Sign in to comment. Sign in to answer this question. Unable to complete the action because of changes made to the page. Reload the page to see its updated state. Choose a web site to get translated content where available and see local events and offers. Based on your location, we recommend that you select:. Select the China site in Chinese or English for best site performance. Other MathWorks country sites are not optimized for visits from your location. You are now following this question You will see updates in your activity feed. You may receive emails, depending on your notification preferences. Add various horizontal lines to a plot. FC93 on 7 Oct Vote 1. Commented: Stephen on 23 Jan Accepted Answer: Marc Jakobi.

How can I add various horizontal lines to a plot? I have a plot and now I want to add several horizontal lines. Could someone show me a way to do it? Thank you. Accepted Answer. Marc Jakobi on 7 Oct Vote Cancel Copy to Clipboard.

## Jupyter Notebook Tutorial in Python

If you want the line to have specific end points, you can use the line function. Starting in Rb, you can use the xline and yline functions to draw vertical and horizontal lines, respectively. The horizontal line extends in both the positive and negative directions with no end points.

Exactly, thank you. Now I included all the horizontal lines I needed.Later, we will almost trivially extend the mathematical details to functions of two- or three-dimensional physical spaces. The approximation 1 is typically used to discretize a problem in space.

Other methods, most notably finite differences, are common for time discretization, although the form 1 can be used in time as well. A natural starting point is to apply the same reasoning as we did for vectors in the section Approximation of general vectors. However, this requires a norm for measuring distances, and a norm is most conveniently defined through an inner product. Note the analogy with 2. We can rewrite 3through similar steps as used for the result 2. The resulting equations are very similar to those we had in the vector case, and we hence end up with a linear system of the form 2.

We may also call it a Galerkin method for approximating functions. Using the same reasoning as in 2. Whether we work with vectors in the plane, general vectors, or functions in function spaces, the least squares principle and the projection or Galerkin method are equivalent. We seek. The coefficient matrix has elements.

Figure Best approximation of a parabola by a straight line displays the parabola and its best approximation in the space of all linear functions. The linear system can be computed either symbolically or numerically a numerical integration rule is needed in the latter case. Observe that we exploit the symmetry of the coefficient matrix: only the upper triangular part is computed. Symbolic integration in sympy is often time consuming, and roughly halving the work has noticeable effect on the waiting time for the function to finish execution.

Let us use the code above to recompute the problem from the section Example: linear approximation where we want to approximate a parabola. The answer is quickly found by running.

Suppose we convert the matrix and right-hand side to floating-point arrays and then solve the system using finite-precision arithmetics, which is what one will almost always do in real life. This time we get astonishing results! We see from the numbers in the table that double precision performs much better than single precision. Nevertheless, when plotting all these solutions the curves cannot be visually distinguished!

This means that the approximations look perfect, despite the partially very wrong values of the coefficients. A matrix has to be non-singular to be invertible, which is a requirement when solving a linear system. Already when the matrix is close to singular, it is ill-conditionedwhich here implies that the numerical solution algorithms are sensitive to round-off errors and may produce very inaccurate results. This phenomenon is illustrated in Figure The 15 first basis functions.

The dark mode beta is finally here. Change your preferences any time. Stack Overflow for Teams is a private, secure spot for you and your coworkers to find and share information. You are confusing Python variables with SymPy symbols. In the second line, the variable f points to a SymPy expression containing the symbol b. In the third line, the variable b points to the integer This doesn't not change any previous lines that used the variable bsince they have already been run.

It's no different than if you ran. You would expect the value of c at the end to be 2not 3. Similarly, when b points to a Symbol, expressions you create with it use a Symbol, but if you change it to point to a number, it doesn't affect previous lines from when it was a Symbol. The recommended way to deal with this in SymPy is to avoid assigning the same variable to a symbol and then later to a non-symbol it's worth pointing out that your definition of f in the first line is completely useless, since you immediately redefine it in the second line.

Exact Areas and Definite Integral with Python

To replace a symbol in an expression, use subs:. Note that subs does not change the original f. It returns a new expression. This document may also help clear this confusion up. If you didn't want to use substitution as in the other answer, you could make f an actual function of course.

Already on GitHub? Sign in to your account. I don't think that matplotlib or numpy are responsible for these sort of problems, but I'd expect sympy to plot something meaningful because it can have educational usage for exploring functions that people are not familiar with. Plotting any arbitrary math expression into something meaningful can be a very difficult problem. But I'd expect that this problem can be divided, to use some information about symbolic derivatives or numeric roots If they can be cheaply computedand use statistical information from the numeric data if computing symbolic things are expensive.

But let's see if there are some reasonable methods studied to use. I was going through the code and I did get better plots.

Where does this singularities function come from? Is it the one from the sympy. IMO using the symbolic capabilities of Sympy may not be the best idea in this particular case: it's almost trivial to find expressions where solveset used internally by singularities IIRC either finds no solutions or, worse, takes an inordinate amount of time. Even singularities tan xx raises a NotImplementedError Both would be problematic if this functionality were to be used by default.

But singularities detection should be enabled by default. So my gut feeling is telling me that a numeric heuristic is probably better suited for the problem at hand. I had a quick look at the code and saw that plot is calling out to LineOver1DRangeSeries which uses an internal sample function to compute the line segments. Those independent segments seem to be collected in a list.

## Simulation using SimPy

Maybe it's possible to simply leave out the problematic vertical segments? So after messing around with the plot function for a while, I've realised that the plot backend which is matplotlib ends up interpolating the points unless it comes across a 'Nan' value. So that's a hack I've used in the previous code. I know its a contrived example but I guess you can see where the logic would break. Moreover, the graphs don't come out good if you do pick an arbitrarily large value as all other points start to seem extremely flat and insignificant, and then the whole purpose of the graph is lost.

