?langb

Returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of general band matrix.

Syntax

val = slangb( norm, n, kl, ku, ab, ldab, work )

val = dlangb( norm, n, kl, ku, ab, ldab, work )

val = clangb( norm, n, kl, ku, ab, ldab, work )

val = zlangb( norm, n, kl, ku, ab, ldab, work )

Include Files

  • Fortran: mkl.fi
  • C: mkl.h

Description

The function returns the value of the 1-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.

Input Parameters

norm

CHARACTER*1. Specifies the value to be returned by the routine:

= 'M' or 'm': val = max(abs(Aij)), largest absolute value of the matrix A.

= '1' or 'O' or 'o': val = norm1(A), 1-norm of the matrix A (maximum column sum),

= 'I' or 'i': val = normI(A), infinity norm of the matrix A (maximum row sum),

= 'F', 'f', 'E' or 'e': val = normF(A), Frobenius norm of the matrix A (square root of sum of squares).

n

INTEGER. The order of the matrix A. n 0. When n = 0, ?langb is set to zero.

kl

INTEGER. The number of sub-diagonals of the matrix A. kl 0.

ku

INTEGER. The number of super-diagonals of the matrix A. ku 0.

ab

REAL for slangb

DOUBLE PRECISION for dlangb

COMPLEX for clangb

DOUBLE COMPLEX for zlangb

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

INTEGER. The leading dimension of the array ab.

ldab kl+ku+1.

work

REAL for slangb/clangb

DOUBLE PRECISION for dlangb/zlangb

Workspace array, DIMENSION (max(1,lwork)), where

lwork n when norm = 'I'; otherwise, work is not referenced.

Output Parameters

val

REAL for slangb/clangb

DOUBLE PRECISION for dlangb/zlangb

Value returned by the function.

For more complete information about compiler optimizations, see our Optimization Notice.