Man page - hetrf_aa_2stage(3)

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Manual

hetrf_aa_2stage

NAME

hetrf_aa_2stage - {he,sy}trf_aa_2stage: triangular factor

SYNOPSIS

Functions

subroutine chetrf_aa_2stage (uplo, n, a, lda, tb, ltb, ipiv, ipiv2, work, lwork, info)
CHETRF_AA_2STAGE
subroutine csytrf_aa_2stage (uplo, n, a, lda, tb, ltb, ipiv, ipiv2, work, lwork, info)
CSYTRF_AA_2STAGE
subroutine dsytrf_aa_2stage (uplo, n, a, lda, tb, ltb, ipiv, ipiv2, work, lwork, info)
DSYTRF_AA_2STAGE
subroutine ssytrf_aa_2stage (uplo, n, a, lda, tb, ltb, ipiv, ipiv2, work, lwork, info)
SSYTRF_AA_2STAGE
subroutine zhetrf_aa_2stage (uplo, n, a, lda, tb, ltb, ipiv, ipiv2, work, lwork, info)
ZHETRF_AA_2STAGE
subroutine zsytrf_aa_2stage (uplo, n, a, lda, tb, ltb, ipiv, ipiv2, work, lwork, info)
ZSYTRF_AA_2STAGE

Detailed Description

Function Documentation

subroutine chetrf_aa_2stage (character uplo, integer n, complex, dimension(lda, * ) a, integer lda, complex, dimension( * ) tb, integer ltb,integer, dimension( * ) ipiv, integer, dimension( * ) ipiv2, complex,dimension( * ) work, integer lwork, integer info)

CHETRF_AA_2STAGE

Purpose:

CHETRF_AA_2STAGE computes the factorization of a real hermitian matrix A
using the Aasen’s algorithm. The form of the factorization is

A = U**T*T*U or A = L*T*L**T

where U (or L) is a product of permutation and unit upper (lower)
triangular matrices, and T is a hermitian band matrix with the
bandwidth of NB (NB is internally selected and stored in TB( 1 ), and T is
LU factorized with partial pivoting).

This is the blocked version of the algorithm, calling Level 3 BLAS.

Parameters

UPLO

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

N is INTEGER
The order of the matrix A. N >= 0.

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, L is stored below (or above) the subdiagonal blocks,
when UPLO is ’L’ (or ’U’).

LDA

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

TB is COMPLEX array, dimension (MAX(1,LTB))
On exit, details of the LU factorization of the band matrix.

LTB

LTB is INTEGER
The size of the array TB. LTB >= MAX(1,4*N), internally
used to select NB such that LTB >= (3*NB+1)*N.

If LTB = -1, then a workspace query is assumed; the
routine only calculates the optimal size of LTB,
returns this value as the first entry of TB, and
no error message related to LTB is issued by XERBLA.

IPIV

IPIV is INTEGER array, dimension (N)
On exit, it contains the details of the interchanges, i.e.,
the row and column k of A were interchanged with the
row and column IPIV(k).

IPIV2

IPIV2 is INTEGER array, dimension (N)
On exit, it contains the details of the interchanges, i.e.,
the row and column k of T were interchanged with the
row and column IPIV(k).

WORK

WORK is COMPLEX workspace of size (MAX(1,LWORK))

LWORK

LWORK is INTEGER
The size of WORK. LWORK >= MAX(1,N), internally used
to select NB such that LWORK >= N*NB.

If LWORK = -1, then a workspace query is assumed; the
routine only calculates the optimal size of the WORK array,
returns this value as the first entry of the WORK array, and
no error message related to LWORK is issued by XERBLA.

