Code covered by the BSD License

### Highlights fromslatec

from slatec by Ben Barrowes
The slatec library converted into matlab functions.

[abd,lda,n,ml,mu,ipvt,det]=sgbdi(abd,lda,n,ml,mu,ipvt,det);
```function [abd,lda,n,ml,mu,ipvt,det]=sgbdi(abd,lda,n,ml,mu,ipvt,det);
%***BEGIN PROLOGUE  SGBDI
%***PURPOSE  Compute the determinant of a band matrix using the factors
%            computed by SGBCO or SGBFA.
%***LIBRARY   SLATEC (LINPACK)
%***CATEGORY  D3A2
%***TYPE      SINGLE PRECISION (SGBDI-S, DGBDI-D, CGBDI-C)
%***KEYWORDS  BANDED, DETERMINANT, INVERSE, LINEAR ALGEBRA, LINPACK,
%             MATRIX
%***AUTHOR  Moler, C. B., (U. of New Mexico)
%***DESCRIPTION
%
%     SGBDI computes the determinant of a band matrix
%     using the factors computed by SBGCO or SGBFA.
%     If the inverse is needed, use SGBSL  N  times.
%
%     On Entry
%
%        ABD     REAL(LDA, N)
%                the output from SBGCO or SGBFA.
%
%        LDA     INTEGER
%                the leading dimension of the array  ABD .
%
%        N       INTEGER
%                the order of the original matrix.
%
%        ML      INTEGER
%                number of diagonals below the main diagonal.
%
%        MU      INTEGER
%                number of diagonals above the main diagonal.
%
%        IPVT    INTEGER(N)
%                the pivot vector from SBGCO or SGBFA.
%
%     On Return
%
%        DET     REAL(2)
%                determinant of original matrix.
%                Determinant = DET(1) * 10.0**DET(2)
%                with  1.0 .LE. ABS(DET(1)) .LT. 10.0
%                or  DET(1) = 0.0 .
%
%***REFERENCES  J. J. Dongarra, J. R. Bunch, C. B. Moler, and G. W.
%                 Stewart, LINPACK Users' Guide, SIAM, 1979.
%***ROUTINES CALLED  (NONE)
%***REVISION HISTORY  (YYMMDD)
%   780814  DATE WRITTEN
%   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  SGBDI
persistent i m ten ;

ipvt_shape=size(ipvt);ipvt=reshape(ipvt,1,[]);
abd_shape=size(abd);abd=reshape([abd(:).',zeros(1,ceil(numel(abd)./prod([lda])).*prod([lda])-numel(abd))],lda,[]);
%
if isempty(ten), ten=0; end;
if isempty(i), i=0; end;
if isempty(m), m=0; end;
%***FIRST EXECUTABLE STATEMENT  SGBDI
m = fix(ml + mu + 1);
det(1) = 1.0e0;
det(2) = 0.0e0;
ten = 10.0e0;
for i = 1 : n;
if( ipvt(i)~=i )
det(1) = -det(1);
end;
det(1) = abd(m,i).*det(1);
if( det(1)==0.0e0 )
break;
end;
if( abs(det(1))>=1.0e0 )
if( abs(det(1))>=ten )
det(1) = det(1)./ten;
det(2) = det(2) + 1.0e0;
goto 60;
end;
else;
det(1) = ten.*det(1);
det(2) = det(2) - 1.0e0;
goto 50;
end;
end;
ipvt_shape=zeros(ipvt_shape);ipvt_shape(:)=ipvt(1:numel(ipvt_shape));ipvt=ipvt_shape;
abd_shape=zeros(abd_shape);abd_shape(:)=abd(1:numel(abd_shape));abd=abd_shape;
end
%DECK SGBFA
```