Provided by: liblapack-doc_3.3.1-1_all

#### NAME

```       LAPACK-3 - 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

```

#### SYNOPSIS

```       DOUBLE PRECISION FUNCTION ZLANTR( NORM, UPLO, DIAG, M, N, A, LDA, WORK )

CHARACTER    DIAG, NORM, UPLO

INTEGER      LDA, M, N

DOUBLE       PRECISION WORK( * )

COMPLEX*16   A( LDA, * )

```

#### 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.

```

#### DESCRIPTION

```        ZLANTR returns the value
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.

```

#### ARGUMENTS

```        NORM    (input) CHARACTER*1
Specifies the value to be returned in ZLANTR as described
above.

UPLO    (input) 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    (input) CHARACTER*1
Specifies whether or not the matrix A has unit diagonal.
= 'N':  Non-unit diagonal
= 'U':  Unit diagonal

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

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

LAPACK auxiliary routine (version 3.2)     April 2011                            ZLANTR(3lapack)
```