[stdlib_math] Add arange function.

[zoziha]

Description

seq returns evenly spaced values within a given interval.

• Add seq function. (see numpy/arange)
  (the API name seq needs to be discussed, arange? I think seq is better, it is shorter.)
  (aready to arange🔰)

Tasks

• by <= 0 condition. (see [stdlib_math] Add arange function. #480 (comment))
• put it in stdlib_math or stdlib_linalg: stdlib_math is better.
• floor or ceiling function: I think floor is better. (see [stdlib_math] Add arange function. #480 (comment))
• by value is a very small amount. (Need to discuss) (see [stdlib_math] Add arange function. #480 (comment)) (let users judge😏)

More routines to do, not this PR

see #476.

[awvwgk]

This looks like a useful addition, but the name seq seems rather short. Why not use arange here? sequence would also be an option, but this is already an attribute for derived types used for memory alignment or creating non-extendible types.

[Jim-215-Fisher]

I will review this one.

[zoziha]

This doesn't sound right for the real values. How about arange(1.0,6.0,2.0) which should give us [1.0, 3.5, 6.0]. Here it gives us [1.0, 3.0, 5.0].

Thanks for your review! @Jim-215-Fisher arange is different with linspace, I think you may be talking about the function of stdlib_math(module):linspace(interface).
(see numpy: arange and linspace)

[Jim-215-Fisher]

This doesn't sound right for the real values. How about arange(1.0,6.0,2.0) which should give us [1.0, 3.5, 6.0]. Here it gives us [1.0, 3.0, 5.0].

Thanks for your review! @Jim-215-Fisher arange is different with linspace, I think you may be talking about the function of stdlib_math(module):linspace(interface).
(see numpy: arange and linspace)

After reading numpy's documents, I understand that arange has a fixed spacing while linspace has fixed number of samples. The fixed number of samples give evenly spaced results. The fixed spacing in arange may give "evenly" spaced results without end point. My suggestion would be to change the wording of description for the function from "evenly spaced values" to "fix spaced values".

Another question is whether this function is elemental. If it is, why not change "pure" to "elemental"? In numpy, 'arange' is suitable to array arguments.

[Jim-215-Fisher]

Another question is whether this function is elemental. If it is, why not change "pure" to "elemental"? In numpy, 'arange' is suitable to array arguments.

Thanks, fixed spaced values is indeed better.

This function is not elemental. It does not seem to meet the definition of elemental function.
I have not used numpy, but it seems that numpy.arange does not state that it supports array arguments.

Do you mean the return value is an array (not only a vector)? In addition, it is difficult for the existing fortran syntax to implement a multi-dimensional array generic interface. (see j3-fortran/fortran_proposals#153)

You are right. numpy.arange does not support array argument. Never mind.

[milancurcic]

Thank you for this PR! I think the API is mostly good, I gave some naming suggestions to use instead of by, and I think there is an issue with using present() inside merge(), so I suggested using optval() instead.

[awvwgk]

Thanks for sharing, looks good to me.

[milancurcic]

With 3 approvals, I'll go ahead and merge. Thank you @zoziha and reviewers!