Man page - hesv_aa_2stage(3)

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Manual

hesv_aa_2stage

NAME

hesv_aa_2stage - {he,sy}sv_aa_2stage: Aasen, blocked 2-stage

SYNOPSIS

Functions

subroutine chesv_aa_2stage (uplo, n, nrhs, a, lda, tb, ltb, ipiv, ipiv2, b, ldb, work, lwork, info)
CHESV_AA_2STAGE computes the solution to system of linear equations A * X = B for HE matrices
subroutine csysv_aa_2stage (uplo, n, nrhs, a, lda, tb, ltb, ipiv, ipiv2, b, ldb, work, lwork, info)
CSYSV_AA_2STAGE computes the solution to system of linear equations A * X = B for SY matrices
subroutine dsysv_aa_2stage (uplo, n, nrhs, a, lda, tb, ltb, ipiv, ipiv2, b, ldb, work, lwork, info)
DSYSV_AA_2STAGE computes the solution to system of linear equations A * X = B for SY matrices
subroutine ssysv_aa_2stage (uplo, n, nrhs, a, lda, tb, ltb, ipiv, ipiv2, b, ldb, work, lwork, info)
SSYSV_AA_2STAGE computes the solution to system of linear equations A * X = B for SY matrices
subroutine zhesv_aa_2stage (uplo, n, nrhs, a, lda, tb, ltb, ipiv, ipiv2, b, ldb, work, lwork, info)
ZHESV_AA_2STAGE computes the solution to system of linear equations A * X = B for HE matrices
subroutine zsysv_aa_2stage (uplo, n, nrhs, a, lda, tb, ltb, ipiv, ipiv2, b, ldb, work, lwork, info)
ZSYSV_AA_2STAGE computes the solution to system of linear equations A * X = B for SY matrices

Detailed Description

Function Documentation

subroutine chesv_aa_2stage (character uplo, integer n, integer nrhs,complex, dimension( lda, * ) a, integer lda, complex, dimension( * )tb, integer ltb, integer, dimension( * ) ipiv, integer, dimension( * )ipiv2, complex, dimension( ldb, * ) b, integer ldb, complex, dimension(* ) work, integer lwork, integer info)

CHESV_AA_2STAGE computes the solution to system of linear equations A * X = B for HE matrices

Purpose:

CHESV_AA_2STAGE computes the solution to a complex system of
linear equations
A * X = B,
where A is an N-by-N Hermitian matrix and X and B are N-by-NRHS
matrices.

Aasen’s 2-stage algorithm is used to factor A as
A = U**H * T * U, if UPLO = ’U’, or
A = L * T * L**H, if UPLO = ’L’,
where U (or L) is a product of permutation and unit upper (lower)
triangular matrices, and T is Hermitian and band. The matrix T is
then LU-factored with partial pivoting. The factored form of A
is then used to solve the system of equations A * X = B.

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.

NRHS

NRHS is INTEGER
The number of right hand sides, i.e., the number of columns
of the matrix B. NRHS >= 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).

B is COMPLEX array, dimension (LDB,NRHS)
On entry, the right hand side matrix B.
On exit, the solution matrix X.

LDB

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

WORK

WORK is COMPLEX workspace of size (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal 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 csysv_aa_2stage (character uplo, integer n, integer nrhs,complex, dimension( lda, * ) a, integer lda, complex, dimension( * )tb, integer ltb, integer, dimension( * ) ipiv, integer, dimension( * )ipiv2, complex, dimension( ldb, * ) b, integer ldb, complex, dimension(* ) work, integer lwork, integer info)

CSYSV_AA_2STAGE computes the solution to system of linear equations A * X = B for SY matrices

Purpose:

CSYSV_AA_2STAGE computes the solution to a complex system of
linear equations
A * X = B,
where A is an N-by-N symmetric matrix and X and B are N-by-NRHS
matrices.

Aasen’s 2-stage algorithm is used to factor A as
A = U**T * T * U, if UPLO = ’U’, or
A = L * T * L**T, if UPLO = ’L’,
where U (or L) is a product of permutation and unit upper (lower)
triangular matrices, and T is symmetric and band. The matrix T is
then LU-factored with partial pivoting. The factored form of A
is then used to solve the system of equations A * X = B.

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.

NRHS

NRHS is INTEGER
The number of right hand sides, i.e., the number of columns
of the matrix B. NRHS >= 0.

