DSPSV(3)              LAPACK driver routine (version 3.1)             DSPSV(3)



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

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

           CHARACTER     UPLO

           INTEGER       INFO, LDB, N, NRHS

           INTEGER       IPIV( * )

           DOUBLE        PRECISION AP( * ), B( LDB, * )

PURPOSE
       DSPSV computes the solution to a real system of linear equations
          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)  tri-
       angular  matrices,  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.


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) DOUBLE PRECISION array, dimension (N*(N+1)/2)
               On  entry,  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)*(2n-j)/2)  =  A(i,j)  for j<=i<=n.  See below for further
               details.

               On exit, 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 DSPTRF, stored as a packed  tri-
               angular 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 DSPTRF.  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) DOUBLE PRECISION 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  factorization
               has  been completed, but the block diagonal 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 ]




 LAPACK driver routine (version 3.N1o)vember 2006                        DSPSV(3)