DGBFARun Method

***PURPOSE Factor a band matrix using Gaussian elimination. ***CATEGORY D2A2 ***TYPE DOUBLE PRECISION (SGBFA-S, DGBFA-D, CGBFA-C) ***KEYWORDS BANDED, LINEAR ALGEBRA, LINPACK, MATRIX FACTORIZATION ***AUTHOR Moler, C. B., (U. of New Mexico) ***DESCRIPTION DGBFA factors a double precision band matrix by elimination. DGBFA is usually called by DGBCO, but it can be called directly with a saving in time if RCOND is not needed. On Entry ABD DOUBLE PRECISION(LDA, N) contains the matrix in band storage. The columns of the matrix are stored in the columns of ABD and the diagonals of the matrix are stored in rows ML+1 through 2*ML+MU+1 of ABD . See the comments below for details. LDA INTEGER the leading dimension of the array ABD . LDA must be .GE. 2*ML + MU + 1 . N INTEGER the order of the original matrix. ML INTEGER number of diagonals below the main diagonal. 0 .LE. ML .LT. N . MU INTEGER number of diagonals above the main diagonal. 0 .LE. MU .LT. N . More efficient if ML .LE. MU . On Return ABD an upper triangular matrix in band storage and the multipliers which were used to obtain it. The factorization can be written A = L*U where L is a product of permutation and unit lower triangular matrices and U is upper triangular. IPVT INTEGER(N) an integer vector of pivot indices. INFO INTEGER = 0 normal value. = K if U(K,K) .EQ. 0.0 . This is not an error condition for this subroutine, but it does indicate that DGBSL will divide by zero if called. Use RCOND in DGBCO for a reliable indication of singularity. Band Storage If A is a band matrix, the following program segment will set up the input. ML = (band width below the diagonal) MU = (band width above the diagonal) M = ML + MU + 1 DO 20 J = 1, N I1 = MAX(1, J-MU) I2 = MIN(N, J+ML) DO 10 I = I1, I2 K = I - J + M ABD(K,J) = A(I,J) 10 CONTINUE 20 CONTINUE This uses rows ML+1 through 2*ML+MU+1 of ABD . In addition, the first ML rows in ABD are used for elements generated during the triangularization. The total number of rows needed in ABD is 2*ML+MU+1 . The ML+MU by ML+MU upper left triangle and the ML by ML lower right triangle are not referenced. ***REFERENCES J. J. Dongarra, J. R. Bunch, C. B. Moler, and G. W. Stewart, LINPACK Users' Guide, SIAM, 1979. ***ROUTINES CALLED DAXPY, DSCAL, IDAMAX ***REVISION HISTORY (YYMMDD) 780814 DATE WRITTEN 890531 Changed all specific intrinsics to generic. (WRB) 890831 Modified array declarations. (WRB) 890831 REVISION DATE from Version 3.2 891214 Prologue converted to Version 4.0 format. (BAB) 900326 Removed duplicate information from DESCRIPTION section. (WRB) 920501 Reformatted the REFERENCES section. (WRB) ***END PROLOGUE DGBFA

public void Run(
	ref double[] ABD,
	int offset_abd,
	int LDA,
	int N,
	int ML,
	int MU,
	ref int[] IPVT,
	int offset_ipvt,
	ref int INFO
)