I am trying to create the following chart in Mathematica.
I would like to somehow generate this based on Ohm's law not just a raw data set.
I would like to be able to switch the resistance value to update the chart and increase the voltage in 5-V steps from 0 to 30 V
Any help would be greatly appreciated I'm totally stuck.
Try this. You will find that the line slope looks the same while the y axis scale changes as the value of r is varied. There are simple plot options you can use to change that effect.
i[v_, r_] := v/r;
Manipulate[
Plot[i[v, r], {v, 1, 5000}, PlotRange -> All], {r, 100, 50000}]
Related
Context: Two sets of data, one is the radius, r, and the other is the velocity, v. v can be positive and negative. The following code
p1=ListLogLogPlot[Table[{r[[i]],v[[i]]},{i,1,number_of_data}]];
p2=ListLogLogPlot[Table[{r[[i]],-v[[i]]},{i,1,number_of_data}],PlotStyle->{Red}];
Show[p1,p2]
is used to give a curve, with positive and negative v both plotted in log-log coordinates.
Question: How to draw a circular, contour-like plot, with Log[r] as the distance to the center of the circle, and the velocities (Log[v]) shown as different, but continuously varying colors, according to v's sign and magnitude?
You may use a DensityPlot function:
v[r_] := Sin[r]*r^2
DensityPlot[v[Norm[{x, y}]], {x, -5, 5}, {y, -5, 5}]
You can deal with the tabular data in two ways. You can either interpolate and use the interpolating function as above or you may use a ListDensityPlot function:
ListDensityPlot[Table[With[{r = RandomReal[{0, 4}], t = RandomReal[{0, 2 Pi}]},
{r Cos[t], r Sin[t], v[r]}], {10^4}]]
I hope this helps.
I guess this is a very basic question.
I have a graph which I created in MATLAB. This is a graph of Power (y-axis) versus Frequency (x-axis).
The range of my x-axis is from 0 to 1000. Now here is my problem. I want to draw a line from specific points on the x-axis to the graph. For example, for points 40, 400, 950.
By using set(gca, 'XTick', [40 400 950]); I am able to mark these particular points. But I want to make it more visible by drawing straight vertical lines from these points.
Any help will be greatly appreciated. Thank you.
Use plot with endpoints with the same x value and different y values. (and don't forget to use myaa to beautify the output).
x = 0:0.1:2*pi;
y = sin(x);
plot(x,y);
hold on;
plot([0.6 0.6], [-1 1], 'Color', [0.7 0.7 0.7], 'LineWidth', 2);
plot([3.6 3.6], [-1 1], 'Color', [0.7 0.7 0.7], 'LineWidth', 2);
If you do this often I would recommend you a great submission from the FileExchange:
hline and vline
Just do:
vline([40 400 950])
Read the function documentation, if you want the line to have different properties than default.
I typically do this using something like this (is powers is a row vector).
powers = randn(1,1000)+40;
plot([1;1]*[40 400 950], [[0 0 0]; [powers([40 400 950])]],'k-')
Here is a tricky problem (or at least so I think). I need to create a histogram, but instead of having the data and it's frequency, I have repeated data (i.e. not binned) and some weight for each data.
One example:
Angle | Weight
90 .... 3/10
93 .... 2/10
180 .... 2/10
180 .... 1/10
95 .... 2/10
I want to create a histogram with bin size 10. The y-values should be the sum of weighted frequencies for angles within a range. How can I do it? Preferably Mathematica or pseudocode...
In Mathematica 9, you can do it using the WeightedData function like this:
Histogram[WeightedData[{90, 93, 180, 180, 95}, {3/10, 2/10, 2/10, 1/10, 2/10}], {10}]
You should then get a graphic like this one:
Since the expected output is not forthcoming I shall adopt Verbeia's interpretation. You might use something like this:
dat = {{90, 3/10}, {93, 1/5}, {180, 1/5}, {180, 1/10}, {95, 1/5}};
bars =
Reap[
Sow[#2, Floor[#, 10]] & ### dat,
_,
{#, Tr##2} &
][[2]]
Graphics[
Rectangle[{#, 0}, {# + 10, #2}] & ### bars,
AspectRatio -> 1/GoldenRatio,
Axes -> True,
AxesOrigin -> {Min#bars[[All, 1]], 0}
]
I did something similar for a different kind of question recently (weighting by balance sheet size).
Assuming your data is in an N * 2 matrix list, I would do something like:
{numbers,weights} = {data[[All,1]], data[[All,2]]*10};
weightednumbers = Flatten# MapThread[
Table[#1, {#2}] &, {numbers, Ceiling[weights]}];
And then use Histogram to draw the histogram on this transformed data.
There might be other ways but this works.
An important point is to make sure the weights are integers, so the Table as the correct iterator. This might require defining weights as data[[All,2]]*Min[data[[All,2]].
I am trying to parametrize a 3D geometry for shape optimization. The structure looks like the following. Another real example is here.
Currently I am using BSplines to create the lower part and using symmetry to create the whole down part of the foil. Here is what I get.
Now I have many control points to take care in order to run a shape optimization. I also don't know how to join the upper part with the bottom hydrofoil part in a sensible way. I don't know how to design a good middle part of the foil (fat nose part of the foil) where the upper part is linked to. I also need to accompany a flap with in the geometry.
