LANGB - 5.2 English - 68552

LANGB returns the value of the 1-norm, Frobenius norm, infinity-norm,

or the largest absolute value of any element of general band matrix.

Purpose:

 LANGB    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 = (fla_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  fla_max(abs(A(i,j)))  is not a consistent matrix norm.

Parameters:

• NORM – [in]

  NORM is CHARACTER*1

  Specifies the value to be returned in SLANGB as described above.

• N – [in]

  N is INTEGER

  The order of the matrix A. N >= 0. When N = 0, SLANGB is set to zero.

• KL – [in]

  KL is INTEGER

  The number of sub-diagonals of the matrix A. KL >= 0.

• KU – [in]

  KU is INTEGER

  The number of super-diagonals of the matrix A. KU >= 0.

• AB – [in]

  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 fla_max(1,j-ku)<=i<=min(n,j+kl).

• LDAB – [in]

  LDAB is INTEGER

  The leading dimension of the array AB. LDAB >= KL+KU+1.

• WORK – [out]

  WORK is REAL array, dimension (MAX(1,LWORK)),

  where LWORK >= N when NORM = ‘I’; otherwise, WORK is not referenced.

Returns:

Returns the value of the norm.