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sspsv

 NAME
      SSPSV - compute the solution to a real system of linear
      equations  A * X = B,

 SYNOPSIS
      SUBROUTINE SSPSV( UPLO, N, NRHS, AP, IPIV, B, LDB, INFO )

          CHARACTER     UPLO

          INTEGER       INFO, LDB, N, NRHS

          INTEGER       IPIV( * )

          REAL          AP( * ), B( LDB, * )

 PURPOSE
      SSPSV computes the solution to a real system of linear equa-
      tions
         A * X = B, where A is an N-by-N symmetric matrix stored
      in packed format 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, D is symmetric and block diago-
      nal 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.

 ARGUMENTS
      UPLO    (input) CHARACTER*1
              = 'U':  Upper triangle of A is stored;
              = 'L':  Lower triangle of A is stored.

      N       (input) INTEGER
              The number of linear equations, i.e., the order of
              the matrix A.  N >= 0.

      NRHS    (input) INTEGER
              The number of right hand sides, i.e., the number of
              columns of the matrix B.  NRHS >= 0.

      AP      (input/output) REAL array, dimension (N*(N+1)/2)
              On entry, the upper or lower triangle of the sym-
              metric 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)*(2n-j)/2) = A(i,j) for j<=i<=n.  See below for
              further details.

              On exit, the block diagonal matrix D and the multi-
              pliers used to obtain the factor U or L from the
              factorization A = U*D*U**T or A = L*D*L**T as com-
              puted by SSPTRF, stored as a packed triangular
              matrix in the same storage format as A.

      IPIV    (output) INTEGER array, dimension (N)
              Details of the interchanges and the block structure
              of D, as determined by SSPTRF.  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       (input/output) 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     (input) INTEGER
              The leading dimension of the array B.  LDB >=
              max(1,N).

      INFO    (output) 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 fac-
              torization has been completed, but the block diago-
              nal matrix D is exactly singular, so the solution
              could not be computed.

 FURTHER DETAILS
      The packed storage scheme is illustrated by the following
      example when N = 4, UPLO = 'U':

      Two-dimensional storage of the symmetric matrix A:

         a11 a12 a13 a14
             a22 a23 a24
                 a33 a34     (aij = aji)
                     a44

      Packed storage of the upper triangle of A:

      AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]