# zlantr.f man page

zlantr.f —

## Synopsis

### Functions/Subroutines

DOUBLE PRECISION functionzlantr(NORM, UPLO, DIAG, M, N, A, LDA, WORK)ZLANTRreturns 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).