SGBFA(3F)							     SGBFA(3F)

NAME    [Toc]    [Back]

     SGBFA   - SGBFA factors a real band matrix	by elimination.

     SGBFA is usually called by	SBGCO, but it can be called directly with a
     saving in time if	RCOND  is not needed.

SYNOPSYS    [Toc]    [Back]

      SUBROUTINE SGBFA(ABD,LDA,N,ML,MU,IPVT,INFO)

DESCRIPTION    [Toc]    [Back]

     On	Entry

     ABD REAL(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 SGBSL will divide	by zero	if
	called.	 Use  RCOND  in	SBGCO for a reliable
	indication of singularity.  Band Storage



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SGBFA(3F)							     SGBFA(3F)



	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 = MAX0(1, J-MU)
	I2 = MIN0(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.  LINPACK.  This
     version dated 08/14/78 .  Cleve Moler, University of New Mexico, Argonne
     National Lab.  Subroutines	and Functions BLAS SAXPY,SSCAL,ISAMAX Fortran
     MAX0,MIN0


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