Please offer some suggestion for parametrization of such a surface so that we can manipulate the geometry from MMA. The less control points are there better the situation is for optimization. May be combination of some analytic function in 3D. But I doubt if that is possible.
BR
I think you have two choices: 1) create the second part of the geometry and then write a face-face intersection algorithm to merge them. 2) create the second part of the geometry and write two functions that return -1 if a query point is inside the geometry and +1 if it is out side (other values will do). Then use RegionPlot3D[ f1[x,y,z]<0 || f2[x,y,z]<0,....]. The idea is the to extract the GraphicsComplex and use that. The question is going to be how well you can approximate the corners with that. Here is an illustration of what I mean.
if1[x_, y_, z_] := If[x^2 + y^2 + z^2 <= 1, -1, 1]
if2[x_, y_, z_] := If[(x - 1)^2 + y^2 <= 1 && -1.5 <= z <= 1.5, -1, 1]
res = RegionPlot3D[
if1[x, y, z] < 0 || if2[x, y, z] < 0, {x, -2, 2}, {y, -2,
2}, {z, -2, 2}, PlotPoints -> 100, Boxed -> False, Axes -> False]
Then extract the coords and the polygons.
coords = res[[1, 1]];
poly = Cases[res[[1]], _Polygon, Infinity];
Graphics3D[GraphicsComplex[coords, poly], Boxed -> False]
Hope this helps.
I am doing this:
ClearAll[matrix];
matrix[p_,q_,nu_:0]:=Module[{sigma},
sigma=p/q;
N#SparseArray[
{{m_,m_}\[Rule]2Cos[2\[Pi]*m*p/q+nu],{i_,j_}/;
Abs[i-j]\[Equal]1\[Rule]1},{q,q}]]
ClearAll[attachsigma]
attachsigma[sigma_,lst_]:={sigma,#}&/#lst
and then execute
fracs = Table[p/q, {q, 2, 30}, {p, 2, q}] // Flatten // DeleteDuplicates;
pq = {Numerator##, Denominator##} & /# fracs;
(ens = Eigenvalues[#] & /#
Normal /# (matrix[#[[1]], #[[2]]] & /# pq);) // Timing
pts = Flatten[#, 1] &#MapThread[attachsigma, {fracs, ens}];
and finally I plot the points as follows (here is the real point of the question):
plot = ListPlot[pts,
PlotMarkers \[Rule] Graphics[{PointSize[Tiny], Point[{0, 0}]}]]
Calculating all the points takes around around 2.6s on my machine, but the plot takes around 25s. If, on the other hand, I plot it like this
ListPlot[pts]
then it is almost instantaneous, as it should (it's just 5256 points). So, it seems PlotMarkers slows things down immensely.
Could anybody
a) explain why (this much I vaguely understand, in analogy with what happens to Sort if you give it custom ordering function) and, more importantly,
b) explain how to avoid this slowdown? I am trying to create plots with quite a bit more points than this so they're really slow; in addition, I am creating lots of them (a movie actually).
One solution would be to not plot all of them, but as I vary parameters it becomes nontrivial to find out which I should include and which not (this would of course work if I only needed this one frame). So, I'd like to speed up the plot creation without removing points.
EDIT: Answered after hints from Sjoerd:
ListPlot[pts] /. Point[List[x___]] \[RuleDelayed] {PointSize[Tiny], Point[List[x]]}
produces the right thing instantaneously. This simply replaces the Points inside the Graphics structure by smaller points by hand.
Now one can increase the upper limit in the table in fracs = Table[p/q, {q, 2, 30}, {p, 2, q}] // Flatten // DeleteDuplicates to 80 or so to get many more points (this thing is the Hofstadter butterfly, and it's a fractal):
PlotMarkers is meant for data plots that contain relatively few points. It is very useful in plots in which you use the markers to identify various conditions. Each individual marker is an Inset as follows:
Inset[Graphics[List[Hue[0.67`,0.6,0.6`],PointSize[Tiny],Point[List[0, 0]]]],10512].
You can imagine this takes up some time and memory.
I also found what seems to be a bug. The plot with PlotMarkers is structured as GraphicsComplex[pointlist,graphicsinstructions]. This point list seems to contain the points in the plot twice!
In[69]:= pts // Length
Out[69]= 5256
In[66]:= plot[[1, 1]] // Length
Out[66]= 10512
In[64]:= Union[plot[[1, 1]]] == Union[pts]
Out[64]= True
In[68]:= Tally[plot[[1, 1]]][[All, 2]] // Mean (*the average number each point occurs*)
Out[68]= 2
Personally, I prefer Graphics to ListPlot, especially when the number of points is large.
Graphics[{Hue[{2/3, 1, 1, .5}], AbsolutePointSize[1.5], Point#pts},
PlotRange -> {{0, 1}, {-4, 4}}, Axes -> False,
AspectRatio -> 1/GoldenRatio]
gives, for example:
Length#pts
102969
I believe the solution you appended to your question can be simplified:
ListPlot[pts] /. x_Point :> {PointSize[Tiny], x}
I voted for both prior answers, but I agree with TomD on the direct use of Graphics.