Man page - lanhb(3)

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Manual

lanhb

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
real function clanhb (character norm, character uplo, integer n, integer k,complex, dimension( ldab, * ) ab, integer ldab, real, dimension( * )work)
real function clansb (character norm, character uplo, integer n, integer k,complex, dimension( ldab, * ) ab, integer ldab, real, dimension( * )work)
double precision function dlansb (character norm, character uplo, integern, integer k, double precision, dimension( ldab, * ) ab, integer ldab,double precision, dimension( * ) work)
real function slansb (character norm, character uplo, integer n, integer k,real, dimension( ldab, * ) ab, integer ldab, real, dimension( * ) work)
double precision function zlanhb (character norm, character uplo, integern, integer k, complex*16, dimension( ldab, * ) ab, integer ldab, doubleprecision, dimension( * ) work)
double precision function zlansb (character norm, character uplo, integern, integer k, complex*16, dimension( ldab, * ) ab, integer ldab, doubleprecision, dimension( * ) work)
Author

NAME

lanhb - 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.

Detailed Description

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.

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.

double precision function dlansb (character norm, character uplo, integern, 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.

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.

double precision function zlanhb (character norm, character uplo, integern, integer k, complex*16, dimension( ldab, * ) ab, integer ldab, doubleprecision, 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.

double precision function zlansb (character norm, character uplo, integern, integer k, complex*16, dimension( ldab, * ) ab, integer ldab, doubleprecision, 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.

Author

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