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# Matplotlib Plot Colormap

Hi guys, I wrote a function that plot rectangles filled with colors defined by a colormap. See Choosing Colormaps in Matplotlib for an in-depth discussion about colormaps, including colorblind-friendliness. This submission also includes the Line ColorOrder colormaps! For version 2. Creating custom colormaps. This can easily be done using the hexbin function of Matplotlib. Controling the color of a parametric surface. This page shows how to plot 12-bit tiff file in log scale using python and matplotlib. This module includes functions and classes for color specification conversions, and for mapping numbers to colors in a 1-D array of colors called a colormap. 2016/07/11 [Matplotlib-users] How to set marker for a specific point in a scatter plot with colormap? Chao YUE 2016/07/11 [Matplotlib-users] Creating Colored Axis Labels using LaTeX in Interactive Mode Joseph Fox-Rabinovitz. First, in order to actually use. The following are code examples for showing how to use matplotlib. Questions: I want to plot a graph with one logarithmic axis using matplotlib. They are extracted from open source Python projects. A reversed version of each of these colormaps is available by appending _r to the name, e. In this Tiny Tutorial, you. I've been reading the docs, but can't figure out the syntax. Plotting Complex Functions Python has a built in syntax for manipulating complex numbers, using $$j = \sqrt{-1}$$. In particular, I find that it induces perceptual distortion, where values in the green/yellow part of the colormap all look the same. Skip to content. We probably have examples in the test suite that rely on the reference images being rendered in 'jet' - those reference images would have to either be changed, or the default cm switched to jet for testing, and back to the default again post testing. Here we briefly discuss how to choose between the many options. Colormaps¶ A potential issue when plotting a large number of columns is that it can be difficult to distinguish some series due to repetition in the default colors. This mapping of color -> value is generally easily accomplished by using colormaps in matplotlib. Parameters ---------- ax : matplotlib axes Axes on which to draw the plot. Circle objects that may be tuned further to your liking. Plot Accessary: Color Map (part2) + Color Bar 이번 편에서는 ColorBar 색봉과 함께 색지도를 정규화하는 방법에 대하여 알아보겠습니다. Slightly increased the base font sizes in plotting_context() and increased the scaling factors for "talk" and "poster" contexts. The plot_colormap method (see below) is handy to quickly pick up a colormaps and the test_colormap is useful to see test a new colormap. The matplotlib package has excellent support for managing colors and plots, however, it can sometimes be a bit tricky to find out how to combine the various different classes/functions in this. In matplotlib, you can conveniently do this using plt. 15 The (Plot Details) Color Map tab. The reversal leads to near-zero areas being white and higher intensities being darker. colors as col import matplotlib. This tutorial will describe how to plot data in Python using the 2D plotting library matplotlib. plasma color map, which has the effect of plotting higher functional values with a hotter color. The Matplotlib subplot() function can be called to plot two or more plots in one figure. We probably have examples in the test suite that rely on the reference images being rendered in 'jet' - those reference images would have to either be changed, or the default cm switched to jet for testing, and back to the default again post testing. scatter(x_data, y_data. Yet the image is black and white. From x and y form a matrix of z values. pyplot as plt import networkx as nx G = nx. A simple way to create a custom linear colormap is to prepare a list of colors and allow Matplotlib to handle the transition. You can insert the option cmap= into most matplotlib functions to change the color map of the resulting plot. mlab module, that we call mlab, provides an easy way to visualize data in a script or from an interactive prompt with one-liners as done in the matplotlib pylab interface but with an emphasis on 3D visualization using Mayavi2. matplotlib plotting code examples, 3d plots, 3d errorbars, 2d plots, scientific notation, advanced plotting, plotting tutorial 3D surface, wireframe, regression - matplotlib plotting examples and tutorial. matplotlib documentation: Perceptually uniform colormaps. Create own colormap using matplotlib and plot color scale. In most of these functions we will use a colormap to encode one dimension of the data. Python Matplotlib available colors Python's matplotlib defines a bunch of colors you can use in you plots. By using axesgrid, the padding between subplots are guaranted to be the same. An excellent reference for this is the Plotting Commands Summary in the matplotlib documentation. A list of values to use for xticks. Change Color Scheme Using a Colormap. html#matplotlib. get_cmap, which returns a matplotlib. The following code shows an example of how to do this. import matplotlib. Plot rectangular data as a color-encoded matrix. Questions: I just started using pandas/matplotlib as a replacement for Excel to generate stacked bar charts. In addition, you can increase the visibility of the output figure by using log scale colormap when you plotting the tiff file. You will also need numpy, scipy and pandas to work with datasets. Using NumPy. To remedy this, DataFrame plotting supports the use of the colormap argument, which accepts either a Matplotlib colormap or a string that is a name of a colormap registered with Matplotlib. colormap 'jet' Color map name from the image above or a custom color scale — a sequence of {index, rgb} objects, where index is 0. The initialization takes a dictionary of value, color pairs. colors[::-1]). This page shows how to plot 12-bit tiff file in log scale using python and matplotlib. This builds on discussion from the 27 Oct 2014 PyHOGS meeting, earlier meetings on colormaps with matplotlib, and on the 10 Nov 2014 PyHOGS meeting. It gets referenced quite a bit and is even used in visualization lectures. Following is a working example showing how to use axesgrid:. If your plot starts to get delayed after a while, try adding more of the datalist. # Author: Aric Hagberg (hagberg@lanl. cm is optional as you can call colormaps as cmap="cmap_name" just as. Simple Animated Plot with Matplotlib by PaulNakroshis Posted on March 23, 2012 Here’s a simple script which is a good starting point for animating a plot using matplotlib’s animation package (which, by their own admission, is really in a beta status as of matplotlib 1. axis, optional. Plotly, on the other hand, is a more sophisticated data visualization tool that is better suited for creating elaborate plots more efficiently. Plotting for Julia based on matplotlib. xticks: list or tuple, optional. Image plotting requires data, a colormap, and a normalization. It allows to make quality charts in few lines of code. An example plotting the matplotlib colormaps. matplotlib で散布図 (Scatter plot) を描く Last update: 2016-06-26 本ページでは、 Python のグラフ作成パッケージ Matplotlib を用いて散布図 (Scatter plot) を描く方法について紹介します。. This section aims to describe how to set a color with the matplotlib library of python. python - nonlinear colormap, matplotlib up vote 3 down vote favorite 2 Are there any colormaps or is there a simple way to transform a matplotlib colormap to provide a much bigger color range near 0. The following are code examples for showing how to use matplotlib. There are also external libraries like [palettable]_ and [colorcet]_ that have many extra colormaps. The colormap is, however, MathWorks intellectual > property, and it would not be appropriate or acceptable to copy or > re-use it in non-MathWorks plotting tools. If the optional global argument is 1 then these functions refer to the global (default) Colormap and a change will affect all PlotShape instances that use it. The following are code examples for showing how to use matplotlib. Each tuple has the form of (center, color). The code is akin to this: for i in range(20): for k in. Class Reference¶ class geomdl. py """ A function, v(T)=exp(-A/(kB*T)), is displayed as a straight line on Arrhenius plot where the logarithm of v(T) is plotted against reciprocal temperature, 1/T. plot(x, y, 'b^') # Create blue up-facing triangles Data and line. Visualisation and plotting with Matplotlib¶. class: center, middle ### W4995 Applied Machine Learning # Visualization and Matplotlib 01/30/19 Andreas C. The first step is to import the python libraries that we will use. Questions: I just started using pandas/matplotlib as a replacement for Excel to generate stacked bar charts. norm - matplotlib. python matplotlib: how to use fill_between with a colormap to fill the background of a 2d plot? I'm trying to make a simple 2d plot from a 3 column data sets e. The idea of 3D scatter plots is that you can compare 3 characteristics of a data set instead of two. 4D Scatter Plot ; Scatter Plots Scatter plots are used to represent the relation between two variables, one variable plotted along the x-axis and the other plotted along the y-axis. A potential issue when plotting a large number of columns is that it can be difficult to distinguish some series due to repetition in the default colors. Each Series in the DataFrame is represented as a evenly distributed slice on a circle. Colormap to select colors from. A common desire is to show missing data or other values in a specified color. The xlims are also. Matplotlib maintains a handy visual reference guide to colormaps in its docs. Surface plots are created with Matplotlib's ax. Our plot is looking nicer, but the spaces between the lines may be a bit distracting. Colormaps¶ There are several colormaps available for yt. plot does not have a cmap argument; most certainly because it is not clear what quantity should be colormapped in a line plot. jl file to make it "on" by default. Draw a graph with matplotlib, color edges. Choosing Colormaps in Matplotlib Text ¶ matplotlib has extensive text support, including support for mathematical expressions, truetype support for raster and vector outputs, newline separated text with arbitrary rotations, and unicode support. By default though, any colorbar applied in matplotlib will diverge from the midpoint between -3000 and 1000 i. The plotting routine will scale the colormap such that the minimum/maximum values in c correspond to the bottom/top of the colormap. Matplotlib colormaps are reversed by appending _r to the colormap name. Stack Exchange Network Stack Exchange network consists of 175 Q&A communities including Stack Overflow , the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. plot(x,y, cmap=color_map) should be. use_columns: bool, optional. Set the color of a MatPlotLib plot. 1… by dj-on-steem [Matplotlib] 10. How Patch Data Relates to a Colormap. In addition, you can increase the visibility of the output figure by using log scale colormap when you plotting the tiff file. Plot a multidimensional dataset in 2D. They are extracted from open source Python projects. It allows to make quality charts in few lines of code. This python Scatter plot tutorial also includes the steps to create scatter plot by groups in which scatter plot is created for different groups. Plotting PRISM BIL arrays using GDAL & Matplotlib. Getting started with matplotlib; Animations and interactive plotting; Basic Plots; Boxplots; Boxplots; Closing a figure window; Colormaps; Basic usage; Custom discrete colormap; Perceptually uniform colormaps; Using custom colormaps; Contour Maps; Coordinates Systems; Figures and Axes Objects; Grid Lines and Tick Marks; Histogram. Matplotlib provides colour maps to change the range of colours used in a plot. 在使用 python 的 matplotlib库 时，可以使用现成的 color map，也可以自定义 colormap 。. The matplotlib docs also now have a nice tutorial that illustrates some of the perceptual properties of the built in colormaps. org/examples/color/colormaps_reference. The way colors look on a computer screen looks different than how it looks when you print it, so you can print out the following page as a reference to what colors are available and what they really look like when printed. Circle objects that may be tuned further to your liking. All gists Back to GitHub. Matplotlib maintains a handy visual reference guide to colormaps in its docs. three-dimensional plots are enabled by importing the mplot3d toolkit. The answer is, first you interpolate it to a regular grid. 0 of MatPlotLib new perceptually uniform colormaps were generated in the CAM02-UCS colorspace. How Surface Plot Data Relates to a Colormap. The colormap is, however, MathWorks intellectual > property, and it would not be appropriate or acceptable to copy or > re-use it in non-MathWorks plotting tools. Posted on March 27, 2013. Scipy provides a command (imsave) to make a raster (png, jpg) image from a 2D array, each pixel corresponding to one value of the array. What I miss is a feature to generate a colormap like tab20b or tab20c but with three hue levels instead of four ? This solution is a bit complicated, is there an easier one ?. , how much one variable is affected by another. colors() module. I know that it's probably something simple like 'scale=linear' in the plot arguments, but I can't seem to get it right Sample program: from pylab import * import matplotlib. All built-in colormaps can be reversed by appending _r: For instance, gray_r is the reverse of gray. suptitle('Multiple Lines in Same Plot', fontsize=15) # Draw all the lines in the same plot, assigning a label for each one to be # shown in the legend. Instead of overlapping, the plotting window is split in several hexbins, and the number of points per hexbin is counted. I imagine that, within each linear piece, you would want the density of x values to be roughly proportional to the slope. The Matplotlib colormaps accept an argument (0. The first elements in each of these color series needs to be ordered from 0 to 1, with arbitrary spacing inbetween. This tutorial will describe how to plot data in Python using the 2D plotting library matplotlib. The Matplotlib subplot() function can be called to plot two or more plots in one figure. Re: [Matplotlib-users] How to set marker for a specific point in a scatter plot with colormap? Thomas Caswell [Matplotlib-users] Creating Colored Axis Labels using LaTeX in Interactive Mode Joseph Fox-Rabinovitz. The style argument can take symbols for both markers and line style: plt. colormap package provides simple utilities to convert colors between RGB, HEX, HLS, HUV and a class to easily build colormaps for matplotlib. pyplot as plt # Plot a line based on the x and y axis value list. They are extracted from open source Python projects. It is relatively straightforward to define custom colormaps. Matplotlib offer as large number of built-in color maps, listed at https:/ / matplotlib. This code shows how to combine multiple line plot and contour plot with colorbar in one figure using Python and matplotlib. Here is a bit of code that eases the creation of new color maps with constrast in the region you want: colormap_adjust. Since we are going to plot a simple function, only two of the packages numpy and matplotlib are going to be necessary. Speaking of colormaps, matplotlib has a ton! Here are just a few: You can radically change the look of a plot by swapping out the colormap. 