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To manipulate a symbolic mathematical expression, you would need to define the symbolic variables first. If using the native Matlab symbolic math toolbox, you can create a symbolic variable by calling sym('var') (scalar) or sym('var',[2,3]) (array). FROST uses the similar syntax to create a symbolic variable.

Overview

SymVariable is an inherited subclass of SymExpression, hence it can be used as any regular symbolic expression in the code. When a SymVariable object is created, it will be associated with one or a group of symbolic variables in Mathematica. You can:

  • create a scalar, 1-D or 2-D array variable
  • reference sub-elements using indices
  • assign special text labels for each elements and reference using labels

Create SymVariable objects

  • Create a scalar variable
>> a = SymVariable('var'); % a is the matlab object that represents a symbolic variable 'var' in Mathematica


ans =

var
  • Create a 1-D array variables:
>> a_vec = SymVariable('var',3)

ans =

{var$1, var$2, var$3}
  • Create a 2-D array variables:
>> a_mat = SymVariable('var',[2,3])

ans =

{{var$1$1, var$1$2, var$1$3}, {var$2$1, var$2$2, var$2$3}}

Use SymVariable objects

Once a SymVariable object is created, you can use it as regular data to perform symbolic math calculation. For example:

>> b = cos(a)

ans =

Cos[var]

>> b + a

ans =

var + Cos[var]

>> b_vec = cos(a_vec)

ans =

{Cos[var$1], Cos[var$2], Cos[var$3]}

>> b_mat = cos(a_mat)

ans =

{{Cos[var$1$1], Cos[var$1$2], Cos[var$1$3]}, {Cos[var$2$1], Cos[var$2$2], Cos[var$2$3]}}

Reference by index

You can access a sub-entries of an array of SymVariable using their indices similar to other Matlab variables. For example:

>> a2 = a_vec(2)

ans =

{var$2}

>> a_1_3 = a_vec([1,3])

ans =

{var$1, var$3}

>> a2_1_3 = a_mat(2,[1,3])

ans =


{{var$2$1, var$2$3}}

Reference by label

Labels can be assigned to each entry of a 2-D array of SymVariable object at initialization.

>> a_vec = SymVariable('var',[3,1],{'alpha','beta','gamma'})

ans =


{{var$1$1}, {var$2$1}, {var$3$1}}

If labels are assigned, then it can be used to reference the individual element in the array. For example:

>> alpha = a_vec('alpha')

ans =

{var$1$1}
Tags: symbolic