A is COMPLEX 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 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).

B is COMPLEX array, dimension (LDB,NRHS)
On entry, the right hand side matrix B.
On exit, the solution matrix X.

LDB

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

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 dsysv_aa_2stage (character uplo, integer n, integer nrhs, doubleprecision, dimension( lda, * ) a, integer lda, double precision,dimension( * ) tb, integer ltb, integer, dimension( * ) ipiv, integer,dimension( * ) ipiv2, double precision, dimension( ldb, * ) b, integerldb, double precision, dimension( * ) work, integer lwork, integerinfo)

DSYSV_AA_2STAGE computes the solution to system of linear equations A * X = B for SY matrices

Purpose:

DSYSV_AA_2STAGE computes the solution to a real system of
linear equations
A * X = B,
where A is an N-by-N symmetric matrix and X and B are N-by-NRHS
matrices.

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.

NRHS

NRHS is INTEGER
The number of right hand sides, i.e., the number of columns
of the matrix B. NRHS >= 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 IPIV(k).

B is DOUBLE PRECISION array, dimension (LDB,NRHS)
On entry, the right hand side matrix B.
On exit, the solution matrix X.

LDB

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

WORK

WORK is DOUBLE PRECISION workspace of size (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal 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 ssysv_aa_2stage (character uplo, integer n, integer nrhs, real,dimension( lda, * ) a, integer lda, real, dimension( * ) tb, integerltb, integer, dimension( * ) ipiv, integer, dimension( * ) ipiv2, real,dimension( ldb, * ) b, integer ldb, real, dimension( * ) work, integerlwork, integer info)

SSYSV_AA_2STAGE computes the solution to system of linear equations A * X = B for SY matrices

Purpose:

SSYSV_AA_2STAGE computes the solution to a real system of
linear equations
A * X = B,
where A is an N-by-N symmetric matrix and X and B are N-by-NRHS
matrices.

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.

NRHS

NRHS is INTEGER
The number of right hand sides, i.e., the number of columns
of the matrix B. NRHS >= 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 (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).

B is REAL array, dimension (LDB,NRHS)
On entry, the right hand side matrix B.
On exit, the solution matrix X.

LDB

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

WORK

WORK is REAL workspace of size (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal 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 zhesv_aa_2stage (character uplo, integer n, integer nrhs,complex16, dimension( lda, ) a, integer lda, complex16, dimension( ) tb, integer ltb, integer, dimension( * ) ipiv, integer, dimension(* ) ipiv2, complex16, dimension( ldb, ) b, integer ldb, complex16,dimension( ) work, integer lwork, integer info)

ZHESV_AA_2STAGE computes the solution to system of linear equations A * X = B for HE matrices

Purpose:

ZHESV_AA_2STAGE computes the solution to a complex system of
linear equations
A * X = B,
where A is an N-by-N Hermitian matrix and X and B are N-by-NRHS
matrices.

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.

NRHS

NRHS is INTEGER
The number of right hand sides, i.e., the number of columns
of the matrix B. NRHS >= 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).

B is COMPLEX*16 array, dimension (LDB,NRHS)
On entry, the right hand side matrix B.
On exit, the solution matrix X.

LDB

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

WORK

WORK is COMPLEX*16 workspace of size (MAX(1,LWORK)).
On exit, if INFO = 0, WORK(1) returns the optimal 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 zsysv_aa_2stage (character uplo, integer n, integer nrhs,complex16, dimension( lda, ) a, integer lda, complex16, dimension( ) tb, integer ltb, integer, dimension( * ) ipiv, integer, dimension(* ) ipiv2, complex16, dimension( ldb, ) b, integer ldb, complex16,dimension( ) work, integer lwork, integer info)

ZSYSV_AA_2STAGE computes the solution to system of linear equations A * X = B for SY matrices

Purpose:

ZSYSV_AA_2STAGE computes the solution to a complex system of
linear equations
A * X = B,
where A is an N-by-N symmetric matrix and X and B are N-by-NRHS
matrices.

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.

NRHS

NRHS is INTEGER
The number of right hand sides, i.e., the number of columns
of the matrix B. NRHS >= 0.

A is COMPLEX*16 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 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).

B is COMPLEX*16 array, dimension (LDB,NRHS)
On entry, the right hand side matrix B.
On exit, the solution matrix X.

LDB

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

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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