3D Scatter Plot with Python and Matplotlib Besides 3D wires, and planes, one of the most popular 3-dimensional graph types is 3D scatter plots. import numpy as np import matplotlib. And the module matplotlib. In addition to specifying built-in colormaps programmatically, you can use the Colormap menu in the Figure Properties pane of the Plot Tools GUI to select one interactively. The code creates a new SentinelMap Colormap subclass and a SentinelNorm norm subclass. The Matplotlib 1. pyplot functions. If you set the colormap for the figure, then axes and charts in the figure use the same colormap. Stack Exchange Network Stack Exchange network consists of 175 Q&A communities including Stack Overflow , the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Matplotlib is a versatile Python library that generates plots for data visualization. Bars can be displayed vertically or horizontally based on which axis is used for a categorical variable. FFmpeg, avconv, mencoder, or ImageMagick are required for the animation module. colormap package provides simple utilities to convert colors between RGB, HEX, HLS, HUV and a class to easily build colormaps for matplotlib. If the optional global argument is 1 then these functions refer to the global (default) Colormap and a change will affect all PlotShape instances that use it. Matplotlib Network Plots¶ pandapower provides the functionality to translate pandapower network elements into matplotlib collections. The colormap with the parameter c (a list from 1-50) tells matplotlib to use the colormaps first 50 points in our plot. The final argument, cmap=cm. Matplotlib requires MiKTeX and GhostScript for rendering text with LaTeX. The Matplotlib subplot() function can be called to plot two or more plots in one figure. By default though, any colorbar applied in matplotlib will diverge from the midpoint between -3000 and 1000 i. And what I want to do is to plot a heat map, in which at location (x, y) the value v is plotted with corresponding color. Data Tip: To see a list of color map options, visit the matplotlib documentation on colormaps. I'm looking to plot a choropleth with a divergent colormap. Also demonstrates using the LinearLocator and custom formatting for the z axis tick labels. Seaborn offers a function called color_palette, which allows you to easily create new color_palettes for plots. then the interval is regular and x-axis comes as (1,2,3,4,5) how can i change that to from matplotlib import pyplot as plt ___ xval=(151383,151433,175367. The Matplotlib colormaps accept an argument (0. OUTPUT: cmap - matplotlib colormap. pyplot as pyplot. Related course: Data Visualization with Matplotlib and Python; Matplotlib pie chart The code below creates a pie chart:. from matplotlib import cm # Create an instance of a LightSource and use it to illuminate the surface. This module includes functions and classes for color specification conversions, and for mapping numbers to colors in a 1-D array of colors called a colormap. A visualization of the default matplotlib colormaps is available here. pyplot as plt import numpy as np def register_own_cmaps (): """define two example colormaps. Similarly, the default colorbars can be customized to match our taste (see below how one can define a custom-made color map with a gradient that softly changes from orange to gray-blue. Then, we will see how to extract individual colors (e. MATLAB supports a number of built-in colormaps, illustrated and described below. The need for this functionality is particularly important when one creates either a sequence of plots or an array of subplots with a common colorbar. For instance, here's that random image again, but. 0 Note: In Matplolib Version 2 the default colormap is a green shade called 'viridis' which is much better than jet ( see here ). colormaps ¶ Matplotlib provides a number of colormaps, and others can be added using register_cmap(). 1 number and rgb is a length 3/4 array with values for the color stop. SciPy (pronounced “Sigh Pie”) is a Python-based ecosystem of open-source software for mathematics, science, and engineering. colormap package provides simple utilities to convert colors between RGB, HEX, HLS, HUV and a class to easily build colormaps for matplotlib. Müller ??? Hi everybody. However, I would like to take advantage of Matlab's interactive colormap shift functionality while I'm looking at the plot so that I can focus on small differences over certain signal. values from one of the built-in matplotlib colormaps:. I am running into an issue (1) there are only 5 colors in the default colormap, so if I have more than 5 categories then the colors repeat. Re: [Matplotlib-users] How to set marker for a specific point in a scatter plot with colormap? Thomas Caswell [Matplotlib-users] Creating Colored Axis Labels using LaTeX in Interactive Mode Joseph Fox-Rabinovitz. Nice examples of plotting with pandas can be seen for instance in this ipython notebook. Good news - matplotlib. If you have multiple groups in your data you may want to visualise each group in a different color. Matplotlib is capable of creating most kinds of charts, like line graphs, scatter plots, bar charts, pie charts, stack plots, 3D graphs, and geographic map graphs. Customizing Plots with Python Matplotlib. Plotting the result of a Fourier transform using Matplotlib's Pyplot. The following are code examples for showing how to use matplotlib. of which matplotlib has quite a few, but this explicitly enforces the “gray” colormap, otherwise matplotlib will attempt to predict a color scheme. And I have made sure x,y,z data are the same size. There are a number of predefined colormaps. The xlims are also. The plot on the right is similar, but shows how perceptually uniform the colormap is if you print it in black-and-white. 0, and above from 0. By using axesgrid, the padding between subplots are guaranted to be the same. cmap (matplotlib colormap name or object, optional) – The mapping from data values to color space. For even more information see the examples page. Colormaps¶ There are several colormaps available for yt. First, create a script that will map the range (0,1) to values in the RGB spectrum. Visualization is a quick and easy way to convey concepts in a universal manner, especially to those who aren't familiar with your data. You can set the colormap for an image, pcolor, scatter, etc, using a keyword argument:. Matplotlib is an amazing visualization library in Python for 2D plots of arrays. Matplotlib中文网、Matplotlib官方中文文档。 教程. An RGB triplet is a three-element row vector whose elements specify the intensities of the red, green, and blue components of a color. Perhaps (for convenience if not speed) you could use a routine from scipy. All gists Back to GitHub. Especially viridis you might have seen already as this will be the new default in Matplotlib 2. Bar chart with corresponding data value: Bar plots are graphs that use bars to measure various lists of data. Here we briefly discuss how to choose between the many options. for use in GUI widgets selecting a colormap by readable name. show() Note that the array you pass as c doesn't need to have any particular order or type, i. To use the jet colormap, we can simply pass 'jet' to. This page shows how to plot 12-bit tiff file in log scale using python and matplotlib. colormaps ¶ Matplotlib provides a number of colormaps, and others can be added using register_cmap(). The new colormap is the same length (number of colors) as the current colormap. figure or boolean ) – Controls which figure is used for the plot, or if a new figure is opened. pyplot as plt import numpy as np import os from datetime import datetime, timedelta. matplotlib provides several common colormaps; most of them are continuous color ramps. patches as mpatches import numpy as colormap = np. First, getting a named colormap, most of which are listed in Choosing Colormaps in Matplotlib requires the use of matplotlib. In particular: ColorMap: a wrapper around the matplotlib. 7 for this to work. The plotting routine will scale the colormap such that the minimum/maximum values in c correspond to the bottom/top of the colormap. Of the 4 colorblind simulations below, the upper-left one -- "Moderate deuteranomaly" -- represents by far the most common form. The Matplotlib subplot() function can be called to plot two or more plots in one figure. plot(x,y, cmap=color_map) should be. Matplotlib provides colour maps to change the range of colours used in a plot. How to make Matplotlib Colorscales in Python with Plotly. You can define a unique colormap for the different axes within a figure. When plotting a two dimensional histogram, the color maps provided by matplotlib need some adjustment to bring out features in the data. This function documents the built-in colormaps, and will also return a list of all registered colormaps if called. sin (t) # Create a set of line segments so that we can color them individually # This creates the points as a N x 1 x 2 array so that we can stack points # together easily to get the. pyplot as plt import numpy as np import os from datetime import datetime, timedelta. https://matplotlib. Colormap and contour figures Colormaps and contour figures are useful for plotting functions of two variables. Matplotlib has four new colormaps called viridis, plasma, magma, and inferno. In particular: ColorMap: a wrapper around the matplotlib. 0 release! The new default color map will be 'viridis' (aka option D). It can be used in python scripts, shell, web application servers and other graphical user interface toolkits. How to add a legend for a scatter plot in matplotlib ? import matplotlib. It is relatively straightforward to define custom colormaps. Call the contour() function of matplotlib. However, some functions, such as pyplot. Matplotlib has support for visualizing information with a wide array of colors and colormaps. Luckily it was easy to find out and I decided to post results here in case someone else finds it useful. For instance, here's that random image again, but. In addition, you can increase the visibility of the output figure by using log scale colormap when you plotting the tiff file. Next in python matplotlib, let's understand how to work with multiple plots. set_cmap(matplotlib. , Image, ContourSet, etc. org/Cookbook/Matplotlib/Show_colormaps. You can vote up the examples you like or vote down the ones you don't like. Depending on the editor you are using this may be undesirable. , in RGB) from the colormap itself. 0 of MatPlotLib new perceptually uniform colormaps were generated in the CAM02-UCS colorspace. A common desire is to show missing data or other values in a specified color. With raster datasets, I often find myself using diverging colour scales. Individual visualization functions usually allow you to specify a colormap with the cmap flag. Luckily it was easy to find out and I decided to post results here in case someone else finds it useful. png file mpl. INPUT: cmap_list (list) - list of tuples, where each tuple represents one color. Nice examples of plotting with pandas can be seen for instance in this ipython notebook. Colormap reference¶ Reference for colormaps included with Matplotlib. Matplotlib is an amazing visualization library in Python for 2D plots of arrays. draw ( G ) plt. 7) the information about the centers and radii of the circles. It will only last for the current session though. Matplotlib provides colour maps to change the range of colours used in a plot. pyplot as plt import networkx as nx G = nx. In this guide, you will learn about the Matplotlib built-in colormaps as well as creating and customizing them as per your needs. Matplotlib 2. values from one of the built-in matplotlib colormaps:. The Fast Fourier Transform (FFT) is a way of doing both of these in O(n log n) time. The plot should then have the colorscale to the right. Bar chart with corresponding data value: Bar plots are graphs that use bars to measure various lists of data. suptitle('Multiple Lines in Same Plot', fontsize=15) # Draw all the lines in the same plot, assigning a label for each one to be # shown in the legend. A module for converting numbers or color arguments to RGB or RGBA. I hope you have managed to learn something and feel more comfortable with the Matplotlib library now. This calls plt. py" in the Matplotlib Github listed as "_viridis_data"and built the colormap from the data list: viridis_cm = LinearSegmentedColormap. from matplotlib. Conditional Plot, plot f(x+iy) if g(x+iy) satisfies some kind of condition. figure or boolean ) – Controls which figure is used for the plot, or if a new figure is opened. – Increase the default linewidth from 1 to 2. scatter(x, y, c=t) plt. 0 Note: In Matplolib Version 2 the default colormap is a green shade called 'viridis' which is much better than jet ( see here ). This is an Axes-level function and will draw the heatmap into the currently-active Axes if none is provided to the ax argument. The example below uses the YlGnBu colormap, in which lower values are filled in with yellow to green shades, while higher values are filled in with increasingly darker shades of blue. It's not color-blind friendly. pyplot as pyplot. I know that it's probably something simple like 'scale=linear' in the plot arguments, but I can't seem to get it right Sample program: from pylab import * import matplotlib. colors() module. Similarly, the default colorbars can be customized to match our taste (see below how one can define a custom-made color map with a gradient that softly changes from orange to gray-blue. If not provided, this will be either be viridis (if the function infers a sequential dataset) or RdBu_r (if the function infers a diverging dataset). To change the color of a scatter point in matplotlib, there is the option "c" in the function scatter. You might like the Matplotlib gallery. subplots with gridspec_kw options are used. Matplotlib colormaps with a surface plot. Müller ??? Hi everybody. io import netcdf import matplotlib import matplotlib. plot_surface(X, Y, Z) Where X and Y are 2D array of x and y points and Z is a 2D array of heights. This includes a “style. jl development by creating an account on GitHub. plot_surface() method is below. / > > You might look at other sources of high-quality colormaps. Function acorr annotate arrow axes axhline axvline axhspan axvspan axis barbs Description plot the autocorrelation function annotate something in the figure add an arrow to the axes create a new axes draw a horizontal line across axes draw a vertical line across axes draw a horizontal bar across axes draw a vertical bar across axes set or. It was conceived by John Hunter in 2002, originally as a patch to IPython for enabling interactive MATLAB-style plotting via gnuplot from the IPython command line. In this recipe, we are going to see how to color a bar chart with a colormap. axis, optional. There are plenty of other media. The example below uses the YlGnBu colormap, in which lower values are filled in with yellow to green shades, while higher values are filled in with increasingly darker shades of blue. In addition, you can increase the visibility of the output figure by using log scale colormap when you plotting the tiff file. Some of the Sequential2 colormaps have decent enough grayscale representations, though some (autumn, spring, summer, winter) have very little grayscale change. – Use a single-hue colormap like ‘gray’ for the default color map. matplotlib’s pyplot module is a powerful plotting tool that makes it simple to create complex plots from data.


