?sygs2/?hegs2

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 4/28/2026

Version

Public

?sygs2/?hegs2

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

Syntax

call ssygs2 ( itype , uplo , n , a , lda , b , ldb , info )

call dsygs2 ( itype , uplo , n , a , lda , b , ldb , info )

call chegs2 ( itype , uplo , n , a , lda , b , ldb , info )

call zhegs2 ( itype , uplo , n , a , lda , b , ldb , info )

Include Files

mkl.fi

Description

The routine ?sygs2 / ?hegs2 reduces a real symmetric-definite or a complex Hermitian positive-definite generalized eigenproblem to standard form.

If itype = 1 , the problem is

A * x = λ* B * x

and A is overwritten by inv(U^{H})*A*inv(U) or inv(L)*A*inv(L^{H}) for complex flavors and by inv(U^{T})*A*inv(U) or inv(L)*A*inv(L^{T}) for real flavors.

If itype = 2 or 3 , the problem is

A*B*x = λ*x , or B*A*x = λ*x ,

and A is overwritten by U*A*U^{H} or L^{H}*A*L for complex flavors and by U*A*U^{T} or L^{T}*A*L for real flavors. Here U^{T} and L^{T} are the transpose while U^{H} and L^{H} are conjugate transpose of U and L .

B must be previously factorized by ?potrf as follows:

U^{H}*U or L*L^{H} for complex flavors U^{T}*U or L*L^{T} for real flavors

Input Parameters

itype: INTEGER . For complex flavors: = 1: compute inv(U^{H})*A*inv(U) or inv(L)*A*inv(L^{H}) ; = 2 or 3: compute U*A*U^{H} or L^{H}*A*L . For real flavors: = 1: compute inv(U^{T})*A*inv(U) or inv(L)*A*inv(L^{T}) ; = 2 or 3: compute U*A*U^{T} or L^{T}*A*L .
uplo: CHARACTER*1 . Specifies whether the upper or lower triangular part of the symmetric/Hermitian matrix A is stored, and how B has been factorized. = ‘U’ : upper triangular = ‘L’ : lower triangular
n: INTEGER . The order of the matrices A and B . n≥ 0 .
a: REAL for ssygs2 DOUBLE PRECISION for dsygs2 COMPLEX for chegs2 DOUBLE COMPLEX for zhegs2 . Array, DIMENSION ( lda , n ). On entry, the symmetric/Hermitian matrix A . If uplo = 'U' , the leading n -by- n upper triangular part of a contains the upper triangular part of the matrix A , and the strictly lower triangular part of a is not referenced. If uplo = 'L' , the leading n -by- n lower triangular part of a contains the lower triangular part of the matrix A , and the strictly upper triangular part of a is not referenced.
lda: INTEGER . The leading dimension of the array a . lda≥ max(1,n) .
b: REAL for ssygs2 DOUBLE PRECISION for dsygs2 COMPLEX for chegs2 DOUBLE COMPLEX for zhegs2 . Array, DIMENSION ( ldb , n ). The triangular factor from the Cholesky factorization of B as returned by ?potrf .
ldb: INTEGER . The leading dimension of the array b . ldb≥ max(1,n) .

Output Parameters

a: On exit, If info = 0 , the transformed matrix, stored in the same format as A .

info

INTEGER .

= 0: successful exit.
< 0: if info = -i , the i -th argument had an illegal value.

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?sygs2/?hegs2

Syntax

Include Files

Description

Input Parameters

Output Parameters