# lanht - Man Page

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.

## 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

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