A statement of truth or a wasted opportunity. Lambda helper functions reluctant to return 2D arrays.

JoeMcDaid 

I was getting there slowly by trial and error, but it is good to have the behaviour confirmed.  It has a logical basis for understanding though I can think of few cases where I would be likely to use the row-major order.  Maybe an escalation calculation where the days are organised by weekday; continuity as one moves down a week could make sense.

lori_m 

Maybe scanning an array with multiple initial values would require separate functions of VSCAN and HSCAN?  In business-based calculation, I suspect that most scanned accumulations would normally be conducted in parallel, but in engineering dynamics there are likely to be multiple position and velocity values required to capture the state of a system and there will be coupling between the system coordinates from step to step.  I wanted to check the simulation of a container port crane moving a load that is free to swing as a pendulum.  

I gave up on that (it requires 4 values), but have attached a worksheet following the motion of a single object.  That only required one position x(t) and the corresponding velocity v(t) to be tracked.  Because SCAN only works the way I need over a single column, I combined the two values as a complex number for the purpose of the calculation.  The job of the Lambda function is to split the string into two numbers, to calculate the two in a way that takes account of the current velocity forces acting on the system (restoring force, control force and damping) and then uses the COMPLEX function to recombine the two forces into one.

= SCAN("2i", F#,
    LAMBDA(coord,F₀,
       LET(
         x₀, IMREAL(coord),
         v₀, IMAGINARY(coord),
         x₁, x₀ + Δt*v₀,
         v₁, v₀ + Δt*F₀/Mass - Δt*Coef*v₀-κ*x₀,
         COMPLEX(x₁,v₁)
       )
    )
  )

The result is generated as a complex number which is absolutely unintelligible, so I split real and imaginary parts (position and velocity) for presentation.  I then hit the problem that IMREAL and IMAGINARY do not accept array arguments, so I have to use MAP.  Map will only transform one column at a time so there are two distinct applications of MAP, which I then combine into an array.

= MAP(p#, LAMBDA(z, IMREAL(z)))

= MAP(p#, LAMBDA(z, IMAGINARY(z)))

= IF({1,0},x#,v#)

There is a lot of tidying up I could do, but VSCAN (or equivalent solution) would be great sometime in the future. 

Meanwhile there is a lot to learn concerning how best to use what we have.  For example, is it good to leave the anonymous Lambda functions at the point at which they are used; is it better to use a LET wrapper to define a local function so that it is more meaningful at the point of application.  A step further and one hides all the working within Name Manager.

tboulden 

What I wanted to achieve was an array of two SCANs, one down each of two columns, with a row of two initial values, so that I could compare the effect of 10% depreciation against 20%.  I had picked up the message that arrays of arrays were not allowed, so expected an error message.  The surprise was that I got numbers at all, then that I couldn't immediately recognise the values returned.

I have used MAP to return each of a 2D array as independent calculations, but order hardly matters there.  What I hadn't realised was that SCAN and REDUCE would also accept 2D arrays in exactly the same way but, given they are accumulating, order is important.  It seems to work like the Persian story of one grain of rice being placed on the first square of a chess board and two on the next.  2⁶⁴ grains are unaffordable.  The modern-day equivalent might be 'on the second week there will be two Covid cases'.  Some of our politicians were noticeably unable to grasp the consequences.