Computes the Cholesky factorization of a symmetric (Hermitian) positive-definite tridiagonal distributed matrix.
call pspttrf(n, d, e, ja, desca, af, laf, work, lwork, info)
call pdpttrf(n, d, e, ja, desca, af, laf, work, lwork, info)
call pcpttrf(n, d, e, ja, desca, af, laf, work, lwork, info)
call pzpttrf(n, d, e, ja, desca, af, laf, work, lwork, info)
The p?pttrf routine computes the Cholesky factorization of an n-by-n real symmetric or complex hermitian positive-definite tridiagonal distributed matrix A(1:n, ja:ja+n-1).
The resulting factorization is not the same factorization as returned from LAPACK. Additional permutations are performed on the matrix for the sake of parallelism.
The factorization has the form:
A(1:n, ja:ja+n-1) = P*L*D*LH*PT, or
A(1:n, ja:ja+n-1) = P*UH*D*U*PT,
where P is a permutation matrix, and U and L are tridiagonal upper and lower triangular matrices, respectively.
(global) INTEGER. The order of the distributed submatrix A(1:n, ja:ja+n-1)
(n ≥ 0).
(local)
REAL for pspttrf
DOUBLE PRECISON for pdpttrf
COMPLEX for pcpttrf
DOUBLE COMPLEX for pzpttrf.
Pointers into the local memory to arrays of dimension (desca(nb_)) each.
On entry, the array d contains the local part of the global vector storing the main diagonal of the distributed matrix A.
On entry, the array e contains the local part of the global vector storing the upper diagonal of the distributed matrix A.
(global) INTEGER. The index in the global array A that points to the start of the matrix to be operated on (which may be either all of A or a submatrix of A).
(global and local) INTEGER array, dimension (dlen_). The array descriptor for the distributed matrix A.
If desca(dtype_) = 501, then dlen_ ≥ 7;
else if desca(dtype_) = 1, then dlen_ ≥ 9.
(local) INTEGER. The dimension of the array af.
Must be laf ≥ NB+2.
If laf is not large enough, an error code will be returned and the minimum acceptable size will be returned in af(1).
(local) Same type as d and e. Workspace array of dimension lwork .
(local or global) INTEGER. The size of the work array, must be at least
lwork ≥ 8*NPCOL.
On exit, overwritten by the details of the factorization.
(local)
REAL for pspttrf
DOUBLE PRECISION for pdpttrf
COMPLEX for pcpttrf
DOUBLE COMPLEX for pzpttrf.
Array, dimension (laf).
Auxiliary Fillin space. Fillin is created during the factorization routine p?pttrf and this is stored in af.
Note that if a linear system is to be solved using p?pttrs after the factorization routine, af must not be altered.
On exit, work(1) contains the minimum value of lwork required for optimum performance.
(global) INTEGER.
If info=0, the execution is successful.
info < 0:
If the i-th argument is an array and the j-th entry had an illegal value, then info = -(i*100+j); if the i-th argument is a scalar and had an illegal value, then info = -i.
info > 0:
If info = k ≤ NPROCS, the submatrix stored on processor info and factored locally was not positive definite, and the factorization was not completed.
If info = k > NPROCS, the submatrix stored on processor info-NPROCS representing interactions with other processors was not nonsingular, and the factorization was not completed.