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## sppsv()

subroutine sppsv | ( | character | uplo,
|  | integer | n,
|  | integer | nrhs,
|  | real, dimension( * ) | ap,
|  | real, dimension( ldb, * ) | b,
|  | integer | ldb,
|  | integer | info )

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

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

Purpose:

      !>
      !> SPPSV computes the solution to a real system of linear equations
      !>    A * X = B,
      !> where A is an N-by-N symmetric positive definite matrix stored in
      !> packed format and X and B are N-by-NRHS matrices.
      !>
      !> The Cholesky decomposition is used to factor A as
      !>    A = U**T* U,  if UPLO = 'U', or
      !>    A = L * L**T,  if UPLO = 'L',
      !> where U is an upper triangular matrix and L is a lower triangular
      !> matrix.  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 REAL 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, if INFO = 0, the factor U or L from the Cholesky
      !>          factorization A = U**T*U or A = L*L**T, in the same storage
      !>          format as A.
      !>

  [in,out]

  B

      !>          B is REAL 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, the leading principal minor of order i
      !>                of A is not positive, so the factorization could not
      !>                be completed, and the solution has not been 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 = conjg(aji))
      !>                 a44
      !>
      !>  Packed storage of the upper triangle of A:
      !>
      !>  AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]
      !>