SSPRFS improves the computed solution to a system of linear


 equations when the coefficient matrix is symmetric indefinite


 and packed, and provides error bounds and backward error estimates


 for the solution.

UPLO

          UPLO is CHARACTER*1


          = 'U':  Upper triangle of A is stored;


          = 'L':  Lower triangle of A is stored.

N

          N is INTEGER


          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 matrices B and X.  NRHS >= 0.

AP

          AP is REAL array, dimension (N*(N+1)/2)


          The upper or lower triangle of the symmetric matrix A, packed


          columnwise in a linear array.  The j-th column of A is stored


          in the array AP as follows:


          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;


          if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.

AFP

          AFP is REAL array, dimension (N*(N+1)/2)


          The factored form of the matrix A.  AFP contains 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 SSPTRF, stored as a packed


          triangular matrix.

IPIV

          IPIV is INTEGER array, dimension (N)


          Details of the interchanges and the block structure of D


          as determined by SSPTRF.

B

          B is REAL array, dimension (LDB,NRHS)


          The right hand side matrix B.

LDB

          LDB is INTEGER


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

X

          X is REAL array, dimension (LDX,NRHS)


          On entry, the solution matrix X, as computed by SSPTRS.


          On exit, the improved solution matrix X.

LDX

          LDX is INTEGER


          The leading dimension of the array X.  LDX >= max(1,N).

FERR

          FERR is REAL array, dimension (NRHS)


          The estimated forward error bound for each solution vector


          X(j) (the j-th column of the solution matrix X).


          If XTRUE is the true solution corresponding to X(j), FERR(j)


          is an estimated upper bound for the magnitude of the largest


          element in (X(j) - XTRUE) divided by the magnitude of the


          largest element in X(j).  The estimate is as reliable as


          the estimate for RCOND, and is almost always a slight


          overestimate of the true error.

BERR

          BERR is REAL array, dimension (NRHS)


          The componentwise relative backward error of each solution


          vector X(j) (i.e., the smallest relative change in


          any element of A or B that makes X(j) an exact solution).

WORK

          WORK is REAL array, dimension (3*N)

IWORK

          IWORK is INTEGER array, dimension (N)

INFO

          INFO is INTEGER


          = 0:  successful exit


          < 0:  if INFO = -i, the i-th argument had an illegal value

  ITMAX is the maximum number of steps of iterative refinement.

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