home
***
CD-ROM
|
disk
|
FTP
|
other
***
search
/
Cream of the Crop 26
/
Cream of the Crop 26.iso
/
os2
/
octa209s.zip
/
octave-2.09
/
libcruft
/
balgen
/
balgen.f
next >
Wrap
Text File
|
1996-07-19
|
3KB
|
103 lines
subroutine balgen (n,ma,a,mb,b,low,igh,cscale,cperm,wk)
c
c *****parameters:
integer igh,low,ma,mb,n
double precision a(ma,n),b(mb,n),cperm(n),cscale(n),wk(n,6)
c
c *****local variables:
c none
c
c *****functions:
c none
c
c *****subroutines called:
c reduce, scaleg, gradeq
c
c ---------------------------------------------------------------
c
c *****purpose:
c this subroutine balances the matrices a and b to improve the
c accuracy of computing the eigensystem of the generalized
c eigenproblem a*x = (lambda)*b*x. the algorithm is specifically
c designed to precede qz type algorithms, but improved performance
c is expected from most eigensystem solvers.
c ref.: ward, r. c., balancing the generalized eigenvalue
c problem, siam j. sci. stat. comput., vol. 2, no. 2, june 1981,
c 141-152.
c
c *****parameter description:
c
c on input:
c
c ma,mb integer
c row dimensions of the arrays containing matrices
c a and b respectively, as declared in the main calling
c program dimension statement;
c
c n integer
c order of the matrices a and b;
c
c a real(ma,n)
c contains the a matrix of the generalized eigenproblem
c defined above;
c
c b real(mb,n)
c contains the b matrix of the generalized eigenproblem
c defined above;
c
c wk real(n,6)
c work array that must contain at least 6*n storage
c locations. wk is altered by this subroutine.
c
c on output:
c
c a,b contain the balanced a and b matrices;
c
c low integer
c beginning -1 of the submatrices of a and b
c containing the non-isolated eigenvalues;
c
c igh integer
c ending -1 of the submatrices of a and b
c containing the non-isolated eigenvalues. if
c igh = 1 (low = 1 also), the a and b matrices have
c been permuted into upper triangular form and have
c not been balanced;
c
c cscale real(n)
c contains the exponents of the column scaling factors
c in its low through igh locations and the reducing
c column permutations in its first low-1 and its
c igh+1 through n locations;
c
c cperm real(n)
c contains the column permutations applied in grading
c the a and b submatrices in its low through igh
c locations;
c
c wk contains the exponents of the row scaling factors
c in its low through igh locations, the reducing row
c permutations in its first low-1 and its igh+1
c through n locations, and the row permutations
c applied in grading the a and b submatrices in its
c n+low through n+igh locations.
c
c *****algorithm notes:
c none
c
c *****history:
c written by r. c. ward.......
c
c ---------------------------------------------------------------
c
call reduce (n,ma,a,mb,b,low,igh,cscale,wk)
if (low .eq. igh) go to 10
call scaleg (n,ma,a,mb,b,low,igh,cscale,cperm,wk)
call gradeq (n,ma,a,mb,b,low,igh,cperm,wk(1,2))
10 continue
return
c
c last line of balgen
c
end