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hegs2(3) Library Functions Manual hegs2(3)

NAME

hegs2 - {he,sy}gs2: reduction to standard form, level 2

SYNOPSIS

Functions


subroutine CHEGS2 (itype, uplo, n, a, lda, b, ldb, info)
CHEGS2 reduces a Hermitian definite generalized eigenproblem to standard form, using the factorization results obtained from cpotrf (unblocked algorithm). subroutine DSYGS2 (itype, uplo, n, a, lda, b, ldb, info)
DSYGS2 reduces a symmetric definite generalized eigenproblem to standard form, using the factorization results obtained from spotrf (unblocked algorithm). subroutine SSYGS2 (itype, uplo, n, a, lda, b, ldb, info)
SSYGS2 reduces a symmetric definite generalized eigenproblem to standard form, using the factorization results obtained from spotrf (unblocked algorithm). subroutine ZHEGS2 (itype, uplo, n, a, lda, b, ldb, info)
ZHEGS2 reduces a Hermitian definite generalized eigenproblem to standard form, using the factorization results obtained from cpotrf (unblocked algorithm).

Detailed Description

Function Documentation

subroutine CHEGS2 (integer itype, character uplo, integer n, complex, dimension( lda, * ) a, integer lda, complex, dimension( ldb, * ) b, integer ldb, integer info)

CHEGS2 reduces a Hermitian definite generalized eigenproblem to standard form, using the factorization results obtained from cpotrf (unblocked algorithm).

Purpose:

!>
!> CHEGS2 reduces a complex Hermitian-definite generalized
!> eigenproblem to standard form.
!>
!> If ITYPE = 1, the problem is A*x = lambda*B*x,
!> and A is overwritten by inv(U**H)*A*inv(U) or inv(L)*A*inv(L**H)
!>
!> If ITYPE = 2 or 3, the problem is A*B*x = lambda*x or
!> B*A*x = lambda*x, and A is overwritten by U*A*U**H or L**H *A*L.
!>
!> B must have been previously factorized as U**H *U or L*L**H by ZPOTRF.
!>

Parameters

ITYPE 

!>          ITYPE is INTEGER
!>          = 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.
!>

UPLO

!>          UPLO is CHARACTER*1
!>          Specifies whether the upper or lower triangular part of the
!>          Hermitian matrix A is stored, and how B has been factorized.
!>          = 'U':  Upper triangular
!>          = 'L':  Lower triangular
!>

N

!>          N is INTEGER
!>          The order of the matrices A and B.  N >= 0.
!>

A

!>          A is COMPLEX array, dimension (LDA,N)
!>          On entry, the 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.
!>
!>          On exit, if INFO = 0, the transformed matrix, stored in the
!>          same format as A.
!>

LDA

!>          LDA is INTEGER
!>          The leading dimension of the array A.  LDA >= max(1,N).
!>

B

!>          B is COMPLEX array, dimension (LDB,N)
!>          The triangular factor from the Cholesky factorization of B,
!>          as returned by CPOTRF.
!>          B is modified by the routine but restored on exit.
!>

LDB

!>          LDB is INTEGER
!>          The leading dimension of the array B.  LDB >= max(1,N).
!>

INFO

!>          INFO is INTEGER
!>          = 0:  successful exit.
!>          < 0:  if INFO = -i, the i-th argument had an illegal value.
!>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 127 of file chegs2.f.

subroutine DSYGS2 (integer itype, character uplo, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( ldb, * ) b, integer ldb, integer info)

DSYGS2 reduces a symmetric definite generalized eigenproblem to standard form, using the factorization results obtained from spotrf (unblocked algorithm).

Purpose:

!>
!> DSYGS2 reduces a real symmetric-definite generalized eigenproblem
!> to standard form.
!>
!> If ITYPE = 1, the problem is A*x = lambda*B*x,
!> and A is overwritten by inv(U**T)*A*inv(U) or inv(L)*A*inv(L**T)
!>
!> If ITYPE = 2 or 3, the problem is A*B*x = lambda*x or
!> B*A*x = lambda*x, and A is overwritten by U*A*U**T or L**T *A*L.
!>
!> B must have been previously factorized as U**T *U or L*L**T by DPOTRF.
!>

Parameters

ITYPE 

!>          ITYPE is INTEGER
!>          = 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

!>          UPLO is CHARACTER*1
!>          Specifies whether the upper or lower triangular part of the
!>          symmetric matrix A is stored, and how B has been factorized.
!>          = 'U':  Upper triangular
!>          = 'L':  Lower triangular
!>

N

!>          N is INTEGER
!>          The order of the matrices A and B.  N >= 0.
!>

A

!>          A is DOUBLE PRECISION array, dimension (LDA,N)
!>          On entry, the symmetric 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.
!>
!>          On exit, if INFO = 0, the transformed matrix, stored in the
!>          same format as A.
!>

