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## dlantr()

double precision function dlantr | ( | character | norm,
|  | character | uplo,
|  | character | diag,
|  | integer | m,
|  | integer | n,
|  | double precision, dimension( lda, * ) | a,
|  | integer | lda,
|  | double precision, dimension( * ) | work )

DLANTR 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.

Download DLANTR + dependencies [TGZ] [ZIP] [TXT]

Purpose:

      !>
      !> DLANTR  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.
      !>

Returns
  DLANTR

      !>
      !>    DLANTR = ( 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 consistent matrix norm.
      !>

Parameters

  [in]

  NORM

      !>          NORM is CHARACTER*1
      !>          Specifies the value to be returned in DLANTR as described
      !>          above.
      !>

  [in]

  UPLO

      !>          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.
      !>

  [in]

  DIAG

      !>          DIAG is CHARACTER*1
      !>          Specifies whether or not the matrix A has unit diagonal.
      !>          = 'N':  Non-unit diagonal
      !>          = 'U':  Unit diagonal
      !>

  [in]

  M

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

  [in]

  N

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

  [in]

  A

      !>          A is DOUBLE PRECISION 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.
      !>

  [in]

  LDA

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

  [out]

  WORK

      !>          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
      !>          where LWORK >= M when NORM = 'I'; otherwise, WORK is not
      !>          referenced.
      !>

Author
  Univ. of Tennessee
  Univ. of California Berkeley
  Univ. of Colorado Denver
  NAG Ltd.