# chesv_rook.f man page

chesv_rook.f —

## Synopsis

### Functions/Subroutines

subroutinechesv_rook(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, LWORK, INFO)CHESV_ROOKcomputes the solution to a system of linear equations A * X = B for HE matrices using the bounded Bunch-Kaufman ('rook') diagonal pivoting method

## Function/Subroutine Documentation

### subroutine chesv_rook (characterUPLO, integerN, integerNRHS, complex, dimension( lda, * )A, integerLDA, integer, dimension( * )IPIV, complex, dimension( ldb, * )B, integerLDB, complex, dimension( * )WORK, integerLWORK, integerINFO)

**CHESV_ROOK** computes the solution to a system of linear equations A * X = B for HE matrices using the bounded Bunch-Kaufman ('rook') diagonal pivoting method

**Purpose:**

```
CHESV_ROOK 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.
The bounded Bunch-Kaufman ("rook") diagonal pivoting method is used
to factor A as
A = U * D * U**T, if UPLO = 'U', or
A = L * D * L**T, if UPLO = 'L',
where U (or L) is a product of permutation and unit upper (lower)
triangular matrices, and D is Hermitian and block diagonal with
1-by-1 and 2-by-2 diagonal blocks.
CHETRF_ROOK is called to compute the factorization of a complex
Hermition matrix A using the bounded Bunch-Kaufman ("rook") diagonal
pivoting method.
The factored form of A is then used to solve the system
of equations A * X = B by calling CHETRS_ROOK (uses BLAS 2).
```

**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 block diagonal matrix D and the
multipliers used to obtain the factor U or L from the
factorization A = U*D*U**H or A = L*D*L**H as computed by
CHETRF_ROOK.
```

*LDA*

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

*IPIV*

```
IPIV is INTEGER array, dimension (N)
Details of the interchanges and the block structure of D.
If UPLO = 'U':
Only the last KB elements of IPIV are set.
If IPIV(k) > 0, then rows and columns k and IPIV(k) were
interchanged and D(k,k) is a 1-by-1 diagonal block.
If IPIV(k) < 0 and IPIV(k-1) < 0, then rows and
columns k and -IPIV(k) were interchanged and rows and
columns k-1 and -IPIV(k-1) were inerchaged,
D(k-1:k,k-1:k) is a 2-by-2 diagonal block.
If UPLO = 'L':
Only the first KB elements of IPIV are set.
If IPIV(k) > 0, then rows and columns k and IPIV(k)
were interchanged and D(k,k) is a 1-by-1 diagonal block.
If IPIV(k) < 0 and IPIV(k+1) < 0, then rows and
columns k and -IPIV(k) were interchanged and rows and
columns k+1 and -IPIV(k+1) were inerchaged,
D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
```

*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 >= 1, and for best performance
LWORK >= max(1,N*NB), where NB is the optimal blocksize for
CHETRF_ROOK.
for LWORK < N, TRS will be done with Level BLAS 2
for LWORK >= N, TRS will be done with Level BLAS 3
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.

**Date:**

November 2013

```
November 2013, Igor Kozachenko,
Computer Science Division,
University of California, Berkeley
September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
School of Mathematics,
University of Manchester.fi
Definition at line 205 of file chesv_rook.f.
```

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

chesv_rook(3) is an alias of chesv_rook.f(3).