bandedmatrices.jl's Introduction

BandedMatrices.jl

A Julia package for representing banded matrices

This package supports representing banded matrices by only the entries on the bands.

One can create banded matrices of type BandedMatrix as follows:

bzeros(m,n,l,u)    # creates a banded matrix of zeros, with l sub-diagonals and u super-diagonals
brand(m,n,l,u)     # creates a random banded matrix, with l sub-diagonals and u super-diagonals
bones(m,n,l,u)     # creates a banded matrix of ones, with l sub-diagonals and u super-diagonals
beye(n,l,u)        # creates a banded  n x n identity matrix, with l sub-diagonals and u super-diagonals

Specialized algebra routines are overriden, include * and \:

A = brand(10000,10000,4,3)  # creates a 10000 x 10000 matrix with 4 sub-diagonals
                            # and 3 super-diagonals
b = randn(10000)
A*b  #   Calls optimized matrix*vector routine
A*A  #   Calls optimized matrix*matrix routine
A\b  #   Calls optimized matrix\vector routine

Implementation

Currently, only column-major ordering is supported: a banded matrix B

[ a_11 a_12
  a_21 a_22 a_23
  a_31 a_32 a_33 a_34
       a_42 a_43 a_44  ]

is represented as a BandedMatrix with a field B.data representing the matrix as

[ *     a_12   a_23    a_34
 a_11   a_22   a_33    a_43
 a_21   a_32   a_43    *
 a_31   a_42   *       *       ]

B.l gives the number of subdiagonals (2) and B.u gives the number of super-diagonals (1). Both B.l and B.u must be non-negative at the moment.

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