitude. Must be an numpy. py from CS 570 at The University of Sydney. NumPy is a Python library used for working with arrays. Next, we'll need to import NumPy, which is a popular library for numerical computing. import numpy, math import scipy. Step 4: Instantiate Optimizer Class. ndarray:return: the value of this feature:return type: float """ return np. dot(vect,vect)) def vnorm(vect. CICE is a computer code developed through years of community collaborations, which solve a collection of mathematical equations that represent the physical processes that occur during sea ice evolution: growth, melting, and movement of sea ice, along with the snow and melt water carried with it. convert ( 'L' )) print (im. def rms_rfft(spectrum, n=None): """ Use Parseval's theorem to find the RMS value of an even-length signal from its rfft, without wasting time doing an inverse real FFT. Linear regression is one of the most popular techniques for modelling a linear relationship between a dependent and one or more independent variables. identity(3)) < 0. store – if True then writes each path (numpy. sum(float_array) Real function: def calc_rms(float_array): return np. Note that Python 3. float32 internally). Download Windows embeddable package (64-bit) Download Windows help file. Waveform class have a time dimension, in which case they are represented as numpy arrays with shape [n_components, T]. A Tensor, floating point value, or a schedule that is a tf. But there is no numpy. Nevertheless, it is sufficiently general to be adopted in any. The library is developed specifically to deal with Magnetic Resonance Imaging (MRI) radiofrequency (RF) coils. Sample code. Let's Get Start. edited Sep 10 '14 at 15:58. In mathematics, the root mean square (abbreviated RMS or rms) is a statistical measure of the magnitude of a varying quantity. 14 Manual ここでは以下の内容について説明する。numpy. , where p is the RMS of the sound wave in Pascals and p0 is 20 micro Pascals. NumPy already has a very large API to maintain. Call the integrate () method on a Function object. Get your technical queries answered by top developers !. it Numpy rms. If a self-described xarray or pandas object, attempts are made to use this array’s metadata to fill in other unspecified arguments. The Kabsch algorithm uses linear and vector algebra to find the optimal rotation and translation of two sets of points in N-dimensional space as to minimize the RMSD between them. matplotlib. fit' # 'dark_25c_1s. @set_property ("fctype", "simple") @set_property ("minimal", True) def root_mean_square (x): """ Returns the root mean square (rms) of the time series. import numpy as np print ("RMS: %r " % np. Right click this link and save the file to a location on your machine. product, np. :param N: Amount of FFT bins. In case you have a higher RMSE value, this would mean that you probably need to change your feature or probably you need to tweak your hyperparameters. amplitude = np. MaskedArray The array for which to calculate the background RMS value. bin_edges (numpy. If not provided or None, a freshly-allocated array is returned. 5」と記述します。その他にも組み込み関数や、mathモジュールやNumPyモジュールの関数を使って平方根を計算することができます。. Hoehn and Niven (1985) show that. safe_isinf(x)¶ numpy. i file is currently located in the numpy/docs/swig sub-directory under the numpy installation directory. sqrt ( (d ** 2 ). A tuple including four items: obs a numpy. GPU tensor. Keras RMSProp Optimizer (Root Mean Square Propagation) 3. The Root Mean Square (RMS) value of a set of values is the square root of the arithmetic mean (average) of the squares of the original values. Paste 2-columns data here (obs vs. Image processing with Python, NumPy. Below is a partial list of third-party and operating system vendor package managers containing NumPy and SciPy packages. Nov 28, 2018 · numpy. mean((predicted - expected) ** 2))) RMS. abstract write (key: str, x: int, y: Union [int, numbers. apply(alt_model. 以下のような簡単なプログラムで fft 関数の使い方を説明していきます。. For simusiodal signals, the RMS value is 0. Numpy rms Numpy rms. py to calculate RMS faster in the frequency domain and example. 4)) TRIMMEAN (a, alpha) Harmonic mean. Ans: RMS Prop is an optimization technique which is not published yet used for Neural Networks. Definition and basic properties. Average is rather a familiar and intuitive concept while RMS is a concept explicitly based on a mathematical definition. See the following example. Numpy rms Numpy rms. NumPy is a popular Python library for data science. Returns the standard deviation, a measure of the spread of a distribution, of the array elements. 本文整理汇总了Python中astropy. Numpy Root-Mean-Squared(RMS)信号平滑 相关文章 原文信息 ： Numpy Root-Mean-Squared(RMS)信号平滑 标签 iteration numpy scipy 栏目 Linux. Parameters (float) (rms) – (bool (power) – optional) (Reference value for decibel scale. , a function mapping arbitrary inputs to a sample of values of some random variable), or of an estimator (i. How to Calculate RMSE in Excel. wrap_at方法的典型用法代码示例。如果您正苦于以下问题：Python Angle. Net Standard 1. CPU tensor. dtype) print (im) (533, 800) uint8 [ [156 159 162 , 135 132 130] [156 155 155 , 133 132 133] [155 153 155. mean(array ** 2))) Generally we prefer to let users write their own helper functions rather than put everything they could conceivably need in NumPy itself. Before I get started let's see some notation that is commonly used in Machine Learning: Summation. It gives a sense for the typical size of the numbers. rgommers closed this on Dec 17, 2018. To make use of NumPy, we have to install it and import it. wrap_at方法的具体用法？. py from CS 570 at The University of Sydney. Get microphone signals and calculates RMS level. Calculate the root mean square. csv') data['rms'] = data. use('ggplot') import seaborn as sns. 本文整理汇总了Python中astropy. mean (block ** 2)) for block in sf. I was recently challenged to make some MLPs with numpy and nothing else. Keras RMSProp Optimizer (Root Mean Square Propagation) 3. ndarray) – the time series to calculate the feature of; param – contains dictionaries {“f_agg”: x, “maxlag”, n} with x str, the name of a numpy function (e. rotran[1])) < 0. Least squares fitting with Numpy and Scipy nov 11, 2015 numerical-analysis optimization python numpy scipy. Then I made functions. coordinates. The same formula can be written with the following, slightly different, notation (Barnston, 1992): Where: Σ = summation (“add up”) (z f. mean(a, axis=None, dtype=None, out=None, keepdims=False) [source] ¶. Using NumPy to get the index of an element in a list.


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# Find the Fourier series for $f(\theta)=\theta^2$ and prove $\Sigma^\infty_{n=1} \frac{1}{n^2}=\frac{\pi^2}{6}$

Find the Fourier series for $$f(\theta)=\theta^2$$ and use Parseval's identity for $$f$$ to derive the identity:

$$\sum^\infty_{n=1} \frac{1}{n^2}=\frac{\pi^2}{6}$$

In addition, find the expansion for $$f$$ in terms of the functions $$\{1, \cos(2\pi \theta), \sin(2\pi \theta), \cos(4\pi \theta),....\}$$

Here is a link explaining Parsevals identity: https://en.wikipedia.org/wiki/Parseval%27s_identity

Can somebody help me with this one? There seems to be a lot going on and a lot of these ideas are really new to me. I'm trying to follow a proof we got in class that we can use the fourier expansion $$f(x)=\theta$$ on $$[0,1)$$ to show that

$$\sum^\infty_{n=1} \frac{1}{n^4}=\frac{\pi^2}{6}$$

But the proof is sort of confusing, and I don't see how I could adapt it. I'd really appreciate some help on this one! Thanks MSE!!