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value.
> 0: if INFO = i, band LU factorization failed on i-th column

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine csytrf_aa_2stage (character uplo, integer n, complex, dimension(lda, * ) a, integer lda, complex, dimension( * ) tb, integer ltb,integer, dimension( * ) ipiv, integer, dimension( * ) ipiv2, complex,dimension( * ) work, integer lwork, integer info)

CSYTRF_AA_2STAGE

Purpose:

CSYTRF_AA_2STAGE computes the factorization of a complex symmetric matrix A
using the Aasen’s algorithm. The form of the factorization is

A = U**T*T*U or A = L*T*L**T

where U (or L) is a product of permutation and unit upper (lower)
triangular matrices, and T is a complex symmetric band matrix with the
bandwidth of NB (NB is internally selected and stored in TB( 1 ), and T is
LU factorized with partial pivoting).

This is the blocked version of the algorithm, calling Level 3 BLAS.

Parameters

UPLO

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

N is INTEGER
The order of the matrix A. N >= 0.

On exit, L is stored below (or above) the subdiagonal blocks,
when UPLO is ’L’ (or ’U’).

LDA

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

TB is COMPLEX array, dimension (LTB)
On exit, details of the LU factorization of the band matrix.

LTB

LTB is INTEGER
The size of the array TB. LTB >= 4*N, internally
used to select NB such that LTB >= (3*NB+1)*N.

IPIV

IPIV is INTEGER array, dimension (N)
On exit, it contains the details of the interchanges, i.e.,
the row and column k of A were interchanged with the
row and column IPIV(k).

IPIV2

IPIV2 is INTEGER array, dimension (N)
On exit, it contains the details of the interchanges, i.e.,
the row and column k of T were interchanged with the
row and column IPIV(k).

WORK

WORK is COMPLEX workspace of size LWORK

LWORK

LWORK is INTEGER
The size of WORK. LWORK >= N, internally used to select NB
such that LWORK >= N*NB.

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value.
> 0: if INFO = i, band LU factorization failed on i-th column

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine dsytrf_aa_2stage (character uplo, integer n, double precision,dimension( lda, * ) a, integer lda, double precision, dimension( * )tb, integer ltb, integer, dimension( * ) ipiv, integer, dimension( * )ipiv2, double precision, dimension( * ) work, integer lwork, integerinfo)

DSYTRF_AA_2STAGE

Purpose:

DSYTRF_AA_2STAGE computes the factorization of a real symmetric matrix A
using the Aasen’s algorithm. The form of the factorization is

A = U**T*T*U or A = L*T*L**T

where U (or L) is a product of permutation and unit upper (lower)
triangular matrices, and T is a symmetric band matrix with the
bandwidth of NB (NB is internally selected and stored in TB( 1 ), and T is
LU factorized with partial pivoting).

This is the blocked version of the algorithm, calling Level 3 BLAS.

Parameters

UPLO

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

N is INTEGER
The order of the matrix A. N >= 0.

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, L is stored below (or above) the subdiagonal blocks,
when UPLO is ’L’ (or ’U’).

LDA

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

TB is DOUBLE PRECISION array, dimension (MAX(1,LTB))
On exit, details of the LU factorization of the band matrix.

LTB

LTB is INTEGER
The size of the array TB. LTB >= MAX(1,4*N), internally
used to select NB such that LTB >= (3*NB+1)*N.

IPIV

IPIV is INTEGER array, dimension (N)
On exit, it contains the details of the interchanges, i.e.,
the row and column k of A were interchanged with the
row and column IPIV(k).

IPIV2

IPIV2 is INTEGER array, dimension (N)
On exit, it contains the details of the interchanges, i.e.,
the row and column k of T were interchanged with the
row and column IPIV2(k).

WORK

WORK is DOUBLE PRECISION workspace of size (MAX(1,LWORK))

LWORK

LWORK is INTEGER
The size of WORK. LWORK >= MAX(1,N), internally used
to select NB such that LWORK >= N*NB.

