man dlangb (Fonctions bibliothèques) - return 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
NAME
DLANGB - return 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
SYNOPSIS
- DOUBLE PRECISION
- FUNCTION DLANGB( NORM, N, KL, KU, AB, LDAB, WORK )
- CHARACTER NORM
- INTEGER KL, KU, LDAB, N
- DOUBLE PRECISION AB( LDAB, * ), WORK( * )
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.
DESCRIPTION
DLANGB returns the value
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 matrix norm.
ARGUMENTS
- NORM (input) CHARACTER*1
- Specifies the value to be returned in DLANGB as described above.
- N (input) INTEGER
- The order of the matrix A. N >= 0. When N = 0, DLANGB is set to zero.
- KL (input) INTEGER
- The number of sub-diagonals of the matrix A. KL >= 0.
- KU (input) INTEGER
- The number of super-diagonals of the matrix A. KU >= 0.
- AB (input) 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 (input) INTEGER
- The leading dimension of the array AB. LDAB >= KL+KU+1.
- WORK (workspace) DOUBLE PRECISION array, dimension (LWORK),
- where LWORK >= N when NORM = 'I'; otherwise, WORK is not referenced.