hegst(3)

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
    !>          = 'U':  Upper triangle of A is stored and B is factored as
    !>                  U**H*U;
    !>          = 'L':  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 = '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.

  subroutine dsygst (integer itype, character uplo, integer n, double precision, 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
    !>          = 'U':  Upper triangle of A is stored and B is factored as
    !>                  U**T*U;
    !>          = 'L':  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 = '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.

  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
    !>          = 'U':  Upper triangle of A is stored and B is factored as
    !>                  U**T*U;
    !>          = 'L':  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 = '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.

  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
    !>          = 'U':  Upper triangle of A is stored and B is factored as
    !>                  U**H*U;
    !>          = 'L':  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 = '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.

Author

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