Man page - lahef_aa(3)

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Manual

lahef_aa

NAME
SYNOPSIS
Functions
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)
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)
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, integerldh, double precision, dimension( * ) work)
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)
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)
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)
Author

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, integerldh, 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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