Visible to Intel only — GUID: GUID-3DE29C39-2BA9-4FB8-BBFF-423281AD553D
Visible to Intel only — GUID: GUID-3DE29C39-2BA9-4FB8-BBFF-423281AD553D
?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(UH)*A*inv(U) or inv(L)*A*inv(LH) for complex flavors and by inv(UT)*A*inv(U) or inv(L)*A*inv(LT)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*UH or LH*A*L for complex flavors and by U*A*UT or LT*A*L for real flavors. Here UT and LT are the transpose while UH and LH are conjugate transpose of U and L.
B must be previously factorized by ?potrf as follows:
UH*U or L*LH for complex flavors
UT*U or L*LT for real flavors
Input Parameters
- itype
-
INTEGER.
For complex flavors:
= 1: compute inv(UH)*A*inv(U) or inv(L)*A*inv(LH);
= 2 or 3: compute U*A*UH orLH*A*L.
For real flavors:
= 1: compute inv(UT)*A*inv(U) or inv(L)*A*inv(LT);
= 2 or 3: compute U*A*UT orLT*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.