# lange - Man Page

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.

## 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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## Info

Tue Nov 28 2023 12:08:43 Version 3.12.0 LAPACK