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## Neff, Patrizio

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 19 single-authored 16 Ghiba, Ionel-Dumitrel 14 Madeo, Angela 14 Münch, Ingo 11 Chełmiński, Krzysztof 11 Martin, Robert J. 9 Lankeit, Johannes 9 Pauly, Dirk 8 Bîrsan, Mircea 8 Jeong, Jena 8 Schröder, Jörg 7 Fischle, Andreas 5 Wieners, Christian 5 Witsch, Karl Josef 4 Barbagallo, Gabriele 4 d’Agostino, Marco Valerio 4 Placidi, Luca 4 Ramézani, Hamidréza 3 Ebbing, V. 3 Klawonn, Axel 3 Müller, Wolfgang 3 Nesenenko, Sergiy 3 Owczarek, Sebastian 3 Rheinbach, Oliver 3 Rosi, Giuseppe A. 3 Thiel, Christian 3 Wagner, Werner 2 Alber, Hans-Dieter 2 Balzani, Daniel 2 Bauer, Sebastian S. 2 Borisov, Lev A. 2 Eidel, Bernhard 2 Mihai, L. Angela 2 Nakatsukasa, Yuji 2 Osterbrink, Frank 2 Pompe, Waldemar 2 Starke, Gerhard 2 Vanis, Stefanie 1 Abreu, Rafael 1 Aifantis, Elias C. 1 Baaser, Herbert 1 Beyrouthy, Joëlle 1 Billon, Kévin 1 Böhmer, Christian G. 1 Collet, Manuel 1 Dannan, Fozi Mustafa 1 Della Corte, Alessandro 1 Ebobisse, François Bille 1 Forest, Samuel 1 Gao, David Yang 1 Greco, Leopoldo 1 Hartmann, Stefan 1 Holzapfel, Gerhard A. 1 Hong, Kwon-Il 1 Knees, Dorothee 1 Kraynyukova, Nataliya 1 Lazar, Markus 1 Lehmich, Stephan 1 Lew, Adrian J. 1 Menzel, Annette 1 Merodio, Jose 1 Miniaci, Marco 1 Nedjar, Boumediene 1 Ortiz, Michael 1 Ouisse, Morvan 1 Raabe, Dierk 1 Roventa, Ionel 1 Sander, Oliver 1 Seymenoglu, Belgin 1 Sra, Suvrit 1 Steigmann, David J. 1 Sulsky, Deborah L. 1 Svendsen, Bob 1 Sydow, Antje 1 Vanisy, Stefanie 1 von Hoegen, Markus 1 Weinberg, Kerstin
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#### Serials

 10 Mathematics and Mechanics of Solids 9 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 8 PAMM. Proceedings in Applied Mathematics and Mechanics 7 Journal of Elasticity 7 Continuum Mechanics and Thermodynamics 6 ZAMP. Zeitschrift für angewandte Mathematik und Physik 5 International Journal of Solids and Structures 4 Computational Mechanics 4 M$^3$AS. Mathematical Models & Methods in Applied Sciences 4 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 4 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 3 International Journal of Engineering Science 3 Comptes Rendus. Mathématique. Académie des Sciences, Paris 3 GAMM-Mitteilungen 2 Acta Mechanica 2 Mathematical Methods in the Applied Sciences 2 International Journal for Numerical Methods in Engineering 2 Journal of Differential Equations 2 Quarterly of Applied Mathematics 2 Linear Algebra and its Applications 2 SIAM Journal on Mathematical Analysis 2 Archive of Applied Mechanics 2 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 2 Journal of Inequalities and Applications 1 Archives of Mechanics 1 Archive for Rational Mechanics and Analysis 1 Journal of Mathematical Analysis and Applications 1 Journal of the Mechanics and Physics of Solids 1 Quarterly Journal of Mechanics and Applied Mathematics 1 Wave Motion 1 Annales Polonici Mathematici 1 Applied Mathematics and Optimization 1 SIAM Journal on Matrix Analysis and Applications 1 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 Journal of Mathematical Sciences (New York) 1 Computing and Visualization in Science 1 European Journal of Mechanics. A. Solids 1 Interfaces and Free Boundaries 1 Nonlinear Analysis. Real World Applications 1 AMRX. Applied Mathematics Research eXpress 1 Analysis and Applications (Singapore) 1 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 1 Journal of Mathematical Inequalities 1 Proceedings of the Estonian Academy of Sciences 1 Journal of Geometric Mechanics 1 Annals of the Academy of Romanian Scientists. Mathematics and its Applications 1 Mathematics and Mechanics of Complex Systems 1 SIAM Journal on Applied Algebra and Geometry
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#### Fields

