---
name: "clantr.f"
section: "3"
platform: "linux"
package: "lapack-doc"
version: "3.12.1-2"
release: "Arch Linux 2026-11-01"
platforms: ["linux"]
url: "https://new.carta.tech/clantr.f"
---

# clantr.f(3)

## NAME

SRC/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 (character norm, character uplo, character diag, integer m, integer n, complex, dimension( lda, \* ) a, integer lda, 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.

Definition at line **140** of file **clantr.f**.

## Author

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