*DECK SNBFA
SUBROUTINE SNBFA (ABE, LDA, N, ML, MU, IPVT, INFO)
C***BEGIN PROLOGUE SNBFA
C***PURPOSE Factor a real band matrix by elimination.
C***LIBRARY SLATEC
C***CATEGORY D2A2
C***TYPE SINGLE PRECISION (SNBFA-S, DNBFA-D, CNBFA-C)
C***KEYWORDS BANDED, LINEAR EQUATIONS, MATRIX FACTORIZATION,
C NONSYMMETRIC
C***AUTHOR Voorhees, E. A., (LANL)
C***DESCRIPTION
C
C SNBFA factors a real band matrix by elimination.
C
C SNBFA is usually called by SNBCO, but it can be called
C directly with a saving in time if RCOND is not needed.
C
C On Entry
C
C ABE REAL(LDA, NC)
C contains the matrix in band storage. The rows
C of the original matrix are stored in the rows
C of ABE and the diagonals of the original matrix
C are stored in columns 1 through ML+MU+1 of ABE.
C NC must be .GE. 2*ML+MU+1 .
C See the comments below for details.
C
C LDA INTEGER
C the leading dimension of the array ABE.
C LDA must be .GE. N .
C
C N INTEGER
C the order of the original matrix.
C
C ML INTEGER
C number of diagonals below the main diagonal.
C 0 .LE. ML .LT. N .
C
C MU INTEGER
C number of diagonals above the main diagonal.
C 0 .LE. MU .LT. N .
C More efficient if ML .LE. MU .
C
C On Return
C
C ABE an upper triangular matrix in band storage
C and the multipliers which were used to obtain it.
C The factorization can be written A = L*U , where
C L is a product of permutation and unit lower
C triangular matrices and U is upper triangular.
C
C IPVT INTEGER(N)
C an integer vector of pivot indices.
C
C INFO INTEGER
C =0 normal value
C =K if U(K,K) .EQ. 0.0 . This is not an error
C condition for this subroutine, but it does
C indicate that SNBSL will divide by zero if
C called. Use RCOND in SNBCO for a reliable
C indication of singularity.
C
C Band Storage
C
C If A is a band matrix, the following program segment
C will set up the input.
C
C ML = (band width below the diagonal)
C MU = (band width above the diagonal)
C DO 20 I = 1, N
C J1 = MAX(1, I-ML)
C J2 = MIN(N, I+MU)
C DO 10 J = J1, J2
C K = J - I + ML + 1
C ABE(I,K) = A(I,J)
C 10 CONTINUE
C 20 CONTINUE
C
C This uses columns 1 through ML+MU+1 of ABE .
C Furthermore, ML additional columns are needed in
C ABE starting with column ML+MU+2 for elements
C generated during the triangularization. The total
C number of columns needed in ABE is 2*ML+MU+1 .
C
C Example: If the original matrix is
C
C 11 12 13 0 0 0
C 21 22 23 24 0 0
C 0 32 33 34 35 0
C 0 0 43 44 45 46
C 0 0 0 54 55 56
C 0 0 0 0 65 66
C
C then N = 6, ML = 1, MU = 2, LDA .GE. 5 and ABE should contain
C
C * 11 12 13 + , * = not used
C 21 22 23 24 + , + = used for pivoting
C 32 33 34 35 +
C 43 44 45 46 +
C 54 55 56 * +
C 65 66 * * +
C
C***REFERENCES J. J. Dongarra, J. R. Bunch, C. B. Moler, and G. W.
C Stewart, LINPACK Users' Guide, SIAM, 1979.
C***ROUTINES CALLED ISAMAX, SAXPY, SSCAL, SSWAP
C***REVISION HISTORY (YYMMDD)
C 800606 DATE WRITTEN
C 890531 Changed all specific intrinsics to generic. (WRB)
C 890831 Modified array declarations. (WRB)
C 890831 REVISION DATE from Version 3.2
C 891214 Prologue converted to Version 4.0 format. (BAB)
C 920501 Reformatted the REFERENCES section. (WRB)
C***END PROLOGUE SNBFA
INTEGER LDA,N,ML,MU,IPVT(*),INFO
REAL ABE(LDA,*)
C
INTEGER ML1,MB,M,N1,LDB,I,J,K,L,LM,LM1,LM2,MP,ISAMAX
REAL T
C***FIRST EXECUTABLE STATEMENT SNBFA
ML1=ML+1
MB=ML+MU
M=ML+MU+1
N1=N-1
LDB=LDA-1
INFO=0
C
C SET FILL-IN COLUMNS TO ZERO
C
IF(N.LE.1)GO TO 50
IF(ML.LE.0)GO TO 7
DO 6 J=1,ML
DO 5 I=1,N
ABE(I,M+J)=0.0E0
5 CONTINUE
6 CONTINUE
7 CONTINUE
C
C GAUSSIAN ELIMINATION WITH PARTIAL ELIMINATION
C
DO 40 K=1,N1
LM=MIN(N-K,ML)
LM1=LM+1
LM2=ML1-LM
C
C SEARCH FOR PIVOT INDEX
C
L=-ISAMAX(LM1,ABE(LM+K,LM2),LDB)+LM1+K
IPVT(K)=L
MP=MIN(MB,N-K)
C
C SWAP ROWS IF NECESSARY
C
IF(L.NE.K)CALL SSWAP(MP+1,ABE(K,ML1),LDA,ABE(L,ML1+K-L),LDA)
C
C SKIP COLUMN REDUCTION IF PIVOT IS ZERO
C
IF(ABE(K,ML1).EQ.0.0E0) GO TO 20
C
C COMPUTE MULTIPLIERS
C
T=-1.0/ABE(K,ML1)
CALL SSCAL(LM,T,ABE(LM+K,LM2),LDB)
C
C ROW ELIMINATION WITH COLUMN INDEXING
C
DO 10 J=1,MP
CALL SAXPY (LM,ABE(K,ML1+J),ABE(LM+K,LM2),LDB,ABE(LM+K,LM2+J),
1 LDB)
10 CONTINUE
GO TO 30
20 CONTINUE
INFO=K
30 CONTINUE
40 CONTINUE
50 CONTINUE
IPVT(N)=N
IF(ABE(N,ML1).EQ.0.0E0) INFO=N
RETURN
END