Error in Assignment

Question

I want to create a matrix with each element updated as per the formula, whose inputs are dependent on the location of element in the matrix.

Zphat[t] = ConstantArray[0, {4, 2, 2}]

The assignment is done using this:

For[i = 1, i < 5, i++, For [j = 1, j < 3, j++ , For [n = 1, n < 3, n++, For[k = 1, k < 5, k++, Zphat[t][[1, j, n]] = Zphat[t][[i, j, n] + D[zdot[t][i,j], {q[t][[1, k]], 1}]*smat[t][[k, n]]]]]] 

I have checked the matrix dimensions used. zdot and smat are the appropriate matrices derived earlier.

Error message: Set::setps: Zphat[t] in the part assignment is not a symbol.

Answer 1

Zphat[t] = ConstantArray[0, {4, 2, 2}] means "whenever you see the expression Zphat[t], replace it with the result of evaluating the ConstantArray expression."

There's a special case of Part that allows you to modify part of an expression that's bound to a symbol. But Zphat[t] isn't a symbol: it's a more complicated expression, so that special case doesn't apply.

Generally, the easy way to construct a matrix according to a formula is to use Table rather than constructing it and modifying it.

To answer the question in the comments:

x = {1, 2};

binds the expression {1,2} to x. This means "when you evaluate x, rewrite it as {1,2}". However, = (Set) holds its left hand side unevaluated, and does a special thing when it's a [[]] (Part) expression:

x[[2]] = 3;
x
(* {1, 3} *)

Note that it can modify any expression this way, not just a List:

x = y + z;
x[[2]] = 3;
x
(* 3 + y *)

Answer 2

I was able to use Table to solve the expression. I have performed the calculation in 2 steps.

Zphat[t] =  Table[D[zdot[t][[i, j]], {q[t][[1, k]], 1}]*smat[t][[k, n ]], {i, 4} , {j, 2}, {n, 2}, {k, 4}]

and for summation over the variable k

Zphatfinal[t] = Table[Sum[Zphat[t][i, j, n, k], {k, 2}], {i, 4} , {j, 2}, {n, 2}]

Also, refer to this before using For - Why should I avoid the For loop in Mathematica?