LANTR - 5.2 English - 68552

LANTR returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,

or the element of largest absolute value of a trapezoidal or triangular matrix.

Purpose:

    LANTR  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.
    \return LANTR
       LANTR = ( fla_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  fla_max(abs(A(i,j)))  is not a consistent matrix norm.

Parameters:

• NORM – [in]

  NORM is CHARACTER*1

  Specifies the value to be returned in SLANTR as described above.

• UPLO – [in]

  UPLO is 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 – [in]

  DIAG is CHARACTER*1

  Specifies whether or not the matrix A has unit diagonal.

  = ‘N’: Non-unit diagonal

  = ‘U’: Unit diagonal

• M – [in]

  M is 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 – [in]

  N is 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 – [in]

  A is 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 – [in]

  LDA is INTEGER

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

• WORK – [out]

  WORK is REAL array, dimension (MAX(1,LWORK)),

  where LWORK >= M when NORM = ‘I’; otherwise, WORK is not referenced.

Returns:

Returns value of the norm.