• No need Parseval for this. See here. Maybe you wish $\sum_{n}\frac{1}{n^4}$ ? – Surb Apr 8 at 14:45
• Why don't you post the proof that you saw in class and how you're attempting to adapt it? – cmk Apr 8 at 14:55
• Thanks @Surb. Does that last equality somehow equal $\frac{\pi^2}{6}$?? They are close with $\frac{\pi^2}{3}$ + extra terms. – HaKuNa MaTaTa Apr 8 at 15:12
• No it's not correct. But Parseval will help you to compute it. – Surb Apr 8 at 15:13
• Ahh okay okay hmm interesting... I don't see a mistake in the computations though.... I'm still a little stuck, could you walk me through this? – HaKuNa MaTaTa Apr 8 at 15:15

You don't need Parseval (which will square your coefficients so it will give you something with $$n^4$$). From this question, $$f(x)=\frac{\pi^2}{3}+4 \ \sum_{n=1}^{+\infty} \frac{(-1)^n}{n^2} \ \cos(nx).$$ As $$f$$ is differentiable everywhere, we have pointwise convergence. Then, evaluating at $$\pi$$, $$\pi^2=f(\pi)=\frac{\pi^2}{3}+4 \ \sum_{n=1}^{+\infty} \frac{(-1)^n}{n^2} \ \cos(n\pi) =\frac{\pi^2}{3}+4 \ \sum_{n=1}^{+\infty} \frac{1}{n^2} .$$ Then $$\sum_{n=1}^{+\infty} \frac{1}{n^2} =\frac14\,\left(\pi^2-\frac{\pi^2}3\right)=\frac{\pi^2}6.$$
If you were to use Parseval for this function, what you get is $$\frac{2\pi^5}5=\int_{-\pi}^\pi (t^2)^2\,dt=\pi\,\left(2{a_0^2}+\sum_{n=0}^\infty a_n^2\right)=\pi\left(\frac{2\pi^4}{9}+\sum_{n=1}^\infty\frac{16}{n^4}\right).$$ Solving, you get $$\sum_{n=1}^\infty\frac{1}{n^4}=\frac1{16}\left(\frac{2\pi^4}5-\frac{2\pi^4}9\right)=\frac{\pi^4}{90}$$
As has been noted, Parseval with this choice of $$f$$ sums $$\tfrac{1}{n^4}$$, not $$\tfrac{1}{n^2}$$. So let's do the latter with Parseval on $$g(\theta)=\theta$$ instead. From here, $$g=-2\sum_{n\ge1}\tfrac{(-1)^n}{n}\sin n\theta$$, so$$\tfrac23\pi^3=\int_{-\pi}^\pi\theta^2 d\theta=4\pi\sum_{n\ge1}\tfrac{1}{n^2}\implies\sum_n\tfrac{1}{n^2}=\tfrac16\pi^2.$$


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# Every neighborhood $N_r(x)$ in $\mathbb{R}^n$ is connected

I am working on an exercise in baby Rudin (Ex 2.20 in particular) and as part of that I am trying to show that any neighborhood in a metric space is connected. I've seen several differing definitions of neighborhoods and connectedness on this site while searching for a solution so I want to be clear about what definition Rudin uses at this point.

In metric space $X$ with metric $d$ a neighborhood of $x \in X$ of radius $r \in \mathbb{R}$ and $r > 0$ is $N_r(x) = \{y \in X \,|\, d(y,x) < r\}$.

The closure of a set $E \subseteq X$ is $\overline{E} = E \cup E'$, where $E'$ is the set of limit points of $E$.

The interior of $E \subseteq X$ is the set of interior points of $E$ and is denoted here by $E^\circ$.

Two subsets of $X$, $A$ and $B$, are separated if $A \cap \overline{B} = \emptyset$ and $\overline{A} \cap B = \emptyset$.

A set $E \subseteq X$ is connected if it is not the union of two separated nonempty sets, i.e. if $\lnot \exists A \exists B (E=A \cup B \land A \neq \emptyset \land B \neq \emptyset \land A \cap \overline{B} = \emptyset \land \overline{A} \cap B = \emptyset)$

This last definition is logically equivalent to $\forall A \forall B ([E=A \cup B \land A \neq \emptyset \land B \neq \emptyset] \to [A \cap \overline{B} \neq \emptyset \lor \overline{A} \cap B \neq \emptyset])$

So if $E$ is some neighborhood in $X$ then consider any $A$ and $B$ where $E = A \cup B$, $A \neq \emptyset$, and $B \neq \emptyset$. We must then show that $A \cap \overline{B} \neq \emptyset \lor \overline{A} \cap B \neq \emptyset$. First if $A \cap B \neq \emptyset$ then clearly they are not separated so we need only worry about the case where $A \cap B = \emptyset$, i.e. they are disjoint. I think I can show this if both $A$ and $B$ are not open because if $A$ is not open then $\breve{A} = A - A^\circ \neq \emptyset$ and I can show that any $x \in \breve{A}$ is a limit point of $B$ thus $A \cup \overline{B} \neq \emptyset$, using the facts that $E=A \cup B$ and $E$, being a neighborhood, is open.

However I am having trouble showing that both $A$ and $B$ cannot both be open despite thinking about it for days. It was shown in a previous exercise that two disjoint open sets are separated but obviously we can't use this since we are trying to show that the arbitrary $A$ and $B$ are not separated. I am thinking that a proof by contradiction is the way to go here and to show that if they are both open then $\exists x \in E (x \not\in A \cup B)$ so that $E \neq A \cup B$ but I cannot pin down how to show this.

Anybody have any insights that might help me out here?

NOTE: It has been brought to my attention below that not every $N_r(x)$ in every metric space is connected, e.g. $X=\mathbb{Z}$ for $r > 1$. So really I am talking specifically about $\mathbb{R}^2$, though I suspect it is true in any $\mathbb{R}^n$. Of course this implies that we'd probably need to use the fact that we are in $\mathbb{R}^n$ in the proof.

• According to my copy, 2.20 asks if closure and interior of a connected set is connected. (Which edition are you using?) – user99914 Jul 6 '15 at 15:44
• Yes, mine is the same. This is regarding the interior part of the question, to which the answer is no. Consider the set he has for the solution here. I am trying to first show that the set he constructs is in fact connected. Showing that its interior is not will be pretty easy. – kyp4 Jul 6 '15 at 16:25
• The rational numbers, $\Bbb Q$, are a perfectly good metric space, and the only connected subsets are the singletons. – Lubin Jul 6 '15 at 16:49

