Assigning symbolic SparseArrays fails

[davidschlegel]

If I want to have a multi-dimensional sparse array. I could define

using Symbolics
using SparseArrayKit

@variables a
 A = SparseArray{Num}(undef, (1,2,3)) #3dimesional array with size 1, 2, and 3 each
A[1,1,1] = a

But this gives the well-known error
ERROR: TypeError: non-boolean used in boolean context
This is due to the fact that in line #34 of sparsearray.jl we have the zero-comparison if v != zero(v).
This however fails for symbolic expressions as == or != defines an equation.
In this context, one should use if v !== zero(v) to evaluate the expression. Then everything works and still works for regular numbers.

[maartenvd]

Sorry for the late reply, I totally forgot about this issue!

that line really should've used iszero, can you verify that everything (the minimal example you provide works, but presumably you do other operations as well) works on the latest master?

[davidschlegel]

The problem is that for symbolic numbers that are defined through Symbolics.jl the function iszero does not have a boolean output but rather defines an equation. Therefore, one should use the double-== to check if symbolic expressions are literally zero.

[davidschlegel]

#7

[Jutho]

The problem is that for symbolic numbers that are defined through Symbolics.jl the function iszero does not have a boolean output but rather defines an equation. Therefore, one should use the double-== to check if symbolic expressions are literally zero.

I am not familiar with Symbolics.jl, but I have to admit that this seems wrong. The documentation of Base.iszero literally states that "Return true if x == zero(x)". If Symbolics.jl choses to have different behaviour, then this is not a method extension of Base.iszero, and thus, it should be a different function.

[davidschlegel]

Sorry, I got confused myself for a second.
From the julia documentation for ===:

Determine whether x and y are identical, in the sense that no program could distinguish them. First the types of x and y are compared. If those are identical, mutable objects are compared by address in memory and
immutable objects (such as numbers) are compared by contents at the bit level. This function is sometimes called "egal". It always returns a Bool value.

Indeed, Symbolics.jl has the behavior that for a symbolic variable, x==0 defines an equation, while isequal(x, 0) gives a boolean.

I think, instead of fiddling with == and === and their negations, one could use isequal to prevent all issues with of non-numeric types.

[Jutho]

I had anticipated that, but one problem with using === or isequal is that, with floating point numbers,

isequal(+0., -0.)

returns false.

[davidschlegel]

Okay, in that case, I would stick to === and !== instead of == and !=.

[Jutho]

Well, but these have the same problem. Also -0. === +0. is false, or thus -0. would not be recognised as a zero entry. I don't know how troublesome that would be in practice.

[davidschlegel]

I agree, then, it is a matter of non-numerical types to adequately define iszero. Submitted an issue in SymbolicUtils.jl for this. This is already working for Num types but not for Sym types.