# langt - Man Page

langt: general matrix, tridiagonal

## Synopsis

### Functions

real function clangt (norm, n, dl, d, du)
CLANGT returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of a general tridiagonal matrix.
double precision function dlangt (norm, n, dl, d, du)
DLANGT returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of a general tridiagonal matrix.
real function slangt (norm, n, dl, d, du)
SLANGT returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of a general tridiagonal matrix.
double precision function zlangt (norm, n, dl, d, du)
ZLANGT returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of a general tridiagonal matrix.

## Function Documentation

### real function clangt (character norm, integer n, complex, dimension( * ) dl, complex, dimension( * ) d, complex, dimension( * ) du)

CLANGT returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of a general tridiagonal matrix.

Purpose:

``` CLANGT  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 tridiagonal matrix A.```
Returns

CLANGT

```    CLANGT = ( 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 CLANGT as described
above.```

N

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

DL

```          DL is COMPLEX array, dimension (N-1)
The (n-1) sub-diagonal elements of A.```

D

```          D is COMPLEX array, dimension (N)
The diagonal elements of A.```

DU

```          DU is COMPLEX array, dimension (N-1)
The (n-1) super-diagonal elements of A.```
Author

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Definition at line 105 of file clangt.f.

### double precision function dlangt (character norm, integer n, double precision, dimension( * ) dl, double precision, dimension( * ) d, double precision, dimension( * ) du)

DLANGT returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of a general tridiagonal matrix.

Purpose:

``` DLANGT  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 tridiagonal matrix A.```
Returns

DLANGT

```    DLANGT = ( 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 DLANGT as described
above.```

N

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

DL

```          DL is DOUBLE PRECISION array, dimension (N-1)
The (n-1) sub-diagonal elements of A.```

D

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

DU

```          DU is DOUBLE PRECISION array, dimension (N-1)
The (n-1) super-diagonal elements of A.```
Author

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Definition at line 105 of file dlangt.f.

### real function slangt (character norm, integer n, real, dimension( * ) dl, real, dimension( * ) d, real, dimension( * ) du)

SLANGT returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of a general tridiagonal matrix.

Purpose:

``` SLANGT  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 tridiagonal matrix A.```
Returns

SLANGT

```    SLANGT = ( 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 SLANGT as described
above.```

N

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

DL

```          DL is REAL array, dimension (N-1)
The (n-1) sub-diagonal elements of A.```

D

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

DU

```          DU is REAL array, dimension (N-1)
The (n-1) super-diagonal elements of A.```
Author

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Definition at line 105 of file slangt.f.

### double precision function zlangt (character norm, integer n, complex*16, dimension( * ) dl, complex*16, dimension( * ) d, complex*16, dimension( * ) du)

ZLANGT returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of a general tridiagonal matrix.

Purpose:

``` ZLANGT  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 tridiagonal matrix A.```
Returns

ZLANGT

```    ZLANGT = ( 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 ZLANGT as described
above.```

N

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

DL

```          DL is COMPLEX*16 array, dimension (N-1)
The (n-1) sub-diagonal elements of A.```

D

```          D is COMPLEX*16 array, dimension (N)
The diagonal elements of A.```

DU

```          DU is COMPLEX*16 array, dimension (N-1)
The (n-1) super-diagonal elements of A.```
Author

Univ. of Tennessee

Univ. of California Berkeley