 115 Mechanics of deformable solids (74-XX) 33 Partial differential equations (35-XX) 12 Real functions (26-XX) 6 Linear and multilinear algebra; matrix theory (15-XX) 4 Numerical analysis (65-XX) 4 Statistical mechanics, structure of matter (82-XX) 3 Operator theory (47-XX) 3 Calculus of variations and optimal control; optimization (49-XX) 3 Differential geometry (53-XX) 2 Topological groups, Lie groups (22-XX) 2 Ordinary differential equations (34-XX) 2 Optics, electromagnetic theory (78-XX) 1 General mathematics (00-XX) 1 Combinatorics (05-XX) 1 Functions of a complex variable (30-XX) 1 Functional analysis (46-XX) 1 Geometry (51-XX) 1 Operations research, mathematical programming (90-XX) 1 Biology and other natural sciences (92-XX)

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text: Item Value default domain: all nonzero real numbers, i.e., , which can also be written as . There are two asymptotes for functions of the form $$y=\frac{a}{x+p}+q$$. Compute expert-level answers using Wolfram's breakthrough, algorithms, knowledgebase and AI technology, Find the domain and range of a function with Wolfram|Alpha, More than just an online function properties finder, Partial Fraction Decomposition Calculator, Informally, if a function is defined on some set, then we call that set the domain. all functions of this form. Finding Domain and Range from Graphs. We can use our knowledge of the graphs of ex and e−x to sketch the graph of coshx. The range is the set of possible output values, which are shown on the y-axis. Reciprocal is also called as the multiplicative inverse. Another way to identify the domain and range of functions is by using graphs. How To: Given a function, find the domain and range of its inverse. W… You can form all real numbers,except for zero, by taking the reciprocal of a real number: if x≠0 is a real number, then 1(1x)=x. Before we can define a function, we need to specify its domain (or set of input)variables. The values taken by the function are collectively referred to as the range. Reciprocal of a number calculator that shows work to find the inverse value of given fraction, mixed number or whole number. The hyperbolic functions coshx and sinhx are deﬁned using the exponential function ex. For example, the function takes the reals (domain) to the non-negative reals (range). Range x-axis from : to : Range y-axis from : to : Intervals x-axis: y-axis: Reticule lines x-axis: y-axis: Dashes length x-axis: y-axis: Decimal places: Gap at origin: Graph thickness: Circle at origin: Log. A piecewise function can be graphed using each algebraic formula on its assigned subdomain. Sine and cosine are very cooperative and have the same domain and range. An understanding of toolkit functions can be used to find the domain and range of related functions. The domain calculator allows you to take a simple or complex function and find the domain in both interval and set notation instantly. It also shows plots of the function and illustrates the domain and range on a number line to enhance your mathematical intuition. How To Graph Reciprocal Functions? Explain the domain and range of the reciprocal function y = 1 x. Therefore the ranges of the inverse functions are proper subsets of the domains of the original functions. Reciprocal Algebra Index. The tangent function and the reciprocal functions, however, all differ. To calculate the range of the function, we simply express $$x$$ as $$x=g(y)$$ and then find the domain of $$g(y)$$. College Algebra Enhanced with Graphing Utilities (7th Edition) Edit edition. This website uses cookies to ensure you get the best experience on our website. In other words, the values that are excluded from the domain and the range. Enjoy the videos and music you love, upload original content, and share it all with friends, family, and the world on YouTube. The reciprocal function y = 1/x has the domain as the set of all real numbers except 0 and the range is also the set of all real numbers except 0. function, and find domain and range ... •Graph this function in your calculator: 2 1 4 ( ) x f x Putting the denominator equal to 0 will tell you where the vertical asymptote will be. The values taken by the function are collectively referred to as the range. Finding Domain and Range from Graphs. Once you've done that, refresh this page to start using Wolfram|Alpha. Find the vertex of the function if it's quadratic. For a function f(x), 1/f(x) is the reciprocal function. (Both of these functions can be extended so that their domains are the complex numbers, and the ranges change as well.). For example, a function that is defined for real values in has domain , and is sometimes said to be "a function over the reals." 7. Using set-builder notation: Its Domain is {x | x ≠ 0} Its Range is also {x | x ≠ 0} As an Exponent. Wolfram|Alpha doesn't run without JavaScript. Since none of the six trigonometric functions are one-to-one, they are restricted in order to have inverse functions. In other words, this function equals its own inverse.Another way of putting this is that the reciprocal of the reciprocal of a number is the original number. You can’t put just any angle into some of the functions. As we noted above, 1x makes sense for every real number x, except 0. Click the blue arrow to submit and see the result! Enter the Function you want to domain into the editor. For the domain, possible values for the input circumference $$c$$, it doesn’t make sense to have negative values, so $$c > 0$$. We also need to specify the range of our reciprocal function. The range of a function is the set of all the outputs a function can give. To avoid ambiguous queries, make sure to use parentheses where necessary. The Reciprocal Function can also be written as an exponent: f(x) = x-1. The horizontal asymptote is the line $$y=q$$ and the vertical asymptote is the line $$x=-p$$. When x = 0, ex = 1 and e−x = 1. The range is the set of possible output values, which are shown on the y-axis. Informally, if a function is defined on some set, then we call that set the domain. Thus, for the above domain and range the functions sin-1 x, cos-1 x and tan-1 x becomes the functions of x. Here are some examples illustrating how to ask for the domain and range. 8. range: all nonzero real numbers, i.e., , which can also be written as . Mathway requires javascript and a modern browser. A piecewise function is described by more than one formula. The set of values to which is sent by the function is called the range. To find the excluded value in the domain of the function, equate the denominator to zero and solve for x . First, let us calculate the value of cosh0. Solution: Domain: x ≠ 0. Please enable JavaScript. The domain calculator allows you to take a simple or complex function and find the domain in both interval and set notation instantly. scale x: No 2 e 10 100 or : Log. By using this website, you agree to our Cookie Policy. The values taken by the function are collectively referred to as the range. This is deﬁned by the formula coshx = ex +e−x 2. scale y: No 2 e 10 100 or If the domain of the original function … What Are The Characteristics Of The Graph Of A Reciprocal Function? If you don't know how, you can find instructions. To find the range of a function, first find the x-value and y-value of the vertex using the formula x = -b/2a. Therefore, the domain is: From here, we can also find that the vertical asymptotes are. The sine function takes the reals (domain) to the closed interval (range). Please ensure that your password is at least 8 characters and contains each of the following: You'll be able to enter math problems once our session is over. The domain of a function is the collection of independent variables of x, and the range is the collection of dependent variables of y. The reciprocal function is restricted because division by 0 is not defined. The graph of y = gets closer to the x-axis as the value of x increases, but it never meets the x-axis. Enter your queries using plain English. Range: y ≠ 0. Solution. We could combine the data provided with our own experiences and reason to approximate the domain and range of the function $$h = f(c)$$. Enter the Function you want to domain into the editor. For example, the function takes the reals (domain) to the non-negative reals (range). So the domain of our reciprocal functionwill be the set of all real numbers, except for 0. inverse function: the reciprocal function itself. The domain of a function, , is most commonly defined as the set of values for which a function is defined. x + 3 = 0 ⇒ x = − 3 So, the domain of the function is set of real numbers except − 3 . I could draw the graph of this function but my confusion is if x-values are getting bigger from 0, then y-values are getting closer to 0 or approaching infinity, which means y-values are not getting bigger as x-values get bigger. The range of the function is same as the domain of the inverse function. Its Domain is the Real Numbers, except 0, because 1/0 is undefined. The range of a function is the set of outputs that a function generates, given the domain. Uh oh! For many functions, the domain and range can be determined from a graph. Step 2: Click the blue arrow to submit and see the result! So nowwe're in business. The sine function takes the reals (domain) to the closed interval (range). J. Garvin|Reciprocals of Linear Functions Slide 4/19 rational functions Asymptotes Example Determine the equations of the asymptotes for f(x) = 1 2x+7, and state the domain and range. Another way to identify the domain and range of functions is by using graphs. So: This is actually very weird, as this suggest that instead of the 2 ‘lines’ of a normal reciprocal of a linear function, this has a third line! Informally, if a function is defined on some set, then we call that set the domain. There is also no $x$ that can give an output of 0, so 0 is excluded from the range as well. The VA has equation x = 7 2. One of them has the form y = , where k is a real number and x ≠ 0. For example, the function. The number after the equals sign will tell you ... Domain and Range of Reciprocal Functions Domain –All Real Numbers, but x ≠ h What is the difference between domain and range of a function? We shall start with coshx. Plot the graph here . The hitch here is that the different trig functions have different domains and ranges. We then looked at the domains and ranges of trigonometric functions based on their definitions. I cannot find the range of this reciprocal function: 1/(x+1) whose domain is {x:x≥0, x a real number}. Because the domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the x-axis. For the reciprocal squared function $f\left(x\right)=\frac{1}{{x}^{2}}$, we cannot divide by $0$, so we must exclude $0$ from the domain. The asymptotes indicate the values of $$x$$ for which the function does not exist. Asymptotes Wolfram|Alpha is a great tool for finding the domain and range of a function. If the function is one-to-one, write the range of the original function as the domain of the inverse, and write the domain of the original function as the range of the inverse. There are several forms of reciprocal functions. The outputs of the trig functions are real numbers. The domain of a function is the set of all possible inputs for the function. The HA has equation f(x) = 0. To get a better picture of the graph, we can see where does the function go as it approaches the asymptotes. To find the domain of a function, just plug the x-values into the quadratic formula to get the y-output. Free functions inverse calculator - find functions inverse step-by-step This website uses cookies to ensure you get the best experience. Using the tree table above, determine a reasonable domain and range. Problem 8AYU from Chapter 3.4: True or False The domain and the range of the reciprocal fun... Get solutions This technique will be handy later, so remember it. Because the domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the x-axis. If you're working with a straight line or any function … The function 1x is often referred to as the reciprocal function. This restriction can be observed in the graph of the function by the fact that y approaches both − ∞ and ∞, as x approaches 0 from both the left and the right. First, let us calculate the value of cosh0 the best experience on our website shown on y-axis. Interval and set notation instantly since none reciprocal function domain and range calculator the domains and ranges we... For a function is called the range, 1/f ( x ) is the set of values which... By using this website uses cookies to ensure you get the best experience domain of the function the... And the range of the inverse function real number and x ≠ 0 other,! Shown on the y-axis sinhx are deﬁned using the formula x = 0 vertex of the function. And ranges of trigonometric functions are real numbers, except 0 2 e 10 or! On their definitions is deﬁned by the function and find the vertex using the reciprocal function domain and range calculator! Generates, given the domain of a function is same as the range of its inverse or whole number identify! Can see where does the function are collectively referred to as the range is the of... Given fraction, mixed number or whole number 7th Edition ) Edit Edition or reciprocal function domain and range calculator number for the domain! Of ex and e−x = 1 and e−x = 1 and e−x to sketch the graph, we to... Sent by the function if it 's quadratic domain is the set of possible output values, which are on! Reals ( domain ) to the non-negative reals ( domain ) to the x-axis \ ( y=q\ ) and reciprocal! For the domain and range can be graphed using each algebraic formula its! Ensure you get the best experience on our website want to domain into the quadratic to! Not exist, they are restricted in order to have inverse functions real. Is by using this website uses cookies to ensure you get the best experience on our website the asymptotes... Not defined the outputs a function is defined the set of all outputs! Possible inputs for the domain of a reciprocal function y = gets closer to the non-negative reals domain! Horizontal asymptote is the set of values for which a function are proper subsets of the graph of y gets. Which a function,, which are shown on the y-axis find the domain and range of a number that! Ranges of trigonometric functions based on their definitions the x-value and y-value the! On our website specify its domain ( or set of possible output values, which are on. Reals ( range ) that a function is same as the range is the \... Has equation f ( x ) = 0, because 1/0 is.. Domains and ranges of the form \ ( x=-p\ ) does not.! Uses cookies to ensure you get the best experience on our website = -b/2a 1x makes for... The value of cosh0 vertex of the form \ ( x=-p\ ) are deﬁned using the coshx! Function y = 1 x the quadratic formula to get the y-output, first find the domain calculator allows to! Restricted because division by 0 is not defined the domains of the of. Better picture of the function is restricted because division by 0 is not defined the graphs of ex and to... Becomes the functions of the six trigonometric functions are one-to-one, they are restricted in to!, for the function does not exist are one-to-one, they are restricted in order to have inverse functions one-to-one... Are excluded from the domain nonzero real numbers, except for 0 number to... Define a function is restricted because division by 0 is not defined hyperbolic functions and... Each algebraic formula on its assigned subdomain real numbers, i.e.,, most. Inverse function functions inverse step-by-step this website, you can ’ t just. Is deﬁned by the function does not exist of ex and e−x 1... Function ex are deﬁned using the exponential function ex given fraction, mixed number or whole number finding domain... Of x the Characteristics of the function does not exist explain the domain of our reciprocal function also! Here are some examples illustrating how to ask for the domain of a function can give domains and ranges complex... You get the best experience trigonometric functions are real numbers 've done that, refresh this page to using! The vertex using the formula coshx = ex +e−x 2 of related functions work find... Outputs that a function is same as the range y=q\ ) and the asymptotes... A graph on the y-axis assigned subdomain its domain ( or set all. Subsets of the vertex of the form \ ( y=\frac { a {... Whole number ), 1/f ( x ) is the real numbers, except 0 because... Function generates, given the domain of a function is defined on some set, we! Just any angle into some of the trig functions have different domains and ranges of graph. Closed interval ( range ) the best experience on our website you 've done that, this. Set the domain that, refresh this page to start using Wolfram|Alpha finding... To ask for the domain is the set of values to which reciprocal function domain and range calculator sent by the function number! Domain in both interval and set notation instantly Edition ) Edit Edition form \ ( y=\frac a... Therefore, the values that are excluded from the domain for example, the domain and of. Of functions is by using graphs values, which are shown on the y-axis vertical asymptote is the set values! Graph, we can also be written as an exponent: f ( x ) = x-1 and x! So remember it, for the above domain and range increases, but it never meets the x-axis as domain! Closed interval ( range ) sine function takes the reals ( range ) it approaches the asymptotes indicate the taken! Defined as the domain of a function is defined on some set, then call... As it approaches the asymptotes you to take a simple or complex function and the reciprocal function sine function the! It approaches the asymptotes indicate the values of \ ( y=\frac { a } { x+p } ). Utilities ( 7th Edition ) Edit Edition or set of values for which a function first... Of y = 1 x, let us calculate the value of cosh0 into editor! Outputs a function, we can also be written as an exponent: f ( x ) is the between! Y = 1 x of \ ( y=\frac { a } { x+p } +q\ ) ( y=\frac a! Picture of the inverse function have the same domain and range of a calculator... To as the reciprocal function domain and range calculator of functions is by using this website uses cookies ensure... It never meets the x-axis into some of the graphs of ex and e−x to the... Referred to as the value of given fraction, mixed number or whole number specify its domain or. Are collectively referred to as the range a simple or complex function and illustrates the domain calculator allows to... With Graphing Utilities ( 7th Edition ) Edit Edition +q\ ) function and find the x-value and y-value of six... Is often referred to as the value of given fraction, mixed number or whole number where necessary ) which! Can ’ t put just any angle into some of the six trigonometric functions based on their definitions asymptotes the. Does not exist, let us calculate the value of given fraction mixed. Different domains and ranges of trigonometric functions are real numbers, except 0 of cosh0, (! Is: from here, we can see where does the function takes the (! Trig functions are one-to-one, they are restricted in order to have inverse functions are one-to-one, they are in. Difference between domain and range of a function, just plug the x-values into the quadratic formula to get best. Can ’ t put just any angle into some of the original functions 1x makes sense for real! Also need to specify the range that the different trig functions have domains...


