lahef_aa(3)

NAME
lahef_aa - la{he,sy}f_aa: triangular factor partial factor

SYNOPSIS

  Functions

subroutine clahef_aa (uplo, j1, m, nb, a, lda, ipiv, h, ldh, work)
CLAHEF_AA
subroutine clasyf_aa (uplo, j1, m, nb, a, lda, ipiv, h, ldh, work)
CLASYF_AA
subroutine dlasyf_aa (uplo, j1, m, nb, a, lda, ipiv, h, ldh, work)
DLASYF_AA
subroutine slasyf_aa (uplo, j1, m, nb, a, lda, ipiv, h, ldh, work)
SLASYF_AA
subroutine zlahef_aa (uplo, j1, m, nb, a, lda, ipiv, h, ldh, work)
ZLAHEF_AA
subroutine zlasyf_aa (uplo, j1, m, nb, a, lda, ipiv, h, ldh, work)
ZLASYF_AA

Detailed Description

Function Documentation

  subroutine clahef_aa (character uplo, integer j1, integer m, integer nb, complex, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, complex, dimension( ldh, * ) h, integer ldh, complex, dimension( * ) work)

CLAHEF_AA

Purpose:

    !>
    !> CLAHEF_AA factorizes a panel of a complex hermitian matrix A using
    !> the Aasen's algorithm. The panel consists of a set of NB rows of A
    !> when UPLO is U, or a set of NB columns when UPLO is L.
    !>
    !> In order to factorize the panel, the Aasen's algorithm requires the
    !> last row, or column, of the previous panel. The first row, or column,
    !> of A is set to be the first row, or column, of an identity matrix,
    !> which is used to factorize the first panel.
    !>
    !> The resulting J-th row of U, or J-th column of L, is stored in the
    !> (J-1)-th row, or column, of A (without the unit diagonals), while
    !> the diagonal and subdiagonal of A are overwritten by those of T.
    !>
    !>

Parameters
    UPLO

    !>          UPLO is CHARACTER*1
    !>          = 'U':  Upper triangle of A is stored;
    !>          = 'L':  Lower triangle of A is stored.
    !>

    J1

    !>          J1 is INTEGER
    !>          The location of the first row, or column, of the panel
    !>          within the submatrix of A, passed to this routine, e.g.,
    !>          when called by CHETRF_AA, for the first panel, J1 is 1,
    !>          while for the remaining panels, J1 is 2.
    !>

    M

    !>          M is INTEGER
    !>          The dimension of the submatrix. M >= 0.
    !>

    NB

    !>          NB is INTEGER
    !>          The dimension of the panel to be facotorized.
    !>

    A

    !>          A is COMPLEX array, dimension (LDA,M) for
    !>          the first panel, while dimension (LDA,M+1) for the
    !>          remaining panels.
    !>
    !>          On entry, A contains the last row, or column, of
    !>          the previous panel, and the trailing submatrix of A
    !>          to be factorized, except for the first panel, only
    !>          the panel is passed.
    !>
    !>          On exit, the leading panel is factorized.
    !>

    LDA

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

    IPIV

    !>          IPIV is INTEGER array, dimension (N)
    !>          Details of the row and column interchanges,
    !>          the row and column k were interchanged with the row and
    !>          column IPIV(k).
    !>

    H

    !>          H is COMPLEX workspace, dimension (LDH,NB).
    !>
    !>

    LDH

    !>          LDH is INTEGER
    !>          The leading dimension of the workspace H. LDH >= max(1,M).
    !>

    WORK

    !>          WORK is COMPLEX workspace, dimension (M).
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

  subroutine clasyf_aa (character uplo, integer j1, integer m, integer nb, complex, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, complex, dimension( ldh, * ) h, integer ldh, complex, dimension( * ) work)

CLASYF_AA

Purpose:

    !>
    !> DLATRF_AA factorizes a panel of a complex symmetric matrix A using
    !> the Aasen's algorithm. The panel consists of a set of NB rows of A
    !> when UPLO is U, or a set of NB columns when UPLO is L.
    !>
    !> In order to factorize the panel, the Aasen's algorithm requires the
    !> last row, or column, of the previous panel. The first row, or column,
    !> of A is set to be the first row, or column, of an identity matrix,
    !> which is used to factorize the first panel.
    !>
    !> The resulting J-th row of U, or J-th column of L, is stored in the
    !> (J-1)-th row, or column, of A (without the unit diagonals), while
    !> the diagonal and subdiagonal of A are overwritten by those of T.
    !>
    !>

