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man pages->IRIX man pages -> complib/SGBFA (3)
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### Contents

```
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

Page 1

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

PPPPaaaaggggeeee 2222```
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