---
name: "lange"
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/lange"
---

# lange(3)

lange: general matrix

## NAME

lange - lange: general matrix

## SYNOPSIS

### Functions

real function **clange** (norm, m, n, a, lda, work)\
 **CLANGE** returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of a general rectangular matrix.  double precision function **dlange** (norm, m, n, a, lda, work)\
 **DLANGE** returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of a general rectangular matrix.  real function **slange** (norm, m, n, a, lda, work)\
 **SLANGE** returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of a general rectangular matrix.  double precision function **zlange** (norm, m, n, a, lda, work)\
 **ZLANGE** returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of a general rectangular matrix.

## Detailed Description

## Function Documentation

### real function clange (character norm, integer m, integer n, complex, dimension( lda, \* ) a, integer lda, real, dimension( \* ) work)

**CLANGE** returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of a general rectangular matrix.

**Purpose:**

```
!>
!> CLANGE  returns the value of the one norm,  or the Frobenius norm, or
!> the  infinity norm,  or the  element of  largest absolute value  of a
!> complex matrix A.
!>
```

**Returns**

CLANGE

```
!>
!>    CLANGE = ( 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 CLANGE as described
!>          above.
!>
```

*M*

```
!>          M is INTEGER
!>          The number of rows of the matrix A.  M >= 0.  When M = 0,
!>          CLANGE is set to zero.
!>
```

*N*

```
!>          N is INTEGER
!>          The number of columns of the matrix A.  N >= 0.  When N = 0,
!>          CLANGE is set to zero.
!>
```

*A*

```
!>          A is COMPLEX array, dimension (LDA,N)
!>          The m by n matrix A.
!>
```

*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 **114** of file **clange.f**.

### double precision function dlange (character norm, integer m, integer n, double precision, dimension( lda, \* ) a, integer lda, double precision, dimension( \* ) work)

**DLANGE** returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of a general rectangular matrix.

**Purpose:**

```
!>
!> DLANGE  returns the value of the one norm,  or the Frobenius norm, or
!> the  infinity norm,  or the  element of  largest absolute value  of a
!> real matrix A.
!>
```

**Returns**

DLANGE

```
!>
!>    DLANGE = ( 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 DLANGE as described
!>          above.
!>
```

*M*

```
!>          M is INTEGER
!>          The number of rows of the matrix A.  M >= 0.  When M = 0,
!>          DLANGE is set to zero.
!>
```

*N*

```
!>          N is INTEGER
!>          The number of columns of the matrix A.  N >= 0.  When N = 0,
!>          DLANGE is set to zero.
!>
```

*A*

```
!>          A is DOUBLE PRECISION array, dimension (LDA,N)
!>          The m by n matrix A.
!>
```

*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.

Definition at line **113** of file **dlange.f**.

### real function slange (character norm, integer m, integer n, real, dimension( lda, \* ) a, integer lda, real, dimension( \* ) work)

**SLANGE** returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of a general rectangular matrix.

**Purpose:**

```
!>
!> SLANGE  returns the value of the one norm,  or the Frobenius norm, or
!> the  infinity norm,  or the  element of  largest absolute value  of a
!> real matrix A.
!>
```

**Returns**

SLANGE

```
!>
!>    SLANGE = ( 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 SLANGE as described
!>          above.
!>
```

*M*

```
!>          M is INTEGER
!>          The number of rows of the matrix A.  M >= 0.  When M = 0,
!>          SLANGE is set to zero.
!>
```

*N*

```
!>          N is INTEGER
!>          The number of columns of the matrix A.  N >= 0.  When N = 0,
!>          SLANGE is set to zero.
!>
```

*A*

```
!>          A is REAL array, dimension (LDA,N)
!>          The m by n matrix A.
!>
```

*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 **113** of file **slange.f**.

### double precision function zlange (character norm, integer m, integer n, complex\*16, dimension( lda, \* ) a, integer lda, double precision, dimension( \* ) work)

**ZLANGE** returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of a general rectangular matrix.

**Purpose:**

```
!>
!> ZLANGE  returns the value of the one norm,  or the Frobenius norm, or
!> the  infinity norm,  or the  element of  largest absolute value  of a
!> complex matrix A.
!>
```

**Returns**

ZLANGE

```
!>
!>    ZLANGE = ( 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 ZLANGE as described
!>          above.
!>
```

*M*

```
!>          M is INTEGER
!>          The number of rows of the matrix A.  M >= 0.  When M = 0,
!>          ZLANGE is set to zero.
!>
```

*N*

```
!>          N is INTEGER
!>          The number of columns of the matrix A.  N >= 0.  When N = 0,
!>          ZLANGE is set to zero.
!>
```

*A*

```
!>          A is COMPLEX*16 array, dimension (LDA,N)
!>          The m by n matrix A.
!>
```

*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.

Definition at line **114** of file **zlange.f**.

## Author

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