1. Manuals
  2. Tumbleweed
  3. lapack-man
  4. lahef_aa(3)

Scroll to navigation

lahef_aa(3) Library Functions Manual 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.

Definition at line 142 of file clahef_aa.f.

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.

Definition at line 142 of file clasyf_aa.f.

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.

Definition at line 142 of file dlasyf_aa.f.

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.

Definition at line 142 of file slasyf_aa.f.

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.

Definition at line 142 of file zlahef_aa.f.

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.

Definition at line 142 of file zlasyf_aa.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.

Version 3.12.0 LAPACK