Purpose
=======
LA_PBSV computes the solution to a linear system of equations
A*X = B, where A has band form and is real symmetric or complex
Hermitian and, in either case, positive definite, and where X and B are
rectangular matrices or vectors. The Cholesky decomposition is used to
factor A as A = U^H*U if UPLO = 'U', or A = L*L^H if UPLO = 'L'
where U is an upper triangular band matrix and L is a lower triangular
band matrix, each with the same number of superdiagonals or subdiagonals
as A. The factored form of A is then used to solve the above system.
=========
SUBROUTINE LA_PBSV( AB, B, UPLO=uplo, INFO=info )
(), INTENT(INOUT) :: AB(:,:),
CHARACTER(LEN=1), INTENT(IN), OPTIONAL :: UPLO
INTEGER, INTENT(OUT), OPTIONAL :: INFO
where
::= REAL | COMPLEX
::= KIND(1.0) | KIND(1.0D0)
::= B(:,:) | B(:)
Arguments
=========
AB (input/output) REAL or COMPLEX array, shape (:,:) with
size(AB,1) = kd + 1 and size(AB,2) = n, where kd is the number
of superdiagonals or subdiagonals in the band and n is the
order of A.
On entry, the upper (if UPLO = 'U') or lower (if UPLO = 'L')
triangle of matrix A in band storage. The (kd + 1) diagonals of
A are stored in the rows of AB so that the j-th column of A is
stored in the j-th column of AB as follows:
if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j
1<=j<=n
if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd)
1<=j<=n.
On exit, the factor U or L from the Cholesky factorization
A = U^H*U = L*L^H in the same storage format as A.
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 .
UPLO Optional (input) CHARACTER(LEN=1)
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
Default value: 'U'.
INFO Optional (output) INTEGER.
= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an illegal value.
> 0: if INFO = i, the leading minor of order i of A is not
positive definite, so the factorization could not be
completed and the solution could not be computed.
If INFO is not present and an error occurs, then the program
is terminated with an error message.