SLANSY (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

SYNOPSIS

  REAL FUNCTION SLANSY( NORM, UPLO, N, A, LDA, WORK )

      CHARACTER NORM, UPLO

      INTEGER   LDA, N

      REAL      A( LDA, * ), WORK( * )

PURPOSE

  SLANSY  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.

DESCRIPTION

  SLANSY returns the value

     SLANSY = ( 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 SLANSY as described above.

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

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

  A       (input) REAL array, dimension (LDA,N)
          The symmetric matrix A.  If UPLO = 'U', the leading n by n upper
          triangular part of A contains the upper triangular part of the
          matrix A, and the strictly lower triangular part of A is not
          referenced.  If UPLO = 'L', the leading n by n lower triangular
          part of A contains the lower triangular part of the matrix A, and
          the strictly upper triangular part of A is not referenced.

  LDA     (input) INTEGER
          The leading dimension of the array A.  LDA >= max(N,1).

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