Numeric containers

Containers that hold a list of numerical values may be constant or variable. It has an incidence on the behaviour of the tensor system using them. Constant propagation may occur in the former case. It is discouraged to use constant containers to store a huge or infinitesimal value (used in finite differences, or penalization methods), even if it is constant, for the risk of rounding surprises: it’s better using a variable one, forcing the system to respect its unknown-value nature.

When variable, a range may constrain the container and the tensor system may take it into account to ensure the validity of some formulations.

Composition of containers are used to form more complex data structures, as is the case with CSR sparse matrices for instance.

Constant containers: NumericList

auto listA = NaturalList{1};      // a constant single value container containing (1)
auto listB = DecimalList{10.1,10.2,10.6};  // a constant 3-values container containing (10.1,1à.2,10.6)

Variable containers: NumericData

auto dataA1 = NaturalData1{"A"};       // a single value container initialized to 0
auto dataB1 = NaturalData1{"B",50};    // a single value container initialized to 50
auto dataC1 = NaturalData1{"C",{1,9}}; // a single value container of values in [1,9] initialized to 1

dataC1.set_value(10); // run-time error
dataC1.set_value(0);  // run-time error
dataC1.set_value(5);  // correct

auto dataAn = NaturalDataN("A",5);        // a 5-values container initialized to 0;
auto dataBn = NaturalDataN{"B",{4,5,6}};  // a 3-values container initialized to (4,5,6);
auto dataCn = DecimalDataN{"C",5,{1,9}};  // a 5-values container of values in [1,9] initialized to 1;

Range constraints

To provide robustness to the formulation engine, assuming a range for some given pack of values may prove useful.

The dummy range

It is not really a container, but the name of a dummy variable within a possible range. When mixing dummy indices, wether they stand for the same one or not does not lead to the same results; thus a name is given to distinguish them.

auto rangeI1 = NaturalRange{"I",{0,9};   // a range of indices in [0,9], named "I"
auto rangeI2 = NaturalRange("I",10);     // the same range: 10 values starting at 0 and named "I"
assert(rangeI1==rangeI2);

Sparse matrices

… to come.