p?syngst

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 3/31/2023

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p?syngst

Reduces a complex Hermitian-definite generalized eigenproblem to standard form.

Syntax

call pssyngst (ibtype, uplo, n, a, ia, ja, desca, b, ib, jb, descb, scale, work, lwork, info )

call pdsyngst (ibtype, uplo, n, a, ia, ja, desca, b, ib, jb, descb, scale, work, lwork, info )

Description

p?syngst reduces a complex Hermitian-definite generalized eigenproblem to standard form.

p?syngst performs the same function as p?hegst, but is based on rank 2K updates, which are faster and more scalable than triangular solves (the basis of p?syngst).

p?syngst calls p?hegst when uplo='U', hence p?hengst provides improved performance only when uplo='L', ibtype=1.

p?syngst also calls p?hegst when insufficient workspace is provided, hence p?syngst provides improved performance only when lwork >= 2 * NP0 * NB + NQ0 * NB + NB * NB

In the following sub( A ) denotes A( ia:ia+n-1, ja:ja+n-1 ) and sub( B ) denotes B( ib:ib+n-1, jb:jb+n-1 ).

If ibtype = 1, the problem is sub( A )*x = lambda*sub( B )*x, and sub( A ) is overwritten by inv(U^H)*sub( A )*inv(U) or inv(L)*sub( A )*inv(L^H)

If ibtype = 2 or 3, the problem is sub( A )*sub( B )*x = lambda*x or sub( B )*sub( A )*x = lambda*x, and sub( A ) is overwritten by U*sub( A )*U^H or L^H*sub( A )*L.

sub( B ) must have been previously factorized as U^H*U or L*L^H by p?potrf.

Input Parameters

ibtype

(global)

INTEGER.

= 1: compute inv(U^H)*sub( A )*inv(U) or inv(L)*sub( A )*inv(L^H);

= 2 or 3: compute U*sub( A )*U^H or L^H*sub( A )*L.

uplo

(global)

CHARACTER.

= 'U': Upper triangle of sub( A ) is stored and sub( B ) is factored as U^H*U;

= 'L': Lower triangle of sub( A ) is stored and sub( B ) is factored as L*L^H.

n

(global)

INTEGER.

The order of the matrices sub( A ) and sub( B ). n >= 0.

a

(local)

REAL for pssyngst

DOUBLE PRECISION for pdsyngst

Pointer into the local memory to an array of size (lld_a,LOCc(ja+n-1)).

On entry, this array contains the local pieces of the n-by-n Hermitian distributed matrix sub( A ). If uplo = 'U', the leading n-by-n upper triangular part of sub( A ) contains the upper triangular part of the matrix, and its strictly lower triangular part is not referenced. If uplo = 'L', the leading n-by-n lower triangular part of sub( A ) contains the lower triangular part of the matrix, and its strictly upper triangular part is not referenced.

ia

(global)

INTEGER.

A's global row index, which points to the beginning of the submatrix which is to be operated on.

ja

(global)

INTEGER.

A's global column index, which points to the beginning of the submatrix which is to be operated on.

desca

(global and local)

INTEGER.

Array of size dlen_.

The array descriptor for the distributed matrix A.

b

(local)

REAL for pssyngst

DOUBLE PRECISION for pdsyngst

Pointer into the local memory to an array of size (lld_b,LOCc(jb+n-1)).

On entry, this array contains the local pieces of the triangular factor from the Cholesky factorization of sub( B ), as returned by p?potrf.

ib

(global)

INTEGER.

B's global row index, which points to the beginning of the submatrix which is to be operated on.

jb

(global)

INTEGER.

B's global column index, which points to the beginning of the submatrix which is to be operated on.

descb

(global and local)

INTEGER.

Array of size dlen_.

The array descriptor for the distributed matrix B.

work

(local)

REAL for pssyngst

DOUBLE PRECISION for pdsyngst

Array, size (lwork)

lwork

(local or global)

INTEGER.

The size of the array work.

lwork is local input and must be at least lwork >= MAX( NB * ( NP0 +1 ), 3 * NB )

When ibtype = 1 and uplo = 'L', p?syngst provides improved performance when lwork >= 2 * NP0 * NB + NQ0 * NB + NB * NB,

where NB = mb_a = nb_a,

NP0 = numroc( n, NB, 0, 0, NPROW ),

NQ0 = numroc( n, NB, 0, 0, NPROW ),

numroc is a ScaLAPACK tool functions

MYROW, MYCOL, NPROW and NPCOL can be determined by calling the subroutine blacs_gridinfo.

If lwork = -1, then lwork is global input and a workspace query is assumed; the routine only calculates the optimal size for all work arrays. Each of these values is returned in the first entry of the corresponding work array, and no error message is issued by pxerbla.

Output Parameters

a	On exit, if info = 0, the transformed matrix, stored in the same format as sub( `A` ).
scale	(global) REAL for pssyngst DOUBLE PRECISION for pdsyngst Amount by which the eigenvalues should be scaled to compensate for the scaling performed in this routine. At present, scale is always returned as 1.0, it is returned here to allow for future enhancement.
work	(local) REAL for pssyngst DOUBLE PRECISION for pdsyngst Array, size (lwork) On exit, work`(1)` returns the minimal and optimal lwork.
info	(global) INTEGER. = 0: successful exit < 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`.

Parent topic: Symmetric Eigenvalue Problems: ScaLAPACK Computational Routines

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

p?syngst