# dsysv_rook (3) - Linux Manuals

dsysv_rook.f -

## SYNOPSIS

### Functions/Subroutines

subroutine dsysv_rook (UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, LWORK, INFO)
DSYSV_ROOK computes the solution to system of linear equations A * X = B for SY matrices

## Function/Subroutine Documentation

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

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

Purpose:

``` DSYSV_ROOK 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.

The 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 symmetric and block diagonal with
1-by-1 and 2-by-2 diagonal blocks.

DSYTRF_ROOK is called to compute the factorization of a real
symmetric 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 DSYTRS_ROOK.
```

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 block diagonal matrix D and the
multipliers used to obtain the factor U or L from the
factorization A = U*D*U**T or A = L*D*L**T as computed by
DSYTRF_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,
as determined by DSYTRF_ROOK.

If UPLO = 'U':
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':
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 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 >= 1, and for best performance
LWORK >= max(1,N*NB), where NB is the optimal blocksize for
DSYTRF_ROOK.

TRS will be done with Level 2 BLAS

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

NAG Ltd.

Date:

April 2012

Contributors:

```   April 2012, Igor Kozachenko,
Computer Science Division,
University of California, Berkeley

September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
School of Mathematics,
University of Manchester
```

Definition at line 204 of file dsysv_rook.f.

## Author

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