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I'm trying to do the following. I have a table, call it TransTable. To give an example 

TransTable = {{0., 6.9, 7., 7.1, 13.9, 14., 14.1, 21.}, {0., 0., 0.100005, 0.20001, 7., 7.1, 7.20001, 14.1}, {0., 0., 0., 0.100005, 6.9, 7., 7.1, 14.}, {0., 0., 0., 0., 6.79999, 6.9, 7., 13.9}, {0., 0., 0., 0., 0., 0.100005, 0.20001, 7.1}, {0., 0., 0., 0., 0., 0., 0.100005, 7.}, {0., 0., 0., 0., 0., 0., 0., 6.9}, {0., 0., 0., 0., 0., 0., 0., 0.}}

What I want to do is as follows. This table has dimensions 8 by 8, or in general x by y. I want to extract all nonzero values, call them z_xy, and define variables according to

Varyx = z_xy

So for example Var21 = -6.9 should follow from this.

Now, I've had a look around and I think some of the ingredients are contained in the answer to Get positions of all non zero matrix elements however I don't really see how to adapt this into naming the variables. Clearly NonzeroPositions can be used to find the positions, but the naming step would then not be obvious to me.

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Function[{n, m}, Evaluate[ ToExpression["Var" <> IntegerString[m] <> IntegerString[n]]] = TransTable[[n, m]]] @@@ Position[Abs@TransTable, _?Positive];

Now you have the variables defined,

Var21 Var83 (* -6.9 *) (* -14. *)

Of course, this isn't usually the best practice. If any of the variables already has a name, then this will throw an error, so you could prepend it with a call to ClearAll,

Function[{n, m}, ClearAll /@ Names["Var" <> IntegerString[m] <> IntegerString[n]]; Evaluate[ ToExpression["Var" <> IntegerString[m] <> IntegerString[n]]] = TransTable[[n, m]]] @@@ Position[Abs@TransTable, _?Positive];

which can be called over and over again.

Usually, there isn't any reason not to use indexed variables, so instead of Var21, you would have Var[2,1]. This makes the code much easier,

Set[Var[#2, #1], TransTable[[#1, #2]]] & @@@ Position[Abs@TransTable, _?Positive];

Either way, it is easy to print the list of variables that have been assigned,

Names["Var*"] (* {"Var", "Var21", "Var31", "Var32", "Var41", "Var42", "Var43", "Var51", "Var52", "Var53", "Var54", "Var61", "Var62", "Var63", "Var64", "Var65", "Var71", "Var72", "Var73", "Var74", "Var75", "Var76", "Var81", "Var82", "Var83", "Var84", "Var85", "Var86", "Var87", "Variables", "Variance", "VarianceEquivalenceTest", "VarianceEstimatorFunction", "VarianceGammaDistribution", "VarianceTest"} *)

for the first method, or for the indexed method,

?Var

Global`Var

Var[2,1]=-6.9

Var[3,1]=-7.

Var[3,2]=-0.100005

Var[4,1]=-7.1

Var[4,2]=-0.20001

Var[4,3]=-0.100005

Var[5,1]=-13.9

Var[5,2]=-7.

Var[5,3]=-6.9

Var[5,4]=-6.79999

Var[6,1]=-14.

Var[6,2]=-7.1

Var[6,3]=-7.

Var[6,4]=-6.9

Var[6,5]=-0.100005

Var[7,1]=-14.1

Var[7,2]=-7.20001

Var[7,3]=-7.1

Var[7,4]=-7.

Var[7,5]=-0.20001

Var[7,6]=-0.100005

Var[8,1]=-21.

Var[8,2]=-14.1

Var[8,3]=-14.

Var[8,4]=-13.9

Var[8,5]=-7.1

Var[8,6]=-7.

Var[8,7]=-6.9

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  • $\begingroup$ That's very nice. I'm just thinking of this now, but perhaps I could add an option that prints which variables have been assigned? I think I should be able to add some conditional to the above right? $\endgroup$ Commented Mar 15, 2016 at 14:27

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