# lanhb - Man Page

lan{hb,sb}: Hermitian/symmetric matrix, banded

## Synopsis

### Functions

real function clanhb (norm, uplo, n, k, ab, ldab, work)
CLANHB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a Hermitian band matrix.
real function clansb (norm, uplo, n, k, ab, ldab, work)
CLANSB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a symmetric band matrix.
double precision function dlansb (norm, uplo, n, k, ab, ldab, work)
DLANSB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a symmetric band matrix.
real function slansb (norm, uplo, n, k, ab, ldab, work)
SLANSB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a symmetric band matrix.
double precision function zlanhb (norm, uplo, n, k, ab, ldab, work)
ZLANHB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a Hermitian band matrix.
double precision function zlansb (norm, uplo, n, k, ab, ldab, work)
ZLANSB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a symmetric band matrix.

## Function Documentation

### real function clanhb (character norm, character uplo, integer n, integer k, complex, dimension( ldab, * ) ab, integer ldab, real, dimension( * ) work)

CLANHB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a Hermitian band matrix.

Purpose:

``` CLANHB  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 hermitian band matrix A,  with k super-diagonals.```
Returns

CLANHB

```    CLANHB = ( 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 CLANHB as described
above.```

UPLO

```          UPLO is CHARACTER*1
Specifies whether the upper or lower triangular part of the
band matrix A is supplied.
= 'U':  Upper triangular
= 'L':  Lower triangular```

N

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

K

```          K is INTEGER
The number of super-diagonals or sub-diagonals of the
band matrix A.  K >= 0.```

AB

```          AB is COMPLEX array, dimension (LDAB,N)
The upper or lower triangle of the hermitian 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 the imaginary parts of the diagonal elements need
not be set and are assumed to be zero.```

LDAB

```          LDAB is INTEGER
The leading dimension of the array AB.  LDAB >= K+1.```

WORK

```          WORK is REAL array, dimension (MAX(1,LWORK)),
where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
WORK is not referenced.```
Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 130 of file clanhb.f.

### real function clansb (character norm, character uplo, integer n, integer k, complex, dimension( ldab, * ) ab, integer ldab, real, dimension( * ) work)

CLANSB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a symmetric band matrix.

Purpose:

``` CLANSB  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 symmetric band matrix A,  with k super-diagonals.```
Returns

CLANSB

```    CLANSB = ( 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 CLANSB as described
above.```

UPLO

```          UPLO is CHARACTER*1
Specifies whether the upper or lower triangular part of the
band matrix A is supplied.
= 'U':  Upper triangular part is supplied
= 'L':  Lower triangular part is supplied```

N

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

K

```          K is INTEGER
The number of super-diagonals or sub-diagonals of the
band matrix A.  K >= 0.```

AB

```          AB is COMPLEX array, dimension (LDAB,N)
The upper or lower triangle of the symmetric 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).```

LDAB

```          LDAB is INTEGER
The leading dimension of the array AB.  LDAB >= K+1.```

WORK

```          WORK is REAL array, dimension (MAX(1,LWORK)),
where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
WORK is not referenced.```
Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 128 of file clansb.f.

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

DLANSB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a symmetric band matrix.

Purpose:

``` DLANSB  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 symmetric band matrix A,  with k super-diagonals.```
Returns

DLANSB

```    DLANSB = ( 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 DLANSB as described
above.```

UPLO

```          UPLO is CHARACTER*1
Specifies whether the upper or lower triangular part of the
band matrix A is supplied.
= 'U':  Upper triangular part is supplied
= 'L':  Lower triangular part is supplied```

N

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

K

```          K is INTEGER
The number of super-diagonals or sub-diagonals of the
band matrix A.  K >= 0.```

AB

```          AB is DOUBLE PRECISION array, dimension (LDAB,N)
The upper or lower triangle of the symmetric 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).```

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' or '1' or 'O'; otherwise,
WORK is not referenced.```
Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 127 of file dlansb.f.

### real function slansb (character norm, character uplo, integer n, integer k, real, dimension( ldab, * ) ab, integer ldab, real, dimension( * ) work)

SLANSB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a symmetric band matrix.

Purpose:

``` SLANSB  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 symmetric band matrix A,  with k super-diagonals.```
Returns

SLANSB

```    SLANSB = ( 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 SLANSB as described
above.```

UPLO

```          UPLO is CHARACTER*1
Specifies whether the upper or lower triangular part of the
band matrix A is supplied.
= 'U':  Upper triangular part is supplied
= 'L':  Lower triangular part is supplied```

N

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

K

```          K is INTEGER
The number of super-diagonals or sub-diagonals of the
band matrix A.  K >= 0.```

AB

```          AB is REAL array, dimension (LDAB,N)
The upper or lower triangle of the symmetric 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).```

LDAB

```          LDAB is INTEGER
The leading dimension of the array AB.  LDAB >= K+1.```

WORK

```          WORK is REAL array, dimension (MAX(1,LWORK)),
where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
WORK is not referenced.```
Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 127 of file slansb.f.

### double precision function zlanhb (character norm, character uplo, integer n, integer k, complex*16, dimension( ldab, * ) ab, integer ldab, double precision, dimension( * ) work)

ZLANHB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a Hermitian band matrix.

Purpose:

``` ZLANHB  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 hermitian band matrix A,  with k super-diagonals.```
Returns

ZLANHB

```    ZLANHB = ( 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 ZLANHB as described
above.```

UPLO

```          UPLO is CHARACTER*1
Specifies whether the upper or lower triangular part of the
band matrix A is supplied.
= 'U':  Upper triangular
= 'L':  Lower triangular```

N

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

K

```          K is INTEGER
The number of super-diagonals or sub-diagonals of the
band matrix A.  K >= 0.```

AB

```          AB is COMPLEX*16 array, dimension (LDAB,N)
The upper or lower triangle of the hermitian 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 the imaginary parts of the diagonal elements need
not be set and are assumed to be zero.```

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' or '1' or 'O'; otherwise,
WORK is not referenced.```
Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 130 of file zlanhb.f.

### double precision function zlansb (character norm, character uplo, integer n, integer k, complex*16, dimension( ldab, * ) ab, integer ldab, double precision, dimension( * ) work)

ZLANSB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a symmetric band matrix.

Purpose:

``` ZLANSB  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 symmetric band matrix A,  with k super-diagonals.```
Returns

ZLANSB

```    ZLANSB = ( 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 ZLANSB as described
above.```

UPLO

```          UPLO is CHARACTER*1
Specifies whether the upper or lower triangular part of the
band matrix A is supplied.
= 'U':  Upper triangular part is supplied
= 'L':  Lower triangular part is supplied```

N

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

K

```          K is INTEGER
The number of super-diagonals or sub-diagonals of the
band matrix A.  K >= 0.```

AB

```          AB is COMPLEX*16 array, dimension (LDAB,N)
The upper or lower triangle of the symmetric 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).```

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' or '1' or 'O'; otherwise,
WORK is not referenced.```
Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 128 of file zlansb.f.

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