NAME

       zlantr.f -

SYNOPSIS

   Functions/Subroutines
       double precision function zlantr (NORM, UPLO, DIAG, M, N, A, LDA, WORK)
           ZLANTR 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

   double precision function zlantr (character NORM, character UPLO, character DIAG, integer M,
       integer N, complex*16, dimension( lda, * ) A, integer LDA, double precision, dimension( *
       ) WORK)
       ZLANTR 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:

            ZLANTR  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:
           ZLANTR

               ZLANTR = ( 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 ZLANTR 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, ZLANTR 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, ZLANTR is set to zero.

           A

                     A is COMPLEX*16 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 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.

       Date:
           September 2012

Author

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