Provided by: liblapack-doc_3.12.0-3build1.1_all 
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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Version 3.12.0 Fri Aug 9 2024 02:33:22 lahef_aa(3)