I'd really appreciate it if someone could explain their working w. I went through the singularities package and it does not find singularities for non-rational functions.

Just for the sake of plotting, could we just use a 5th or 6th order Taylor Expansion to get an approximate rational function and then use the singularities package? That would make things a lot easier. I think that it still makes sense to use helpers for easy stuff like rational polynomials or sinusoid, and it would not be that much difficult to tell some formulas are easy Though it may not be able to catch up all the formulas that can be supposed to be easy, but it's fine.

Just for further clarification, would you want to creat a new method that helps in plotting polynomials, and a new method that helps in plotting trigonometric functions or edit the existing ones to include the same i. If not we could probably find out the magnitude of the finite differences and sample accordingly.

### SymPy TUTORIAL for the Second Course in Applied Differential Equations

Yes, this is exactly what I hope so.Coffee shops are generally a popular place to hangout. Starbucks, Colectivo, Anodyne, Stone Creek, etc. It is not just the rejuvenating coffee that attracts customers, but the ambience draws people who want to read, work on their laptops, write, do some deep thinking, carry on conversation, or just relax.

However, sometimes getting a cup of coffee can take a long wait. Coffee shops try to minimize the wait times so that customers leave satisfied. In this tutorial we will simulate a simple coffee shop. The purpose of this simulation is to see how the number of cashiers and baristas affect the wait times of customers. We will use Python with some relevant libraries to model this simulation. When a customer arrives they go to the cashier to place the order and make the payment.

The cashier accepts payments through cash or cards. It generally takes 15 to 30 seconds to service a payment by cash and 10 to 20 seconds to service a payment by card.

Once the payment is made the item is prepared by the barista. The numbers in brackets indicate how many seconds it takes to prepare the item. When the item is ready the customer picks up the order. There are two wait periods in the above process. The first is the queue at the cashier and the second is the queue at the barista. The wait times at both the queues depend on the number of cashiers and baristas at work.

More the number of cashiers and baristas, shorter will be the wait time. However, economic factors would stipulate that the shop could employ only a certain number of staff. This balance between number of staff and customer wait times is important for customer satisfaction as well as business viability.

Python is a popular general purpose programming language with many libraries to boot. In this simulation tutorial we will use random for generating random numbers that correspond to customer traffic, etc. Finally, we will use MatPlotLib to plot the results of the simulation.Documentation Help Center. New plots use the next colors and line styles based on the ColorOrder and LineStyleOrder properties of the axes. If axes do not exist, then the hold command creates them.

The next plot added to the axes uses the first color and line style based on the ColorOrder and LineStyleOrder properties of the axes. This option is the default behavior. This syntax will be removed in a future release. Use hold on instead. Specify ax before all other arguments in any of the previous syntaxes. Use single quotes around the 'on' and 'off' inputs, such as hold ax,'on'. Create a line plot.

Use hold on to add a second line plot without deleting the existing line plot. The new plot uses the next color and line style based on the ColorOrder and LineStyleOrder properties of the axes.

Then reset the hold state to off. When the hold state is off, new plots delete existing plots. New plots start from the beginning of the color order and line style order. Starting in Rb, you can display a tiling of plots using the tiledlayout and nexttile functions. Call the tiledlayout function to create a 2-by-1 tiled chart layout.

Call the nexttile function to create the axes objects ax1 and ax2. Plot a sine wave plot in each axes. Create a 1-by-2 tiled chart layout.The plotting module allows you to make 2-dimensional and 3-dimensional plots.

Presently the plots are rendered using matplotlib as a backend. The above functions are only for convenience and ease of use. It is possible to plot any plot by passing the corresponding Series class to Plot as argument.

For interactive work the function plot is better suited. This class permits the plotting of sympy expressions using numerous backends matplotlib, textplot, the old pyglet module for sympy, Google charts api, etc. The figure can contain an arbitrary number of plots of sympy expressions, lists of coordinates of points, etc. The customization of the figure is on two levels. Global options that concern the figure as a whole eg title, xlabel, scale, etc and per-data series options eg name and aesthetics eg. The difference between options and aesthetics is that an aesthetic can be a function of the coordinates or parameters in a parametric plot. The supported values for an aesthetic are: - None the backend uses default values - a constant - a function of one variable the first coordinate or parameter - a function of two variables the first and second coordinate or parameters - a function of three variables only in nonparametric 3D plots Their implementation depends on the backend so they may not work in some backends.

If the plot is parametric and the arity of the aesthetic function permits it the aesthetic is calculated over parameters and not over coordinates. If the arity does not permit calculation over parameters the calculation is done over coordinates.

Only cartesian coordinates are supported for the moment, but you can use the parametric plots to plot in polar, spherical and cylindrical coordinates. The per data series options and aesthetics are: There are none in the base series. See below for options for subclasses. Consider two Plot objects, p1 and p2. To add the second plot to the first, use the extend method, like so:.

Plots a function of a single variable and returns an instance of the Plot class also, see the description of the show keyword argument below. The plotting uses an adaptive algorithm which samples recursively to accurately plot the plot. The adaptive algorithm uses a random point near the midpoint of two points that has to be further sampled. Hence the same plots can appear slightly different.

Default range may change in the future if a more advanced default range detection algorithm is implemented. The default value is set to True. Set show to False and the function will not display the plot. The returned instance of the Plot class can then be used to save or display the plot by calling the save and show methods respectively.

Used when the adaptive is set to False. Specifies the color for the plot. See Plot to see how to set color for the plots. If there are multiple plots, then the same series series are applied to all the plots.

If you want to set these options separately, you can index the Plot object returned and set it. Title of the plot. It is set to the latex representation of the expression, if the plot has only one expression.