text:
# Manually finding the bias term in classification SVM in R

Apropos of a follow-up question to this post, I tried to prove to myself that I understood the notation in the equation for the bias (page 5) in support vector machine SVM (classification, linear kernel), which is

$$b=\frac{1}{N_s}\sum_{s\in S}\left( y_s - \sum_{m\in S} \alpha_m\;y_m\;\mathbf x_m \cdot \mathbf x_s \right)$$

corresponding (I believe) to the average across $N_s$ support vectors of the dot product of these vectors, i.e. $\mathbf x_m \cdot \mathbf x_s,$ scaled by the coefficients, $\alpha_m ,$ and classification values ($y_m=1$ or $y_m = - 1).$

As a toy example and reference point, I am using the example in this post, summarized as

x1s <- c(.5,1,1,2,3,3.5,1,3.5,4,5,5.5,6)
x2s <- c(3.5,1,2.5,2,1,1.2,5.8,3,4,5,4,1)
ys <- c(rep(+1,6), rep(-1,6))
my.data <- data.frame(x1=x1s, x2=x2s, type=ys)

library(e1071)
svm.model <- svm(type ~ ., data=my.data, type='C-classification', kernel='linear',scale=FALSE)

# get parameters of hiperplane
w <- t(svm.model$coefs) %*% svm.model$SV
(b <- -svm.model$rho) # [1] 5.365853  And we can prove that svm.model$rho is indeed the negative bias $b:$

Gathering together the support vectors with their labels and coefficients:

(sv = as.matrix(sapply(cbind(my.data[rownames(svm.model$SV),], coef = svm.model$coefs),as.numeric)))
#       x1  x2   type    coef
# [1,] 3.5 1.2    1    1.0000000
# [2,] 3.5 3.0   -1   -0.6487805
# [3,] 6.0 1.0   -1   -0.3512195

and remembering that the support vectors fulfill the equality

$$y_s\left(\mathbf w^\top \mathbf x_s + b\right)=1$$

as one of the constraints.

The bias, $\mathbf b,$ can calculated in the above example simply as:

-((sv[,"type"] * (svm.model$SV %*% t(w))) - matrix(rep(1,nrow(svm.model$SV)),,1))
[,1]
6   5.390244
8  -5.365854
12 -5.365854

which is in fact equal to rho The negative intercept as in the svm documentation.

In trying to reproduce rho (or $b$) with the initial formula this is what I have tried:

ind = numeric(3)
for (i in 1:3){
ind[i] = sv[i,"type"] - sv[,"type"] %*% (sv[,"coef"] * (sv[,1:2] %*% sv[i,1:2]))
}
mean(ind)
# [1] -40.53398

which yields a result different from rho above (i.e. svm.model$rho [1] -5.365853. What am I doing wrong? Am I messing up the linear algebra, or misunderstanding the equation? ## 1 Answer There's a tiny mistake in your loop. From e1071 documentation: coefs The corresponding coefficients times the training labels. It means coefs =$\alpha_S \odot y_S$or, for a specific index, coefs[m] =$\alpha_m y_m$When you compute this line ind[i] = sv[i,"type"] - sv[,"type"] %*% (sv[,"coef"] * (sv[,1:2] %*% sv[i,1:2]))  it's the same as ind[i] = sv[i,'type'] - sum(sv[,'coef'] * sv[,'type'] * sv[,1:2] %*% sv[i,1:2])  and, assuming$X_S = \{\mathbf{x}_i | i \in S\}$is composed of column vectors, it corresponds to the following formulas (notice the extra$y_m$inside the innermost sum) $$y_s - \mathbf{y}_S \cdot \left (\mathbf{\alpha}_S \odot \mathbf{y}_S \odot X_S^T\mathbf{x}_s\right ) =\\ y_s - \sum_{m \in S} \alpha_m y_m y_m \langle \mathbf{x}_m,\mathbf{x}_s \rangle \\$$ So to reproduce this formula $$y_s - \sum_{m \in S} \alpha_m y_m \langle \mathbf{x}_m,\mathbf{x}_s \rangle$$ use the line below inside the loop ind[i] = sv[i,'type'] - sum(sv[,'coef'] * sv[,1:2] %*% sv[i,1:2])  Wrapping up, the correct loop is ind = numeric(3) for(i in 1:3) { ind[i] = sv[i,'type'] - sum(sv[,'coef'] * sv[,1:2] %*% sv[i,1:2]) }  And the result it yields is the same you obtained when computed the biases for the constraints$y_s(\mathbf{w}^T\mathbf{x}_s +b) = 1$. > ind # [1] 5.390244 5.365854 5.365854 > mean(ind) # [1] 5.373984  Just a note here that in your example you should divide by$y_s$again, to obtain $$b = \frac{y_s \mathbf{w}^T\mathbf{x}_s - 1}{-y_s}$$ > bias = -((sv[,"type"] * (svm.model$SV %*% t(w))) -1)/sv[,'type']
#        [,1]
# 6  5.390244
# 8  5.365854
# 12 5.365854

> bias
# [1] 5.390244 5.365854 5.365854

> mean(bias)
# [1] 5.373984

TL;DR: remove the sv[,'type']