No, not all neighbourhoods are connected. For example, in $\mathbb R$ with the usual metric, $(-1,1) \cup (2,3)$ is a disconnected neighbourhood of $0$. A neighbourhood of $x$ is not $N_r(x)$, it's any set that contains $N_r(x)$.
But it's also not true that $N_r(x)$ is connected. For example, in $\mathbb Z$ with the usual metric, $N_r(x)$ is disconnected if $r > 1$.
It's also not true that in a connected metric space, $N_r(x)$ is connected. A counterexample is the "topologist's sine curve".
• I am using Rudin's definition of neighborhood, which unless I am mistaken about his definition at the top of page 32, is just $N_r(x)$ as defined above and does not include any points outside of $N_r(x)$. You are right about $\mathbb{Z}$ though, good point. In particular I am trying to show this for any $N_r(x)$ in $\mathbb{R}^2$, though I suspect any such neighborhood (as defined above) is connected in any $\mathbb{R}^n$. – kyp4 Jul 6 '15 at 16:29
• I was very surprised that baby Rudin used this non-standard definition of "neighborhood", which everybody else would call "open ball". When you get to grown-up Rudin ("Real and Complex Analysis") you'll see "A neighborhood of a point $x$ is, by definition, an open set that contains $x$". But even that is not the usual definition: a neighborhood of $x$ is a set that contains an open set that contains $x$; it doesn't have to be open itself. en.wikipedia.org/wiki/Neighbourhood_%28mathematics%29 – Robert Israel Jul 9 '15 at 15:54
It would seem that a good strategy for this is to first prove that any convex set in $\mathbb{R}^n$ is connected. The proof of this is similar to that presented here.
Then show that any $N_r(x)$ in $\mathbb{R}^n$ is convex, from which it follows that $N_r(x)$ is connected. Since $N_r(x)$ is an open ball, this proof is rather trivial and is actually presented at the bottom of page 31 in Rudin.


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# rmh.default

0th

Percentile

##### Simulate Point Process Models using the Metropolis-Hastings Algorithm.

Generates a random point pattern, simulated from a chosen point process model, using the Metropolis-Hastings algorithm.

Keywords
spatial, datagen
##### Usage
## S3 method for class 'default':
rmh(model, start, control, verbose=TRUE, \dots)
##### Arguments
model
Data specifying the point process model that is to be simulated.
start
Data determining the initial state of the algorithm.
control
Data controlling the iterative behaviour and termination of the algorithm.
verbose
Logical flag indicating whether to print progress reports.
...
Further arguments which will be passed to any trend functions in model.
##### Details

This function generates simulated realisations from any of a range of spatial point processes, using the Metropolis-Hastings algorithm. It is the default method for the generic function rmh.

This function executes a Metropolis-Hastings algorithm with birth, death and shift proposals as described in Geyer and Moller (1994).

The argument model specifies the point process model to be simulated. It is either a list, or an object of class "rmhmodel", with the following components:

[object Object],[object Object],[object Object],[object Object],[object Object] For full details of these parameters, see rmhmodel.

The argument start determines the initial state of the Metropolis-Hastings algorithm. It is either a list, or an object of class "rmhstart", with the following components:

[object Object],[object Object] For full details of these parameters, see rmhstart.

The third argument control controls the simulation procedure (including conditional simulation), iterative behaviour, and termination of the Metropolis-Hastings algorithm. It is either a list, or an object of class "rmhcontrol", with components: [object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object] For full details of these parameters, see rmhcontrol.

##### Value

• A point pattern (an object of class "ppp", see ppp.object).

The returned value has an attribute info containing modified versions of the arguments model, start, and control which together specify the exact simulation procedure.

The value of .Random.seed at the start of the simulations is also saved and returned as an attribute seed.

##### Conditional Simulation

There are several kinds of conditional simulation.

• Simulationconditional upon the number of points, that is, holding the number of points fixed. To do this, setcontrol$p(the probability of a shift) equal to 1. The number of points is then determined by the starting state, which may be specified either by settingstart$n.startto be a scalar, or by setting the initial patternstart$x.start. • In the case of multitype processes, it is possible to simulate the modelconditionally upon the number of points of each type, i.e. holding the number of points of each type to be fixed. To do this, setcontrol$pequal to 1 andcontrol$fixallto beTRUE. The number of points is then determined by the starting state, which may be specified either by settingstart$n.startto be an integer vector, or by setting the initial patternstart$x.start. • Simulationconditional on the configuration observed in a sub-window, that is, requiring that, inside a specified sub-window$V$, the simulated pattern should agree with a specified point pattern$y$.To do this, setcontrol$x.condto equal the specified point pattern$y$, making sure that it is an object of class"ppp"and that the windowas.owin(control$x.cond)is the conditioning window$V$. • Simulationconditional on the presence of specified points, that is, requiring that the simulated pattern should include a specified set of points. This is simulation from the Palm distribution of the point process given a pattern$y$. To do this, setcontrol$x.condto be adata.framecontaining the coordinates (and marks, if appropriate) of the specified points.
For further information, see rmhcontrol. Note that, when we simulate conditionally on the number of points, or conditionally on the number of points of each type, no expansion of the window is possible.

##### Warnings

There is never a guarantee that the Metropolis-Hastings algorithm has converged to its limiting distribution.

If start$x.start is specified then expand is set equal to 1 and simulation takes place in x.start$window. Any specified value for expand is simply ignored.

The presence of both a component w of model and a non-null value for x.start$window makes sense ONLY if w is contained in x.start$window.

For multitype processes make sure that, even if there is to be no trend corresponding to a particular type, there is still a component (a NULL component) for that type, in the list.

##### Other models

In theory, any finite point process model can be simulated using the Metropolis-Hastings algorithm, provided the conditional intensity is uniformly bounded.

In practice, the list of point process models that can be simulated using rmh.default is limited to those that have been implemented in the package's internal C code. More options will be added in the future.

Note that the lookup conditional intensity function permits the simulation (in theory, to any desired degree of approximation) of any pairwise interaction process for which the interaction depends only on the distance between the pair of points.

##### Reproducible simulations

If the user wants the simulation to be exactly reproducible (e.g. for a figure in a journal article, where it is useful to have the figure consistent from draft to draft) then the state of the random number generator should be set before calling rmh.default. This can be done either by calling set.seed or by assigning a value to .Random.seed. In the examples below, we use set.seed.

If a simulation has been performed and the user now wants to repeat it exactly, the random seed should be extracted from the simulated point pattern X by seed <- attr(x, "seed"), then assigned to the system random nunber state by .Random.seed <- seed before calling rmh.default.

##### References

Baddeley, A. and Turner, R. (2000) Practical maximum pseudolikelihood for spatial point patterns. Australian and New Zealand Journal of Statistics 42, 283 -- 322.

Diggle, P. J. (2003) Statistical Analysis of Spatial Point Patterns (2nd ed.) Arnold, London.

Diggle, P.J. and Gratton, R.J. (1984) Monte Carlo methods of inference for implicit statistical models. Journal of the Royal Statistical Society, series B 46, 193 -- 212.

Diggle, P.J., Gates, D.J., and Stibbard, A. (1987) A nonparametric estimator for pairwise-interaction point processes. Biometrika 74, 763 -- 770.

Geyer, C.J. and Moller, J. (1994) Simulation procedures and likelihood inference for spatial point processes. Scandinavian Journal of Statistics 21, 359--373.

