SLANGB (3lapack)

return 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

SYNOPSIS

  REAL FUNCTION SLANGB( NORM, N, KL, KU, AB, LDAB, WORK )

      CHARACTER NORM

      INTEGER   KL, KU, LDAB, N

      REAL      AB( LDAB, * ), WORK( * )

PURPOSE

  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.

DESCRIPTION

  SLANGB returns the value

     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  matrix norm.

ARGUMENTS

  NORM    (input) CHARACTER*1
          Specifies the value to be returned in SLANGB as described above.

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

  KL      (input) INTEGER
          The number of sub-diagonals of the matrix A.  KL >= 0.

  KU      (input) INTEGER
          The number of super-diagonals of the matrix A.  KU >= 0.

  AB      (input) 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    (input) INTEGER
          The leading dimension of the array AB.  LDAB >= KL+KU+1.

  WORK    (workspace) REAL array, dimension (LWORK),
          where LWORK >= N when NORM = 'I'; otherwise, WORK is not
          referenced.