Built-in Array Functions

1 Array Dimension and Size Functions

The following examples illustrate built-in functions that return the number of dimensions of an array (ndims(A)), the sizes of its dimensions (size(A, i)), or the size of a specific dimension (size(A)).

class DimSize parameter Real[4, 1, 6] x = fill(1., 4, 1, 6); parameter Real dim = ndims(x); // Returns 3 parameter Real dimsize = size(x, 1); // Returns 4 parameter Real specsize[3] = size(x); // Returns the vector {4, 1, 6} equation // size(2*x + x) = size(x); // This equation holds end DimSize;

1.1 Simulation of DimSize

simulate( DimSize )

Take a look at an array element value at time=1:

val(x[4,1,4],1)
plot(x[4,1,4])

2 Dimensionality Conversion Functions

The following conversion functions convert scalars, vectors, and arrays to scalars or matrices by adding or removing 1-sized dimensions.

class DimConvert Real[3] v1 = {1.0, 2.0, 3.0}; Real[3,1] m1 = matrix(v1); // m1 contains {{1.0}, {2.0}, {3.0}} Real[3] v2 = vector(m1); // v2 contains {1.0, 2.0, 3.0} Real[1,1,1] m2 = {{{4}}}; Real s1 = scalar(m2); // s1 contains 4.0 Real[2,2,1] m3 = {{{1.0}, {2.0}}, {{3.0}, {4.0}}}; Real[2,2] m4 = matrix(m3); // m4 contains {{1.0, 2.0}, {3.0, 4.0}} end DimConvert;

2.1 Simulation of DimConvert

simulate( DimConvert )

Take a look at an array element value at time=1:

val(m1[3,1],1)
plot({m1[3,1],s1})

3 Specialized Constructor Functions

An array constructor function constructs and returns an array computed from its arguments. Most of the constuctor functions in the table below construct an array by filling in values according to a certain pattern.

class ConstructFunc Real z[2,3] = zeros(2, 3); // Constructs the matrix {{0,0,0}, {0,0,0}} Real o[3] = ones(3); // Constructs the vector {1, 1, 1} Real f[2,2] = fill(2.1,2,2); // Constructs the matrix {{2.1, 2.1}, {2.1, 2.1}} Boolean check[3, 4] = fill(true, 3, 4); // Fills a Boolean matrix Real id[3,3] = identity(3); // Creates the matrix {{1,0,0}, {0,1,0}, {0, 0, 1}} Real di[3,3] = diagonal({1, 2, 3}); // Creates the matrix {{1, 0, 0}, {0, 2, 0}, {0, 0, 3}} Real ls[5] = linspace(0.0, 8.0, 5); // Computes the vector {0.0, 2.0, 4.0, 6.0, 8.0} end ConstructFunc;

3.1 Simulation of ConstructFunc

simulate( ConstructFunc )

Take a look at an array element value at time=0:

val(di[3,2],0)
plot({di[3,2],f[2,2]})

4 Reduction Functions

An array reduction function "reduces" an array to a scalar value, i.e. computes a scalar value from the array.

class Reduce Real minimum, maximum, summ, prod; equation minimum = min({1, -1, 7}); // Gives the value -1 maximum = max([1, 2, 3; 4, 5, 6]); // Gives the value 6 summ = sum({{1, 2, 3}, {4, 5, 6}}); // Gives the value 21 prod = product({3.14, 2, 2}); // Gives the value 12.56 end Reduce;

4.1 Simulation of Reduce

simulate( Reduce )

Take a look at the value at time=0:

val(summ,0)
plot({summ,prod})

5 Matrix and Vector Algebra Functions

The following set of functions are rather common in matrix and vector algebra, but are not associated with any Modelica operator symbol.

class AlgebraFunc Real transp1[2,2] = transpose([1, 2; 3, 4]); // Gives [1, 2; 3, 4] of type Integer[2, 2] Real transp2[2,2,1] = transpose({{{1},{2}},{{3},{4}}}); // Gives {{{1},{2}},{{3},{4}}} of type Integer[2, 2, 1] Real out[2, 2] = outerProduct({2,1}, {3,2}); // Gives {{6, 4}, {3, 2}} Real symm[2, 2] = symmetric({{1, 2}, {3, 1}}); // Gives {{1, 2}, {2, 1}} Real c[3] = cross({1, 0, 0}, {0, 1, 0}); // Gives {0, 0, 1} Real s[3, 3] = skew({1, 2, 3}); // Gives {{0, -3, 2}, {3, 0, -1}, {-2, 1, 0}}; end AlgebraFunc;

5.1 Simulation of AlgebraFunc

simulate( AlgebraFunc )

Take a look at the value at time=0:

val(transp2[2,1,1],0)
val(s[3,3],0)
plot({s[3,3],c[3]})