# chesv_aa_2stage.f - Man Page

SRC/chesv_aa_2stage.f

## Synopsis

### Functions/Subroutines

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

## Function/Subroutine 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

```          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

```          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

```          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.

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

```          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.

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

NAG Ltd.

Definition at line 183 of file chesv_aa_2stage.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page chesv_aa_2stage(3) is an alias of chesv_aa_2stage.f(3).

Tue Nov 28 2023 12:08:41 Version 3.12.0 LAPACK