SLANTB (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 triangular band matrix A, with ( k + 1 ) diagonals

SYNOPSIS

  REAL FUNCTION SLANTB( NORM, UPLO, DIAG, N, K, AB, LDAB, WORK )

      CHARACTER DIAG, NORM, UPLO

      INTEGER   K, LDAB, N

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

PURPOSE

  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.

DESCRIPTION

  SLANTB returns the value

     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  matrix norm.

ARGUMENTS

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

  UPLO    (input) CHARACTER*1
          Specifies whether the matrix A is upper or lower triangular.  =
          'U':  Upper triangular
          = 'L':  Lower triangular

  DIAG    (input) CHARACTER*1
          Specifies whether or not the matrix A is unit triangular.  = 'N':
          Non-unit triangular
          = 'U':  Unit triangular

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

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

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