Man page - hegst(3)

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Manual

hegst

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
subroutine chegst (integer itype, character uplo, integer n, complex,dimension( lda, * ) a, integer lda, complex, dimension( ldb, * ) b,integer ldb, integer info)
subroutine dsygst (integer itype, character uplo, integer n, doubleprecision, dimension( lda, * ) a, integer lda, double precision,dimension( ldb, * ) b, integer ldb, integer info)
subroutine ssygst (integer itype, character uplo, integer n, real,dimension( lda, * ) a, integer lda, real, dimension( ldb, * ) b,integer ldb, integer info)
subroutine zhegst (integer itype, character uplo, integer n, complex*16,dimension( lda, * ) a, integer lda, complex*16, dimension( ldb, * ) b,integer ldb, integer info)
Author

NAME

hegst - {he,sy}gst: reduction to standard form

SYNOPSIS

Functions

subroutine chegst (itype, uplo, n, a, lda, b, ldb, info)
CHEGST
subroutine dsygst (itype, uplo, n, a, lda, b, ldb, info)
DSYGST
subroutine ssygst (itype, uplo, n, a, lda, b, ldb, info)
SSYGST
subroutine zhegst (itype, uplo, n, a, lda, b, ldb, info)
ZHEGST

Detailed Description

Function Documentation

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

CHEGST

Purpose:

CHEGST 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 CPOTRF.

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
= ā€™Uā€™: Upper triangle of A is stored and B is factored as
U**H*U;
= ā€™Lā€™: Lower triangle of A is stored and B is factored as
L*L**H.

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

DSYGST

Purpose:

DSYGST 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
= ā€™Uā€™: Upper triangle of A is stored and B is factored as
U**T*U;
= ā€™Lā€™: Lower triangle of A is stored and B is factored as
L*L**T.

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

SSYGST

Purpose:

SSYGST 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
= ā€™Uā€™: Upper triangle of A is stored and B is factored as
U**T*U;
= ā€™Lā€™: Lower triangle of A is stored and B is factored as
L*L**T.

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

ZHEGST

Purpose:

ZHEGST 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
= ā€™Uā€™: Upper triangle of A is stored and B is factored as
U**H*U;
= ā€™Lā€™: Lower triangle of A is stored and B is factored as
L*L**H.

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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