Geyer, C.J. (1999) Likelihood Inference for Spatial Point Processes. Chapter 3 in O.E. Barndorff-Nielsen, W.S. Kendall and M.N.M. Van Lieshout (eds) Stochastic Geometry: Likelihood and Computation, Chapman and Hall / CRC, Monographs on Statistics and Applied Probability, number 80. Pages 79--140.

rmh, rmh.ppm, rStrauss, ppp, ppm, Strauss, Softcore, StraussHard, MultiStrauss, MultiStraussHard, DiggleGratton

• rmh.default
##### Examples
nr   <- 1e5
nv  <- 5000
<testonly>nr  <- 10
nv <- 5</testonly>
set.seed(961018)

# Strauss process.
mod01 <- list(cif="strauss",par=c(beta=2,gamma=0.2,r=0.7),
w=c(0,10,0,10))
X1.strauss <- rmh(model=mod01,start=list(n.start=80),
control=list(nrep=nr,nverb=nv))

# Strauss process, conditioning on n = 80:
X2.strauss <- rmh(model=mod01,start=list(n.start=80),
control=list(p=1,nrep=nr,nverb=nv))

# Strauss process equal to pure hardcore:
mod02 <- list(cif="strauss",par=c(beta=2,gamma=0,r=0.7),w=c(0,10,0,10))
X3.strauss <- rmh(model=mod02,start=list(n.start=60),
control=list(nrep=nr,nverb=nv))

# Strauss process in a polygonal window.
x     <- c(0.55,0.68,0.75,0.58,0.39,0.37,0.19,0.26,0.42)
y     <- c(0.20,0.27,0.68,0.99,0.80,0.61,0.45,0.28,0.33)
mod03 <- list(cif="strauss",par=c(beta=2000,gamma=0.6,r=0.07),
w=owin(poly=list(x=x,y=y)))
X4.strauss <- rmh(model=mod03,start=list(n.start=90),
control=list(nrep=nr,nverb=nv))

# Strauss process in a polygonal window, conditioning on n = 80.
X5.strauss <- rmh(model=mod03,start=list(n.start=90),
control=list(p=1,nrep=nr,nverb=nv))

# Strauss process, starting off from X4.strauss, but with the
# polygonal window replace by a rectangular one.  At the end,
# the generated pattern is clipped to the original polygonal window.
xxx <- X4.strauss
xxx\$window <- as.owin(c(0,1,0,1))
X6.strauss <- rmh(model=mod03,start=list(x.start=xxx),
control=list(nrep=nr,nverb=nv))

# Strauss with hardcore:
mod04 <- list(cif="straush",par=c(beta=2,gamma=0.2,r=0.7,hc=0.3),
w=c(0,10,0,10))
X1.straush <- rmh(model=mod04,start=list(n.start=70),
control=list(nrep=nr,nverb=nv))

# Another Strauss with hardcore (with a perhaps surprising result):
mod05 <- list(cif="straush",par=c(beta=80,gamma=0.36,r=45,hc=2.5),
w=c(0,250,0,250))
X2.straush <- rmh(model=mod05,start=list(n.start=250),
control=list(nrep=nr,nverb=nv))

# Pure hardcore (identical to X3.strauss).
mod06 <- list(cif="straush",par=c(beta=2,gamma=1,r=1,hc=0.7),
w=c(0,10,0,10))
X3.straush <- rmh(model=mod06,start=list(n.start=60),
control=list(nrep=nr,nverb=nv))

# Soft core:
par3 <- c(0.8,0.1,0.5)
w    <- c(0,10,0,10)
mod07 <- list(cif="sftcr",par=c(beta=0.8,sigma=0.1,kappa=0.5),
w=c(0,10,0,10))
X.sftcr <- rmh(model=mod07,start=list(n.start=70),
control=list(nrep=nr,nverb=nv))

# Area-interaction process:
mod42 <- rmhmodel(cif="areaint",par=c(beta=2,eta=1.6,r=0.7),
w=c(0,10,0,10))
X.area <- rmh(model=mod42,start=list(n.start=70),
control=list(nrep=nr,nverb=nv))

# Multitype Strauss:
beta <- c(0.027,0.008)
gmma <- matrix(c(0.43,0.98,0.98,0.36),2,2)
r    <- matrix(c(45,45,45,45),2,2)
w=c(0,250,0,250))
X1.straussm <- rmh(model=mod08,start=list(n.start=80),
control=list(ptypes=c(0.75,0.25),nrep=nr,nverb=nv))

# Multitype Strauss conditioning upon the total number
# of points being 80:
X2.straussm <- rmh(model=mod08,start=list(n.start=80),
control=list(p=1,ptypes=c(0.75,0.25),nrep=nr,
nverb=nv))

# Conditioning upon the number of points of type 1 being 60
# and the number of points of type 2 being 20:
X3.straussm <- rmh(model=mod08,start=list(n.start=c(60,20)),
control=list(fixall=TRUE,p=1,ptypes=c(0.75,0.25),
nrep=nr,nverb=nv))

# Multitype Strauss hardcore:
rhc  <- matrix(c(9.1,5.0,5.0,2.5),2,2)
mod09 <- list(cif="straushm",par=list(beta=beta,gamma=gmma,
X.straushm <- rmh(model=mod09,start=list(n.start=80),
control=list(ptypes=c(0.75,0.25),nrep=nr,nverb=nv))

# Multitype Strauss hardcore with trends for each type:
beta  <- c(0.27,0.08)
tr3   <- function(x,y){x <- x/250; y <- y/250;
exp((6*x + 5*y - 18*x^2 + 12*x*y - 9*y^2)/6)
}
tr4   <- function(x,y){x <- x/250; y <- y/250;
exp(-0.6*x+0.5*y)}
# log linear trend
mod10 <- list(cif="straushm",par=list(beta=beta,gamma=gmma,
trend=list(tr3,tr4))
X1.straushm.trend <- rmh(model=mod10,start=list(n.start=350),
control=list(ptypes=c(0.75,0.25),
nrep=nr,nverb=nv))

# Multitype Strauss hardcore with trends for each type, given as images:
bigwin <- square(250)
i1 <- as.im(tr3, bigwin)
i2 <- as.im(tr4, bigwin)
mod11 <- list(cif="straushm",par=list(beta=beta,gamma=gmma,
trend=list(i1,i2))
X2.straushm.trend <- rmh(model=mod11,start=list(n.start=350),
control=list(ptypes=c(0.75,0.25),expand=1,
nrep=nr,nverb=nv))

# Diggle, Gates, and Stibbard:
mod12 <- list(cif="dgs",par=c(beta=3600,rho=0.08),w=c(0,1,0,1))
X.dgs <- rmh(model=mod12,start=list(n.start=300),
control=list(nrep=nr,nverb=nv))

# Diggle-Gratton:
mod13 <- list(cif="diggra",
par=c(beta=1800,kappa=3,delta=0.02,rho=0.04),
w=square(1))
X.diggra <- rmh(model=mod13,start=list(n.start=300),
control=list(nrep=nr,nverb=nv))

# Geyer:
mod14 <- list(cif="geyer",par=c(beta=1.25,gamma=1.6,r=0.2,sat=4.5),
w=c(0,10,0,10))
X1.geyer <- rmh(model=mod14,start=list(n.start=200),
control=list(nrep=nr,nverb=nv))

