Man page - hesv_aa(3)

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Manual

hesv_aa

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
subroutine chesv_aa (character uplo, integer n, integer nrhs, complex,dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv,complex, dimension( ldb, * ) b, integer ldb, complex, dimension( * )work, integer lwork, integer info)
subroutine csysv_aa (character uplo, integer n, integer nrhs, complex,dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv,complex, dimension( ldb, * ) b, integer ldb, complex, dimension( * )work, integer lwork, integer info)
subroutine dsysv_aa (character uplo, integer n, integer nrhs, doubleprecision, dimension( lda, * ) a, integer lda, integer, dimension( * )ipiv, double precision, dimension( ldb, * ) b, integer ldb, doubleprecision, dimension( * ) work, integer lwork, integer info)
subroutine ssysv_aa (character uplo, integer n, integer nrhs, real,dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, real,dimension( ldb, * ) b, integer ldb, real, dimension( * ) work, integerlwork, integer info)
subroutine zhesv_aa (character uplo, integer n, integer nrhs, complex*16,dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv,complex*16, dimension( ldb, * ) b, integer ldb, complex*16, dimension(* ) work, integer lwork, integer info)
subroutine zsysv_aa (character uplo, integer n, integer nrhs, complex*16,dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv,complex*16, dimension( ldb, * ) b, integer ldb, complex*16, dimension(* ) work, integer lwork, integer info)
Author

NAME

hesv_aa - {he,sy}sv_aa: Aasen

SYNOPSIS

Functions

subroutine chesv_aa (uplo, n, nrhs, a, lda, ipiv, b, ldb, work, lwork, info)
CHESV_AA computes the solution to system of linear equations A * X = B for HE matrices
subroutine csysv_aa (uplo, n, nrhs, a, lda, ipiv, b, ldb, work, lwork, info)
CSYSV_AA computes the solution to system of linear equations A * X = B for SY matrices
subroutine dsysv_aa (uplo, n, nrhs, a, lda, ipiv, b, ldb, work, lwork, info)
DSYSV_AA computes the solution to system of linear equations A * X = B for SY matrices
subroutine ssysv_aa (uplo, n, nrhs, a, lda, ipiv, b, ldb, work, lwork, info)
SSYSV_AA computes the solution to system of linear equations A * X = B for SY matrices
subroutine zhesv_aa (uplo, n, nrhs, a, lda, ipiv, b, ldb, work, lwork, info)
ZHESV_AA computes the solution to system of linear equations A * X = B for HE matrices
subroutine zsysv_aa (uplo, n, nrhs, a, lda, ipiv, b, ldb, work, lwork, info)
ZSYSV_AA computes the solution to system of linear equations A * X = B for SY matrices

Detailed Description

Function Documentation

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

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

Purpose:

CHESV_AA 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 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 tridiagonal. The factored form
of A is then used to solve the system of equations A * X = B.

Parameters

UPLO

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

N

N is INTEGER
The number of linear equations, i.e., 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

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, if INFO = 0, the tridiagonal matrix T and the
multipliers used to obtain the factor U or L from the
factorization A = U**H*T*U or A = L*T*L**H as computed by
CHETRF_AA.

LDA

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

B

B is COMPLEX array, dimension (LDB,NRHS)
On entry, the N-by-NRHS right hand side matrix B.
On exit, if INFO = 0, the N-by-NRHS solution matrix X.

LDB

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

WORK

WORK is COMPLEX array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK

LWORK is INTEGER
The length of WORK. LWORK >= MAX(1,2*N,3*N-2), and for best
performance LWORK >= MAX(1,N*NB), where NB is the optimal
blocksize for CHETRF.

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, D(i,i) is exactly zero. The factorization
has been completed, but the block diagonal matrix D is
exactly singular, so the solution could not be computed.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

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

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

Purpose:

CSYSV 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 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 tridiagonal. The factored
form of A is then used to solve the system of equations A * X = B.

Parameters

UPLO

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

N

N is INTEGER
The number of linear equations, i.e., 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

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, if INFO = 0, the tridiagonal matrix T and the
multipliers used to obtain the factor U or L from the
factorization A = U**T*T*U or A = L*T*L**T as computed by
CSYTRF.

LDA

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

B

B is COMPLEX array, dimension (LDB,NRHS)
On entry, the N-by-NRHS right hand side matrix B.
On exit, if INFO = 0, the N-by-NRHS solution matrix X.

LDB

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

WORK

WORK is COMPLEX array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK

LWORK is INTEGER
The length of WORK. LWORK >= MAX(2*N, 3*N-2), and for
the best performance, LWORK >= max(1,N*NB), where NB is
the optimal blocksize for CSYTRF_AA.

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, D(i,i) is exactly zero. The factorization
has been completed, but the block diagonal matrix D is
exactly singular, so the solution could not be computed.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine dsysv_aa (character uplo, integer n, integer nrhs, doubleprecision, dimension( lda, * ) a, integer lda, integer, dimension( * )ipiv, double precision, dimension( ldb, * ) b, integer ldb, doubleprecision, dimension( * ) work, integer lwork, integer info)

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

Purpose:

DSYSV 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.

