DSYSV  -  compute  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)  triangular matrices, and D is symmetric and block
       diagonal with 1-by-1 and 2-by-2 diagonal blocks.  The fac­
       tored  form of A is then used to solve the system of equa­
       tions 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 con­
               tains  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 tri­
               angular  part  of  the  matrix A, and the strictly


               On exit, if INFO = 0, 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 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  struc­
               ture  of D, as determined by DSYTRF.  If IPIV(k) >
               0, then rows and columns k and IPIV(k) were inter­
               changed,  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 inter­
               changed 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 inter­
               changed  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 (LWORK)
               On  exit, if INFO = 0, WORK(1) returns the optimal
               LWORK.

       LWORK   (input) INTEGER
               The length of WORK.  LWORK >= 1, and for best per­
               formance  LWORK  >=  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  ille­
               gal value

               factorization has been completed,  but  the  block
               diagonal  matrix  D  is  exactly  singular, so the
               solution could not be computed.


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