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1 Matrices and Square Matrices Internal Layout We choose to use row-major contiguous storage for our Matrix_ class: this reflects our emphasis on maximal efficiency of access and minimal allocation calls, at the expense of inefficient resizing (since the values must be shuffled around whenever the number of columns changes). We make several requirements of Matrix_: • It must produce ephemeral Row_ and Column_ sub-objects which view or manipulate its data; • These must have ConstRow_ and ConstColumn_ relatives for viewing only; • It must support an ephemeral SubMatrix_ which sees part of its data, and which also produces Row_s and Column_s.

H 5 namespace Matrix { template void Append (Matrix_* above, const Matrix_& below); } For all other combinations, we write a generic function to glue matrices together in a user-specified format. This functionality is bulky enough that we confine it to a source file, exporting it only for the types commonly held in matrices – double, String_ and Cell_. h 5 namespace Matrix { Matrix_ Merge(const String_& format, const Vector_*>& vals); Matrix_ Merge(const String_& format, const Vector_*>& vals); Matrix_ Merge(const String_& format, const Vector_*>& vals); } These functions take a vector-of-pointers, rather than a vector, as input to avoid unnecessary copying; they do not own or memory manage the pointers.

1 Tables and Cells A table is a two-dimensional matrix of cells. We will use the same template Matrix_ class for all element types – see Sec. 7 – so we focus here on defining the CELL. Boost supplies a variant type which implements a discriminated union; a class boost::empty (equivalent to the OCaml unit) is provided to serve as the type of a variant object with no contents. h typedef variant Cell_; The type of a variant is queried using the visitor pattern which supplies functionality for each type.

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