Aasen’s 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 tridiagonal. The factored
form of A is then used to solve the system of equations A * X = B.

Parameters

UPLO

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

N

N is INTEGER
The number of linear equations, i.e., 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

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, if INFO = 0, the tridiagonal matrix T and the
multipliers used to obtain the factor U or L from the
factorization A = U**T*T*U or A = L*T*L**T as computed by
DSYTRF.

LDA

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

B

B is DOUBLE PRECISION array, dimension (LDB,NRHS)
On entry, the N-by-NRHS right hand side matrix B.
On exit, if INFO = 0, the N-by-NRHS solution matrix X.

LDB

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

WORK

WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK

LWORK is INTEGER
The length of WORK. LWORK >= MAX(1,2*N,3*N-2), and for
the best performance, LWORK >= MAX(1,N*NB), where NB is
the optimal blocksize for DSYTRF_AA.

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, D(i,i) is exactly zero. The factorization
has been completed, but the block diagonal matrix D is
exactly singular, so the solution could not be computed.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine ssysv_aa (character uplo, integer n, integer nrhs, real,dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, real,dimension( ldb, * ) b, integer ldb, real, dimension( * ) work, integerlwork, integer info)

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

Purpose:

SSYSV 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.

Aasen’s 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 tridiagonal. The factored
form of A is then used to solve the system of equations A * X = B.

Parameters

UPLO

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

N

N is INTEGER
The number of linear equations, i.e., 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

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, if INFO = 0, the tridiagonal matrix T and the
multipliers used to obtain the factor U or L from the
factorization A = U**T*T*U or A = L*T*L**T as computed by
SSYTRF.

LDA

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

B

B is REAL array, dimension (LDB,NRHS)
On entry, the N-by-NRHS right hand side matrix B.
On exit, if INFO = 0, the N-by-NRHS solution matrix X.

LDB

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

WORK

WORK is REAL array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK

LWORK is INTEGER
The length of WORK. LWORK >= MAX(1,2*N,3*N-2), and for
the best performance, LWORK >= MAX(1,N*NB), where NB is
the optimal blocksize for SSYTRF_AA.

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, D(i,i) is exactly zero. The factorization
has been completed, but the block diagonal matrix D is
exactly singular, so the solution could not be computed.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine zhesv_aa (character uplo, integer n, integer nrhs, complex*16,dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv,complex*16, dimension( ldb, * ) b, integer ldb, complex*16, dimension(* ) work, integer lwork, integer info)

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

Purpose:

ZHESV_AA 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 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 tridiagonal. The factored form
of A is then used to solve the system of equations A * X = B.

Parameters

UPLO

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

N

N is INTEGER
The number of linear equations, i.e., 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

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, if INFO = 0, the tridiagonal matrix T and the
multipliers used to obtain the factor U or L from the
factorization A = U**H*T*U or A = L*T*L**H as computed by
ZHETRF_AA.

LDA

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

B

B is COMPLEX*16 array, dimension (LDB,NRHS)
On entry, the N-by-NRHS right hand side matrix B.
On exit, if INFO = 0, the N-by-NRHS solution matrix X.

LDB

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

WORK

WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK

LWORK is INTEGER
The length of WORK. LWORK >= MAX(1,2*N,3*N-2), and for best
performance LWORK >= max(1,N*NB), where NB is the optimal
blocksize for ZHETRF_AA.

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, D(i,i) is exactly zero. The factorization
has been completed, but the block diagonal matrix D is
exactly singular, so the solution could not be computed.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine zsysv_aa (character uplo, integer n, integer nrhs, complex*16,dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv,complex*16, dimension( ldb, * ) b, integer ldb, complex*16, dimension(* ) work, integer lwork, integer info)

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

Purpose:

ZSYSV 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 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 tridiagonal. The factored
form of A is then used to solve the system of equations A * X = B.

Parameters

UPLO

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

N

N is INTEGER
The number of linear equations, i.e., 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

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, if INFO = 0, the tridiagonal matrix T and the
multipliers used to obtain the factor U or L from the
factorization A = U**T*T*U or A = L*T*L**T as computed by
ZSYTRF.

LDA

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

B

B is COMPLEX*16 array, dimension (LDB,NRHS)
On entry, the N-by-NRHS right hand side matrix B.
On exit, if INFO = 0, the N-by-NRHS solution matrix X.

LDB

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

WORK

WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK

LWORK is INTEGER
The length of WORK. LWORK >= MAX(1,2*N,3*N-2), and for
the best performance, LWORK >= MAX(1,N*NB), where NB is
the optimal blocksize for ZSYTRF_AA.

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, D(i,i) is exactly zero. The factorization
has been completed, but the block diagonal matrix D is
exactly singular, so the solution could not be computed.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Author

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