Parameters
    UPLO

    !>          UPLO is CHARACTER*1
    !>          = 'U':  Upper triangle of A is stored;
    !>          = 'L':  Lower triangle of A is stored.
    !>

    J1

    !>          J1 is INTEGER
    !>          The location of the first row, or column, of the panel
    !>          within the submatrix of A, passed to this routine, e.g.,
    !>          when called by CSYTRF_AA, for the first panel, J1 is 1,
    !>          while for the remaining panels, J1 is 2.
    !>

    M

    !>          M is INTEGER
    !>          The dimension of the submatrix. M >= 0.
    !>

    NB

    !>          NB is INTEGER
    !>          The dimension of the panel to be facotorized.
    !>

    A

    !>          A is COMPLEX array, dimension (LDA,M) for
    !>          the first panel, while dimension (LDA,M+1) for the
    !>          remaining panels.
    !>
    !>          On entry, A contains the last row, or column, of
    !>          the previous panel, and the trailing submatrix of A
    !>          to be factorized, except for the first panel, only
    !>          the panel is passed.
    !>
    !>          On exit, the leading panel is factorized.
    !>

    LDA

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

    IPIV

    !>          IPIV is INTEGER array, dimension (M)
    !>          Details of the row and column interchanges,
    !>          the row and column k were interchanged with the row and
    !>          column IPIV(k).
    !>

    H

    !>          H is COMPLEX workspace, dimension (LDH,NB).
    !>
    !>

    LDH

    !>          LDH is INTEGER
    !>          The leading dimension of the workspace H. LDH >= max(1,M).
    !>

    WORK

    !>          WORK is COMPLEX workspace, dimension (M).
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

  subroutine dlasyf_aa (character uplo, integer j1, integer m, integer nb, double precision, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, double precision, dimension( ldh, * ) h, integer ldh, double precision, dimension( * ) work)

DLASYF_AA

Purpose:

    !>
    !> DLATRF_AA factorizes a panel of a real symmetric matrix A using
    !> the Aasen's algorithm. The panel consists of a set of NB rows of A
    !> when UPLO is U, or a set of NB columns when UPLO is L.
    !>
    !> In order to factorize the panel, the Aasen's algorithm requires the
    !> last row, or column, of the previous panel. The first row, or column,
    !> of A is set to be the first row, or column, of an identity matrix,
    !> which is used to factorize the first panel.
    !>
    !> The resulting J-th row of U, or J-th column of L, is stored in the
    !> (J-1)-th row, or column, of A (without the unit diagonals), while
    !> the diagonal and subdiagonal of A are overwritten by those of T.
    !>
    !>

Parameters
    UPLO

    !>          UPLO is CHARACTER*1
    !>          = 'U':  Upper triangle of A is stored;
    !>          = 'L':  Lower triangle of A is stored.
    !>

    J1

    !>          J1 is INTEGER
    !>          The location of the first row, or column, of the panel
    !>          within the submatrix of A, passed to this routine, e.g.,
    !>          when called by DSYTRF_AA, for the first panel, J1 is 1,
    !>          while for the remaining panels, J1 is 2.
    !>

    M

    !>          M is INTEGER
    !>          The dimension of the submatrix. M >= 0.
    !>

    NB

    !>          NB is INTEGER
    !>          The dimension of the panel to be facotorized.
    !>

    A

    !>          A is DOUBLE PRECISION array, dimension (LDA,M) for
    !>          the first panel, while dimension (LDA,M+1) for the
    !>          remaining panels.
    !>
    !>          On entry, A contains the last row, or column, of
    !>          the previous panel, and the trailing submatrix of A
    !>          to be factorized, except for the first panel, only
    !>          the panel is passed.
    !>
    !>          On exit, the leading panel is factorized.
    !>

