regular array and vector constructor functions

[bob-carpenter]

Summary:

Create functions to create regular arrays.

Here's one from MATLAB (also related to Python range):

/**
 * Return vector of evenly spaced elements with given minimum and maximum.  Behavior for size = 0 and size = 1 to be determined.  Requires min <= max.
 */
vector linspace_vector(real min, real max, int size);

There could also be linspace_array and linspace_row_vector versions. It might be possible to call the vector or array version just linspace.

Python provides range, which is a bit different.

/**
 * Return sequence of numbers min, min + by, min + 2*by, ...
 * up to but not including max.  Requires min <= max and by > 0.
 */
vector range_vector(real min, real max, real by);

In R, there's a function seq that allows either of these parameterizations, but we don't want to follow that redundant pattern.

This one's a suggestion from peterzh on http://discourse.mc-stan.org/t/create-vector-from-a-number-range/3760.

This will then get pushed through to Stan.

Current Version:

v2.17.0

[linwangidd]

function for creating regular arrays is still not available?

[bob-carpenter]

Correct. It's easy to write one yourself and Stan gets compiled to efficient code, so we haven't prioritized this. If someone builds it, we'll accept a PR for this.

[mcol]

In #1636 we have added spaced_vector and friends, but I now think that linspace_vector could be a better name, as it matches what matlab, numpy and Eigen use. This will allow us to add a logspace_vector if we ever wanted. @bob-carpenter do you have an opinion?

[bob-carpenter]

I like the idea of matching MATLAB, numpy, and Eigen and am happy to review the changes. I'm also OK just leaving it spaced_vector with "linear" as a default. Is it really linspace_vector and not linspaced_vector? I like the adjectival form better! I'm OK doing whatever, but if the current ones escaped to a language release, they're going to need to be deprecated.

[mcol]

These are not exposed yet, so we are free to pick what we want. I also think 'linspaced_vector would work well, so we could go with that.

[mcol]

The range function as described here (with size of the resulting vector deduced rather than predeclared) would limit the uses of this function to only some contexts (see #1666 (comment), and #1666 (comment)).