SRC/ssysv.f(3)

NAME
SRC/ssysv.f

SYNOPSIS

  Functions/Subroutines
subroutine ssysv (uplo, n, nrhs, a, lda, ipiv, b, ldb, work, lwork, info)
SSYSV computes the solution to system of linear equations A * X = B for SY matrices

Function/Subroutine Documentation

  subroutine ssysv (character uplo, integer n, integer nrhs, real, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, real, dimension( ldb, * ) b, integer ldb, real, dimension( * ) work, integer lwork, integer info)

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

Purpose:

    !>
    !> SSYSV 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.  The factored form of A is then
    !> used to solve the system of equations A * X = B.
    !>

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 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, 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
    !>          SSYTRF.
    !>

    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 SSYTRF.  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 UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0,
    !>          then rows and columns k-1 and -IPIV(k) were interchanged and
    !>          D(k-1:k,k-1:k) is a 2-by-2 diagonal block.  If UPLO = 'L' and
    !>          IPIV(k) = IPIV(k+1) < 0, then rows and columns k+1 and
    !>          -IPIV(k) were interchanged and D(k:k+1,k:k+1) is a 2-by-2
    !>          diagonal block.
    !>

    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))
    !>          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
    !>          SSYTRF.
    !>          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.

Definition at line 169 of file ssysv.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.