# Geyer; same as a Strauss process with parameters
# (beta=2.25,gamma=0.16,r=0.7):

mod15 <- list(cif="geyer",par=c(beta=2.25,gamma=0.4,r=0.7,sat=10000),
w=c(0,10,0,10))
X2.geyer <- rmh(model=mod15,start=list(n.start=200),
control=list(nrep=nr,nverb=nv))

mod16 <- list(cif="geyer",par=c(beta=8.1,gamma=2.2,r=0.08,sat=3))
data(redwood)
X3.geyer <- rmh(model=mod16,start=list(x.start=redwood),
control=list(periodic=TRUE,nrep=nr,nverb=nv))

# Geyer, starting from the redwood data set, simulating
# on a torus, and conditioning on n:
X4.geyer <- rmh(model=mod16,start=list(x.start=redwood),
control=list(p=1,periodic=TRUE,nrep=nr,nverb=nv))

# Lookup (interaction function h_2 from page 76, Diggle (2003)):
r <- seq(from=0,to=0.2,length=101)[-1] # Drop 0.
h <- 20*(r-0.05)
h[r<0.05] <- 0
h[r>0.10] <- 1
mod17 <- list(cif="lookup",par=list(beta=4000,h=h,r=r),w=c(0,1,0,1))
X.lookup <- rmh(model=mod17,start=list(n.start=100),
control=list(nrep=nr,nverb=nv))

# Strauss with trend
tr <- function(x,y){x <- x/250; y <- y/250;
exp((6*x + 5*y - 18*x^2 + 12*x*y - 9*y^2)/6)
}
beta <- 0.3
gmma <- 0.5
r    <- 45
mod17 <- list(cif="strauss",par=c(beta=beta,gamma=gmma,r=r),
w=square(1), trend=tr3)
X1.strauss.trend <- rmh(model=mod17,start=list(n.start=90),
control=list(nrep=nr,nverb=nv))
r <- seq(0,0.2,length=8)[-1]
gmma <- c(0.5,0.6,0.7,0.8,0.7,0.6,0.5)
w=square(1))
control=list(nrep=nr,nverb=nv))
par=list(beta=4000, gamma=gmma,r=r,sat=1e4),
w=square(1))
set.seed(1329)
control=list(nrep=nr,nverb=nv))

# Check:
h <- ((prod(gmma)/cumprod(c(1,gmma)))[-8])^2
hs <- stepfun(r,c(h,1))
mod20 <- list(cif="lookup",par=list(beta=4000,h=hs),w=square(1))
set.seed(1329)
X.check <- rmh(model=mod20,start=list(n.start=100),
control=list(nrep=nr,nverb=nv))
# X2.badgey and X.check will be identical.

r=c(0.035,0.07,0.14),sat=5), w=square(1))
control=list(nrep=nr,nverb=nv))
# Same result as Geyer model with beta=300, gamma=0.4, r=0.07,
# sat = 5 (if seeds and control parameters are the same)

# Or more simply:
# Same again --- i.e. the BadGey model includes the Geyer model.


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# Chapter 2 – Features of Time Series Data

## 2.1 Stochastic Process and Time Series

A time series is an observed sequence of realizations of chronologically stored random variables. The sequence of random variables indexed by time, $$\{\ldots,Y_{-1},Y_0,Y_1,\ldots,Y_T,Y_{T+1}\ldots\}$$, is referred to as the stochastic process. Thus, a time series is a realization of a stochastic process.

We can think of a time series as a finite sample from an underlying doubly–infinite sequence: $$\{\ldots,y_{-1},y_{0},y_1,y_2,\ldots,y_T,y_{T+1},y_{T+2},\ldots\}$$. This is to say that the history extends beyond the starting and ending time periods of the sample at hand.

But we don’t observe, or choose not to observe, those time periods. Instead, we observe and work with the sample of time series $$\{y_1,y_2,\ldots,y_T\}$$, which we can also denote as $$\{y_t\}_{t=1}^{T}$$ or simply $$\{y_t\}$$. Similarly, we denote the stochastic process over the observed time periods as $$\{Y_t\}_{t=1}^{T}$$ or $$\{Y_t\}$$.

## 2.2 Stationarity

If all random variables, from where the time series are drawn, have the same distribution, then we refer to such data as stationary time series. Stationarity is an important feature, and the assumption on which time series econometrics heavily relies.

Consider a simplest kind of a time series comprised of realizations from independent and identically distributed (iid) normal random variable with zero mean and constant variance: $$Y_t \sim iid~\text{N}\left(0,\sigma^2\right)$$. The following graph plots the realized time series from this process:

Such time series is a realization of what is referred to as a white noise process.8 Technically, this is a Gaussian white noise process as the random variables are iid normally distributed. Without the normality assumption we would have an Independent white noise process. Without the indepence assumption we would have simply a white noise process. That is, $$\{Y_t\}$$, is a white noise process if: \begin{align*} & E(Y_t) = 0,\;~\forall~t\\ & Var(Y_t) = \sigma^2,\;~\forall~t\\ & Cov(Y_t,Y_{t-k}) = 0,\;~\forall~k \ne 0 \end{align*}

Because each observation is drawn from the same distribution, white noise is a stationary process. Indeed, it is a special type of the stationary process insofar as its mean, variance, and covariance are time-invariant. Note, for stationarity, neither the mean nor the covariances are required to be equal to zero. Thus, $$\{Y_t\}$$ is a stationary process9 To be precise, this is a definition of covariance-stationarity or weak form of stationarity. Strict stationarity is defined by time invariant joint distribution of random variables. if its mean and variance are independent of $$t$$, and the autocovariances are independent of $$t$$ for all $$k$$.

Why should we care about stationarity? The gist of the matter is that in each time period we only observe one realization of the respective random variable. We don’t have the sample of observations for that period—just a single observation is all we have. Of course, over time, we have many such observations—one for each period. The question then is, could we use this sample of time series and conclude something about the moments of the stochastic process? Stationarity in conjunction with ergodicity enables us to do just this.

Ergodicity implies independence of two random variables that are far apart from each other in the stochastic process. That is, if $$\{Y_t\}$$ is stationary and ergodic with $$E(Y_t)=\mu$$, then $$Cov(Y_t,Y_{t-k}) = 0$$ for some large integer $$k$$. More importantly, when the process is stationary and ergodic, the mean of the sample of time series converges to the mean of the stochastc process as the sample size increases.

## 2.3 Serial Dependence

It is more of the norm rather than the exception for a time series to be correlated over time. Indeed, because of the sequential nature of the stochastic process, we commonly observe dependence among the temporally adjacent random variables. That is, we expect $$Y_t$$ and $$Y_{t-k}$$ to be correlated for a reasonably small integer $$k$$. Such correlation, referred to as the autocorrelation, or more specifically, the $$k^{th}$$ order autocorrelation is given by: $\rho_k=Cor(Y_{t},Y_{t-k}) = \frac{Cov(Y_{t},Y_{t-k})}{\sqrt{Var(Y_{t})}\sqrt{Var(Y_{t-k})}},\;~~k=1,2,\ldots$

Under the assumption of stationarity, $$Var(Y_{t})=Var(Y_{t-k})$$, so the autocorrelation can be simplified to: $$\rho_k= \frac{Cov(Y_{t},Y_{t-k})}{Var(Y_{t})}.$$

Autocorrelations are commonly illustrated via the so-called autocorrelogram, which plots the sequence of autocorrelation coefficients against the lags at which these coefficients are obtained. The following figure illustrates an autocorrelogram for a sample of time series with 240 observations:

For each lag, $$k$$, the vertical line extending from zero represents an estimate of the autocorrelation coefficient at that lag. The dashed lines denote the 95% confidence interval, given by $$\pm 1.96/\sqrt{T}$$, where $$T$$ is the size of the time series sample.

