At minimum, tspan must be a two element vector [t0 tf] specifying the initial and final times. To obtain solutions at specific times between t0 and tf, use a longer vector of the form [t0,t1,t2, The elements in tspan must be all increasing or all decreasing. The solver imposes the initial conditions given by y0 at the initial time tspan 1then integrates from tspan 1 to tspan end:

The Problem People frequently ask how to show vastly different values in a single chart. Usually they ask because a few very large values for instance, Paris in June or Madrid in May in the chart below overwhelm the other, relatively much smaller, values.

Logarithmic Scale One suggestion is to use a logarithmic scale.

For scientific data presented to scientific audiences, this is often an excellent suggestion. For the general public, and for general data, this may not be so useful.

Especially in a bar chart, where the length of bars is important to comprehension, not some mathematical abstraction of length.

Panel Chart A better suggestion than either a log scale or a broken axis is to plot the data in a panel chart. This chart has two panels, one with an axis that shows all the data, the other with an axis that focuses on the small values. I generally advise strongly against using any kind of gradient in a chart, because the gradients are pretty much meaningless.

In this chart, the gradient at the tops of the truncated large values are not meaningless, but are intended to show the large values extending high up into the clouds.

If you want to play along at home, the data is located in BrokenYData. Here is the data for the chart. The first step is to plot all of the data in one chart. By default, all series are plotted on the primary axis. The second step is to move the three extra series to the secondary axis.

They block the primary axis data… … but if I format the secondary axis series with outlines and no fills, you can see the primary axis data.

Back to solid fill colors. I have rescaled the vertical axes.

Add the secondary horizontal axis. Excel by default puts it at the top of the chart, and the bars hang from the axis down to the values they represent.

Format the secondary vertical axis right of chartand change the Crosses At setting to Automatic. This makes the added axis cross at zero, at the bottom of the chart. Now we need to apply custom number formats to the vertical axes.

Each comma knocks a set of three zeros off the displayed value, making for example 1, appear as 1. The M will be shown after the number of millions. The semicolon indicates that this format is for positive values, and nothing after the semicolon indicates that negative values are not to be shown.

Since no special format is indicated for zero which would be after a second semicolonit is shown with the same format as a positive number. The first format in the string is normally for positive numbers, but square brackets indicate a non-default condition for the first string.

This means that any values less than 8 million will appear as the number of millions folloewd by capital M. The semicolon with nothing following means that any other numbers will not be displayed. The primary and secondary axis scales conveniently have the right spacing so that the primary horizontal gridlines work for the secondary axis as well.

To format just one point in a series, click once to select the series, then click again to select the particular point column to format. This gradient makes the bars extend upward, and fade as they reached into the clouds.

Finally I deleted the duplicate legend entries. To delete an unwanted legend entry, click once to select the legend, then click again to select the particular legend entry, then press the Delete key.

This is the finished panel chart. The top panel shows that the two outlying values are drastically larger than the others, while the bottom panel allows comparison between the smaller values. However, I am under no obligation to share something that I do not want to share.

I do not even have the old tutorial, so I cannot send it to you, nor will I recreate a new version of the tutorial.BER for BPSK in OFDM modultion with a Rayleigh distributed channel of duration lower than the cyclic prefix.

Matlab/Octave simulation scripts also provided. Last update: 10th May Fixed a mistake in handling reflection case. Finding the optimal/best rotation and translation between two sets of corresponding 3D point data, so that they are aligned/registered, is a common problem I come across.

An illustration of the problem is shown below for the simplest case of 3 corresponding points (the minimum required points to solve). Have you ever wondered why Matlab does not have standard GUI date-handling components?

Matlab has many built-in date-handling functions (calendar, date, datestr, datenum, datetick, datevec etc.).Unfortunately, this built-in support does not extend to Matlab GUI.

Using Matlab's posibility to search a file in the complete list of folders in the path leads to such strange effects. It is recommended to use absolute file names instead: It is recommended to use absolute .

For nonnegative integers n and m, the value of n m is the number of functions from a set of m elements to a set of n elements (see cardinal exponentiation).Such functions can be represented as m-tuples from an n-element set (or as m-letter words from an n-letter alphabet).Some examples for particular values of m and n are given in the following table.

Introduction. This is the home page of high-performance C++ interface for MPFR monstermanfilm.com library allows user to conduct floating-point calculations with virtually any (restricted by available memory only) precision with correct rounding.

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The libsndfile API