gblpy.gblnum.BorderedBandMatrix Class Reference

(Symmetric) Bordered Band Matrix. More...

Inheritance diagram for gblpy.gblnum.BorderedBandMatrix:

Public Member Functions
def	__init__ (self, nSize, nBorder=1, nBand=7)
	Create new BBmatrix. More...
def	addBlockMatrix (self, aIndex, aMatrix)
	Add (compressed) block to BBmatrix: More...
def	getBlockMatrix (self, aIndex)
	Retrieve (compressed) block from BBmatrix: More...
def	getBandCond (self)
	Get condition from band part decomposition. More...
def	printMatrix (self)
	Print BBmatrix. More...
def	solveAndInvertBorderedBand (self, aRightHandSide)
	Solve linear equation A*x=b system with BBmatrix A, calculate BB part of inverse of A. More...

Private Attributes
	__numSize
	size of matrix; int More...
	__numBorder
	size of border; int More...
	__numBand
	size of border; int More...
	__numCol
	size of band part of matrix; int More...
	__border
	border part B; matrix(float) More...
	__mixed
	mixed part M; matrix(float) More...
	__band
	band part C; matrix(float) More...

Detailed Description

(Symmetric) Bordered Band Matrix.

Separate storage of border, mixed and band parts.

  Example for matrix size=8 with border size and band width of two:
  
     +-                                 -+
     |  B11 B12 M13 M14 M15 M16 M17 M18  |
     |  B12 B22 M23 M24 M25 M26 M27 M28  |
     |  M13 M23 C33 C34 C35  0.  0.  0.  |
     |  M14 M24 C34 C44 C45 C46  0.  0.  |
     |  M15 M25 C35 C45 C55 C56 C57  0.  |
     |  M16 M26  0. C46 C56 C66 C67 C68  |
     |  M17 M27  0.  0. C57 C67 C77 C78  |
     |  M18 M28  0.  0.  0. C68 C78 C88  |
     +-                                 -+
     
  Is stored as: 
  
     +-         -+     +-                         -+
     |  B11 B12  |     |  M13 M14 M15 M16 M17 M18  | 
     |  B12 B22  |     |  M23 M24 M25 M26 M27 M28  |
     +-         -+     +-                         -+
     
                       +-                         -+
                       |  C33 C44 C55 C66 C77 C88  |
                       |  C34 C45 C56 C67 C78  0.  |
                       |  C35 C46 C57 C68  0.  0.  |
                       +-                         -+

Definition at line 65 of file gblnum.py.

Constructor & Destructor Documentation

__init__()

def gblpy.gblnum.BorderedBandMatrix.__init__	(		self,
			nSize,
			nBorder = 1,
			nBand = 7
	)

Create new BBmatrix.

Parameters

nSize	size of matrix; int
nBorder	size of border (default: 1, 'curvature'); int
nBand	(maximal) band width (7); int

Definition at line 73 of file gblnum.py.

Member Function Documentation

addBlockMatrix()

def gblpy.gblnum.BorderedBandMatrix.addBlockMatrix	(		self,
			aIndex,
			aMatrix
	)

Add (compressed) block to BBmatrix:

BBmatrix(aIndex(i),aIndex(j)) += aMatrix(i,j)

Parameters

aIndex	list of indices; list(int)
aMatrix	(compressed) matrix; matrix(float)

Definition at line 98 of file gblnum.py.

References gblpy.gblnum.BorderedBandMatrix.__band, gblpy.gblnum.BorderedBandMatrix.__border, gblpy.gblnum.BorderedBandMatrix.__mixed, gblpy.gblnum.BorderedBandMatrix.__numBand, and gblpy.gblnum.BorderedBandMatrix.__numBorder.

getBandCond()

def gblpy.gblnum.BorderedBandMatrix.getBandCond

(

self

)

Get condition from band part decomposition.

Returns

condition (ratio largest to smallest eigenvalue, or 0. if fit failed)

Definition at line 152 of file gblnum.py.

