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

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

     CHARACTER UPLO

     INTEGER INFO, LDB, N, NRHS

     INTEGER IPIV( * )

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



     #include <sunperf.h>

     void cspsv(char uplo, int n, int  nrhs,  complex  *cap,  int
               *ipivot, complex *cb, int ldb, int *info) ;

PURPOSE
     CSPSV 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) triangular matrices, D is symmetric and block diago-
     nal 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     array,     dimension
               (N*(N+1)/2)
               On entry, the upper or lower triangle of the  sym-
               metric  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  mul-
               tipliers used to obtain the factor U or L from the
               factorization A = U*D*U**T or A = L*D*L**T as com-
               puted  by  CSPTRF,  stored  as a packed triangular
               matrix in the same storage format as A.

     IPIV      (output) INTEGER array, dimension (N)
               Details of the interchanges and the  block  struc-
               ture  of D, as determined by CSPTRF.  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) COMPLEX 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 ille-
               gal 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 ]

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