Another relevant measure of the time series dependence is partial autocorrelation, which is correlation between $$Y_t$$ and $$Y_{t-k}$$ net of any correlations between $$Y_t$$ and $$Y_{t-k+j}$$, for all $$j=1,\ldots,k-1$$. Similar to autocorrelations, partial autocorrelations, here denoted by $$\pi$$, can also be illustrated using autocorrelograms:

Autocorrelogram is a useful tool for detecting dynamic properties of a time series. For example, autocorrelations of the stationary and ergodic stochastic process dissipate to zero as $$k$$ increases. Thus, by observing autocorrelograms, in conjunction with a visual inspection of the time series, we can get an idea whether the process is stationary.10 There are, of course, formal tests of stationarity, which we will discuss in one of the subsequent chapters. If a time series appear nonstationary, we can make changes to it, so that the transformed series becomes stationary.

## 2.4 Transformations

It is common to transform time series by taking logarithms (if applicable), by first-differencing the series, or by first-differencing the logarithms of the series. Such transformations are done to work with a suitable variable for the desired econometric analysis, or to address some underlying issues of the series (e.g., nonstationarity).

Consider the Dow Jones Industrial Average (commonly referred to as the Dow Jones Index), for example. In levels, the series are clearly nonstationary. This is because the series are trending upward (on average), and also because the series become more volatile over time.

Could first-differencing resolve the issue of nonstationarity? Turns out, not exactly. The first-differenced Dow Jones Index, while no longer trending, reveals increasing volatility over time.

As it turns out, we can largely resolve the issue if we first-difference the log-transformed series. When we log-transform the series, the difference in observations from two different period is no longer measured in absolute terms, rather it is measured in relative terms. Then, by first-differencing the log-transformed series we, in effect, obtain a measure of a growth rate of the original series. The growth rate of the Dow Jones Index appears to be stationary.

Page built: 2022-11-30 using R version 4.1.2 (2021-11-01)


text:
# $\chi(G) \cdot \chi(\bar{G})\geq n$ [duplicate]

Prove that $\chi(G) \cdot \chi(\bar{G})\geq n$

$\chi(G)$: number of colors required for a graph $G$.

Here $\bar{G}$ is a graph that consists of all the edges that are not in $G$.


text:
# KL Divergence and Maximum Likelihood

Posted by GwanSiu on June 12, 2019

## 1. KL Divergence

### 1.1 Definition of KL Divergence

The Kullback-Leibler (KL) divergence is a measure of how a probability distribution differs from another probability distribution. In Bayesian learning, data sample is assumed to be generated from the underlying distribution $P$, and we would like to estimate it with an approximated distribution $Q_{\theta}$ with parameter $\theta$. In this case, KL divergence can be applied to measure the distance between the approximated distribution $Q_{\theta}$ and the true distribution $P$.

In formal words, consider two probability distribution $P(X)$ and $Q_{\theta}(X)$. The KL divergence is defined as

$$$\begin{split} D_{KL}(P(X)\Arrowvert Q_{\theta}(X)) &= \int P(X)\log \frac{P(X)}{Q_{\theta}(X)}\mathrm{d}x \\ &=\mathbb{E}_{x\sim P(X)}[\log\frac{P(X)}{Q_{\theta}(X)}] \end{split}$$$

KL divergence is not symmetric, i.e. $D_{KL}(Q_{\theta\Arrowvert P})\neq D_{KL}(P\Arrowvert Q_{\theta})$. Therefore, KL divergence is not a well-defined measure. If $P$ and $Q_{\theta}$ are exact the same, i.e. $P=Q_{\theta}$, then $D_{KL}(Q_{\theta\Arrowvert P})= D_{KL}(P\Arrowvert Q_{\theta})=0$.

The range of KL divergence is $[0,\infty]$. In order for KL divergence to be finite, e.g. $D_{KL}(P\Arrowvert Q_{\theta})$, the support of $P$ needs to be contained in the support of $Q_{\theta}$. If a point $x$ exists with $Q(x)=0$ but $P(x)>0$, then $D_{KL}(P\Arrowvert Q_{\theta})=\infty$.

### 1.2 Forward and Reverse KL

As I mentioned earlier, the KL divergence is not symmetric measure. Thus, from optimization perspective, minimize $D_{KL}(Q_{\theta\Arrowvert P})$ and minimize $D_{KL}(P\Arrowvert Q_{\theta})$ has different physical meanings.

Note:

• Forward KL divergence:$D_{KL}(P\Arrowvert Q_{\theta})$ Mean-seeking behavior, inclusive (more principle because approximates the full distribution)
• Reversed KL divergence: $D_{KL}(Q_{\theta}\Arrowvert P)$ Mode seeking, exclusive.

## 2. Forward KL

Let’s consider optimizing the forward KL divergence with respect to $Q_{\theta}$

$$$\begin{split} \arg\min_{\theta} D_{KL}(P\Arrowvert Q_{\theta}) &=\arg\min_{\theta}\mathbb{E}_{x\sim P}[-\log Q_{\theta}(X)]-\mathcal{H}(P(X)) \\ &=\arg\min_{\theta}\mathbb{E}_{x\sim P}[-\log Q_{\theta}(X)]-const \\ &\Rightarrow\arg\max_{\theta}\mathbb{E}_{x\sim P}[\log Q_{\theta}(X)] \end{split}$$$

Notice that this is identical to the maximum likelihood estimation objective. Translated into words, the objective above will sample points from $P(X)$ and try to maximize the probability of these points under $Q(X)$. A good approximation under the forward KL objective thus satisfies

Whenever $P(\cdot)$ has high probability, $Q(\cdot)$ must also have high probability.

We consider this mean-seeking behaviour, because the approximate distribution Q must cover all the modes and regions of high probability in P. The optimal “approximate” distribution for our example is shown below. Notice that the approximate distribution centers itself between the two modes, so that it can have high coverage of both. The forward KL divergence does not penalize Q for having high probability mass where P does not.

Note that the objective function of forward KL is

$$$\arg\max_{\theta}\mathbb{E}_{x\sim P}[\log Q_{\theta}(X)]$$$

To be able to evaluate this objective, we need either a dataset of samples from true distribution $P$, or a machanism for sampling from the true distribution $P$.

## 3. Reverse KL

Now consider optimizing the reverse KL objective with respect to $Q_{\theta}$:

$$$\begin{split} \arg\min_{\theta} D_{KL}(Q_{\theta}\Arrowvert P) &=\arg\min_{\theta}\mathbb{E}_{x\sim Q_{\theta}}[-\log P(X)]-\mathcal{H}(Q_{\theta}(X)) \\ &=\arg\max_{\theta}\mathbb{E}_{x\sim Q_{\theta}} \end{split}$$$

Let’s translate the objective above into words. The objective above will sample points from $Q_{\theta}(X)$, and try to maximize the probability of these points under $P(X)$. The entropy term encourages the approximate distribution to be as wide as possible. A good approximation under the reverse KL objective thus satisfies

Whenever $Q_{\theta}(\cdot)$ has high probability, $P(\cdot)$ must also have high probability.