    LDA

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

    IPIV

    !>          IPIV is INTEGER array, dimension (M)
    !>          Details of the row and column interchanges,
    !>          the row and column k were interchanged with the row and
    !>          column IPIV(k).
    !>

    H

    !>          H is DOUBLE PRECISION workspace, dimension (LDH,NB).
    !>
    !>

    LDH

    !>          LDH is INTEGER
    !>          The leading dimension of the workspace H. LDH >= max(1,M).
    !>

    WORK

    !>          WORK is DOUBLE PRECISION workspace, dimension (M).
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

  subroutine slasyf_aa (character uplo, integer j1, integer m, integer nb, real, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, real, dimension( ldh, * ) h, integer ldh, real, dimension( * ) work)

SLASYF_AA

Purpose:

    !>
    !> DLATRF_AA factorizes a panel of a real symmetric matrix A using
    !> the Aasen's algorithm. The panel consists of a set of NB rows of A
    !> when UPLO is U, or a set of NB columns when UPLO is L.
    !>
    !> In order to factorize the panel, the Aasen's algorithm requires the
    !> last row, or column, of the previous panel. The first row, or column,
    !> of A is set to be the first row, or column, of an identity matrix,
    !> which is used to factorize the first panel.
    !>
    !> The resulting J-th row of U, or J-th column of L, is stored in the
    !> (J-1)-th row, or column, of A (without the unit diagonals), while
    !> the diagonal and subdiagonal of A are overwritten by those of T.
    !>
    !>

Parameters
    UPLO

    !>          UPLO is CHARACTER*1
    !>          = 'U':  Upper triangle of A is stored;
    !>          = 'L':  Lower triangle of A is stored.
    !>

    J1

    !>          J1 is INTEGER
    !>          The location of the first row, or column, of the panel
    !>          within the submatrix of A, passed to this routine, e.g.,
    !>          when called by SSYTRF_AA, for the first panel, J1 is 1,
    !>          while for the remaining panels, J1 is 2.
    !>

    M

    !>          M is INTEGER
    !>          The dimension of the submatrix. M >= 0.
    !>

    NB

    !>          NB is INTEGER
    !>          The dimension of the panel to be facotorized.
    !>

    A

    !>          A is REAL array, dimension (LDA,M) for
    !>          the first panel, while dimension (LDA,M+1) for the
    !>          remaining panels.
    !>
    !>          On entry, A contains the last row, or column, of
    !>          the previous panel, and the trailing submatrix of A
    !>          to be factorized, except for the first panel, only
    !>          the panel is passed.
    !>
    !>          On exit, the leading panel is factorized.
    !>

    LDA

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

    IPIV

    !>          IPIV is INTEGER array, dimension (M)
    !>          Details of the row and column interchanges,
    !>          the row and column k were interchanged with the row and
    !>          column IPIV(k).
    !>

    H

    !>          H is REAL workspace, dimension (LDH,NB).
    !>
    !>

    LDH

    !>          LDH is INTEGER
    !>          The leading dimension of the workspace H. LDH >= max(1,M).
    !>

    WORK

    !>          WORK is REAL workspace, dimension (M).
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

  subroutine zlahef_aa (character uplo, integer j1, integer m, integer nb, complex*16, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, complex*16, dimension( ldh, * ) h, integer ldh, complex*16, dimension( * ) work)

ZLAHEF_AA

Purpose:

    !>
    !> DLAHEF_AA factorizes a panel of a complex hermitian matrix A using
    !> the Aasen's algorithm. The panel consists of a set of NB rows of A
    !> when UPLO is U, or a set of NB columns when UPLO is L.
    !>
    !> In order to factorize the panel, the Aasen's algorithm requires the
    !> last row, or column, of the previous panel. The first row, or column,
    !> of A is set to be the first row, or column, of an identity matrix,
    !> which is used to factorize the first panel.
    !>
    !> The resulting J-th row of U, or J-th column of L, is stored in the
    !> (J-1)-th row, or column, of A (without the unit diagonals), while
    !> the diagonal and subdiagonal of A are overwritten by those of T.
    !>
    !>

Parameters
    UPLO

    !>          UPLO is CHARACTER*1
    !>          = 'U':  Upper triangle of A is stored;
    !>          = 'L':  Lower triangle of A is stored.
    !>

