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## dsysv_rk()

subroutine dsysv_rk | ( | character | uplo,
|  | integer | n,
|  | integer | nrhs,
|  | double precision, dimension( lda, * ) | a,
|  | integer | lda,
|  | double precision, dimension( * ) | e,
|  | integer, dimension( * ) | ipiv,
|  | double precision, dimension( ldb, * ) | b,
|  | integer | ldb,
|  | double precision, dimension( * ) | work,
|  | integer | lwork,
|  | integer | info )

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

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

Purpose:

      !> DSYSV_RK 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 bounded Bunch-Kaufman (rook) diagonal pivoting method is used
      !> to factor A as
      !>    A = P*U*D*(U**T)*(P**T),  if UPLO = 'U', or
      !>    A = P*L*D*(L**T)*(P**T),  if UPLO = 'L',
      !> where U (or L) is unit upper (or lower) triangular matrix,
      !> U**T (or L**T) is the transpose of U (or L), P is a permutation
      !> matrix, P**T is the transpose of P, and D is symmetric and block
      !> diagonal with 1-by-1 and 2-by-2 diagonal blocks.
      !>
      !> DSYTRF_RK is called to compute the factorization of a real
      !> symmetric matrix.  The factored form of A is then used to solve
      !> the system of equations A * X = B by calling BLAS3 routine DSYTRS_3.
      !>

Parameters

  [in]

  UPLO

      !>          UPLO is CHARACTER*1
      !>          Specifies whether the upper or lower triangular part of the
      !>          symmetric matrix A is stored:
      !>          = '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 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, diagonal of the block diagonal
      !>          matrix D and factors U or L  as computed by DSYTRF_RK:
      !>            a) ONLY diagonal elements of the symmetric block diagonal
      !>               matrix D on the diagonal of A, i.e. D(k,k) = A(k,k);
      !>               (superdiagonal (or subdiagonal) elements of D
      !>                are stored on exit in array E), and
      !>            b) If UPLO = 'U': factor U in the superdiagonal part of A.
      !>               If UPLO = 'L': factor L in the subdiagonal part of A.
      !>
      !>          For more info see the description of DSYTRF_RK routine.
      !>

  [in]

  LDA

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

  [out]

  E

      !>          E is DOUBLE PRECISION array, dimension (N)
      !>          On exit, contains the output computed by the factorization
      !>          routine DSYTRF_RK, i.e. the superdiagonal (or subdiagonal)
      !>          elements of the symmetric block diagonal matrix D
      !>          with 1-by-1 or 2-by-2 diagonal blocks, where
      !>          If UPLO = 'U': E(i) = D(i-1,i), i=2:N, E(1) is set to 0;
      !>          If UPLO = 'L': E(i) = D(i+1,i), i=1:N-1, E(N) is set to 0.
      !>
      !>          NOTE: For 1-by-1 diagonal block D(k), where
      !>          1 <= k <= N, the element E(k) is set to 0 in both
      !>          UPLO = 'U' or UPLO = 'L' cases.
      !>
      !>          For more info see the description of DSYTRF_RK routine.
      !>

  [out]

  IPIV

      !>          IPIV is INTEGER array, dimension (N)
      !>          Details of the interchanges and the block structure of D,
      !>          as determined by DSYTRF_RK.
      !>
      !>          For more info see the description of DSYTRF_RK routine.
      !>

  [in,out]

  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.
      !>

  [in]

  LDB

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

  [out]

  WORK

      !>          WORK is DOUBLE PRECISION array, dimension ( MAX(1,LWORK) ).
      !>          Work array used in the factorization stage.
      !>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
      !>

  [in]

  LWORK

      !>          LWORK is INTEGER
      !>          The length of WORK.  LWORK >= 1. For best performance
      !>          of factorization stage LWORK >= max(1,N*NB), where NB is
      !>          the optimal blocksize for DSYTRF_RK.
      !>
      !>          If LWORK = -1, then a workspace query is assumed;
      !>          the routine only calculates the optimal size of the WORK
      !>          array for factorization stage, 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 = -k, the k-th argument had an illegal value
      !>
      !>          > 0: If INFO = k, the matrix A is singular, because:
      !>                 If UPLO = 'U': column k in the upper
      !>                 triangular part of A contains all zeros.
      !>                 If UPLO = 'L': column k in the lower
      !>                 triangular part of A contains all zeros.
      !>
      !>               Therefore D(k,k) is exactly zero, and superdiagonal
      !>               elements of column k of U (or subdiagonal elements of
      !>               column k of L ) are all zeros. The factorization has
      !>               been completed, but the block diagonal matrix D is
      !>               exactly singular, and division by zero will occur if
      !>               it is used to solve a system of equations.
      !>
      !>               NOTE: INFO only stores the first occurrence of
      !>               a singularity, any subsequent occurrence of singularity
      !>               is not stored in INFO even though the factorization
      !>               always completes.
      !>

Author
  Univ. of Tennessee
  Univ. of California Berkeley
  Univ. of Colorado Denver
  NAG Ltd.

Contributors:

      !>
      !>  December 2016,  Igor Kozachenko,
      !>                  Computer Science Division,
      !>                  University of California, Berkeley
      !>
      !>  September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
      !>                  School of Mathematics,
      !>                  University of Manchester
      !>
      !>