We consider this mode-seeking behaviour, because any sample from the approximate distribution $Q_{\theta}$ must lie within a mode of P (since it’s required that samples from $Q_{\theta}$ have high probability under $P$). Notice that unlike the forward KL objective, there’s nothing requiring the approximate distribution to try to cover all the modes. The entropy term prevents the approximate distribution from collapsing to a very narrow mode; typically, behaviour when optimizing this objective is to find a mode of $P$ with high probability and wide support, and mimic it exactly.

The optimal “approximate” distribution for our example is shown below. Notice that the approximate distribution essentially encompasses the right mode of $P$. The reverse KL divergence does not penalize $Q_{\theta}$ for not placing probability mass on the other mode of P.

Note that the simplified objective function of reverse KL divergence is

$$$\arg\max_{\theta}\mathbb{E}_{x\sim Q_{\theta}}[\log P(X)]+\mathcal{H}(Q_{\theta}(X))$$$

To be able to evaluate this objective, we need to be able to evaluate probabilities of data-points under the true model $P(X)$.


text:
Engineering

Just Enough Kafka for the Elastic Stack, Part 1

The Elastic Stack and Apache Kafka share a tight-knit relationship in the log/event processing realm. A number of companies use Kafka as a transport layer for storing and processing large volumes of data. In many deployments we've seen in the field, Kafka plays an important role of staging data before making its way into Elasticsearch for fast search and analytical capabilities. Through a series of blog posts, we'd like to shine more light on how to set up and manage Kafka when integrating with the Elastic Stack. Specifically, we'll discuss our experiences operating Kafka and Logstash under high volume.

Note: For the purposes of these posts, we refer to Kafka's 0.8.x version. Some of the functionality has changed in Kafka's latest 0.9.x version, but 0.8.x is still very popular and widely used.

The Basics

Let's get some basic concepts out of the way. From Kafka's documentation:

Apache Kafka is publish-subscribe messaging rethought as a distributed commit log

Kafka was created at LinkedIn to handle large volumes of event data. Like many other message brokers, it deals with publisher-consumer and queue semantics by grouping data into topics. As an application, you write to a topic and consume from a topic. An important distinction, or a shift in design with Kafka is that the complexity moves from producer to consumers, and it heavily uses the file system cache. These design decisions, coupled with it being distributed from scratch, makes it a winner in many high volume streaming use cases.

Logstash integrates natively with Kafka using the Java APIs. It provides both input and output plugins so you can read and write to Kafka from Logstash directly. The configuration to get started is pretty simple:

kafka {
zk_connect => "hostname:port"
topic_id => "apache_logs"
...
}

Kafka has a dependency on Apache ZooKeeper, so if you are running Kafka, you'll need access to a ZooKeeper cluster. More on that later.

When To Use Kafka With The Elastic Stack?

Scenario 1: Event Spikes

Log data or event based data rarely have a consistent, predictable volume or flow rates. Consider a scenario where you upgraded an application on a Friday night (why you shouldn't upgrade on a Friday is for a different blog :) ). The app you deployed has a bad bug where information is logged excessively, flooding your logging infrastructure. This spike or a burst of data is fairly common in other multi-tenant use cases as well, for example, in the gaming and e-commerce industries. A message broker like Kafka is used in this scenario to protect Logstash and Elasticsearch from this surge.

In this architecture, processing is typically split into 2 separate stages — the Shipper and Indexer stages. The Logstash instance that receives data from different data sources is called a Shipper as it doesn't do much processing. Its responsibility is to immediately persist data received to a Kafka topic, and hence, its a producer. On the other side, a Logstash instance — a beefier one — will consume data, at its own throttled speed, while performing expensive transformations like Grok, DNS lookup and indexing into Elasticsearch. This instance is called the Indexer.

While Logstash has traditionally been used as the Shipper, we strongly recommend using the suite of Elastic Beats products available as specialized shippers. Filebeat, for example, is a lightweight, resource friendly agent which can follow files and ship to Kafka via a Logstash receiver.

Note: At this time, Filebeat cannot write directly to Kafka, but starting with 5.0.0 (currently in pre-release state), you'll be able to configure Kafka as one of the outputs. This enhancement further simplifies the above architecture in use cases that ingest data using beats. Please try out this and other awesome new features in our alpha releases, and let us know what you think! Word on the street is that you can even win a free pass to Elastic{ON}17 by helping us test these!

Scenario 2: Elasticsearch not reachable

Consider another scenario. You're planning to upgrade your multi-node Elasticsearch cluster from 1.7 to 2.3 which requires a full cluster restart. Or, a situation where Elasticsearch is down for a longer period of time than you expected. If you have a number of data sources streaming into Elasticsearch, and you can't afford to stop the original data sources, a message broker like Kafka could be of help here! If you use the Logstash shipper and indexer architecture with Kafka, you can continue to stream your data from edge nodes and hold them temporarily in Kafka. As and when Elasticsearch comes back up, Logstash will continue where it left off, and help you catch up to the backlog of data. In fact, this bodes well with the Elastic nature of our software — you can temporarily increase your processing and indexing power by adding extra Logstash instances to consume from the same Kafka topic. You could additionally add extra nodes in Elasticsearch as well. Scaling horizontally without too much hand-holding is one of the core features of Elasticsearch. Once you are caught up, you can scale down to your original number of instances.

Anti-pattern: When not to use Kafka with Elastic Stack

Just as it is good to know when to use Kafka, it is also good knowledge to know when not to use it. Everything has a cost — Kafka is yet another piece of software you need to tend to, in your production environment. This involves monitoring, reacting to alerts, upgrading and everything else that comes with running a software successfully in production. You are monitoring all your production software, aren't you?

When it comes to centralized log management, there is often a blanket statement made that logs need to be shipped off your edge nodes as soon as possible. While this may be true for some use cases, ask yourself if this is really a requirement for you! If you can tolerate a relaxed search latency, you can completely skip the use of Kafka. Filebeat, which follows and ships file content from edge nodes, is resilient to log rotations. This means if your application is emitting more logs than Logstash/Elasticsearch can ingest at real time, logs can be rotated — using Log4j or logrotate, for example — across files, but they will still be indexed. Of course, this brings in a separate requirement of having sufficient disk space to house these logs on your server machines. In other words, in this scenario, your local filesystem will become the temporary buffer.

Design Considerations For Kafka And Logstash

Below we describe some design considerations while using Kafka with Logstash. Logstash input uses the high level Kafka consumer API and Logstash Output uses the new producer API.

Topics

Topics are logical grouping of messages. They provide a way to isolate data from other consumers if necessary. Note, in 0.8 version of Kafka, there is no in-built security, so any consumer can access from any topic available on the broker. How many topics you need and how do you model your data, is, well, dependent on your data. Here are some strategies:

User based data flow: In this case you would be creating a topic per user. Please remember that Kafka registers all partitions in ZooKeeper, so there is a cost of creating hundreds and thousands of topics. If your users are small in number — for example, departments — this strategy of partitioning per user works well.