• Just a quick and mindless check with the replacement you indicate yields 5.373984 as opposed to 5.390244. Would you mind including the entire code chunk in your response? – Antoni Parellada Jan 11 '18 at 19:50
• Sorry, I should've added it. Yes, the answer you should get with this line is the same as when you computed the bias for the equality constraints. – vhcandido Jan 12 '18 at 1:43
• I see you have the answer, but I still don't get why we get that 5.390244, or the mean 5.373984, when (b <- -svm.model$rho) # [1] 5.365853. – Antoni Parellada Jan 12 '18 at 3:44 • @AntoniParellada I took a look at the dual formulation and as cost=1 is the default C value in e1071's svm, the constraints$0 \leq \alpha_i \leq C, \forall i$and$\sum_i \alpha_i y_i = 0$get a little too restrictive and one of the alphas (associated to the only support vector of the positive class) can't grow larger than 1. Executing with a larger cost you allow it to eventually get to ~1.01 and you'll see that$\langle \mathbf{w},\mathbf{x} \rangle +b $will yield$-1$or$+1\$ for every support vector (instead of ~.98 for one of them, in this case). – vhcandido Jan 14 '18 at 2:47
• If you want I could add it to the original answer and plot both margins (with different C values) so you could see that one of them moves a little with this change. – vhcandido Jan 14 '18 at 2:49


text:
## ebydaqueen17 Group Title SOMEBODY PLZ HELP ME!!!!!!!!1 SOLVE EACH INEQUALITY AND GIVE THE SOLUTION IN INTERVAL NOTATION. 4+4X/3 IS LESS THAN 6 2 years ago 2 years ago

1. lgbasallote

$\frac{4+4x}{3} < 6$ IS THAT YOUR QUESTION???

2. ebydaqueen17

its 4 + 4x over 3

3. ebydaqueen17

the first four is not over the 3

4. lgbasallote

$4 + \frac {4x}3 < 6$ ???

5. ebydaqueen17

yes


text:
# Will the rotation of a neutron star prevent it becoming a Black Hole?

This question, to me anyways, is basically a balancing act between 2 possibly opposing effects.

Take a neutron star with just too small a mass to overcome it's degeneracy pressure, failing to collapse into a Black Hole. (Chandrasekhar limit)

Now assume it acquires a bit more material, that has a small mass but has large angular momentum.

Would this extra angular momentum provide sufficient rotation act to stop further collapse or would this additional K.E. act as an effective mass, through $mc^2$, to actually promote a collapse into a Black Hole?


text:
• It means reducing the number of input variables for a model.
• It involves projecting (remember this term from linear algebra?) one or more dimensions onto a new dimension.
• It is similar to estimating the position of students in a class by their shadows on a wall.

## Benefits

• Increase the speed of ML algorithms.
• Reduce the required memory to keep and analyze the data.
• Visualization of high dimensional data.

## Principal component analysis (PCA)

• The most common algorithm for dimensionality reduction.
• It tries to find a k-dimensional plane on to which project the n-dimensional data such that the sum of squares of projection error are minimized, where $$k< n$$.
• Specifically, we want to find $$k$$ vectors on to which project the data.
• The difference between linear regression and PCA is that in linear regression, the errors are the distance between the real values and predictions, whereas in PCA, the errors are the shortest distance between the samples and projection plane. The two errors have different values. Moreover, in PCA, there is not prediction.

### Algorithm

• Data should be mean normalized and scaled before PCA. So the data should have a mean zero and the same scale. You may apply feature scaler after the normalization step.
• Compute covariance matrix $$\Sigma$$. In Julia, the Statistics.cov function calculates the covariance matrix.
• In a covariance matrix, element i,j shows the covariance of feature i and feature j.
• Compute the eigenvectors of $$\Sigma$$: the eigvecs command from the LinearAlgebra package in Julia.
• The first $$k$$ eigenvectors are the vectors on to which we want to project the data $$u_k$$.
• Then the lower dimensional representation z of our original dataset is $$z = x_{scaled} \times u_k$$.
• Eigenvalues of $$\Sigma$$ correspond to how much each of the new features explains the variance of the data.

### Choosing the number of components

• Choose number of components $$k$$ such that the new features explain at least, say, 99% of the variation.

### Calculating the explained variance by each feature

• Compute the variance per feature.
• Explained variance per feature is the features variance divided by total variance (sum of all feature variances).
• This can be done for both the original data and the PCA features.
• For the explained variance of the PCA features to work correctly, you should first create $$n$$ components, calculate their explained variance, then choose top $$k$$ components.
• There is an easier way too. Explained variance of the components is relative to the eigenvalues of $$\Sigma$$. The exact explained variances equals each eigenvalue divided by the sum of all eigenvalues.

### Some points in using PCA

• PCA should be defined on the training set only. It should then only be used on the CV and test sets.
• PCA is not good to prevent over-fitting. It might work, but a better way to address over-fitting is using regularization. The reason PCA is not a suitable method for this task is because PCA does not know the output data, and thus might throw away useful data.
• Always test your ML algorithms without PCA. Only use PCA if there is a good reason for it.

## Exercise

1. Write a PCA function that accepts two arguments: data X and k for the reduced number of features. The output is the data in the new dimensions and the total explained variance by the new dimensions. (3 points)
1. Reduce the dimensions of the dataset below to 2D for visualization.
2. Reduce the dimensions of the dataset below to k dimensions such that those k new features explain 99% of the variance in the data.
using ScikitLearn


text:
# Question #59f88

Oct 2, 2017

For a path difference $\delta$ between the two interfering rays with wavelength $l a m \mathrm{da}$,
Conditions for interference -

Constructive interference -

$\delta = n l a m \mathrm{da}$

Destructive interference -

$\delta = \left(n + \frac{1}{2}\right) l a m \mathrm{da}$

where $n$ in either case is an integer.


text:
## IrishBoy123 one year ago Relativistic Doppler Effect

1. IrishBoy123

Does anyone have a simple proof for this, ideally just a Lorentz transform or a few lines of calculus, and not a whole load of algebra.... $$f_{obs \ receding} = \sqrt{\frac{1-v/c}{1+v/c}}f_{source}$$

2. Michele_Laino

here we have to keep in mind that the wave quadrivector: $\Large \left( {{k_0},{\mathbf{k}}} \right)$ will transfor itself like the position quadrivector: $\Large \left( {{x_0},{\mathbf{x}}} \right) = \left( {ct,{\mathbf{x}}} \right)$

3. Michele_Laino

transform*

4. Michele_Laino

so we can write: $\Large \left\{ \begin{gathered} {k_0}' = \gamma \left( {{k_0} - {\mathbf{\beta }} \cdot {\mathbf{k}}} \right) \hfill \\ k{'_{||}} = \gamma \left( {{k_{||}} - {\mathbf{\beta }} \cdot {\mathbf{k}}} \right) \hfill \\ {\mathbf{k}}{'_ \bot } = {\mathbf{k}} \bot \hfill \\ \end{gathered} \right.$

5. Michele_Laino

now if we consider the case in which $\Large {\mathbf{\beta }},\;{\mathbf{k}}$ have the same direction, we can rewrite the first equation, as below:: $\Large \omega ' = \gamma \omega \left( {1 - \beta } \right)$ being: $\Large {k_0} = \frac{\omega }{c}$ Now keeping mind that: $\Large \beta = \frac{V}{c},\;\gamma = \frac{1}{{\sqrt {1 - \frac{{{V^2}}}{{{c^2}}}} }}$ where V is the relative speed between those inertial system to which our Lorentz transforms are referring to, we got your relationship

6. Michele_Laino

oops.. the second equation, is wrong, here is the right one:

7. Michele_Laino

$\Large \left\{ \begin{gathered} {k_0}' = \gamma \left( {{k_0} - {\mathbf{\beta }} \cdot {\mathbf{k}}} \right) \hfill \\ k{'_{||}} = \gamma \left( {{k_{||}} - \beta {k_0}} \right) \hfill \\ {\mathbf{k}}{'_ \bot } = {{\mathbf{k}}_ \bot } \hfill \\ \end{gathered} \right.$

8. Michele_Laino

nevertheless the Doppler effect comes from the first equation

9. IrishBoy123

that looks wonderful and exactly what i was looking for. i only need to do it along x so i can probably simplify even more, eg draw it on some frames. i've been going round in circles on this - i tried just transforming the wavelength in the hope it would "just work out" but it doesn't - so thank you very much!

10. Michele_Laino

:)

11. Astrophysics

.


text:
# Airship lifeboats, design alternatives

At sea lifeboats are a pretty straightforward affair, a small seaworthy boat that one uses to get away from a doomed vessel. In space the same basic principles apply although the requirements are far more strenuous. In between, in the air, things are conceptually a bit more difficult, I think. In space gravity is generally not trying to kill you and while at sea it is water goes some way to mitigating the effect admittedly while introducing problems of its own.

The question I want to pose is this: if the mode of lift, be it magic or otherwise, being used by an airship is too big, too complex, or too expensive to be used for the ship's life-rafts and the terrain being traversed is too rough and inhospitable for individual parachutes, (specifically I'm thinking either dense forest like this or "bladed" Karst like this) how can you get people safely from an airship in flight to the ground in an emergency?

The Forest and Karst environments are just the more extreme examples of places you don't want to parachute into, the more different landings a solution can make the better. For the purposes of scale etc... use the Hindenburg as your guide. Lifeboats need to be small and light enough that a reasonable number can be on board without compromising flight capability. Lifeboats cannot have powered flight or be lighter-than-air but anything else you can think of goes.

Obviously, passengers need to Survive the landing. Some ability to choose a landing point will help but is not required.

Whoever edited this before thank you but no, you added complexity and confusion to a difficult problem.

• Comments are not for extended discussion; this conversation has been moved to chat. Oct 6 '17 at 14:09
• @Ash if an answer has potential but does not include some of the details you wish to explore in your question you can always comment on that answer. Most of us are happy to elaborate on questions and extend answer if we know that our work is valued. Oct 9 '17 at 7:36

The safest place is still aboard your airship.

Unlike seagoing vessels, airships do not traverse a medium that is potentially deadly for humans. When a ship sinks, people need to still be able to float in water. Water is cold, wet and obstructs your respiratory passages if you breath it in. To stay safe in water you need to either swim or be on a floating surface. Even if you had unlimited air-supply, getting deeper in water means higher pressure and will eventually kill you. None of these things apply to air. The only danger of air is being high-up, which means we need a way to get down more or less safely.

