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



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

SYNOPSIS
       SUBROUTINE DSYSV( UPLO,  N,  NRHS,  A,  LDA, IPIV, B, LDB, WORK, LWORK,
                         INFO )

           CHARACTER     UPLO

           INTEGER       INFO, LDA, LDB, LWORK, N, NRHS

           INTEGER       IPIV( * )

           DOUBLE        PRECISION A( LDA, * ), B( LDB, * ), WORK( * )

PURPOSE
       DSYSV 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) tri-
       angular 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.


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.

       A       (input/output) DOUBLE PRECISION 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  mul-
               tipliers  used  to obtain the factor U or L from the factoriza-
               tion A = U*D*U**T or A = L*D*L**T as computed by DSYTRF.

       LDA     (input) INTEGER
               The leading dimension of the array A.  LDA >= max(1,N).

       IPIV    (output) INTEGER array, dimension (N)
               Details of the interchanges and the block structure  of  D,  as
               determined  by DSYTRF.  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).

       WORK       (workspace/output)   DOUBLE   PRECISION   array,   dimension
       (MAX(1,LWORK))
               On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

       LWORK   (input) INTEGER
               The length of WORK.  LWORK >= 1, and for best performance LWORK
               >= max(1,N*NB), where NB is the optimal blocksize for DSYTRF.

               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    (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.



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