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## csysv_rook()

subroutine csysv_rook | ( | 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_ROOK computes the solution to system of linear equations A * X = B for SY matrices

Download CSYSV_ROOK + dependencies [TGZ] [ZIP] [TXT]

Purpose:

      !>
      !> CSYSV_ROOK 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.
      !>
      !> 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.
      !>
      !> CSYTRF_ROOK is called to compute the factorization of a complex
      !> symmetric matrix A using the bounded Bunch-Kaufman () diagonal
      !> pivoting method.
      !>
      !> The factored form of A is then used to solve the system
      !> of equations A * X = B by calling CSYTRS_ROOK.
      !>

Parameters

  [in]

  UPLO

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

  [in]

  N

      !>          N is INTEGER
      !>          The number of linear equations, i.e., the order of the
      !>          matrix A.  N >= 0.
      !>

  [in]

  NRHS

      !>          NRHS is INTEGER
      !>          The number of right hand sides, i.e., the number of columns
      !>          of the matrix B.  NRHS >= 0.
      !>

  [in,out]

  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 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
      !>          CSYTRF_ROOK.
      !>

  [in]

  LDA

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

  [out]

  IPIV

      !>          IPIV is INTEGER array, dimension (N)
      !>          Details of the interchanges and the block structure of D,
      !>          as determined by CSYTRF_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.
      !>

  [in,out]

  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.
      !>

  [in]

  LDB

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

  [out]

  WORK

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

  [in]

  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
      !>          CSYTRF_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.
      !>

  [out]

  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.

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
      !>
      !>