---
name: "lanht"
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/lanht"
---

# lanht(3)

lan{ht,st}: Hermitian/symmetric matrix, tridiagonal

## NAME

lanht - lan{ht,st}: Hermitian/symmetric matrix, tridiagonal

## SYNOPSIS

### Functions

real function **clanht** (norm, n, d, e)\
 **CLANHT** returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex Hermitian tridiagonal matrix.  double precision function **dlanst** (norm, n, d, e)\
 **DLANST** returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric tridiagonal matrix.  real function **slanst** (norm, n, d, e)\
 **SLANST** returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric tridiagonal matrix.  double precision function **zlanht** (norm, n, d, e)\
 **ZLANHT** returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex Hermitian tridiagonal matrix.

## Detailed Description

## Function Documentation

### real function clanht (character norm, integer n, real, dimension( \* ) d, complex, dimension( \* ) e)

**CLANHT** returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex Hermitian tridiagonal matrix.

**Purpose:**

```
!>
!> CLANHT  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 Hermitian tridiagonal matrix A.
!>
```

**Returns**

CLANHT

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

*N*

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

*D*

```
!>          D is REAL array, dimension (N)
!>          The diagonal elements of A.
!>
```

*E*

```
!>          E is COMPLEX array, dimension (N-1)
!>          The (n-1) sub-diagonal or super-diagonal elements of A.
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **100** of file **clanht.f**.

### double precision function dlanst (character norm, integer n, double precision, dimension( \* ) d, double precision, dimension( \* ) e)

**DLANST** returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric tridiagonal matrix.

**Purpose:**

```
!>
!> DLANST  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 symmetric tridiagonal matrix A.
!>
```

**Returns**

DLANST

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

*N*

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

*D*

```
!>          D is DOUBLE PRECISION array, dimension (N)
!>          The diagonal elements of A.
!>
```

*E*

```
!>          E is DOUBLE PRECISION array, dimension (N-1)
!>          The (n-1) sub-diagonal or super-diagonal elements of A.
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **99** of file **dlanst.f**.

### real function slanst (character norm, integer n, real, dimension( \* ) d, real, dimension( \* ) e)

**SLANST** returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric tridiagonal matrix.

**Purpose:**

```
!>
!> SLANST  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 symmetric tridiagonal matrix A.
!>
```

**Returns**

SLANST

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

*N*

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

*D*

```
!>          D is REAL array, dimension (N)
!>          The diagonal elements of A.
!>
```

*E*

```
!>          E is REAL array, dimension (N-1)
!>          The (n-1) sub-diagonal or super-diagonal elements of A.
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **99** of file **slanst.f**.

### double precision function zlanht (character norm, integer n, double precision, dimension( \* ) d, complex\*16, dimension( \* ) e)

**ZLANHT** returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex Hermitian tridiagonal matrix.

**Purpose:**

```
!>
!> ZLANHT  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 Hermitian tridiagonal matrix A.
!>
```

**Returns**

ZLANHT

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

*N*

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

*D*

```
!>          D is DOUBLE PRECISION array, dimension (N)
!>          The diagonal elements of A.
!>
```

*E*

```
!>          E is COMPLEX*16 array, dimension (N-1)
!>          The (n-1) sub-diagonal or super-diagonal elements of A.
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **100** of file **zlanht.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.