slantr.f(3)

NAME
slantr.f -

SYNOPSIS

  Functions/Subroutines

real function slantr (NORM, UPLO, DIAG, M, N, A, LDA, WORK)
SLANTR 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.

Function/Subroutine Documentation

  real function slantr (characterNORM, characterUPLO, characterDIAG, integerM, integerN, real, dimension( lda, * )A, integerLDA, real, dimension( * )WORK)

SLANTR 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:

     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.

Returns:
    SLANTR

        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 consistent matrix norm.

Parameters:
    NORM

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

    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.

    DIAG

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

    M

              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

              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

              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

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

    WORK

              WORK is REAL 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.

Date:
    September 2012

Definition at line 141 of file slantr.f.

Author

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