slangb.f (3) - Linux Man Pages
REAL function slangb (characterNORM, integerN, integerKL, integerKU, real, dimension( ldab, * )AB, integerLDAB, real, dimension( * )WORK)
SLANGB returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of general band matrix.
SLANGB 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.
SLANGB = ( 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 SLANGB as described above.
N is INTEGER The order of the matrix A. N >= 0. When N = 0, SLANGB is set to zero.
KL is INTEGER The number of sub-diagonals of the matrix A. KL >= 0.
KU is INTEGER The number of super-diagonals of the matrix A. KU >= 0.
AB is REAL 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 is INTEGER The leading dimension of the array AB. LDAB >= KL+KU+1.
WORK is REAL array, dimension (MAX(1,LWORK)), where LWORK >= N when NORM = 'I'; otherwise, WORK is not referenced.
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Univ. of Colorado Denver
- September 2012
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