# clantr.f(3) [centos man page]

```clantr.f(3)							      LAPACK							       clantr.f(3)

NAME
clantr.f -

SYNOPSIS
Functions/Subroutines
REAL function clantr (NORM, UPLO, DIAG, M, N, A, LDA, WORK)
CLANTR 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 clantr (characterNORM, characterUPLO, characterDIAG, integerM, integerN, complex, dimension( lda, * )A, integerLDA, real,
dimension( * )WORK)
CLANTR 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:

CLANTR  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:
CLANTR

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

A

A is COMPLEX 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 142 of file clantr.f.

Author
Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2							  Tue Sep 25 2012						       clantr.f(3)```

## Check Out this Related Man Page

```CLANTR(l)								 )								 CLANTR(l)

NAME
CLANTR  -  return  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
REAL FUNCTION CLANTR( NORM, UPLO, DIAG, M, N, A, LDA, WORK )

CHARACTER DIAG, NORM, UPLO

INTEGER   LDA, M, N

REAL      WORK( * )

COMPLEX   A( LDA, * )

PURPOSE
CLANTR returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a trape-
zoidal or triangular matrix A.

DESCRIPTION
CLANTR returns the value

CLANTR = ( 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  matrix norm.

ARGUMENTS
NORM    (input) CHARACTER*1
Specifies the value to be returned in CLANTR 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, CLANTR 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, CLANTR is set to zero.

A       (input) COMPLEX 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  con-
tains 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) REAL array, dimension (LWORK),
where LWORK >= M when NORM = 'I'; otherwise, WORK is not referenced.

LAPACK version 3.0						   15 June 2000 							 CLANTR(l)```
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