---
name: "dlantb.f"
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/dlantb.f"
---

# dlantb.f(3)

## NAME

SRC/dlantb.f

## SYNOPSIS

### Functions/Subroutines

double precision function **dlantb** (norm, uplo, diag, n, k, ab, ldab, work)\
 **DLANTB** returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular band matrix.

## Function/Subroutine Documentation

### double precision function dlantb (character norm, character uplo, character diag, integer n, integer k, double precision, dimension( ldab, \* ) ab, integer ldab, double precision, dimension( \* ) work)

**DLANTB** returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular band matrix.

**Purpose:**

```
!>
!> DLANTB  returns the value of the one norm,  or the Frobenius norm, or
!> the  infinity norm,  or the element of  largest absolute value  of an
!> n by n triangular band matrix A,  with ( k + 1 ) diagonals.
!>
```

**Returns**

DLANTB

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

*UPLO*

```
!>          UPLO is CHARACTER*1
!>          Specifies whether the matrix A is upper or lower triangular.
!>          = 'U':  Upper triangular
!>          = 'L':  Lower triangular
!>
```

*DIAG*

```
!>          DIAG is CHARACTER*1
!>          Specifies whether or not the matrix A is unit triangular.
!>          = 'N':  Non-unit triangular
!>          = 'U':  Unit triangular
!>
```

*N*

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

*K*

```
!>          K is INTEGER
!>          The number of super-diagonals of the matrix A if UPLO = 'U',
!>          or the number of sub-diagonals of the matrix A if UPLO = 'L'.
!>          K >= 0.
!>
```

*AB*

```
!>          AB is DOUBLE PRECISION array, dimension (LDAB,N)
!>          The upper or lower triangular band matrix A, stored in the
!>          first k+1 rows of AB.  The j-th column of A is stored
!>          in the j-th column of the array AB as follows:
!>          if UPLO = 'U', AB(k+1+i-j,j) = A(i,j) for max(1,j-k)<=i<=j;
!>          if UPLO = 'L', AB(1+i-j,j)   = A(i,j) for j<=i<=min(n,j+k).
!>          Note that when DIAG = 'U', the elements of the array AB
!>          corresponding to the diagonal elements of the matrix A are
!>          not referenced, but are assumed to be one.
!>
```

*LDAB*

```
!>          LDAB is INTEGER
!>          The leading dimension of the array AB.  LDAB >= K+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 **138** of file **dlantb.f**.

## Author

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