@aryan_ams Earlier you wrote that,

 [A]+[B] N+[C] N^(2)+[D] N^(3)+...+[H] N^(8) = 0

and now you write that the equation is, instead,

 ( [A]+[B] N+[C] N^(2)+[D] N^(3)+...+[J] N^(8) ) . X = 0

  K . X = 0

  K = ( [A]+[B] N+[C] N^(2)+[D] N^(3)+...+[J] N^(8) )

And you think that X will be eigenvectors of K? Are you completely sure that you now have the right equation? Why isn't the equation K.X = Lambda.X for an eigenvalue of K and X an eigenvector of K? Have you been trying to say that you want to solve,

 | K | = 0    where |..| means determinant?

so that you could perhaps solve,

  Linearalgebra:-Determinant(K) = 0

  Linearalgebra:-Determinant(A+B*N+C*N^2+DD*N^3+...+J*N^(8)) = 0

If that is so, then can't you construct a procedure and fsolve it for N,

  z := N ->  Linearalgebra:-Determinant(A+B*N+C*N^2+DD*N^3+...+J*N^(8));

  fsolve(z, a..b); # for some sensible numbers a and b.

@aryan_ams Oh, thanks for the detail. So, what is the Matrix for which you want eigenvalues and eigenvectors?

Does N take only integer values, or float values? Can't you just create a procedure,

N -> LinearAlgebra:-Norm(A + B*N + ... + H*N^7 + J*N^8)

and pass that to fsolve?

I'd like to add that the size of plots inlined in the worksheet is not (as of Maple 13?) important. Some small plotted symbols will not show up, not matter how densely they appear in the plot, below a certain symbolsize and plot size. In other words, for inlined plots the size of the display afffects whether small symbols get seen or not. So if you want to export with the right-click context-menu of the plot, it matters what size it is! (I find this behaviour to be unhelpful, and it is not how "images" work in other software or even some other Maple contexts.)

acer

I think that you're right: mouse/pointer manipulation of a plot (whether in a Component or not) will not necessarily result in the GUI changing anything that the kernel knows by name.

In other words, even changing a plot's qualities in a Component %Plot0 doesn't affect what GetProperty('Plot0','value') will return. That command will simply return whatever was assigned to the Component by use of DocumentTools. Manipulating the plot with the cursor doesn't change the value. So, any such manipulations are lost, in programmatic terms. Hence, if you need programmatic access to any changes to the stored plot, then those changes better all have been made programmatically in the first place.

Have I understood you rightly?

Maple is in rather serious need of a mutable plot data structure, so that such two-way communincation can be done properly and efficiently. If the Standard GUI can access rtables by "handle", then it should be possible to access some new (module or Record based?) plot data structure in a similar fashion. Hey, a fellow can dream.

acer

I don't see an equation, because I don't see an equals sign (or any statement of things being equal).

What is N? It is a Matrix, or a scalar? Is it known, or unknown?

Do you mean that [A]+[B] N+[C] N^(2)+[D] N^(3)+...+[J] N^(8) is equal to something else, say Q? If so, then is Q known while N is unknown?

Which Matrix is it for which you want the eigenvalues and eigenvectors? N, or Q?

I suspect that you want to know the eigenvalues/vectors of Matrix N, and that you might well know Q. But the post is quite unclear, and your could clarify. 

acer

@gretchenp08@gmail.com Can you run the attached worksheet and get the same output?

I created this with Maple 14.01, as a Document with 2D Math input.

DEplot01.mw

@gretchenp08@gmail.com Can you run the attached worksheet and get the same output?

I created this with Maple 14.01, as a Document with 2D Math input.

DEplot01.mw

It would be interesting to know what grade Kitonum gets for completing a significant portion of the assignment.

acer

It would be interesting to know what grade Kitonum gets for completing a significant portion of the assignment.

acer

@elango8 I don't have DirectSearch installed, so don't have much to say about how uou might use it. But in my Answer above I showed that fsolve could reasonably quickly find solutions for a1..a6 and t, given a w (less than w_critical which drives a6 to zero, which I computed using `Q`).

@elango8 I don't have DirectSearch installed, so don't have much to say about how uou might use it. But in my Answer above I showed that fsolve could reasonably quickly find solutions for a1..a6 and t, given a w (less than w_critical which drives a6 to zero, which I computed using `Q`).

@Christopher2222 Well, this post was about rotating the whole view, and you seem to be asking about rotating objects. (If I've understood you, then this earlier post on more efficient rotation of GRID and MESH might pertain.)

This reminds me that there may be yet another efficient way (in recent versions of Maple) to get rotation of the whole plot (objects + axes). That is to use the ?plot3d,viewpoint option to control the path. It might look the same, for the observer to move in a particular path about the "plot" as it would be for the observer to stay fixed and have the orientation change dynamically.

So then we have a vector calculus computation, in general. Suppose that we want to animate a "rotation" (movement) of a plot, and using the `orientation` option we'd have a parameterization like,

orientation=[f(t),g(t),h(t)]

as a `plot3d` optional argument. Here the center is (0,0,0), I suppose. How shall we most naturally convert this to a `viewpoint` optional argument of another `plotd3` call?

This has almost as good performance as the third (best) version in the post above. But, what could a sequence of `upvectors` be instead, to get a view where the axes appear always tilted and pointing in the same direction (relative to the user!) like above?

restart:
st,ba:=time(),kernelopts(bytesalloc):
plot3d(1+x+1*x^2-1*y+1*y^2+1*x*y, x=-5..5, y=-5..5,
          axes=normal, labels=[x,y,z],
          viewpoint=[look = [0,0,0],
                     upvector=[0,0,1],
                     location=[seq([3000*cos(t),3000*sin(t),0],
                               t=0..evalf(2*Pi),.02)], fieldofview=0.4]);
time()-st,kernelopts(bytesalloc)-ba;

                         0.062, 2096768

@elango8 Sorry, but I don't understand exactly what you mean. Could you post whatever code that you're running, and show how it isn't doing what you need? Thanks.

@elango8 Sorry, but I don't understand exactly what you mean. Could you post whatever code that you're running, and show how it isn't doing what you need? Thanks.

At the risk of being a bore, I ought to mention that the performance improvements may depend on the actual example to be plotted.

That is to say, for a very expensive expression or procedure then the cost of computing the data for just the first frame would be much higher. And so the total time saved by not recomputing those numeric results for each and every subsequent frame would be much greater.

Also, the memory savings would depend on the resolution of each plotted frame, be that in terms of grid-size or number of points plotted, etc. The greater the resolution and data per frame, the greater the savings.

The timing and memory allocation for the given example might seem small and unimportant. But more costly 3D plotting examples do arise. Also, there is the matter of scaling. If we want Maple's plotting to scale up well (or, just better) to huge examples then we should always strive to improve performance when practical.

acer