References gblpy.gblnum.BorderedBandMatrix.__band.

getBlockMatrix()

def gblpy.gblnum.BorderedBandMatrix.getBlockMatrix	(		self,
			aIndex
	)

Retrieve (compressed) block from BBmatrix:

aMatrix(i,j) = BBmatrix(aIndex(i),aIndex(j))

Parameters

aIndex

list of indices; list(int)

Returns

(compressed) matrix; matrix(float)

Definition at line 124 of file gblnum.py.

References gblpy.gblnum.BorderedBandMatrix.__band, gblpy.gblnum.BorderedBandMatrix.__border, gblpy.gblnum.BorderedBandMatrix.__mixed, gblpy.gblnum.BorderedBandMatrix.__numBand, and gblpy.gblnum.BorderedBandMatrix.__numBorder.

printMatrix()

def gblpy.gblnum.BorderedBandMatrix.printMatrix

(

self

)

Print BBmatrix.

Definition at line 159 of file gblnum.py.

References gblpy.gblnum.BorderedBandMatrix.__band, gblpy.gblnum.BorderedBandMatrix.__border, gblpy.gblnum.BorderedBandMatrix.__mixed, gblpy.gblnum.BorderedBandMatrix.__numBand, and gblpy.gblnum.BorderedBandMatrix.__numBorder.

solveAndInvertBorderedBand()

def gblpy.gblnum.BorderedBandMatrix.solveAndInvertBorderedBand	(		self,
			aRightHandSide
	)

Solve linear equation A*x=b system with BBmatrix A, calculate BB part of inverse of A.

Parameters

aRightHandSide

right hand side 'b' of linear equation system; vector(float)

Returns

solution; vector(float)

Exceptions

ZeroDivisionError

Band matrix is not positive definite

Note

BBmatrix is replaced by BB part of it's inverse

Definition at line 179 of file gblnum.py.

Member Data Documentation

__band

gblpy.gblnum.BorderedBandMatrix.__band

private

band part C; matrix(float)

Definition at line 88 of file gblnum.py.

Referenced by gblpy.gblnum.BorderedBandMatrix.addBlockMatrix(), gblpy.gblnum.BorderedBandMatrix.getBandCond(), gblpy.gblnum.BorderedBandMatrix.getBlockMatrix(), and gblpy.gblnum.BorderedBandMatrix.printMatrix().

__border

gblpy.gblnum.BorderedBandMatrix.__border

private

border part B; matrix(float)

Definition at line 84 of file gblnum.py.

Referenced by gblpy.gblnum.BorderedBandMatrix.addBlockMatrix(), gblpy.gblnum.BorderedBandMatrix.getBlockMatrix(), and gblpy.gblnum.BorderedBandMatrix.printMatrix().

__mixed

gblpy.gblnum.BorderedBandMatrix.__mixed

private

mixed part M; matrix(float)

Definition at line 86 of file gblnum.py.

Referenced by gblpy.gblnum.BorderedBandMatrix.addBlockMatrix(), gblpy.gblnum.BorderedBandMatrix.getBlockMatrix(), and gblpy.gblnum.BorderedBandMatrix.printMatrix().

__numBand

gblpy.gblnum.BorderedBandMatrix.__numBand

private

size of border; int

Definition at line 80 of file gblnum.py.

Referenced by gblpy.gblnum.BorderedBandMatrix.addBlockMatrix(), gblpy.gblnum.BorderedBandMatrix.getBlockMatrix(), and gblpy.gblnum.BorderedBandMatrix.printMatrix().

__numBorder

gblpy.gblnum.BorderedBandMatrix.__numBorder

private

size of border; int

Definition at line 78 of file gblnum.py.

Referenced by gblpy.gblnum.BorderedBandMatrix.addBlockMatrix(), gblpy.gblnum.BorderedBandMatrix.getBlockMatrix(), and gblpy.gblnum.BorderedBandMatrix.printMatrix().

__numCol

gblpy.gblnum.BorderedBandMatrix.__numCol

private

size of band part of matrix; int

Definition at line 82 of file gblnum.py.

__numSize

gblpy.gblnum.BorderedBandMatrix.__numSize

private

size of matrix; int

Definition at line 76 of file gblnum.py.

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The documentation for this class was generated from the following file:

• gblnum.py