SLANTR (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 trapezoidal or triangular matrix A

SYNOPSIS

  REAL FUNCTION SLANTR( NORM, UPLO, DIAG, M, N, A, LDA, WORK )

      CHARACTER DIAG, NORM, UPLO

      INTEGER   LDA, M, N

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

PURPOSE

  SLANTR  returns the value of the one norm,  or the Frobenius norm, or the
  infinity norm,  or the  element of  largest absolute value  of a
  trapezoidal or triangular matrix A.

DESCRIPTION

  SLANTR returns the value

     SLANTR = ( 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 SLANTR as described above.

  UPLO    (input) CHARACTER*1
          Specifies whether the matrix A is upper or lower trapezoidal.  =
          'U':  Upper trapezoidal
          = 'L':  Lower trapezoidal Note that A is triangular instead of
          trapezoidal if M = N.

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

  M       (input) INTEGER
          The number of rows of the matrix A.  M >= 0, and if UPLO = 'U', M
          <= N.  When M = 0, SLANTR is set to zero.

  N       (input) INTEGER
          The number of columns of the matrix A.  N >= 0, and if UPLO = 'L',
          N <= M.  When N = 0, SLANTR is set to zero.

  A       (input) REAL array, dimension (LDA,N)
          The trapezoidal matrix A (A is triangular if M = N).  If UPLO =
          'U', the leading m by n upper trapezoidal part of the array A
          contains the upper trapezoidal matrix, and the strictly lower
          triangular part of A is not referenced.  If UPLO = 'L', the leading
          m by n lower trapezoidal part of the array A contains the lower
          trapezoidal matrix, and the strictly upper triangular part of A is
          not referenced.  Note that when DIAG = 'U', the diagonal elements
          of A are not referenced and are assumed to be one.

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

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