DLANSP (3lapack)

return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric matrix A, supplied in packed form

SYNOPSIS

  DOUBLE PRECISION FUNCTION DLANSP( NORM, UPLO, N, AP, WORK )

      CHARACTER    NORM, UPLO

      INTEGER      N

      DOUBLE       PRECISION AP( * ), WORK( * )

PURPOSE

  DLANSP  returns the value of the one norm,  or the Frobenius norm, or the
  infinity norm,  or the  element of  largest absolute value  of a real
  symmetric matrix A,  supplied in packed form.

DESCRIPTION

  DLANSP returns the value

     DLANSP = ( max(abs(A(i,j))), NORM = 'M' or 'm'
              (
              ( norm1(A),         NORM = '1', 'O' or 'o'
              (
              ( normI(A),         NORM = 'I' or 'i'
              (
              ( normF(A),         NORM = 'F', 'f', 'E' or 'e'

  where  norm1  denotes the  one norm of a matrix (maximum column sum), normI
  denotes the  infinity norm  of a matrix  (maximum row sum) and normF
  denotes the  Frobenius norm of a matrix (square root of sum of squares).
  Note that  max(abs(A(i,j)))  is not a  matrix norm.

ARGUMENTS

  NORM    (input) CHARACTER*1
          Specifies the value to be returned in DLANSP as described above.

  UPLO    (input) CHARACTER*1
          Specifies whether the upper or lower triangular part of the
          symmetric matrix A is supplied.  = 'U':  Upper triangular part of A
          is supplied
          = 'L':  Lower triangular part of A is supplied

  N       (input) INTEGER
          The order of the matrix A.  N >= 0.  When N = 0, DLANSP is set to
          zero.

  AP      (input) DOUBLE PRECISION array, dimension (N*(N+1)/2)
          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.

  WORK    (workspace) DOUBLE PRECISION array, dimension (LWORK),
          where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise, WORK is
          not referenced.