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LinearAlgebra

  

FromSplitForm

  

translate split form to native Maple form

 

Calling Sequence

Parameters

Options

Description

Examples

Compatibility

Calling Sequence

FromSplitForm(Ai, B, opts)

Parameters

Ai

-

list of integer index Vectors

B

-

data Vector

opts

-

optional equations controlling the details of the computation

Options

• 

dimensions = [d1, ..., dn]

  

This option controls the dimensions of . Its value needs to be a list of  positive integers, giving the dimensions of . For example, when constructing a sparse Vector, the value should be a list containing a single positive integer, and for a Matrix it should be a list of two positive integers. If the option is not specified, Maple uses the maximal value in the th index vector  as the th dimension.

• 

scan = true or scan = false

  

This option determines whether or not  is scanned for zeroes. If scan = true, the default, then  is scanned to test if it contains any entries that are equal to 0. If this is the case, the operation is aborted with an error message: such entries are not allowed. If you are certain that there are no entries equal to 0, you can save a little bit of processing time by disabling this scan by passing scan = false to the procedure. Use this option with extreme caution.

Description

• 

The FromSplitForm function constructs a sparse rtable  from its split form, performing the opposite function to SplitForm.

• 

The split form of an -dimensional rtable  with  nonzero entries consists of  Vectors, , , ..., , and , each with  entries: for every nonzero entry , there is an index  such that , , ..., , and . (If  is a Vector, then ; if  is a Matrix, then .)

• 

The Vectors  need to be of word-size integer data type; that is, on 32-bit platforms they will have data type  and on 64-bit platforms data type . The Vector  needs to have a data type compatible with NAG-sparse rtables; that is, the datatype of  as returned by rtable_options needs to be one of these values:

  

Examples

Let us examine the split form of an arbitrary matrix.

(1)

(2)

(3)

(4)

If  has a dimension  such that all entries where index  is at its maximal value, are zero, then these are not reflected in the split form. For example, if the last entry in a sparse Vector is zero, or the last row or column of a Matrix.

(5)

(6)

(7)

(8)

Therefore, to recover the original rtable, you may need to use the dimensions option.

(9)

(10)

To construct the Vectors  from scratch in a cross-platform way, one can use kernelopts to find the right integer data type.

(11)

(12)

(13)

(14)

(15)

Compatibility

• 

The LinearAlgebra[FromSplitForm] command was introduced in Maple 17.

• 

For more information on Maple 17 changes, see Updates in Maple 17.

See Also

LinearAlgebra[CompressedSparseForm]

LinearAlgebra[FromCompressedSparseForm]

LinearAlgebra[SplitForm]

 


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