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value.
> 0: if INFO = i, band LU factorization failed on i-th column

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine ssytrf_aa_2stage (character uplo, integer n, real, dimension(lda, * ) a, integer lda, real, dimension( * ) tb, integer ltb, integer,dimension( * ) ipiv, integer, dimension( * ) ipiv2, real, dimension( *) work, integer lwork, integer info)

SSYTRF_AA_2STAGE

Purpose:

SSYTRF_AA_2STAGE computes the factorization of a real symmetric matrix A
using the Aasen’s algorithm. The form of the factorization is

A = U**T*T*U or A = L*T*L**T

This is the blocked version of the algorithm, calling Level 3 BLAS.

Parameters

UPLO

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

N is INTEGER
The order of the matrix A. N >= 0.

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, L is stored below (or above) the subdiagonal blocks,
when UPLO is ’L’ (or ’U’).

LDA

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

TB is REAL array, dimension (LTB)
On exit, details of the LU factorization of the band matrix.

LTB

LTB is INTEGER
The size of the array TB. LTB >= MAX(1,4*N), internally
used to select NB such that LTB >= (3*NB+1)*N.

IPIV

IPIV is INTEGER array, dimension (N)
On exit, it contains the details of the interchanges, i.e.,
the row and column k of A were interchanged with the
row and column IPIV(k).

IPIV2

IPIV2 is INTEGER array, dimension (N)
On exit, it contains the details of the interchanges, i.e.,
the row and column k of T were interchanged with the
row and column IPIV(k).

WORK

WORK is REAL workspace of size (MAX(1,LWORK))

LWORK

LWORK is INTEGER
The size of WORK. LWORK >= MAX(1,N), internally used to
select NB such that LWORK >= N*NB.

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value.
> 0: if INFO = i, band LU factorization failed on i-th column

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine zhetrf_aa_2stage (character uplo, integer n, complex16,dimension( lda, ) a, integer lda, complex16, dimension( ) tb,integer ltb, integer, dimension( * ) ipiv, integer, dimension( * )ipiv2, complex16, dimension( ) work, integer lwork, integer info)

ZHETRF_AA_2STAGE

Purpose:

ZHETRF_AA_2STAGE computes the factorization of a double hermitian matrix A
using the Aasen’s algorithm. The form of the factorization is

A = U**H*T*U or A = L*T*L**H

This is the blocked version of the algorithm, calling Level 3 BLAS.

Parameters

UPLO

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

N is INTEGER
The order of the matrix A. N >= 0.

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, L is stored below (or above) the subdiagonal blocks,
when UPLO is ’L’ (or ’U’).

LDA

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

TB is COMPLEX*16 array, dimension (MAX(1,LTB))
On exit, details of the LU factorization of the band matrix.

LTB

LTB is INTEGER
The size of the array TB. LTB >= MAX(1,4*N), internally
used to select NB such that LTB >= (3*NB+1)*N.

IPIV

IPIV is INTEGER array, dimension (N)
On exit, it contains the details of the interchanges, i.e.,
the row and column k of A were interchanged with the
row and column IPIV(k).

IPIV2

IPIV2 is INTEGER array, dimension (N)
On exit, it contains the details of the interchanges, i.e.,
the row and column k of T were interchanged with the
row and column IPIV(k).

WORK

WORK is COMPLEX*16 workspace of size (MAX(1,LWORK))

LWORK

LWORK is INTEGER
The size of WORK. LWORK >= MAX(1,N), internally used to
select NB such that LWORK >= N*NB.

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value.
> 0: if INFO = i, band LU factorization failed on i-th column

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine zsytrf_aa_2stage (character uplo, integer n, complex16,dimension( lda, ) a, integer lda, complex16, dimension( ) tb,integer ltb, integer, dimension( * ) ipiv, integer, dimension( * )ipiv2, complex16, dimension( ) work, integer lwork, integer info)

ZSYTRF_AA_2STAGE

Purpose:

ZSYTRF_AA_2STAGE computes the factorization of a complex symmetric matrix A
using the Aasen’s algorithm. The form of the factorization is

A = U**T*T*U or A = L*T*L**T

This is the blocked version of the algorithm, calling Level 3 BLAS.

