Purpose
=======
LA_GBSV computes the solution to a real or complex linear system
of equations A*X = B, where A is a square band matrix and X and B are
rectangular matrices or vectors. The LU decomposition with row
interchanges is used to factor A as A = L*U , where L is a product of
permutation and unit lower triangular matrices with kl subdiagonals,
and U is upper triangular with kl + ku superdiagonals. The factored
form of A is then used to solve the above system.
=========
SUBROUTINE LA_GBSV( AB, B, KL=kl, IPIV=ipiv, INFO=info )
(), INTENT(INOUT) :: AB(:,:),
INTEGER, INTENT(IN), OPTIONAL :: KL
INTEGER, INTENT(OUT), OPTIONAL :: IPIV(:)
INTEGER, INTENT(OUT), OPTIONAL :: INFO
where
::= REAL | COMPLEX
::= KIND(1.0) | KIND(1.0D0)
::= B(:,:) | B(:)
Arguments
=========
AB (input/output) REAL or COMPLEX rectangular array, shape (:,:)
with size(AB,1) = 2*kl+ku+1 and size(AB,2) = n, where kl and ku
are, respectively, the numbers of subdiagonals and
superdiagonals in the band of A, and n is the order of A.
On entry, the matrix A in band storage. The (kl + ku + 1)
diagonals of A are stored in rows (kl + 1) to (2*kl + ku + 1)
of AB, so that the j-th column of A is stored in the j-th
column of AB as follows:
AB(kl+ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(n,j+kl)
1<=j<=n
The remaining elements in AB need not be set.
On exit, details of the factorization. U is an upper triangular
band matrix with (kl + ku + 1) diagonals. These are stored in
the first (kl + ku + 1) rows of AB. The multipliers that arise
during the factorization are stored in the remaining rows.
B (input/output) REAL or COMPLEX array, shape (:,:) with
size(B,1) = n or shape (:) with size(B) = n.
On entry, the matrix B.
On exit, the solution matrix X.
KL Optional (input) INTEGER.
The number of subdiagonals in the band of A (KL = kl).
The number of superdiagonals in the band is given by
ku = size(AB,1) - 2 * kl - 1.
Default value: (size(AB,1)-1)/3.
IPIV Optional (output) INTEGER array, shape (:) with size(IPIV) = n.
The pivot indices that define the row interchanges; row i of the
matrix was interchanged with row IPIV(i).
INFO Optional (output) INTEGER
= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an illegal value.
> 0: if INFO = i, U(i,i) = 0. The factorization has been
completed, but the factor U is singular, so the solution could
not be computed.
If INFO is not present and an error occurs, then the program
is terminated with an error message.