Man page - langb(3)

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Manual

langb

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
real function clangb (character norm, integer n, integer kl, integer ku,complex, dimension( ldab, * ) ab, integer ldab, real, dimension( * )work)
double precision function dlangb (character norm, integer n, integer kl,integer ku, double precision, dimension( ldab, * ) ab, integer ldab,double precision, dimension( * ) work)
real function slangb (character norm, integer n, integer kl, integer ku,real, dimension( ldab, * ) ab, integer ldab, real, dimension( * ) work)
double precision function zlangb (character norm, integer n, integer kl,integer ku, complex*16, dimension( ldab, * ) ab, integer ldab, doubleprecision, dimension( * ) work)
Author

NAME

langb - langb: general matrix, banded

SYNOPSIS

Functions

real function clangb (norm, n, kl, ku, ab, ldab, work)
CLANGB returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of general band matrix.
double precision function dlangb (norm, n, kl, ku, ab, ldab, work)
DLANGB returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of general band matrix.
real function slangb (norm, n, kl, ku, ab, ldab, work)
SLANGB returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of general band matrix.
double precision function zlangb (norm, n, kl, ku, ab, ldab, work)
ZLANGB returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of general band matrix.

Detailed Description

Function Documentation

real function clangb (character norm, integer n, integer kl, integer ku,complex, dimension( ldab, * ) ab, integer ldab, real, dimension( * )work)

CLANGB returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of general band matrix.

Purpose:

CLANGB 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 band matrix A, with kl sub-diagonals and ku super-diagonals.

Returns

CLANGB

CLANGB = ( 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 CLANGB as described
above.

N

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

KL

KL is INTEGER
The number of sub-diagonals of the matrix A. KL >= 0.

KU

KU is INTEGER
The number of super-diagonals of the matrix A. KU >= 0.

AB

AB is COMPLEX array, dimension (LDAB,N)
The band matrix A, stored in rows 1 to KL+KU+1. The j-th
column of A is stored in the j-th column of the array AB as
follows:
AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(n,j+kl).

LDAB

LDAB is INTEGER
The leading dimension of the array AB. LDAB >= KL+KU+1.

WORK

WORK is REAL 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.

double precision function dlangb (character norm, integer n, integer kl,integer ku, double precision, dimension( ldab, * ) ab, integer ldab,double precision, dimension( * ) work)

DLANGB returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of general band matrix.

Purpose:

DLANGB 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 band matrix A, with kl sub-diagonals and ku super-diagonals.

Returns

DLANGB

DLANGB = ( 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 DLANGB as described
above.

N

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

KL

KL is INTEGER
The number of sub-diagonals of the matrix A. KL >= 0.

KU

KU is INTEGER
The number of super-diagonals of the matrix A. KU >= 0.

AB

AB is DOUBLE PRECISION array, dimension (LDAB,N)
The band matrix A, stored in rows 1 to KL+KU+1. The j-th
column of A is stored in the j-th column of the array AB as
follows:
AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(n,j+kl).

LDAB

LDAB is INTEGER
The leading dimension of the array AB. LDAB >= KL+KU+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.

real function slangb (character norm, integer n, integer kl, integer ku,real, dimension( ldab, * ) ab, integer ldab, real, dimension( * ) work)

SLANGB returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of general band matrix.

Purpose:

SLANGB 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 band matrix A, with kl sub-diagonals and ku super-diagonals.

Returns

SLANGB

SLANGB = ( 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 SLANGB as described
above.

N

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

KL

KL is INTEGER
The number of sub-diagonals of the matrix A. KL >= 0.

KU

KU is INTEGER
The number of super-diagonals of the matrix A. KU >= 0.

AB

AB is REAL array, dimension (LDAB,N)
The band matrix A, stored in rows 1 to KL+KU+1. The j-th
column of A is stored in the j-th column of the array AB as
follows:
AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(n,j+kl).

LDAB

LDAB is INTEGER
The leading dimension of the array AB. LDAB >= KL+KU+1.

WORK

WORK is REAL 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.

double precision function zlangb (character norm, integer n, integer kl,integer ku, complex*16, dimension( ldab, * ) ab, integer ldab, doubleprecision, dimension( * ) work)

ZLANGB returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of general band matrix.

Purpose:

ZLANGB 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 band matrix A, with kl sub-diagonals and ku super-diagonals.

Returns

ZLANGB

ZLANGB = ( 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 ZLANGB as described
above.

N

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

KL

KL is INTEGER
The number of sub-diagonals of the matrix A. KL >= 0.

KU

KU is INTEGER
The number of super-diagonals of the matrix A. KU >= 0.

AB

AB is COMPLEX*16 array, dimension (LDAB,N)
The band matrix A, stored in rows 1 to KL+KU+1. The j-th
column of A is stored in the j-th column of the array AB as
follows:
AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(n,j+kl).

LDAB

LDAB is INTEGER
The leading dimension of the array AB. LDAB >= KL+KU+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.

Author

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