SLANTP (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 triangular matrix A, supplied in packed form

SYNOPSIS

  REAL FUNCTION SLANTP( NORM, UPLO, DIAG, N, AP, WORK )

      CHARACTER DIAG, NORM, UPLO

      INTEGER   N

      REAL      AP( * ), WORK( * )

PURPOSE

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

DESCRIPTION

  SLANTP returns the value

     SLANTP = ( 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 SLANTP as described above.

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

  DIAG    (input) CHARACTER*1
          Specifies whether or not the matrix A is unit triangular.  = 'N':
          Non-unit triangular
          = 'U':  Unit triangular

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

  AP      (input) REAL array, dimension (N*(N+1)/2)
          The upper or lower triangular 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.  Note that
          when DIAG = 'U', the elements of the array AP corresponding to the
          diagonal elements of the matrix A are not referenced, but are
          assumed to be one.

  WORK    (workspace) REAL array, dimension (LWORK),
          where LWORK >= N when NORM = 'I'; otherwise, WORK is not
          referenced.