Create Determinant Guide (detguide) for pxp Matrix

Description

A determinant guide is a list of 2 levels, each of which contains a list of p!/2 levels, which codes the use of each element of a pxp matrix in the calculation of the determinant of that matrix. From the guide, the symbolic representation of the determinant can be produced directly.

Usage

   anewdetguide(p,storage,verbose=TRUE)

Arguments

Details

Each determinant guide (detguide) is created by cofactor expansion from the detguide of the next smaller square matrix. If p is set larger than any existing detguide, all lower detguides larger than the largest existing one are first created in turn.

Value

"list"

Author(s)

William R. Fairweather

Examples

anewdetguide(p=5,storage=tempdir(),verbose=TRUE)

Create Determinant Guide (Minidetguide) for pxp Matrix

Description

A minidetguide is a series of p directories, each of which contains a matrix of size (p-1) x (p-1)!/2, which codes the use of each element of a pxp matrix in the calculation of the determinant of that matrix. From the minidetguide, the symbolic representation of the determinant can be produced directly.

Usage

   anewminidet(p,storage,cols,verbose=TRUE)

Arguments

Details

Each determinant guide (minidetguide) is created by creating the set of all possible permutations of the numbers 1 through p except j and storing them as a matrix in subdirectory R1Cj. This represents the set of columns corresponding to rows 2 through p of the products with leading element 1,j of the determinant.

Value

matrix described in details above

Author(s)

William R. Fairweather

Examples

   anewminidet(p=5,storage=tempdir(),cols=1:5,verbose=TRUE)

Confirm Accuracy of Symbolic Determinant Created by anewdetguide() Function

Description

Compares the determinant calculated by multiplying eigenvalues of a matrix to that calculated by applying the symbolic representation created by this package.

Usage

confirm.det(x=NULL, p, storage, verbose=TRUE)

Arguments

Value

Determinant of x produced obtained by multiplying its eigenvalues and determinant of x obtained by applying the detguide defined by p

Author(s)

William R. Fairweather

Examples

confirm.det(x=NULL, p=5,storage=tempdir(),verbose=TRUE)

Confirm Accuracy of Symbolic Determinant Created by anewminidet Function

Description

Compares the determinant calculated by multiplying eigenvalues of a matrix to that calculated by applying the symbolic representation created by this package

Usage

confirm.minidet(x=NULL, p, storage, verbose=TRUE)

Arguments

Value

Determinantof x produced obtained by multiplying its eigenvalues and determinant of x obtained by applying the minidetguide defined by p

Author(s)

William R. Fairweather

Examples

confirm.minidet(x=NULL, p=5,storage=tempdir(),verbose=TRUE)

Index of Determinant Guides and Symbolic Representation Files

Description

Produces a table of existing detguides and parsed detguides for all p or a list of minidetguides and parsed minidetguides for a particular p

Usage

detindex(storage,  mini=c("B","D","M"), pmini=1, verbose=TRUE)

Arguments

Details

Provide full path in storage. Example: storage="c:/determinants". If storage directory "name" is in same folder as R Workspace, storage="./name" is sufficient.

Value

Author(s)

William R. Fairweather

Examples

detindex(storage=tempdir(),mini="B",pmini=5,verbose=TRUE)

Display Symbolic Representation of Determinant of pxp Matrix

Description

Produces symbolic (textual) representation of determinant of pxp matrix from previously defined determinant guide (detguide) for that matrix

Usage

parsedetguide(p, storage, 
    browser="C:/Program Files (x86)/Microsoft/Edge/Application/msedge.exe", 
    symmetric=FALSE, verbose=TRUE)

Arguments

Value

Returns symbolic representation to screen and to existing external storage.

Author(s)

William R. Fairweather

Examples

## Not run: parsedetguide(p=5, storage=tempdir(), 
       browser="C:/Program Files (x86)/Microsoft/Edge/Application/msedge.exe",
       symmetric=FALSE,verbose=TRUE)
## End(Not run)

Display Symbolic Representation of Determinant of pxp Matrix

Description

Produces symbolic (textual) representation of determinant of pxp matrix from previously defined determinant guide (minidetguide) for that matrix

Usage

parsemini(p, storage, symmetric, cols=1:p, verbose=TRUE)

Arguments

Value

Returns symbolic representation to screen and to existing external storage.

Author(s)

William R. Fairweather

Examples

parsemini(p=5, storage=tempdir(), symmetric=FALSE,cols=1:5, verbose=TRUE)

Calculates Size of Elements of Determinant Guide and of Symbolic Representation

Description

In order to anticipate the impact of p on calculation time and storage, some indication can be found from size.predictor( ).

Usage

predictor(p,verbose=TRUE)

Arguments

Details

Provide full path in storage, using double backslashes. Example: storage="c:\determinants". If storage directory is in same folder as R Workspace, storage=".\name" is sufficient.

Value

Summary of calculations in other functions of this package and their relationship to p, including the number of levels of positive terms and of negative terms, the number of elements of the matrix in each term of the determinant, and the number of lines of text required for the symbolic representation of the determinant.

Author(s)

William R. Fairweather

Examples

predictor(p=10,verbose=TRUE)

Retrieve Specific Detguide or Parsed Detguide

Description

Retrieves a specified file from storage directory

Usage

retrieve(p, storage, 
   browser="C:/Program Files (x86)/Microsoft/Edge/Application/msedge.exe", verbose=TRUE)

Arguments

Details

Provide full path to storage. Example: storage="c:/determinants". File to be retrieved is indicated interactively from console.

Value

Selects and retrieves a detguide file from the storage/p/ subdirectory or displays the symbolic determinant in an HTML editor

Author(s)

William R. Fairweather

Examples

## Not run: retrieve(p=5,storage=tempdir(), 
    browser="C:/Program Files (x86)/Microsoft/Edge/Application/msedge.exe",   
    verbose=TRUE)
## End(Not run)

Retrieve Specific Minidetguide or Parsed Minidetguide

Description

Retrieves a specified file from storage directory

Usage

retrieve.mini(p, storage, 
    browser="C:/Program Files (x86)/Microsoft/Edge/Application/msedge.exe", 
    verbose=TRUE)

Arguments

Details

Provide full path in storage. Example: storage="c:/determinants". File to be retrieved is indicated interactively from console.

Value

Selects and retrieves a minidetguide file from the storage/p/ subdirectory or displays the symbolic determinant in an HTML editor

Author(s)

William R. Fairweather

Examples

## Not run: retrieve.mini(p=5,storage=tempdir(), 
    browser="C:/Program Files (x86)/Microsoft/Edge/Application/msedge.exe", 
    verbose=TRUE)
## End(Not run)