Alger

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11 years, 70 days

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These are replies submitted by Alger

@acer 

Yes, it is less time and memory consuming to use Eignevectors(V) and apply sqrt to the result than using MatrixPower. Thank you.

I corrected also the repetition in matrix inversion.

But, I should give high Digits for large value for N in this case also to get accurate results.

I will also investigate the position of the command Digits in the code.

When you have time, please give me other ideas to improve the computation.

Best regards

Kamel

 

@Kitonum 

Maple 18 gives the same error. 

Maple 15 gives the solution with no problem.

@Alejandro Jakubi 

Yes, I think the two environnements are differents (Maple and Matlab).

I use generally Maple for symbolic calculations (I appreciat it) and Matlab for numerical calculations. From the answers, I think it is simple to continue to do that.

I wanted to do all my calculations by Maple.

Thank you

@acer Thank you acer

Yes, it is what I want. It work well.

Thank you again

 

@Kitonum Thank you

But, I am interesting in the polar plot as given in:

R:=5:

freq:=4:

plots:-display(plot(R,theta=0..2*Pi,color=blue,coords=polar),plot(R+cos(freq*theta),theta=0..2*Pi,color=red,coords=polar),gridlines=false,scaling=constrained);

Now, I do not know if it is possible to correct the axis as explained in my above post.

 

@acer 

When we plot(cos(theta),theta=0..2*Pi), theta vary from 0 to 2*Pi in the X axis and cos(theta) vary from -1 to 1 in the Y axis.

When we plot the function cos(theta) with polar coordinates as:

R:=5:

freq:=5:
plots:-display(plot(R,theta=0..2*Pi,color=blue,coords=polar),plot(R+cos(freq*theta),theta=0..2*Pi,color=red,coords=polar),gridlines=false,scaling=constrained);

The X axis and Y axis varies from -6 to 6. These axis represent the function R+cos(theta).

Is it possible to remove theses axis which correspond to R+cos(theta) and replace them with new axis X and Y where origines are at the radius R.

From the polar plot, I want to get in the figure, 0 replaced by -3, 2 by -2 and 4 by -1, to get the variation of cos(theta) between -1 and 1.

I hope it is clear now.

 

@acer 

Is it possible to get on the axis of ordinate only the magnetude of the function cos(theta) and not R+cos(theta) ?

Thank you

@Carl Love 

Yes, this is what I want

Thank you

@acer 

Yes your first code do the work (sorry). I have not understand the effect of the frequency.

I am very happy, thank you 

@acer : Thanks for the answer:

I want to plot a function where the axis of abscisse theta is the radius R (for example cos(theta)). As in the figure below in red.

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Download plot.mw

 

 

@Kitonum Thank for the answer.

But, I want plot the function cos(theta) where the axis theta of the function is represented by the contour (perimeter) of radius R (not inside the circle). I do not know if my explanations are good.

@acer 

Thank you

The command

plots:-matrixplot( Y, heights=histogram, gap=0.5,
                   color=((x,y)->1-y/3+0.2),
                   orientation=[-55,55,0], labels=["","",""] );

 is what I want.

@Markiyan Hirnyk 

I have Maple 18 and I can not find the command.

dataplot does not exists in Maple 18

@Markiyan Hirnyk @Carl Love 8142: Thank you

Yes, OrthogonalExpansions package can be used to determine 2D Fourier series coefficients. Now, I can read the help from Maple18.

From DiscreteTransforms, are matrices (3) and (4) represent the coefficients of 2D Fourier expansion ?  The matrices are the Fourier transform and we need to do an inverse Fourier transform to get the coefficients ?

Can you help me to plot the 2D Fourier expansion function issued from Discrete Transforms with the original function f(x,y).

Thank you

I am using OrthogonalExpansion currently. It can not give the Fourier expansion from 2D Fourier transform.

I want to use 2D Fourier transform to obtain the coefficients of the 2D Fourier expansion of a surface as done in http://www.mapleprimes.com/questions/121551-Fourier-Serie-And-Discrete-Fourier-Transform for curves.

 

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