slantb.f (3)  Linux Manuals
NAME
slantb.f 
SYNOPSIS
Functions/Subroutines
REAL function slantb (NORM, UPLO, DIAG, N, K, AB, LDAB, WORK)
SLANTB returns the value of the 1norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular band matrix.
Function/Subroutine Documentation
REAL function slantb (characterNORM, characterUPLO, characterDIAG, integerN, integerK, real, dimension( ldab, * )AB, integerLDAB, real, dimension( * )WORK)
SLANTB returns the value of the 1norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular band matrix.
Purpose:

SLANTB 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:

SLANTB
SLANTB = ( 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 SLANTB as described above.
UPLOUPLO is CHARACTER*1 Specifies whether the matrix A is upper or lower triangular. = 'U': Upper triangular = 'L': Lower triangular
DIAGDIAG is CHARACTER*1 Specifies whether or not the matrix A is unit triangular. = 'N': Nonunit triangular = 'U': Unit triangular
NN is INTEGER The order of the matrix A. N >= 0. When N = 0, SLANTB is set to zero.
KK is INTEGER The number of superdiagonals of the matrix A if UPLO = 'U', or the number of subdiagonals of the matrix A if UPLO = 'L'. K >= 0.
ABAB is REAL array, dimension (LDAB,N) The upper or lower triangular band matrix A, stored in the first k+1 rows of AB. The jth column of A is stored in the jth column of the array AB as follows: if UPLO = 'U', AB(k+1+ij,j) = A(i,j) for max(1,jk)<=i<=j; if UPLO = 'L', AB(1+ij,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.
LDABLDAB is INTEGER The leading dimension of the array AB. LDAB >= K+1.
WORKWORK 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.
Date:
 September 2012
Definition at line 140 of file slantb.f.
Author
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