Previous: zsprfs Up: ../lapack-z.html Next: zspsvx


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


          CHARACTER     UPLO

          INTEGER       INFO, LDB, N, NRHS

          INTEGER       IPIV( * )

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

      ZSPSV computes the solution to a complex system of linear
         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.

      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 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 multi-
              pliers 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 ZSPTRF, 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 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

      LDB     (input) INTEGER
              The leading dimension of the array B.  LDB >=

      INFO    (output) INTEGER
              = 0:  successful exit
              < 0:  if INFO = -i, the i-th argument had an illegal
              > 0:  if INFO = i, D(i,i) is exactly zero.  The fac-
              torization has been completed, but the block diago-
              nal matrix D is exactly singular, so the solution
              could not be computed.

      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)

      Packed storage of the upper triangle of A:

      AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]