p?sygs2/p?hegs2

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 3/22/2024

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p?sygs2/p?hegs2

Reduces a symmetric/Hermitian positive-definite generalized eigenproblem to standard form, using the factorization results obtained from p?potrf (local unblocked algorithm).

Syntax

void pssygs2 (MKL_INT *ibtype , char *uplo , MKL_INT *n , float *a , MKL_INT *ia , MKL_INT *ja , MKL_INT *desca , float *b , MKL_INT *ib , MKL_INT *jb , MKL_INT *descb , MKL_INT *info );

void pdsygs2 (MKL_INT *ibtype , char *uplo , MKL_INT *n , double *a , MKL_INT *ia , MKL_INT *ja , MKL_INT *desca , double *b , MKL_INT *ib , MKL_INT *jb , MKL_INT *descb , MKL_INT *info );

void pchegs2 (MKL_INT *ibtype , char *uplo , MKL_INT *n , MKL_Complex8 *a , MKL_INT *ia , MKL_INT *ja , MKL_INT *desca , MKL_Complex8 *b , MKL_INT *ib , MKL_INT *jb , MKL_INT *descb , MKL_INT *info );

void pzhegs2 (MKL_INT *ibtype , char *uplo , MKL_INT *n , MKL_Complex16 *a , MKL_INT *ia , MKL_INT *ja , MKL_INT *desca , MKL_Complex16 *b , MKL_INT *ib , MKL_INT *jb , MKL_INT *descb , MKL_INT *info );

Include Files

mkl_scalapack.h

Description

The p?sygs2/p?hegs2function reduces a real symmetric-definite or a complex Hermitian positive-definite generalized eigenproblem to standard form.

Here 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^T)*sub(A)*inv(U) or inv(L)*sub(A)*inv(L^T) - for real flavors, and

inv(U^H)*sub(A)*inv(U) or inv(L)*sub(A)*inv(L^H) - for complex flavors.

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^T or L**T*sub(A)*L- for real flavors and

U*sub(A)*U^H or L**H*sub(A)*L- for complex flavors.

The matrix sub(B) must have been previously factorized as U^T*U or L*L^T (for real flavors), or as U^H*U or L*L^H (for complex flavors) by p?potrf.

Input Parameters

ibtype

(global)

= 1:

compute inv(U^T)*sub(A)*inv(U), or inv(L)*sub(A)*inv(L^T) for real functions,

and inv(U^H)*sub(A)*inv(U), or inv(L)*sub(A)*inv(L^H) for complex functions;

= 2 or 3:

compute U*sub(A)*U^T, or L^T*sub(A)*L for real functions,

and U*sub(A)*U^H or L^H*sub(A)*L for complex functions.

uplo

(global)

Specifies whether the upper or lower triangular part of the symmetric/Hermitian matrix sub(A) is stored, and how sub(B) is factorized.

= 'U': Upper triangular of sub(A) is stored and sub(B) is factorized as U^T*U (for real functions) or as U^H*U (for complex functions).

= 'L': Lower triangular of sub(A) is stored and sub(B) is factorized as L*L^T (for real functions) or as L*L^H (for complex functions)

n

(global)

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

a

(local)

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 symmetric/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 the strictly lower triangular part of sub(A) 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 the strictly upper triangular part of sub(A) is not referenced.

ia, ja

(global)

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

desca

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

B

(local)

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, jb

(global)

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

descb

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

Output Parameters

a

(local)

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

info

= 0: successful exit.

< 0: if the i-th argument is an array and the j-th entry, indexed j-1, 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: ScaLAPACK Auxiliary Routines

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Developer Reference for Intel® oneAPI Math Kernel Library for C

p?sygs2/p?hegs2

Syntax

Include Files

Description

Input Parameters

Output Parameters

See Also