p?hegst

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?hegst

Reduces a Hermitian positive-definite generalized eigenvalue problem to the standard form.

Syntax

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

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

Include Files

Description

The p?hegst routine reduces complex Hermitian positive-definite generalized eigenproblems to the standard form.

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 = λ*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 = λ*x, or sub(B)*sub(A)*x = λ*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. Must be 1 or 2 or 3.

If itype = 1, compute inv(U^H)*sub(A)*inv(U), or inv(L)*sub(A)*inv(L^H);

If itype = 2 or 3, compute U*sub(A)*U^H, or L^H*sub(A)*L.

uplo

(global) CHARACTER. Must be 'U' or 'L'.

If uplo = 'U', the upper triangle of sub(A) is stored and sub (B) is factored as U^H*U.

If uplo = 'L', the 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 pchegst

DOUBLE COMPLEX for pzhegst.

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

(global) INTEGER. The row and column indices in the global matrix A indicating the first row and the first column of the submatrix A, respectively.

desca

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

b

(local)

COMPLEX for pchegst

DOUBLE COMPLEX for pzhegst.

Pointer into the local memory to an array of size (lld_b,LOCc(jb+n-1)). On entry, the array contains the local pieces of the triangular factor from the Cholesky factorization of sub (B) as returned by p?potrf.

ib, jb

(global) INTEGER. The row and column indices in the global matrix B indicating the first row and the first column of the submatrix B, respectively.

descb

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

Output Parameters

a

On exit, if info = 0, the transformed matrix, stored in the same format as sub(A).

scale

(global)

REAL for pchegst

DOUBLE PRECISION for pzhegst.

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.

info

(global) INTEGER.

If info = 0, the execution is successful. If 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.

Parent topic: Generalized Symmetric-Definite Eigenvalue Problems: ScaLAPACK Computational Routines

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p?hegst

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