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## zspsv()

subroutine zspsv | ( | character | uplo,
|  | integer | n,
|  | integer | nrhs,
|  | complex*16, dimension( * ) | ap,
|  | integer, dimension( * ) | ipiv,
|  | complex*16, dimension( ldb, * ) | b,
|  | integer | ldb,
|  | integer | info )

ZSPSV computes the solution to system of linear equations A * X = B for OTHER matrices

Download ZSPSV + dependencies [TGZ] [ZIP] [TXT]

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)
      !> triangular 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.
      !>

Parameters

  [in]

  UPLO

      !>          UPLO is CHARACTER*1
      !>          = 'U':  Upper triangle of A is stored;
      !>          = 'L':  Lower triangle of A is stored.
      !>

  [in]

  N

      !>          N is INTEGER
      !>          The number of linear equations, i.e., the order of the
      !>          matrix A.  N >= 0.
      !>

  [in]

  NRHS

      !>          NRHS is INTEGER
      !>          The number of right hand sides, i.e., the number of columns
      !>          of the matrix B.  NRHS >= 0.
      !>

  [in,out]

  AP

      !>          AP is 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 triangular matrix in the same storage format as A.
      !>

  [out]

  IPIV

      !>          IPIV is 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.
      !>

  [in,out]

  B

      !>          B is 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.
      !>

  [in]

  LDB

      !>          LDB is INTEGER
      !>          The leading dimension of the array B.  LDB >= max(1,N).
      !>

  [out]

  INFO

      !>          INFO is 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.
      !>

Author
  Univ. of Tennessee
  Univ. of California Berkeley
  Univ. of Colorado Denver
  NAG Ltd.

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 ]
      !>