zlantr.f man page

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 (characterNORM, characterUPLO, characterDIAG, integerM, integerN, complex*16, dimension( lda, * )A, integerLDA, 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

Definition at line 142 of file zlantr.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.

Referenced By

zlantr(3) is an alias of zlantr.f(3).

Sat Nov 16 2013 Version 3.4.2 LAPACK