p?dttrf

Computes the LU factorization of a diagonally dominant-like tridiagonal distributed matrix.

Syntax

call psdttrf(n, dl, d, du, ja, desca, af, laf, work, lwork, info)

call pddttrf(n, dl, d, du, ja, desca, af, laf, work, lwork, info)

call pcdttrf(n, dl, d, du, ja, desca, af, laf, work, lwork, info)

call pzdttrf(n, dl, d, du, ja, desca, af, laf, work, lwork, info)

Include Files

Description

The p?dttrf routine computes the LU factorization of an n-by-n real/complex diagonally dominant-like tridiagonal distributed matrix A(1:n, ja:ja+n-1) without pivoting for stability.

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*U*PT,

where P is a permutation matrix, and L and U are banded lower and upper triangular matrices, respectively.

Optimization Notice

Intel's compilers may or may not optimize to the same degree for non-Intel microprocessors for optimizations that are not unique to Intel microprocessors. These optimizations include SSE2, SSE3, and SSSE3 instruction sets and other optimizations. Intel does not guarantee the availability, functionality, or effectiveness of any optimization on microprocessors not manufactured by Intel. Microprocessor-dependent optimizations in this product are intended for use with Intel microprocessors. Certain optimizations not specific to Intel microarchitecture are reserved for Intel microprocessors. Please refer to the applicable product User and Reference Guides for more information regarding the specific instruction sets covered by this notice.

Notice revision #20110804

Input Parameters

n

(global) INTEGER. The number of rows and columns to be operated on, that is, the order of the distributed submatrix A(1:n, ja:ja+n-1) (n 0).

dl, d, du

(local)

REAL for pspttrf

DOUBLE PRECISON for pdpttrf

COMPLEX for pcpttrf

DOUBLE COMPLEX for pzpttrf.

Pointers to the local arrays of size nb_a each.

On entry, the array dl contains the local part of the global vector storing the subdiagonal elements of the matrix. Globally, dl(1) is not referenced, and dl must be aligned with d.

On entry, the array d contains the local part of the global vector storing the diagonal elements of the matrix.

On entry, the array du contains the local part of the global vector storing the super-diagonal elements of the matrix. du(n) is not referenced, and du must be aligned with d.

ja

(global) INTEGER. The index in the global matrix A indicating the start of the matrix to be operated on (which may be either all of A or a submatrix of A).

desca

(global and local) INTEGER array of size dlen_. The array descriptor for the distributed matrix A.

If dtype_a = 501, then dlen_ 7;

else if dtype_a = 1, then dlen_ 9.

laf

(local) INTEGER. The size of the array af.

Must be laf 2*(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).

work

(local) Same type as d. Workspace array of size lwork.

lwork

(local or global) INTEGER. The size of the work array, must be at least lwork 8*NPCOL.

Output Parameters

dl, d, du

On exit, overwritten by the information containing the factors of the matrix.

af

(local)

REAL for psdttrf

DOUBLE PRECISION for pddttrf

COMPLEX for pcdttrf

DOUBLE COMPLEX for pzdttrf.

Array of size laf.

Auxiliary fill-in space. The fill-in space is created in a call to the factorization routine p?dttrf and is stored in af.

Note that if a linear system is to be solved using p?dttrs after the factorization routine,af must not be altered.

work(1)

On exit, work(1) contains the minimum value of lwork required for optimum performance.

info

(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 = kNPROCS, the submatrix stored on processor info and factored locally was not diagonally dominant-like, 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.

See Also

For more complete information about compiler optimizations, see our Optimization Notice.