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dlantb.f(3) LAPACK dlantb.f(3)

NAME

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.

Date:

December 2016

Definition at line 142 of file dlantb.f.

Author

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Tue Nov 14 2017 Version 3.8.0