# hetrf_aa - Man Page

{he,sy}trf_aa: triangular factor

## Synopsis

### Functions

subroutine chetrf_aa (uplo, n, a, lda, ipiv, work, lwork, info)
CHETRF_AA
subroutine csytrf_aa (uplo, n, a, lda, ipiv, work, lwork, info)
CSYTRF_AA
subroutine dsytrf_aa (uplo, n, a, lda, ipiv, work, lwork, info)
DSYTRF_AA
subroutine ssytrf_aa (uplo, n, a, lda, ipiv, work, lwork, info)
SSYTRF_AA
subroutine zhetrf_aa (uplo, n, a, lda, ipiv, work, lwork, info)
ZHETRF_AA
subroutine zsytrf_aa (uplo, n, a, lda, ipiv, work, lwork, info)
ZSYTRF_AA

## Function Documentation

### subroutine chetrf_aa (character uplo, integer n, complex, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, complex, dimension( * ) work, integer lwork, integer info)

CHETRF_AA

Purpose:

``` CHETRF_AA computes the factorization of a complex 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

where U (or L) is a product of permutation and unit upper (lower)
triangular matrices, and T is a hermitian tridiagonal matrix.

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

```          N is INTEGER
The order of the matrix A.  N >= 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, the tridiagonal matrix is stored in the diagonals
and the subdiagonals of A just below (or above) the diagonals,
and L is stored below (or above) the subdiagonals, when UPLO
is 'L' (or 'U').```

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).```

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 >= 2*N. For optimum performance
LWORK >= N*(1+NB), where NB is the optimal blocksize.

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.```
Author

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Definition at line 131 of file chetrf_aa.f.

### subroutine csytrf_aa (character uplo, integer n, complex, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, complex, dimension( * ) work, integer lwork, integer info)

CSYTRF_AA

Purpose:

``` CSYTRF_AA 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 tridiagonal matrix.

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

```          N is INTEGER
The order of the matrix A.  N >= 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, the tridiagonal matrix is stored in the diagonals
and the subdiagonals of A just below (or above) the diagonals,
and L is stored below (or above) the subdiagonals, when UPLO
is 'L' (or 'U').```

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).```

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). For optimum performance
LWORK >= N*(1+NB), where NB is the optimal blocksize.

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.```
Author

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Definition at line 131 of file csytrf_aa.f.

### subroutine dsytrf_aa (character uplo, integer n, double precision, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, double precision, dimension( * ) work, integer lwork, integer info)

DSYTRF_AA

Purpose:

``` DSYTRF_AA 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 tridiagonal matrix.

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

```          N is INTEGER
The order of the matrix A.  N >= 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, the tridiagonal matrix is stored in the diagonals
and the subdiagonals of A just below (or above) the diagonals,
and L is stored below (or above) the subdiagonals, when UPLO
is 'L' (or 'U').```

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).```

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). For optimum performance
LWORK >= N*(1+NB), where NB is the optimal blocksize.

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.```
Author

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Definition at line 131 of file dsytrf_aa.f.

### subroutine ssytrf_aa (character uplo, integer n, real, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, real, dimension( * ) work, integer lwork, integer info)

SSYTRF_AA

Purpose:

``` SSYTRF_AA 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 tridiagonal matrix.

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

```          N is INTEGER
The order of the matrix A.  N >= 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, the tridiagonal matrix is stored in the diagonals
and the subdiagonals of A just below (or above) the diagonals,
and L is stored below (or above) the subdiagonals, when UPLO
is 'L' (or 'U').```

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).```

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). For optimum performance
LWORK >= N*(1+NB), where NB is the optimal blocksize.

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.```
Author

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Definition at line 131 of file ssytrf_aa.f.

### subroutine zhetrf_aa (character uplo, integer n, complex*16, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, complex*16, dimension( * ) work, integer lwork, integer info)

ZHETRF_AA

Purpose:

``` ZHETRF_AA computes the factorization of a complex 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

where U (or L) is a product of permutation and unit upper (lower)
triangular matrices, and T is a hermitian tridiagonal matrix.

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

```          N is INTEGER
The order of the matrix A.  N >= 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, the tridiagonal matrix is stored in the diagonals
and the subdiagonals of A just below (or above) the diagonals,
and L is stored below (or above) the subdiagonals, when UPLO
is 'L' (or 'U').```

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).```

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). For optimum performance
LWORK >= N*(1+NB), where NB is the optimal blocksize.

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.```
Author

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Definition at line 131 of file zhetrf_aa.f.

### subroutine zsytrf_aa (character uplo, integer n, complex*16, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, complex*16, dimension( * ) work, integer lwork, integer info)

ZSYTRF_AA

Purpose:

``` ZSYTRF_AA 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 tridiagonal matrix.

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

```          N is INTEGER
The order of the matrix A.  N >= 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, the tridiagonal matrix is stored in the diagonals
and the subdiagonals of A just below (or above) the diagonals,
and L is stored below (or above) the subdiagonals, when UPLO
is 'L' (or 'U').```

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).```

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). For optimum performance
LWORK >= N*(1+NB), where NB is the optimal blocksize.

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.```
Author

Univ. of Tennessee

Univ. of California Berkeley