F406: Banded Linear Equations

Author(s): G.A. Erskine	Library: KERNLIB
Submitter:	Submitted: 01.09.1983
Language: Fortran	Revised: 27.11.1984

Subroutine subprograms RBEQN and DBEQN solve a system of N simultaneous linear equations with K right-hand sides, the coefficient matrix being a band matrix with bandwidth 2M+1:

Only those coefficients for which need be supplied on entry (see Usage).

Structure:

SUBROUTINE subprograms
User Entry Names: RBEQN, DBEQN
Files Referenced: Printer
External References: KERMTR, ABEND

Usage:

For (type REAL), (type DOUBLE PRECISION),

    CALL tBEQN(N,M,ABAND,IDIM,IFAIL,K,B)

N

(INTEGER) Number of equations.

M

(INTEGER) Band parameter M.

ABAND

(type according to t) Two-dimensional array whose first dimension has the value IDIM.

IDIM

(INTEGER) First dimension of array ABAND (and of array B if ).

IFAIL

(INTEGER) On exit, IFAIL will be set to -1 if the coefficient matrix is singular, and to 0 otherwise.

K

(INTEGER) Number of right-hand sides in array B.

B

(type according to t) In general, a two-dimensional array whose first dimension has the value IDIM. B may be one-dimensional if .

On entry, ABAND must contain the packed form of the coefficient matrix as described below, and array B must contain the matrix of right-hand sides . Then, provided the coefficient matrix is non-singular, IFAIL will be set to 0 and the solution will replace in B. The contents of ABAND are destroyed. If the coefficient matrix is singular, IFAIL will be set to -1. In this case the contents of ABAND and B are unpredictable.

The storage convention for ABAND is that it must contain, on entry, those coefficients for which , stored "left-justified" as an array of N rows and at most columns. For example, if and , the coefficient matrix

where X denotes elements whose value need not to be set.

If ALPHA(I,J) is a function subprogram or statement function which computes , the following Fortran statements will set ABAND correctly:

      DO 2 I =1,N
      L = 1
      DO 1 J = MAX(I-M,1),MIN(I+M,N)
      ABAND(I,L) = ALPHA(I,J)
      L = L+1
    1 CONTINUE
    2 CONTINUE

Method:

Gaussian elimination with row interchanges. The storage organization is as described in the reference.

Error handling:

If the integer arguments do not satisfy the conditions , a message is printed and program execution is terminated by calling ABEND (Z035).

References:

1. J.H. Wilkinson and C. Reinsch (eds.), Handbook for automatic computation, Vol.2: Linear algebra (Springer-Verlag, New York 1971) 54.