---
name: "lanhs"
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/lanhs"
---

# lanhs(3)

lanhs: Hessenberg

## NAME

lanhs - lanhs: Hessenberg

## SYNOPSIS

### Functions

real function **clanhs** (norm, n, a, lda, work)\
 **CLANHS** returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of an upper Hessenberg matrix.  double precision function **dlanhs** (norm, n, a, lda, work)\
 **DLANHS** returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of an upper Hessenberg matrix.  real function **slanhs** (norm, n, a, lda, work)\
 **SLANHS** returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of an upper Hessenberg matrix.  double precision function **zlanhs** (norm, n, a, lda, work)\
 **ZLANHS** returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of an upper Hessenberg matrix.

## Detailed Description

## Function Documentation

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

**CLANHS** returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of an upper Hessenberg matrix.

**Purpose:**

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

**Returns**

CLANHS

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

*N*

```
!>          N is INTEGER
!>          The order of the matrix A.  N >= 0.  When N = 0, CLANHS is
!>          set to zero.
!>
```

*A*

```
!>          A is COMPLEX array, dimension (LDA,N)
!>          The n by n upper Hessenberg matrix A; the part of A below the
!>          first sub-diagonal is not referenced.
!>
```

*LDA*

```
!>          LDA is INTEGER
!>          The leading dimension of the array A.  LDA >= max(N,1).
!>
```

*WORK*

```
!>          WORK is REAL array, dimension (MAX(1,LWORK)),
!>          where LWORK >= N 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 **108** of file **clanhs.f**.

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

**DLANHS** returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of an upper Hessenberg matrix.

**Purpose:**

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

**Returns**

DLANHS

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

*N*

```
!>          N is INTEGER
!>          The order of the matrix A.  N >= 0.  When N = 0, DLANHS is
!>          set to zero.
!>
```

*A*

```
!>          A is DOUBLE PRECISION array, dimension (LDA,N)
!>          The n by n upper Hessenberg matrix A; the part of A below the
!>          first sub-diagonal is not referenced.
!>
```

*LDA*

```
!>          LDA is INTEGER
!>          The leading dimension of the array A.  LDA >= max(N,1).
!>
```

*WORK*

```
!>          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
!>          where LWORK >= N 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 **107** of file **dlanhs.f**.

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

**SLANHS** returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of an upper Hessenberg matrix.

**Purpose:**

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

**Returns**

SLANHS

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

*N*

```
!>          N is INTEGER
!>          The order of the matrix A.  N >= 0.  When N = 0, SLANHS is
!>          set to zero.
!>
```

*A*

```
!>          A is REAL array, dimension (LDA,N)
!>          The n by n upper Hessenberg matrix A; the part of A below the
!>          first sub-diagonal is not referenced.
!>
```

*LDA*

```
!>          LDA is INTEGER
!>          The leading dimension of the array A.  LDA >= max(N,1).
!>
```

*WORK*

```
!>          WORK is REAL array, dimension (MAX(1,LWORK)),
!>          where LWORK >= N 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 **107** of file **slanhs.f**.

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

**ZLANHS** returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of an upper Hessenberg matrix.

**Purpose:**

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

**Returns**

ZLANHS

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

*N*

```
!>          N is INTEGER
!>          The order of the matrix A.  N >= 0.  When N = 0, ZLANHS is
!>          set to zero.
!>
```

*A*

```
!>          A is COMPLEX*16 array, dimension (LDA,N)
!>          The n by n upper Hessenberg matrix A; the part of A below the
!>          first sub-diagonal is not referenced.
!>
```

*LDA*

```
!>          LDA is INTEGER
!>          The leading dimension of the array A.  LDA >= max(N,1).
!>
```

*WORK*

```
!>          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
!>          where LWORK >= N 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 **108** of file **zlanhs.f**.

## Author

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