LDA

!>          LDA is INTEGER
!>          The leading dimension of the array A.  LDA >= max(1,N).
!>

B

!>          B is DOUBLE PRECISION array, dimension (LDB,N)
!>          The triangular factor from the Cholesky factorization of B,
!>          as returned by DPOTRF.
!>

LDB

!>          LDB is INTEGER
!>          The leading dimension of the array B.  LDB >= max(1,N).
!>

INFO

!>          INFO is INTEGER
!>          = 0:  successful exit.
!>          < 0:  if INFO = -i, the i-th argument had an illegal value.
!>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 126 of file dsygs2.f.

subroutine SSYGS2 (integer itype, character uplo, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( ldb, * ) b, integer ldb, integer info)

SSYGS2 reduces a symmetric definite generalized eigenproblem to standard form, using the factorization results obtained from spotrf (unblocked algorithm).

Purpose:

!>
!> SSYGS2 reduces a real symmetric-definite generalized eigenproblem
!> to standard form.
!>
!> If ITYPE = 1, the problem is A*x = lambda*B*x,
!> and A is overwritten by inv(U**T)*A*inv(U) or inv(L)*A*inv(L**T)
!>
!> If ITYPE = 2 or 3, the problem is A*B*x = lambda*x or
!> B*A*x = lambda*x, and A is overwritten by U*A*U**T or L**T *A*L.
!>
!> B must have been previously factorized as U**T *U or L*L**T by SPOTRF.
!>

Parameters

ITYPE 

!>          ITYPE is INTEGER
!>          = 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

!>          UPLO is CHARACTER*1
!>          Specifies whether the upper or lower triangular part of the
!>          symmetric matrix A is stored, and how B has been factorized.
!>          = 'U':  Upper triangular
!>          = 'L':  Lower triangular
!>

N

!>          N is INTEGER
!>          The order of the matrices A and B.  N >= 0.
!>

A

!>          A is REAL array, dimension (LDA,N)
!>          On entry, the symmetric 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.
!>
!>          On exit, if INFO = 0, the transformed matrix, stored in the
!>          same format as A.
!>

LDA

!>          LDA is INTEGER
!>          The leading dimension of the array A.  LDA >= max(1,N).
!>

B

!>          B is REAL array, dimension (LDB,N)
!>          The triangular factor from the Cholesky factorization of B,
!>          as returned by SPOTRF.
!>

LDB

!>          LDB is INTEGER
!>          The leading dimension of the array B.  LDB >= max(1,N).
!>

INFO

!>          INFO is INTEGER
!>          = 0:  successful exit.
!>          < 0:  if INFO = -i, the i-th argument had an illegal value.
!>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 126 of file ssygs2.f.

subroutine ZHEGS2 (integer itype, character uplo, integer n, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( ldb, * ) b, integer ldb, integer info)

ZHEGS2 reduces a Hermitian definite generalized eigenproblem to standard form, using the factorization results obtained from cpotrf (unblocked algorithm).

Purpose:

!>
!> ZHEGS2 reduces a complex Hermitian-definite generalized
!> eigenproblem to standard form.
!>
!> If ITYPE = 1, the problem is A*x = lambda*B*x,
!> and A is overwritten by inv(U**H)*A*inv(U) or inv(L)*A*inv(L**H)
!>
!> If ITYPE = 2 or 3, the problem is A*B*x = lambda*x or
!> B*A*x = lambda*x, and A is overwritten by U*A*U**H or L**H *A*L.
!>
!> B must have been previously factorized as U**H *U or L*L**H by ZPOTRF.
!>

Parameters

ITYPE 

!>          ITYPE is INTEGER
!>          = 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.
!>

UPLO

!>          UPLO is CHARACTER*1
!>          Specifies whether the upper or lower triangular part of the
!>          Hermitian matrix A is stored, and how B has been factorized.
!>          = 'U':  Upper triangular
!>          = 'L':  Lower triangular
!>

N

!>          N is INTEGER
!>          The order of the matrices A and B.  N >= 0.
!>

A

!>          A is COMPLEX*16 array, dimension (LDA,N)
!>          On entry, the 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.
!>
!>          On exit, if INFO = 0, the transformed matrix, stored in the
!>          same format as A.
!>

LDA

!>          LDA is INTEGER
!>          The leading dimension of the array A.  LDA >= max(1,N).
!>

B

!>          B is COMPLEX*16 array, dimension (LDB,N)
!>          The triangular factor from the Cholesky factorization of B,
!>          as returned by ZPOTRF.
!>          B is modified by the routine but restored on exit.
!>

LDB

!>          LDB is INTEGER
!>          The leading dimension of the array B.  LDB >= max(1,N).
!>

INFO

!>          INFO is INTEGER
!>          = 0:  successful exit.
!>          < 0:  if INFO = -i, the i-th argument had an illegal value.
!>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 127 of file zhegs2.f.

Author

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