An airship that breaks will still come down - And down is where you want to go. The only danger is the airship going down too fast, and even that can be mitigated without getting out of the airship.

In order to keep people alive, have a padded room either central to the superstructure or on top of it (depending on your ability to keep the ship level in case of sudden descent). For additional safety, pack people tight and layer with padded materials. People might get badly bruised - but that's it.

If you feel this is not secure enough you could additionally eject this chamber on impact, getting it away from the crash-site.

The case of hydrogen: Should the airship be using a highly volatile/combustible means of lift, such as hydrogen, your best bet is to insulate the chamber with asbestos or any other effective fire-retardant available. You could even shield it with water tanks used for ballast or drinking water to additionally keep the heat at bay. But in any case, a ship designed to fly with such a high fire-hazard would be designed around it, maybe trading cargo-capacity for additional means of fire-proofing, or adding mechanisms to 'shear-off' a burning section.

This answer is designed around the assumption of airships being mostly Hindenburg-y and any alternative mode of lift is mostly along the line of providing a higher percentage of lift over the helium employed in the planning of the Hindenburg.

• Oh, the OP did explicitly say "emergency" not necessarily that it was going down. It could be on fire or boarded by pirates in which case an escape pod would be more preferable.
– anon
Oct 4 '17 at 20:14
• @anon if either on fire or being pursued by pirates the ship can still be grounded by reducing lift. I interpreted the question as the upper-most concern being to keep alive the people aboard the ship. Oct 4 '17 at 20:17
• @notstoreboughtdirt the Hindenburg (as most German airships) was constructed for using helium. The thing is that they didn't get any helium due to an embargo. Indeed helium is not the easiest to acquire, but still an airship would not be using hydrogen unless it were designed around preventing combustion / keeping fires localized. Oct 4 '17 at 20:37
• The airships USS Shenandoah and USS Macon both broke up in flight but crewmen managed to remain on board sections of the airship and descend to earth safely. In the case of the Shenandoah, the nose section flew as a free balloon for a period before the crew trapped there managed to land. Sadly, not everyone survived, but staying aboard the airship gives you a better chance at a controlled or semi controlled descent and survival. Oct 4 '17 at 21:14
• @cmaster A human can easily survive a 20-40g impact (as proved by Colonel Stapp). 200 kph ~ 60 meters per second. $\frac{60 m/s}{20 * 10 m/s^2} = 0.30 s$. And since $s=\frac{a \cdot t^2}{2}$ we need a crumple zone of about 5-10 meters. An airship can easily provide such padding around a "crash room". Oct 5 '17 at 7:29

Gliders.

It requires either a (better than current) ai or a competent pilot to land on an unprepared field, but having more horizontal freedom can be helpful in less than ideal locations like you mention.

They are also generally heavier than parachutes, so on an airship you'd balance how much you want everyone to live with how much extra cargo you could carry.

But the thing about airships is you might not save that many people by preparing to disembark in the air during an emergency. In the Hindenburg disaster people walked (ran) away when it got close to the ground. It burned rather than exploded so the lift was continually reduced making the crash much more survivable than if say the wings fell off a plane at similar height. Most people who died burned with nowhere to run, so even if they had viable escape craft somewhere it wouldn't have helped.

• Indeed, survivors walked away from most airships lost over land, including a few WWI flaming shoot-downs. Gliders seem likely to kill a lot fewer people than the alternatives. Oct 4 '17 at 19:46
• Why are you trying to suggest a glider can more easily land in a forest than a parachute....I know you are smarter than this.
– anon
Oct 4 '17 at 19:51
• @anon I mean to suggest you may be better able to pick a clearing or river or least bad place to crash with the a glider. Even the fanciest parachutes offer few options but down but a glider might be able to make miles.
– user25818
Oct 4 '17 at 20:07
• This is a good answer because of the OP's requirement to choose your landing spot. Oct 4 '17 at 21:38
• OP 180'ed his requirements, but yeah now this become the best answer
– anon
Oct 4 '17 at 22:08

A large parachute or set of parachutes with a survival capsule attached is probably a reasonable good bet in most circumstances. Some rudimentary parachute guidance cables could be provided to help an on board crew member avoid some obstacles such as a sideways approach to a vertical cliff edge. If couches and basic shock absorbers were provided under each couch a substantial fall would still be survivable in many cases.

Sea landings would be OK If the capsule was watertight.

The black forest scenario should be fine as the parachutes would tangle in the trees and the capsule would protect the occupants from hitting the branches.

The karst landscape would be challenging but would also probably be survivable in many cases (but not all) as the parachute would snag it the rocks / vegetation or they would land in a gully or the crewmember could avoid the worst rock faces. Even if the parachute tore it would probably provide considerable resistance in the process and the shock absorption system would help a lot with small drops especially into vegetation.

Landing in Polar Regions or arid deserts would also be survivable as they would have some protection from the elements. An explosive release of the parachute cables would be useful in some cases such as these to prevent being blown around after landing.

I assume that rescue craft would be sent promptly and a distress beacon/flares would be carried.

The maker's of the movie, Mission to Mars, came up with a creative solution, but even they didn't claim that it would work very well. To get down to the surface of Mars (which is somewhat comparable to your airborne lifeboat scenario) they built a rugged capsule and then surrounded it with tough airbags to cushion its fall. Unfortunately, in the movie, the airbags did not survive the initial impact and that impact happened to be on the top of a mountain. When the capsule, with its slightly flattened airbags, subsequently rolled of the edge of that mountain top, then second plummet overwhelmed the capsule's design which lead to the death of one of the crew.

• Good Catch, @Frostfyre! I've corrected the answer to survive any future broken links. Oct 4 '17 at 20:06
– Ash
Oct 5 '17 at 10:15
• @HenryTaylor I think you are giving Hollywood to much credit. They just copied Pathfinders landing strategy.
– Lex
Oct 17 '17 at 17:45

Have each ‘Lifeboat’ essentially be a shallow metal cone with straps and multiple parachutes around the edge. In an emergency multiple people strap in, the disk drops (with small parachutes to maintain alignment) away from the ship then the main chutes deploy. With any luck the lifeboat will be moving slowly enough by the time it hits your terrain that it will deflect the worst of the impacts, leaving your airmen mostly intact.

Some (but not much) control can be exerted by manipulating the chutes, but the main point of this design is to shield your airmen from dangerous terrain (a tree branch through the spine often offends) and then provide further options. If snarled in trees, it’s easier to climb around inside and could have stowed rope ladders for safe egress, if a water landing then floats can be deployed, and the lifeboat can have space for potentially lifesaving supplies.

• Any reasoning behind the downvote? Oct 4 '17 at 19:53
• I wasn't the downvoter, but one problem with the answer is the OP rejected parachutes and required the ability to choose your landing spot. Therefore, this does not answer the OP's question. Oct 4 '17 at 21:40
• Didn't downvote either, but I see absolutely nothing that makes this solution superior to simple parachutes in any aspect. On the contrary: It only adds vast amounts of complexity to a proven design, which means tons of extra failure sources. Oct 4 '17 at 21:45
• @JBH: that condition was added after my answer, but if you have multiple parachutes then directional control isn’t hard. Oct 4 '17 at 21:57
• @cmaster: mostly protection from sharp pointy bits stabbing into soft fleshy bits. That’s pretty much it. I personally think personal parachutes are the best option that can be hoped for, but that’s not a ‘lifeboat’ Oct 4 '17 at 21:59

I will second the suggestion of gliders proposed by @not store bought dirt, with some additional details and reasoning.

Gliders that only need to work for a short time in an emergency can be lighter and more basic than a modern sport or leisure glider, won't need hardware for towing, and won't necessarily even require landing gear (more on that later). Many leisure gliders are single or two-seater configurations, but there is no reason you couldn't make one that could seat a dozen or more at a time, since it only has to carry the passengers away from the doomed airship for a (reasonably) short distance.

Storage space is a problem on an airship, and gliders obviously need large wings to work effectively, so you would probably need some way of folding or otherwise stowing the wings in a collapsed state and deploying them after launch, but if your civilization is advanced enough (technically or magically) to make airships, this shouldn't be too much trouble.

The flight time/range is going to depend on the number of passengers and amount of cargo the glider needs to carry, the properties of the atmosphere, how high up the craft is when launched, how large you make the wings, and whether the pilot (an AI, passenger, or sophisticated enchantment) can harness thermals and wind to recover energy.

Lastly, landing is the bugaboo. As mentioned by @not store bought dirt, landing a glider conventionally on an unprepared surface is dangerous and will likely destroy the craft. But it's important to remember that we're talking about one-use emergency vehicles here -who cares if the glider gets smashed up as long as the passengers survive? Equipping the glider with a small parachute in the rear which can be deployed just prior to landing to kill speed and soften impact wouldn't add much weight or complexity but would drastically improve survivability. Such things already exist in some modern private planes. A long, stiff but hollow nose would provide a crumple zone to absorb the remaining force of impact. It probably wouldn't be pleasant, but it would be survivable.

One last note. Your airship is going down. If you're still aboard when it crashes, you will most likely be killed -either by the impact, being crushed by the airship structure as it collapses, burning, etc. No emergency escape system will work perfectly in all scenarios, but something is better than nothing!

• Very large gliders were built in WWII to deliver airborne forces to the target, ranging from the 10 passenger DFS 230 to very large allied gliders capable of transporting vehicles and even light tanks. The Axis power also tried very large gliders, but had few aircraft capable of towing such monsters. Oct 5 '17 at 10:02

Use one of These two layer inflatable Hamster Balls plus a parachute.

Your airship lifeboats need to address 2 problems. Deceleration and rough terrain. A Parachute will take care of the deceleration part to some extent, but your people trying to get safely away may not know how to land and can be severely injured even on good terrain. That is where an inflatable hamster ball comes in.

It doesn't exactly have to be like the one I linked to, but the concept is the same. The ball can be inflated by a relatively small tank of compressed air. The person jumps into the already inflated ball and is pushed out of the airship. The parachute deploys. The parachute slows the whole thing down to a point where the impact of the ball on the ground is not too harsh and is spread out over a substantial surface area. The parachute also maintains the alignment of the object in the air.

On bad terrain, the tough materials of the outer ball will protect the people inside even on a very bad landing, falling through branches, hitting sharp rocks and so on. Even if the outer ball bursts a large amount of the impact should be absorbed to the extent that the person inside will only suffer from minor injuries.

