Man page - hegs2(3)

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Manual

hegs2

NAME
SYNOPSIS
Functions
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)
subroutine dsygs2 (integer itype, character uplo, integer n, doubleprecision, dimension( lda, * ) a, integer lda, double precision,dimension( ldb, * ) b, integer ldb, integer info)
subroutine ssygs2 (integer itype, character uplo, integer n, real,dimension( lda, * ) a, integer lda, real, dimension( ldb, * ) b,integer ldb, integer info)
subroutine zhegs2 (integer itype, character uplo, integer n, complex*16,dimension( lda, * ) a, integer lda, complex*16, dimension( ldb, * ) b,integer ldb, integer info)
Author

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.
= ā€™Uā€™: Upper triangular
= ā€™Lā€™: 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 = ā€™Uā€™, 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 = ā€™Lā€™, 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.

subroutine dsygs2 (integer itype, character uplo, integer n, doubleprecision, 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.
= ā€™Uā€™: Upper triangular
= ā€™Lā€™: 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 = ā€™Uā€™, 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 = ā€™Lā€™, 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.

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.
= ā€™Uā€™: Upper triangular
= ā€™Lā€™: 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 = ā€™Uā€™, 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 = ā€™Lā€™, 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.

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.
= ā€™Uā€™: Upper triangular
= ā€™Lā€™: 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 = ā€™Uā€™, 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 = ā€™Lā€™, 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.

Author

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