@vv 

Thank you! It make sense. I'll play with it.

@mmcdara 

>At the evidence your line is not a regression line, excepted if the points above have very high weights.

It is certainly not a regression. I don't need a best-fitting line *through* the data cloud. I need it through (approximately) its upper-right boundary (the hypothenuse). Thus, in my fitting-by-eye, there is only one point above the line, the yellow circle.  The data points labelled by triangles should be neglected.

> Second question: your points have different colors, "what do they mean?"
 

It is irrelevant. The data cloud is formed by all circles of any colour.

@Kitonum 

I believe that you are right. But the reviewer has a different opinion :(((. Hence what need is to justify the fitting somehow.

@acer 

Here it is. The first colimn is x, the right one is y. (The fitting I need is on the log-log plot).

data.txt

@Wavish 

I forgot to say that the dashed line was made "by eye".

@Carl Love 

To be specific, I need to justify more or less rigorously this orange dashed line in the image. Some data points could be above it. The data points labelled by triangles should be neglected.

Robert, aha, I see. Having the matrix A, how can I make a 1D array of its row or column, and then how can I make a plot of this 1D array? Thanks!

Robert, aha, I see. Having the matrix A, how can I make a 1D array of its row or column, and then how can I make a plot of this 1D array? Thanks!

Aha, great. I did it. Now, U is a function, and I can look at it's values at a certain (x,t) point:

> U(-1.3,0.2);

   0.18889255096658836

But, when I am trying to make a plot of this function for a fixed value of, e.g., t, I am getting:

> plot(U(x,t=0.2),x=-5..5);

"Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct"

What am I doing wrong? I have also tried >plot(U(x,t),x=-5..5,t=0.2); with no effect.

Also, when I am looking at the value of an element of A, I am getting

> A[1,3];

   0.960789439152323

which seems to be correct. But, can I make a 1D array with a certain line or column of the matrix A? If so, how should I plot it?

Thanks!

Aha, great. I did it. Now, U is a function, and I can look at it's values at a certain (x,t) point:

> U(-1.3,0.2);

   0.18889255096658836

But, when I am trying to make a plot of this function for a fixed value of, e.g., t, I am getting:

> plot(U(x,t=0.2),x=-5..5);

"Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct"

What am I doing wrong? I have also tried >plot(U(x,t),x=-5..5,t=0.2); with no effect.

Also, when I am looking at the value of an element of A, I am getting

> A[1,3];

   0.960789439152323

which seems to be correct. But, can I make a 1D array with a certain line or column of the matrix A? If so, how should I plot it?

Thanks!

Thank you for the answers, but, I am afraid, I am still struggling to understand Maple's philosophy. (My main analytical tool is IDL). I followed your suggestion, and got the array A. I check its dimensions by ArrayNumDims(A)and ArrayNumElems(A), it turned to be 2 and 441, respectively. I understand that 441=21*21, hence I have 21 points in both x and t directions.

But, when I print elements of the array, I am getting confused: print(A(1,1)) gives me 1. If these indices, (1,1), correspond to x=-10, t=0, the answer is not correct. Hence, I clearly don't understand what is in the array A. Also, when I am trying to plot it, plot3d(A,x=-10..10,t=0..4.5) I am getting "Error, (in plot3d) first argument must be either in standard or parametric form
". Hence, I am doing something wrong again...  Also, having the array A, how can I make a plot of, e.g. A(*,0) - all possible values of x and t=0.

Sorry for silly questions! Thanks!

Thank you for the answers, but, I am afraid, I am still struggling to understand Maple's philosophy. (My main analytical tool is IDL). I followed your suggestion, and got the array A. I check its dimensions by ArrayNumDims(A)and ArrayNumElems(A), it turned to be 2 and 441, respectively. I understand that 441=21*21, hence I have 21 points in both x and t directions.

But, when I print elements of the array, I am getting confused: print(A(1,1)) gives me 1. If these indices, (1,1), correspond to x=-10, t=0, the answer is not correct. Hence, I clearly don't understand what is in the array A. Also, when I am trying to plot it, plot3d(A,x=-10..10,t=0..4.5) I am getting "Error, (in plot3d) first argument must be either in standard or parametric form
". Hence, I am doing something wrong again...  Also, having the array A, how can I make a plot of, e.g. A(*,0) - all possible values of x and t=0.

Sorry for silly questions! Thanks!