slantb.f(3) LAPACK slantb.f(3)
REAL function slantb (NORM, UPLO, DIAG, N, K, AB, LDAB, WORK)
SLANTB 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.
REAL function slantb (characterNORM, characterUPLO, characterDIAG, integerN, integerK, real,
dimension( ldab, * )AB, integerLDAB, real, dimension( * )WORK)
SLANTB 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.
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.
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.
NORM is CHARACTER*1
Specifies the value to be returned in SLANTB as described
UPLO is CHARACTER*1
Specifies whether the matrix A is upper or lower triangular.
= 'U': Upper triangular
= 'L': Lower triangular
DIAG is CHARACTER*1
Specifies whether or not the matrix A is unit triangular.
= 'N': Non-unit triangular
= 'U': Unit triangular
N is INTEGER
The order of the matrix A. N >= 0. When N = 0, SLANTB is
set to zero.
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 is REAL 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 is INTEGER
The leading dimension of the array AB. LDAB >= K+1.
WORK is REAL array, dimension (MAX(1,LWORK)),
where LWORK >= N when NORM = 'I'; otherwise, WORK is not
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
Definition at line 140 of file slantb.f.
Generated automatically by Doxygen for LAPACK from the source code.
Version 3.4.2 Tue Sep 25 2012 slantb.f(3)