p?hengst

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 11/07/2023

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p?hengst

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

Syntax

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

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

Description

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

p?hengst 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?hengst).

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

p?hengst also calls p?hegst when insufficient workspace is provided, hence p?hengst provides improved performance only when lwork is sufficient (as described in the parameter descriptions).

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

COMPLEX for pchengst

DOUBLE COMPLEX for pzhengst

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.

Global row index of matrix A, which points to the beginning of the submatrix on which to operate.

ja

(global)

INTEGER.

Global column index of matrix A, which points to the beginning of the submatrix on which to operate.

desca

(global and local)

INTEGER.

Array of size dlen_.

The array descriptor for the distributed matrix A.

b

(local)

COMPLEX for pchengst

DOUBLE COMPLEX for pzhengst

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

ib

(global)

INTEGER.

Global row index of matrix B, which points to the beginning of the submatrix on which to operate.

jb

(global)

INTEGER.

Global column index of matrix B, which points to the beginning of the submatrix on which to operate.

descb

(global and local)

INTEGER.

Array of size dlen_.

The array descriptor for the distributed matrix B.

work

(local)

COMPLEX for pchengst

DOUBLE COMPLEX for pzhengst

Array, size (lwork)

On exit, work( 1 ) returns the minimal and optimal lwork.

lwork

(local)

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?hengst 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 ), and numroc is a ScaLAPACK tool function.

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 pchengst DOUBLE PRECISION for pzhengst Amount by which the eigenvalues should be scaled to compensate for the scaling performed in this routine. scale is always returned as 1.0.
work	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`-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?hengst

Syntax

Description

Input Parameters

Output Parameters