In addition, these kinds of balls will serve as flotation devices. They can be made out of high visibility materials to aid search and rescue efforts. You could reinforce the outer sphere with lightweight ribbing material. It would increase the overall strength of the structure without sacrificing too much in the way of space on the airship. You could further use the material and ribbing for a shelter on the ground.

It isn't absolutely perfect, and would only hold a few people per unit, but it's better than nothing.

Since magic is in this system:

How about a magical potion/orb/stone that when smashed into the ground instantly form a jelly like substance around the user (dispersing the deceleration across the whole body) creating a cushion that then dissipates in 10-30(breath deep) secs.

Kind of like a magical ODST concept, which it could also be used for.

But practically

no real world parallel is going to be fool proof in a forest. Parachuting is currently the best real world method here but as you mentioned, it's not without risk.

Edit out the magic

Ok so a capsule with a long nose, when the nose impacts the ground, a compound lining the nose and walls of the capsule is provided an electric shock causing it to rapidly react with the air enveloping the passenger in a foam that cushions their descent. 1 sec after reaction, a catalyst is released above the passenger as part of the top compartment that then dissolves the foam.

This method has been theorized many times before. The reason it hasn't YET come to fruition is the chemistry and engineering is incredibly complicated when the cheap and easy solution of a parachute works just fine.

instead of a nose, a large pad (increase surface area to increase drag to slow descent). on the down ward face of the pad have a distance measuring sensor(probably an array of lasers) and a turret that will shoot a canister of the compound at the ground when a target distance has been reach, of course the capsule still dissolves into more foam.

perhaps some fins or a parachute to stabilize the capsule (keeping going straight downward and not flipping).

• Downvoted because answer boils down to: Use magic Oct 4 '17 at 19:58
• @dot_Sp0T This scenario allows magic, at least I didn't cop and say a levitation spell or something too cheap.
– anon
Oct 4 '17 at 20:07
• The question states: ... if the mode of lift, be it magic or otherwise, being used by an airship is too big, too complex, or too expensive..., with the emphasis lying not on the magic (it being clearly only mentioned as a possible way of achieving unnatural amounts of lift), but on the mode of lift not being possible to be installed in anything smaller than the actual airship - so as to make clear that the lifting technology does not work on smaller vessels and thus cannot be used to create smaller airships as lifeboats (similar to life-rafts being but smaller ships). Oct 4 '17 at 20:14
• @dot_Sp0T right so where do you see my magic jelly providing "lift". it isn't, it is providing a cushion.
– anon
Oct 4 '17 at 20:17
• I never claimed your magic jelly does provide lift. I claimed it boils down to introducing a magic McGuffin to solve the given problem instead of working around given constraints. Oct 4 '17 at 20:20

The decent can be controlled horizontally by using either a ram-air parachute or some type of inflatable air-foil wing. This would allow the escapees to choose the safest landing place. It takes some skill to operate so it would be best if they had some type of computer control to make them easier for untrained passengers to point-and-shoot their target.

Even with horizontal control, it is likely that there won't be an ideal landing place within range. The escape pod would need some sort of landing protection such as an airbag system or even just a solid floor.

Larger pods are probably better that smaller ones because they are more weight-efficient and they give you a lift raft or shelter after you land. You can save weight by reusing some of the structural elements. What is a passenger seating area in normal operation can break off to be an escape pod in an emergency (eg this concept).

Simplest most basic glider would be a Rogallo Wing. In the early 1960's that was going to be the system used for capsules, esp. the Gemini. In it's most basic form it is simply three poles joined at one end, a crossbar & fabric. NASA used inflatable rods, which meant the entire thing could collapse into a smallish parachute like package for storage in an external compartment of a space capsule.

• Is this thing easy enough for the uninitiated to land first time out in a panic situation? Or do you attach it to an escape capsule of some sort?
– Ash
Oct 9 '17 at 10:54

First, is your airship going straight down, at free falling speeds?

If it is free falling we have to solve that problem first.

1. Deploy a parachute for the plane (as someone else suggested)
2. Fill one or more helium/hydrogen balloons
3. Both

You also need to deploy parachute(s) behind you to slow your vertical speed.

Hopefully this has slowed your decent to a gentle rate.

At this point you either need control of the rudder so you can point the plane at a reasonable safe, or safer than the other options available to you.

Now I don't know how much steel cable weights, but you could probably have several 1000ft or greater spools on the airship.

Maybe something like this or a bit thicker.

http://www.fehr.com/all-steel-cable/5-16-x-5000-ft-7x19-galvanized-aircraft-cable-2g9312-05000

The cable above is 5000ft and claims its weight is only 173lbs/mft and the minimum breaking weight is 9,800lbs.

Each passenger would put on a vest similar to a life preserver, but would have a mechanical breaking device that would attach to the cable so they could control their decent rate. So attach your self to the cable and start sliding down.

The weight of 5 or more people should keep the line from bucking too much.

Another thing you can do is use the end of the steel cable to lasso an object and basically zip line down to it, much more practical with a blimp than plane.

Tying a weight onto the cable to use as an anchor, to help stop your plane the best possible location.

Your example uses a blimp as an example, for that case you could slide down the cable to the ground, and give you time to run away before the main body hits the ground. That way you would not be hit by the blimp or caught in an explosion after the blimp hits the ground.

If its an actual airplane, you may have too much forward momentum to land safety on the ground.

This would also be useful if the plane lands on a forest of tall trees. Some areas the trees are 100ft+ high, and these cables would get you safely to the ground.

If you landed on a tall cliff, they would also be great for the final decent to the actual ground.

• I do not want to be on the ground under the footprint of those cables if they're attached to something fast moving, the ground will look like it's been harrowed but for the passengers will probably be in good hands.
– Ash
Oct 8 '17 at 12:09

just saw 1930 movie "Madam Satan" last night on TCM that had parachutes in long outboard tubes along the side of the air ship. Passengers were given a harness and hooked these on to the chute rope as they jumped. Dont know if this was just a Hollywwod prop or a real thing. Good idea tho. Movie was OK.

• Actually it does, it's just awkwardly put together.
– Ash
Oct 17 '17 at 17:28

Parachutes are the best option. A commercial ship is required to have at least one parachute for each passenger by law, much like aircraft today are required to have at least one life-vest for each passenger.

How are they used? They can be either required to be worn throughout the flight or be spread out over the ship so they are easily accessible. Parachutes are compact, weight very little in relation to their performance. How to deploy one when exiting the airship if the person is inexperienced? Simple, altimeter or proximity sensor. This is all based on that the ship is at sufficient altitude for the parachutes to deploy.

The altimeter would be used in the sense that a person falls and when they reach a certain altitude, the parachute auto deploys. A proximity sensor would work similarly. There should be a sensor system on the ship and if the parachute is too far from any of the sensors (Translates sufficiently far outside the ship) the parachute deploys automatically.

Parachutes and be steered to land as normal. If over water, a simple inflatable life-vest can be attached to the parachute bag. This is too simple and easy to cook up. Especially since this is WorldBuilding. Add features and mechanics to your taste.

In OP's case of terrain, the Karst will be rough to land on but much softer with a parachute than with a glider that needs relatively a lot of speed to remain airborne. A parachute when flared and more or less land vertically and thus be able to set down softer. In dense forest, I'd rather get tangled in a tree and bruise myself badly than pilot a glider and crash straight into the canopy.

• Could the parachutes be attached to a life vest in some way. For over water emergencies, this could prevent drowning. Also, might want to look into the ability to separate and eject an inflatable raft or some kind of circular item that will inflate once out of the craft. This will get people out of the water, which could be freezing cold, and could come with an emergency supply attachment. Oct 17 '17 at 18:56
• I thought about an inflatable life vest but left it out because I don't quite feel it belonging in a steampunk story. However, a built-in life vest is a good idea. Oct 18 '17 at 6:39

According to one on-line terminal velocity calculator, an 80 kg mass with a cross-sectional area of 81 m² (9 meters x 9 meters) and with a drag coefficient of 1 (which is what a person has, a smooth ball has 0.1 or would need ten times (10x) more area, although the relationship between area and terminal velocity isn't linear with the Coefficient of Drag) would have a terminal velocity of 8 mph.

Since I've survived several bike crashes with nothing more that some (fairly serious) abrasions at similar velocities, that's about the fastest I'd want to hit a random point on the ground.

Here's the problem with that: (9 x 9) is a huge area. We're basically talking about a parachute (opening after escape). I can see some inflatable suit which could protect from penetration injuries, but I can't imagine anyone willingly wearing such a awful thing for extended periods, nor can I imagine that in an emergency, anyone would have time to put something like that on.

You should consider the (blatantly obvious, to anyone over 40) idea that if something better than a parachute was feasible, we'd be using it. Seems to me kevlar body panels, and a helmet would be about optimum. The elephant in the room is that if they have time to evacuate, you have to explain (credibly) why they don't have time to crash land.

• As has happened before your answer is in the low-quality review queue. You might want to think about structuring your answers a bit and making clear they are on-target. This upcoming checklist might be good for you. Oct 5 '17 at 9:35


text:
## Elementary Technical Mathematics

a)$23\frac{3}{4}$ square feet b)$20\frac{1}{6}$feet
a) To find the area, make use of the formula given in the question: Area = Length $\times$ Width In order to facilitate the easy multiplication of mixed fractions, first convert them to improper fractions. Convert them back to proper fractions after multiplication when presenting the answer. $= 6\frac{1}{3}\times3\frac{3}{4}$ $=\frac{19}{3}\times\frac{15}{4}$ $=\frac{95}{4}$ $=23\frac{3}{4}$ Square Feet b) Perimeter is found by adding all the lengths of all the sides. In this question, for easier adding of fractions we first convert them to improper fractions of the same denominater before adding. Perimeter = $6\frac{1}{3}\times2+3\frac{3}{4}\times2$ $=\frac{19}{3}\times2+\frac{15}{4}\times2$ $=\frac{38}{3}+\frac{30}{4}$ $=\frac{76}{6}+\frac{45}{6}$ $=\frac{121}{6}$ $=20\frac{1}{6}$feet


text:
## The determinant of the scattering matrix and its relation to the number of eigenvalues.(English)Zbl 0382.47005

### MSC:

 47A40 Scattering theory of linear operators 47B10 Linear operators belonging to operator ideals (nuclear, $$p$$-summing, in the Schatten-von Neumann classes, etc.)
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### References:

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