_BANDR(3F)_BANDR(3F)NAME
BANDR, SBANDR - EISPACK routine. This subroutine reduces a REAL
SYMMETRIC BAND matrix to a symmetric tridiagonal matrix using and
optionally accumulating orthogonal similarity transformations.
SYNOPSYS
subroutine bandr(nm, n, mb, a, d, e, e2, matz, z)
integer nm, n, mb, z
double precision a(nm,mb), d(n), e(n), e2(n), z(nm,n)
logical matz
subroutine sbandr(nm, n, mb, a, d, e, e2, matz, z)
integer nm, n, mb, z
real a(nm,mb), d(n), e(n), e2(n), z(nm,n)
logical matz
DESCRIPTION
On INPUT
NM must be set to the row dimension of two-dimensional array parameters
as declared in the calling program dimension statement.
N is the order of the matrix.
MB is the (half) band width of the matrix, defined as the number of
adjacent diagonals, including the principal diagonal, required to specify
the non-zero portion of the lower triangle of the matrix.
A contains the lower triangle of the symmetric band input matrix stored
as an N by MB array. Its lowest subdiagonal is stored in the last N+1-MB
positions of the first column, its next subdiagonal in the last N+2-MB
positions of the second column, further subdiagonals similarly, and
finally its principal diagonal in the N positions of the last column.
Contents of storages not part of the matrix are arbitrary.
MATZ should be set to .TRUE. if the transformation matrix is to be
accumulated, and to .FALSE. otherwise. On OUTPUT
A has been destroyed, except for its last two columns which contain a
copy of the tridiagonal matrix.
D contains the diagonal elements of the tridiagonal matrix.
E contains the subdiagonal elements of the tridiagonal matrix in its last
N-1 positions. E(1) is set to zero.
E2 contains the squares of the corresponding elements of E. E2 may
coincide with E if the squares are not needed.
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Z contains the orthogonal transformation matrix produced in the reduction
if MATZ has been set to .TRUE. Otherwise, Z is not referenced.
Questions and comments should be directed to B. S. Garbow, Applied
Mathematics Division, ARGONNE NATIONAL LABORATORY
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