histogram | Fast multi-dimensional generalized histogram | SDK library

You could loop through the bars and test whether it is completely to the right of the separation, completely to the left or crosses it. You change the bar's color correspondingly.

When a bar crosses the separator, the bar gets the color for the left area and its size is narrowed to touch the separator. A copy of the bar can be added, with the right-area color and its x-position moved.

edit: Found another solution emulating what insertUI does but with renderUI:

This is what I achieved:

I'm not entirely sure if you wanted x to range from [-pi,pi] or [0,2pi]. If you want the range [0,2pi] instead, just comment out the lines ax.set_xlim and ax.set_xticks.

You can concatenate the input from two text in onclick -

In a histogram, a "rectangle"'s height represents how many values are in the given range which is in turn described by the width of the rectangle. You can get the width of each rectangle by (max - min) / number_of_rectangles.

For example, in the matplotlib's output, there are 10 rectangles (bins). Since your data has a minimum around 3 and maximum around 50, each width is around 4.7 units wide. Now, to get the 3rd rectangles range, for example, we start from minimum and add this width until we get there, i.e., 3 + 4.7*2 = 12.4. It then ends at 12.4 + 4.7 = 17.1. So, the counts corresponding to 3rd bin is the number of values in tips_df.total_bill that fall in this range. Let's find it manually:

IIUC:

try:

As far as I can tell, boundary specifies a spot to be a split between two bins. The rest of bins are set according to the number of bins or supplied break points. If the supplied boundary is outside the range of the data, some clever shifting is done according to the documentation. Maybe with the following examples it becomes clear what boundary does.

if you set limits for the x axis, you can circumvent the issue, although not a very elegant solution.

Restating the problem - My understanding given the different comments and your updates is the following:

• someone other than you is in possession of data, which as it happens is 2D data, i.e. an Nx2 matrix;
• using the covariance matrix, they are effectively saying something about the joint distribution of these two dimensions, specifically about the variance;
• if they assume a Gaussian distribution, as is implied by your comment regarding 68%, 95% and 99.7% for 1sigma, 2sigma and 3sigma, they can draw ellipses which represent the 2D-normal distribution: these are in fact some of the contour lines associated with the 3D "bell" surface;
• you have obtained the contour lines in a graph and are trying to obtain the covariance matrix (not the original data...);
• you are concerned about the complexity of having to extract the information from each ellipsis.

Partial answer:

• It is impossible to recover the original data, I hope you are already aware of that, but in case you are not let's just note that the covariance matrix is a summary statistic of the data, much like the average, and although it says something about the data many different datasets could happen to have the same summary statistic (the same way many different sets of numbers can give you an average of 10).
• It is possible to somewhat recover the covariance matrix, i.e. the 3 numbers a, b and c in the matrix [a,b;b,c], though the error in doing so will likely be large because of how imprecise the pixel representation is. Essentially, you will be looking for the dimensions of the two axes, for the variances, as well as the angle of one of the axes, for the covariance.
• Unless I am mistaken, under the Gaussian assumption above, you only need to measure this for one of the three ellipses, and then factor by whatever number of sigmas that contour represents. Here you might want to either use the best-defined ellipse, or attempt to use the largest one, which will provide the maximum precision for your measurements (cf. pixelization).
• Also, the problem of finding the axes and angle for the ellipse need not be as complex as what it seems like in your first trials: instead of trying to find the contour of the ellipses, find the bounding rectangle.
• In order to further simplify this process, if your images are color-coded the way you show, then a filter on blue pixels might be enough in terms of image processing. Then simply take the minimum and maximum (x,y) coordinates in order to obtain the bounding rectangle.
• Once the bounding rectangle is obtained, find the equation to your ellipse (that's a question for a math group, but you could start here for example).

Happy filtering!

Wrap it in a div as

titlePanel(div("Old Faithful Geyser Data", style = "color: #FF0000"))