Array Indexing

1 General Description

The indexing operator ....[....] takes two or more operands, where the first operand is the array to be indexed and the rest of the operands are index expressions. It is used to access array elements for retrieval of their values or for updating these values. In class ArrayIndex: arrayname[indexexpr1, indexexpr2, ......];

1.1 ArrayIndex Class

class ArrayIndex Real[2, 2] A = {{2, 3}, {4, 5}}; // Definition of array A Real A_Retrieval = A[2, 2]; // Retrieves the array element value 5 Real B[2, 2]; Real c; algorithm B := fill(1,2,2); // B will have the values {{1, 1}, {1, 1}} B[2, 1] := 8; // Assignment to the array element B[2, 1] c := A[1, 1]; end ArrayIndex;

1.2 Simulation of ArrayIndex

Here we simulate the class ArrayIndex above.

simulate( ArrayIndex )

We see that B[2, 1] now has the value 8.

plot( { c, B[2,1] } )

2 Indexing with Scalar Index Expressions

Array indexing using scalar integer index expressions is usually used to retrieve or update single array elements. The value of the index expression for the i:th dimension of an array X must be within the bounds of the size of that dimension, i.e. 1.Since multi-dimensional arrays are defined as arrays of arrays in Modelica, it is also possible to access sub-arrays using simple scalar indexing. For example, the array b can also be regarded as a one-dimensional array of vectors.

class ScalarIndex Real[2, 2] b = {{1, 2}, {4, 5}}; Real[2] v = {10, 11}; Real[4, 2] m; Real b_Ret1 = b[1, 2]; // Retrieves the value 2 //Real b_Ret2[2] = b[2]; // Retrieves b[2] giving {4, 5} Real v_Ret1 = v[2]; // Retrieves the value 11 // Real v_Ret2 = v[4]; // Error, index out of range! algorithm m := fill(5, 4, 2); m[4] := v; // Updates m to become // {{5, 5}, {5, 5}, {5, 5}, {10, 11}} end ScalarIndex;
simulate(ScalarIndex)
{val(m[4,1],1.0), val(m[4,2],1.0)}

3 Accessing Array Slices with Index Vectors

When at least one of the index expressions in an array indexing operation is a vector expression, a subsection (slice) of the array is accessed rather than a single element. Such an index vector must be a vector of integer values, where each value must be within the size bounds for the particular array dimension. An index vector can be constructed in any way but it is often convenient to use the colon operator to construct a range vector of index values. A single colon without operands used as an index expression at a dimension k of an array of X denotes all indices of that dimension and is equivalent to the index vector 1:size(X, k).

class ArraySlice Real x1 = X[2, 1]; // Retrieves the value 3 Real x2[3] = X[:, 1]; // Gets the first column of X as the vector {1,3,8} Real x3[2] = X[2, :]; // Gets the second row of X as the vector {3, 4} Real x4[2] = X[2, 1:2]; // Same as above, i.e. {3, 4} Real x5[2] = X[2, {1, 2}]; // Same as above, i.e. {3, 4} Real x6[1] = X[2, {2}]; // Half of the above vector, i.e. {4} Real x7[3, 1] = X[:, 1:1]; // Gets the first column of X as // column matrix {{1}, {3}, {8}} Real x8[1, 2] = X[{2}, :]; // Gets the second row of X as the row matrix {{3, 4}} Real x9[2, 2] = X[{2, 3}, {1, 2}]; // Extract submatrix given {{3, 4}, {8, 9}} Real w1[3] = w[2:4]; // Get the 2:nd through 4:th elements as {16,17,18} Real w2[2] = w[{1, 3}]; // Get the 1:st and 3:rd elements as {15, 17} Real w3[2] = w[1:2:4]; // Get the 1:st to 4:th step 2 elements as {15,17} Real X[3, 2] = {{1, 2}, {3, 4}, {8, 9}}; Real w[4] = {15, 16, 17, 18}; Real[4] y = fill(1, 4); end ArraySlice;
simulate(ArraySlice)

4 Array Field Slices of Record Arrays

If A is an array of records and m is a field of that record type, the expression A.m is interpreted as an array field slice operation of that record array. It returns the array of fields: {A[1].m, A[2].m, A[3].m, ...}. For example, given a record Person with three fields: name, age and children.

4.1 Record Person, Function mkperson and Class p

record Person String name; Integer age; String[2] children; end Person;

We have defined a record constructor function: mkperson(name, age, children) in Modelica returning a Person record, which is used to define the contents of a small array persons consisting of Person records.

function mkperson input String name; input Integer age; input String[2] children; output Person p; algorithm p.name := name; p.age := age; p.children := children; end mkperson;

4.2 Calling mkperson

mkperson("John",35,{"Carl","Eva"})

4.3 Classes PersonList and getPerson

class PersonList Person[3] persons = {mkperson("John", 35, {"Carl", "Eva"} ), mkperson("Karin", 40, {"Anders", "Dan"} ), mkperson("Lisa", 37, {"John", "Daniel"} ) }; end PersonList;

The field slices persons.name, persons.age and persons.children give the following results:

class getPerson PersonList pList; String name[3]; Integer age[3]; String[3, 2] children; equation name = pList.persons.name; // Returns: {"John", "Karin", "Lisa"} age = pList.persons.age; // Returns: {35, 40, 37} children = pList.persons.children; // Returns: {{"Carl", "Eva"}, // {"Anders", "Dan"}, // {"John", "Daniel"}} end getPerson;