Purpose
 =======
 
    LA_SPSVX computes the solution to a linear system of equations
 A*X = B, where A is a real or complex symmetric matrix stored in packed
 format and X and B are rectangular matrices or vectors.
    LA_HPSVX computes the solution to a linear system of equations 
 A*X = B, where A is a complex Hermitian matrix stored in packed format 
 and X and B are rectangular matrices or vectors.
    LA_SPSVX and LA_HPSVX can also optionally estimate the condition 
 number of A and compute error bounds.
 
 =========
 
       SUBROUTINE LA_SPSVX / LA_HPSVX( AP, B, X, UPLO=uplo, AFP=afp, &
                         IPIV=ipiv, FACT=fact, FERR=ferr, BERR=berr, &
                         RCOND=rcond, INFO=info )
            <type>(<wp>), INTENT(IN) :: AP(:), <rhs>
            <type>(<wp>), INTENT(OUT) :: <sol>
            CHARACTER(LEN=1), INTENT(IN), OPTIONAL :: UPLO
            <type>(<wp>), INTENT(INOUT), OPTIONAL :: AFP(:)
            INTEGER, INTENT(INOUT), OPTIONAL :: IPIV(:)
            CHARACTER(LEN=1), INTENT(IN), OPTIONAL :: FACT
            REAL(<wp>), INTENT(OUT), OPTIONAL :: <err>, RCOND
            INTEGER, INTENT(OUT), OPTIONAL :: INFO
       where
            <type> ::= REAL | COMPLEX
            <wp>   ::= KIND(1.0) | KIND(1.0D0)
            <rhs>  ::= B(:,:) | B(:)
            <sol>  ::= X(:,:) | X(:)
            <err>  ::= FERR(:), BERR(:) | FERR, BERR
 
 Arguments
 =========
 
 AP       (input) REAL or COMPLEX array, shape (:) with size(AP ) = 
          n*(n + 1)/2, where n is the order of A.
          On entry, the upper or lower triangle of matrix A in packed 
 	  storage. The elements are stored columnwise as follows:
          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j<=n;
 	  if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for 1<=j<=i<=n.
 B        (input) REAL or COMPLEX array, shape (:,:) with 
          size(B,1) = n or shape (:) with size(B) = n.
          The matrix B.
 X        (output) REAL or COMPLEX array, shape (:,:) with 
          size(X,1) = n and size(X,2) = size(B,2), or shape (:) with 
 	  size(X) = n.
          The solution matrix X .
 UPLO     Optional (input) CHARACTER(LEN=1).
            = 'U': Upper triangle of A is stored;
            = 'L': Lower triangle of A is stored.
          Default value: 'U'.
 AFP      Optional (input or output) REAL or COMPLEX array, shape (:,:)
          with the same size as AP.
          If FACT = 'F', then AFP is an input argument that contains 
 	  the block diagonal matrix D and the multipliers used to 
 	  obtain the factor L or U from the factorization of A, returned
 	  by a previous call to LA_SPSVX or LA_HPSVX and stored as a 
 	  packed triangular matrix in the same storage format as A.
          If FACT = 'N', then AFP is an output argument that contains 
 	  the block diagonal matrix D and the multipliers used to obtain
 	  the factor L or U from the factorization of A, stored as a
          packed triangular matrix in the same storage format as A.
 IPIV     Optional (input or output) INTEGER array, shape (:) with 
          size(IPIV) = size(A,1).
          If FACT = 'F', then IPIV is an input argument that contains 
 	  details of the row and column interchanges and the block 
 	  structure of D.
          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 IPIV(k) < 0 , then there are two cases:
           1. 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.
           2. 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.
          If FACT = 'N', then IPIV is an output argument and on exit 
 	  contains details of the interchanges and the block structure
 	  of D (as described above).
 FACT     Optional (input) CHARACTER(LEN=1).
          Specifies whether the factored form of A has been supplied 
 	   on entry.
            = 'N': The matrix A will be copied to AFP and factored.
            = 'F': AFP and IPIV contain the factored form of A.
          Default value: 'N'.
 FERR     Optional (output) REAL array of shape (:), with size(FERR)=
          size(X,2), or REAL scalar.
          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     Optional (output) REAL array of shape (:), with size(BERR) =
          size(X,2), or REAL scalar.
          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).
 RCOND    Optional (output) REAL
          The estimate of the reciprocal condition number of A. If RCOND
 	  is less than the machine precision, the matrix is singular to
 	  working precision. This condition is indicated by a return
          code of INFO > 0.
 INFO     (output) INTEGER
          = 0: successful exit.
          < 0: if INFO = -i, the i-th argument had an illegal value.
          > 0: if INFO = i, and i is
             <= n: D(i,i) = 0. The factorization has been completed, but
 	         the block diagonal matrix D is singular, so the 
 		 solution could not be computed.
             = n+1: D is nonsingular, but RCOND is less than machine 
 	         precision, so the matrix is singular to working 
 		 precision. Nevertheless, the solution and error bounds
 		 are computed because the computed solution can be more
 		 accurate than the value of RCOND would suggest.
            n is the order of A.
          If INFO is not present and an error occurs, then the program
          is terminated with an error message.