man slansb (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 symmetric band matrix A, with k super-diagonals
NAME
SLANSB - 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 symmetric band matrix A, with k super-diagonals
SYNOPSIS
- REAL FUNCTION
- SLANSB( NORM, UPLO, N, K, AB, LDAB, WORK )
- CHARACTER NORM, UPLO
- INTEGER K, LDAB, N
- REAL AB( LDAB, * ), WORK( * )
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.
DESCRIPTION
SLANSB returns the value
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 matrix norm.
ARGUMENTS
- NORM (input) CHARACTER*1
- Specifies the value to be returned in SLANSB as described above.
- UPLO (input) 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 (input) INTEGER
- The order of the matrix A. N >= 0. When N = 0, SLANSB is set to zero.
- K (input) INTEGER
- The number of super-diagonals or sub-diagonals of the band matrix A. K >= 0.
- AB (input) 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 (input) INTEGER
- The leading dimension of the array AB. LDAB >= K+1.
- WORK (workspace) REAL array, dimension (LWORK),
- where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise, WORK is not referenced.