ssysv_rk.f(3)

NAME
ssysv_rk.f

SYNOPSIS

  Functions/Subroutines
subroutine ssysv_rk (UPLO, N, NRHS, A, LDA, E, IPIV, B, LDB, WORK, LWORK, INFO)
SSYSV_RK computes the solution to system of linear equations A * X = B for SY matrices

Function/Subroutine Documentation

  subroutine ssysv_rk (character UPLO, integer N, integer NRHS, real, dimension( lda, * ) A, integer LDA, real, dimension( * ) E, integer, dimension( * ) IPIV, real, dimension( ldb, * ) B, integer LDB, real, dimension( * ) WORK, integer LWORK, integer INFO)

Purpose:

     SSYSV_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.
     SSYTRF_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 SSYTRS_3.

Parameters
    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.

    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 REAL 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 SSYTRF_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.

    LDA

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

    E

              E is REAL 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.

    IPIV

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

    B

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

    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.

    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

Definition at line 226 of file ssysv_rk.f.

Author

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