13.1 Mathematic_Vector Class

The Mathematic_Vector Class is used to describe a Mathematic Vector in the CÆSAR Code Package. A Mathematic_Vector differs from a Distributed_Vector in several ways:

• A Mathematic_Vector has operations which allow it to calculate various mathematic functions (norms, averages, etc.).
• A Mathematic_Vector is used with a matrix class to define a matvec operation.
• A Distributed_Vector can interoperate with other CÆSAR parallel data structures (Assembled_Vector, Overlapped_Vector, Collected_Array).

Note that a Mathematic_Vector contains a Distributed_Vector and a vector of Overlapped_Vectors which it uses for matvecs.

The Mathematic_Vector methods section describes the methods used in the Mathematic_Vector Class.

Mathematic_Vector public procedures:

	Fundamental procedures
	Initialize		Initializes a Mathematic_Vector object.
	Finalize		Finalizes a Mathematic_Vector object.
	Valid_State		Returns false iff a Mathematic_Vector object is in an invalid state.
	Initialized		Returns true iff a Mathematic_Vector object has been initialized.
	Operations
	Average		Returns the arithmetic mean of the Mathematic_Vector object.
	Add_Values		Increments the values of a Mathematic_Vector object.
	DotProduct		Returns the global dot product of two Mathematic_Vector objects.
	Duplicate		Makes an exact copy of a Mathematic_Vector (except for the internal DV's and OV's, which will be generated if needed). This procedure is also useful when a compatible Mathematic_Vector is needed.
	First_PE		Returns the global number of the first entry on this PE of the Mathematic_Vector object.
	Get_Values		Returns the values for a Mathematic_Vector object (also has an assignment interface).
	Infinity_Norm		Returns the infinity norm of the Mathematic_Vector object.
	Last_PE		Returns the global number of the last entry on this PE of the Mathematic_Vector object.
	Length_PE		Returns the length on this PE of the Mathematic_Vector object.
	Length_Total		Returns the total length (all PEs) of the Mathematic_Vector object.
	Locus		Returns the locus of the Mathematic_Vector object.
	Maximum		Returns the maximum of the Mathematic_Vector object.
	Mean		Returns the mean value of the Mathematic_Vector object.
	Minimum		Returns the minimum of the Mathematic_Vector object.
	Name		Returns the name of the Mathematic_Vector object.
	Norm		Returns the two norm of the Mathematic_Vector object.
	One_Norm		Returns the one norm of the Mathematic_Vector object.
	Orthogonal		Returns true if the two Mathematic_Vector objects are orthogonal.
	Output		Writes out the Mathematic_Vector object.
	P_Norm		Returns the P-norm of the Mathematic_Vector object.
	Two_Norm		Returns the two norm of the Mathematic_Vector object.
	Set_Not_Up_to_Date		Puts a Mathematic Vector into a ``not up-to-date'' state. Can be used externally to force recalculation of norms, extrema, etc.
	Set_Value		Sets all values to a specified scalar (often zero) for a Mathematic_Vector object.
	Set_Values		Sets the values for a Mathematic_Vector object.
	Sum		Returns the sum of the Mathematic_Vector object.
	Total		Returns the sum of the Mathematic_Vector object.
	Update_DV		Updates the Distributed Vector inside of a Mathematic_Vector object.

Mathematic_Vector public defined types:

	Mathematic_Vector type
	Average		Global average of the Mathematic Vector.
	Average_is_Updated		Updated? toggle for Average.
	Dimensionality		Number of dimensions for the Mathematic Vector (always unity).
	DV		Distributed Vector that is used for matvecs.
	Infinity_Norm		Infinity norm of the Mathematic Vector.
	Infinity_Norm_is_Updated		Updated? toggle for Infinity_Norm.
	Initialized		Initialization status.
	Maximum		Global maximum of the Mathematic Vector.
	Maximum_is_Updated		Updated? toggle for Maximum.
	Minimum		Global minimum of the Mathematic Vector.
	Minimum_is_Updated		Updated? toggle for Minimum.
	Name		The name for this variable (especially useful in a vector of Mathematic Vectors).
	One_Norm		One norm of the Mathematic Vector.
	One_Norm_is_Updated		Updated? toggle for One_Norm.
	OV		A vector of Overlapped Vectors that is used for matvecs.
	DV_is_Updated		Updated? toggle for DV.
	P_Norm		P norm of the Mathematic Vector.
	P_Norm_Exponent		Exponent used in taking the P norm.
	P_Norm_is_Updated		Updated? toggle for P_Norm.
	Structure		Basic data structure for the Mathematic Vector.
	Sum		Global sum of the Mathematic Vector.
	Sum_is_Updated		Updated? toggle for Sum.
	Two_Norm		Two norm of the Mathematic Vector.
	Two_Norm_is_Updated		Updated? toggle for Two_Norm.
	Values		Values for the Mathematic Vector.

Mathematic_Vector public variables:

Number_of_OVs_in_an_MV

A parameter specifying the number of Overlapped_Vector objects in a Mathematic_Vector object. This number limits the number of different matrices that MatVecs can be done with quickly. For example, if a Mathematic_Vector object is to be multipied by three matrices, all with the same Column_Structure but with different Data_Indices (Columns arrays), then the set up for all three can be stored as long as Number_of_OVs_in_an_MV is equal to or greater than three. Otherwise, multiplication can still be done, but set up phases will have to be repeated.

The Mathematic_Vector Class code listing contains additional documentation. The Mathematic_Vector Class also contains a Unit Test Program.