Parameters

UPLO

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

N is INTEGER
The order of the matrix A. N >= 0.

On exit, L is stored below (or above) the subdiagonal blocks,
when UPLO is ’L’ (or ’U’).

LDA

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

TB is COMPLEX*16 array, dimension (LTB)
On exit, details of the LU factorization of the band matrix.

LTB

LTB is INTEGER
The size of the array TB. LTB >= 4*N, internally
used to select NB such that LTB >= (3*NB+1)*N.

IPIV

IPIV is INTEGER array, dimension (N)
On exit, it contains the details of the interchanges, i.e.,
the row and column k of A were interchanged with the
row and column IPIV(k).

IPIV2

IPIV2 is INTEGER array, dimension (N)
On exit, it contains the details of the interchanges, i.e.,
the row and column k of T were interchanged with the
row and column IPIV(k).

WORK

WORK is COMPLEX*16 workspace of size LWORK

LWORK

LWORK is INTEGER
The size of WORK. LWORK >= N, internally used to select NB
such that LWORK >= N*NB.

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value.
> 0: if INFO = i, band LU factorization failed on i-th column

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Author

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Man page - hetrf_aa_2stage(3)

Packages contains this manual

Manual

hetrf_aa_2stage

NAME

SYNOPSIS

Functions

Detailed Description

Function Documentation

subroutine chetrf_aa_2stage (character uplo, integer n, complex, dimension(lda, * ) a, integer lda, complex, dimension( * ) tb, integer ltb,integer, dimension( * ) ipiv, integer, dimension( * ) ipiv2, complex,dimension( * ) work, integer lwork, integer info)

subroutine csytrf_aa_2stage (character uplo, integer n, complex, dimension(lda, * ) a, integer lda, complex, dimension( * ) tb, integer ltb,integer, dimension( * ) ipiv, integer, dimension( * ) ipiv2, complex,dimension( * ) work, integer lwork, integer info)

subroutine dsytrf_aa_2stage (character uplo, integer n, double precision,dimension( lda, * ) a, integer lda, double precision, dimension( * )tb, integer ltb, integer, dimension( * ) ipiv, integer, dimension( * )ipiv2, double precision, dimension( * ) work, integer lwork, integerinfo)

subroutine ssytrf_aa_2stage (character uplo, integer n, real, dimension(lda, * ) a, integer lda, real, dimension( * ) tb, integer ltb, integer,dimension( * ) ipiv, integer, dimension( * ) ipiv2, real, dimension( *) work, integer lwork, integer info)

subroutine zhetrf_aa_2stage (character uplo, integer n, complex*16,dimension( lda, * ) a, integer lda, complex*16, dimension( * ) tb,integer ltb, integer, dimension( * ) ipiv, integer, dimension( * )ipiv2, complex*16, dimension( * ) work, integer lwork, integer info)

subroutine zsytrf_aa_2stage (character uplo, integer n, complex*16,dimension( lda, * ) a, integer lda, complex*16, dimension( * ) tb,integer ltb, integer, dimension( * ) ipiv, integer, dimension( * )ipiv2, complex*16, dimension( * ) work, integer lwork, integer info)

Author

subroutine zhetrf_aa_2stage (character uplo, integer n, complex16,dimension( lda, ) a, integer lda, complex16, dimension( ) tb,integer ltb, integer, dimension( * ) ipiv, integer, dimension( * )ipiv2, complex16, dimension( ) work, integer lwork, integer info)

subroutine zsytrf_aa_2stage (character uplo, integer n, complex16,dimension( lda, ) a, integer lda, complex16, dimension( ) tb,integer ltb, integer, dimension( * ) ipiv, integer, dimension( * )ipiv2, complex16, dimension( ) work, integer lwork, integer info)