Solves the symmetric positive definitive banded linear system Ax = b.

Syntax

x = LSolveSPDB(M, k, b)

Arguments

Name

Description

M

Symmetric compressed diagonal storage matrix form of the banded square matrix A.  Use SymBandMatrix to create it and SymBandMatrixIndices to populate it.

k

The number of super- or sub-diagonals in the lower or upper band of the original matrix.  It should include off-diagonals with zero entries that are in between diagonals with non zero entries.

b

The right-hand side column vector or a matrix.  If it is a matrix, each column is considered a separate vector and the system is solved separately for each column, resulting in multiple solutions.  The number of columns must be equal to the row/column size of the square matrix A.

Output

Name

Description

x

The solution(s) to the system(s).  It will have the same dimensions as the right-hand side argument b.  For each column in b, there will be a solution in the corresponding column in x.

Example

Solve symmetric banded linear system Ax=b.

Syntax

M = [40, 40, 40; 2, 4, 0];
k = 1;
b = [1, 1; 11, 11; 21, 21];
x = LSolveSPDB(M, k, b);
print("LSolveSPDB\:\n", x);
 
LSolveSPDB:
[Matrix] 3 x 2
0.013797 0.013797
0.22405 0.22405
0.50259 0.50259

Result

A matrix of the solution to the system.

[Matrix] 3 x 2
0.013797 0.013797
0.22405  0.22405
0.50259  0.50259

Comments

LSolveSPDB is based on dpbsv from the LAPACK library.

See Also:

SymBandMatrix

SymBandMatrixIndices

LSolve

LSolveB

LSolveT