Computes the indices for the compressed diagonal storage  matrix equivalent of a banded matrix.  This needs to be called for each of the original matrix entries within the band.

Syntax

row, col = BandMatrixIndices(i, j, size, kl, ku)

Arguments

Name

Description

i

The row index of the element of the original matrix.

j

The column index of the element of the original matrix.

size

The size of each dimension of the original square matrix.

kl

Number of sub-diagonals in the lower band of the original matrix.  This should include zero entry off-diagonals that are placed in-between.

ku

Number of super diagonals in the upper band of the original matrix.  This should include zero entry off-diagonals that are placed in-between.

Output

Name

Description

row

The corresponding row index in the compressed diagonal storage format for index i in source matrix.

col

The corresponding column index in the compressed diagonal storage format for index j in source matrix.

Example

Construct the compressed diagonal storage matrix for A, where A is a 3x3 matrix with one sub- and super-diagonal.

Syntax

A = [1,2,0;41,15,6;0,8,9]; // 3x3 band matrix

kl=1; ku=1; // off diagonal bandwidths

M = BandMatrix(3,kl,ku); // This will hold the compressed matrix

// For each band entry (i,j) of A do the following two operations

row,col = BandMatrixIndices(i,j,3,kl,ku);

M(row,col) = A(i,j);

Result

M will be the compressed diagonal storage matrix version of A.

[Matrix] 4 x 3

0               0               0            

0               2               6              

1               15              9

41              8               0              

Comments

The matrix M becomes an input to a function such as LSolveB.

See Also:

BandMatrix

SymBandMatrix

SymBandMatrixIndices