Attributes based data flow: For logging and event driven data, you could also group multiple users in one topic based on attributes like data volume and expected search latency. Remember that more time events spend in the queue while not getting indexed into Elasticsearch, the longer are the latency for searching these. One solution is to create topics based on expected SLAs — “high”, “medium” and “low” topics. Similarly based on data volume. Do you have a customer/user who is known to produce bursty data? Give them a new topic. In a multi-tenant deployment, it's good practice to have a “bursty” topic, so when a user violates their data volume, or produces too much bursty data in the last X minutes/hours, you can move them, at runtime, to this topic. This way you'll keep other topics clear of unnecessary traffic, thereby not slowing everybody down. A good analogy here is an expressway — you mostly want the fast lane to be free flowing, so slower vehicles are expected to move to other lanes. Think of Kafka topics as lanes and events as cars!

In general, separate topics per data source allows for isolation of sources. In Kafka, you can configure number of partitions per topic. This also means you can scale Logstash instances per topic. If you expect certain sources to grow to a higher volume in the future, you can always over-partition to future proof it.

Topics can be created on the fly when data is first published to a non-existent one, or can be manually pre-created.

kafka-topics.sh --zookeeper zk_host:port --create --topic user1
--partitions 8 --replication-factor 1

Partitions

Now's a good time to talk about partitions! From Kafka's documentation:

“The partition count controls how many logs the topic will be sharded into. There are several impacts of the partition count. First each partition must fit entirely on a single server. So if you have 20 partitions the full data set (and read and write load) will be handled by no more than 20 servers (no counting replicas). Finally the partition count impacts the maximum parallelism of your consumers.”

In essence, the more partitions you have, the more throughput you get when consuming data. From the producer standpoint, Kafka provides you an option for controlling which data ends up in which partition. By default, when using Logstash, data is assigned to a partition in a round-robin fashion. By specifying the message_key in Logstash config, you can control how your data is assigned to a partition. In some cases it can be efficient to have fewer topic/partitions to workaround the ZooKeeper limitation, but group multiple users under fixed partitions by using user_id as message_key. If key is specified, a partition will be chosen using a hash of the key.

Another important property to be aware in Kafka is the order of messages. Kafka only guarantees message order within the same partition. So if messages from data source has no key, it gets sprayed across partitions, and Kafka will not guarantee ordering when consuming. Where data is immutable, and in particular, for logging use cases, this can be an acceptable property. If you need strong ordering, make sure that data is pinned to a single partition.

Consumer Groups: Scalability And Fault Tolerance

Multiple Kafka consumers which process data from similar topics form a consumer group designated by unique name in the cluster. Messages published to Kafka are distributed across instances in the group, but each message is handled by just one consumer in the group, i.e. there is no overlap. Logstash instances reading from Kafka form a consumer group with a default group ID called logstash. You can spin up new Logstash instances at any time to scale read throughput for the subscribed topic. By default, the new Logstash instance started will join the logstash consumer group. This process — when a new consumer joins a consumer group — triggers a rebalancing in Kafka. we mentioned before that Logstash uses the high level Kafka consumer, so it delegates rebalancing logic to the Kafka library. This process automatically reassigns the partitions to current consumers based on metadata available in Zookeeper. Another reason to use multiple Logstash instances is to add fault tolerance. If one instance goes down, Kafka goes through rebalancing process and distributes assignments to existing Logstash instances.

All this closely relates to consumer_threads setting in Logstash input. This setting controls the number of threads consuming from Kafka partitions. Ideally you should have as many threads as the number of partitions for a perfect balance — more threads than partitions means that some threads will not have anything do. Fewer threads than partition means some threads are consuming from more than one partition.

Consider a scenario where topic apache_logs that has 16 partitions. I could spin up one Logstash instance on an 8 core machine with this configuration:

input {
kafka {
zk_connect => "kafka:2181"
group_id => "logstash"
topic_id => "apache_logs"
}
}

Or we could spin up 2 Logstash instances on 2 machines with consumer_threads set to 8 each. The latter deployment is a better choice — it fully utilizes the machine's CPU, but also adds fault tolerance in case of catastrophic failures.

Usually, try to ensure that the number of partitions is a multiple of the number of Logstash threads/instances. This ensures instances are balanced. Partitioning, similar to Elasticsearch sharding, means we can add more processing capacity (Logstash instances) later.

Serialization Formats

Kafka persists messages using byte arrays in its queue. So you can pretty much throw any format at Kafka, but in general its is recommended to use a serialization format which is compact and fast. Kafka has a way to deal with serialized message formats by specifying the value_serializer in outputs, and decoder_class in inputs. If you are a savvy Logstash user, you must surely be thinking about codecs by now. It is both possible to leverage Logstash codecs as well as Kafka serializers to manage message representation into and out of Kafka topics.

Other Logstash codecs that are relevant to the Kafka ecosystem are plain, avro, and avro_schema_registry.

If you wish to write your own serializer/deserializer you can do so in your favorite JVM language. Since these classes are not in Logstash's classpath, you must explicitly add the appropriate library into your java classpath

export CLASSPATH=\$CLASSPATH:/path/to/kafkaserializers.jar; bin/logstash -f ..

Please note that decoding of messages in Logstash input is single threaded, so an expensive serialization format like json will decrease the overall performance of the pipeline.

Conclusion

In this post, we've covered few basic concepts in Kafka and presented its use with the Elastic Stack. In the next post, we'll jump right into the operational aspects, and provide tips for running Kafka with Logstash. Meanwhile, if you have any questions, feel free to reach us on our forum or on twitter!

Update: Want more? Read part 2 of this series for operational and monitoring tips.


text:
# Observation of light echoes around very young stars - Astrophysics > Solar and Stellar Astrophysics

Observation of light echoes around very young stars - Astrophysics > Solar and Stellar Astrophysics - Descarga este documento en PDF. Documentación en PDF para descargar gratis. Disponible también para leer online.

Abstract: The goal of the paper is to present new results on light echoes from youngstellar objects. Broad band CCD images were obtained over three months atone-to-two week intervals for the field of NGC 6726, using the largefield-of-view remotely-operated telescope on top of Cerro Burek. We detectedscattered light echoes around two young, low-amplitude, irregular variablestars. Observations revealed not just one, but multiple light echoes frombrightness pulses of the T Tauri star S CrA and the Herbig Ae-Be star R CrA.Analysis of S CrA-s recurring echoes suggests that the star is located 138 +-16 pc from Earth, making these the closest echoes ever detected. Theenvironment that scatters the stellar light from S CrA is compatible with anincomplete dust shell or an inclined torus some 10,000 AU in radius andcontaining $\sim$ $2 \times 10^{-3}$ $M {\sun}$ of dust. The cause of suchconcentration at $\sim$ 10,000AU from the star is unknown. It could be theremnant of the envelope from which the star formed, but the distance of thecloud is remarkably similar to the nominal distance of the Oort cloud to theSun, leading us to also speculate that the dust or ice seen around S CrAmight have the same origin as the Solar System Oort cloud.

Autor: J.L. Ortiz, B.E.K. Sugerman, I. de la Cueva, P. Santos-Sanz, R. Duffard, R. Gil-Hutton, M. Melita, N. Morales

Fuente: https://arxiv.org/