    J1

    !>          J1 is INTEGER
    !>          The location of the first row, or column, of the panel
    !>          within the submatrix of A, passed to this routine, e.g.,
    !>          when called by ZHETRF_AA, for the first panel, J1 is 1,
    !>          while for the remaining panels, J1 is 2.
    !>

    M

    !>          M is INTEGER
    !>          The dimension of the submatrix. M >= 0.
    !>

    NB

    !>          NB is INTEGER
    !>          The dimension of the panel to be facotorized.
    !>

    A

    !>          A is COMPLEX*16 array, dimension (LDA,M) for
    !>          the first panel, while dimension (LDA,M+1) for the
    !>          remaining panels.
    !>
    !>          On entry, A contains the last row, or column, of
    !>          the previous panel, and the trailing submatrix of A
    !>          to be factorized, except for the first panel, only
    !>          the panel is passed.
    !>
    !>          On exit, the leading panel is factorized.
    !>

    LDA

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

    IPIV

    !>          IPIV is INTEGER array, dimension (N)
    !>          Details of the row and column interchanges,
    !>          the row and column k were interchanged with the row and
    !>          column IPIV(k).
    !>

    H

    !>          H is COMPLEX*16 workspace, dimension (LDH,NB).
    !>
    !>

    LDH

    !>          LDH is INTEGER
    !>          The leading dimension of the workspace H. LDH >= max(1,M).
    !>

    WORK

    !>          WORK is COMPLEX*16 workspace, dimension (M).
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

  subroutine zlasyf_aa (character uplo, integer j1, integer m, integer nb, complex*16, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, complex*16, dimension( ldh, * ) h, integer ldh, complex*16, dimension( * ) work)

ZLASYF_AA

Purpose:

    !>
    !> DLATRF_AA factorizes a panel of a complex symmetric matrix A using
    !> the Aasen's algorithm. The panel consists of a set of NB rows of A
    !> when UPLO is U, or a set of NB columns when UPLO is L.
    !>
    !> In order to factorize the panel, the Aasen's algorithm requires the
    !> last row, or column, of the previous panel. The first row, or column,
    !> of A is set to be the first row, or column, of an identity matrix,
    !> which is used to factorize the first panel.
    !>
    !> The resulting J-th row of U, or J-th column of L, is stored in the
    !> (J-1)-th row, or column, of A (without the unit diagonals), while
    !> the diagonal and subdiagonal of A are overwritten by those of T.
    !>
    !>

Parameters
    UPLO

    !>          UPLO is CHARACTER*1
    !>          = 'U':  Upper triangle of A is stored;
    !>          = 'L':  Lower triangle of A is stored.
    !>

    J1

    !>          J1 is INTEGER
    !>          The location of the first row, or column, of the panel
    !>          within the submatrix of A, passed to this routine, e.g.,
    !>          when called by ZSYTRF_AA, for the first panel, J1 is 1,
    !>          while for the remaining panels, J1 is 2.
    !>

    M

    !>          M is INTEGER
    !>          The dimension of the submatrix. M >= 0.
    !>

    NB

    !>          NB is INTEGER
    !>          The dimension of the panel to be facotorized.
    !>

    A

    !>          A is COMPLEX*16 array, dimension (LDA,M) for
    !>          the first panel, while dimension (LDA,M+1) for the
    !>          remaining panels.
    !>
    !>          On entry, A contains the last row, or column, of
    !>          the previous panel, and the trailing submatrix of A
    !>          to be factorized, except for the first panel, only
    !>          the panel is passed.
    !>
    !>          On exit, the leading panel is factorized.
    !>

    LDA

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

    IPIV

    !>          IPIV is INTEGER array, dimension (M)
    !>          Details of the row and column interchanges,
    !>          the row and column k were interchanged with the row and
    !>          column IPIV(k).
    !>

    H

    !>          H is COMPLEX*16 workspace, dimension (LDH,NB).
    !>
    !>

    LDH

    !>          LDH is INTEGER
    !>          The leading dimension of the workspace H. LDH >= max(1,M).
    !>

    WORK

    !>          WORK is COMPLEX*16 workspace, dimension (M).
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Author

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