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



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

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

           CHARACTER     UPLO

           INTEGER       INFO, LDB, N, NRHS

           INTEGER       IPIV( * )

           COMPLEX*16    AP( * ), B( LDB, * )

PURPOSE
       ZSPSV computes the solution to a complex 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) COMPLEX*16 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 ZSPTRF, 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 ZSPTRF.  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) COMPLEX*16 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                        ZSPSV(3)