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## dlansb()

double precision function dlansb | ( | character | norm,
|  | character | uplo,
|  | integer | n,
|  | integer | k,
|  | double precision, dimension( ldab, * ) | ab,
|  | integer | ldab,
|  | double precision, dimension( * ) | work )

DLANSB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a symmetric band matrix.

Download DLANSB + dependencies [TGZ] [ZIP] [TXT]

Purpose:

      !>
      !> DLANSB  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 symmetric band matrix A,  with k super-diagonals.
      !>

Returns
  DLANSB

      !>
      !>    DLANSB = ( 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.
      !>

Parameters

  [in]

  NORM

      !>          NORM is CHARACTER*1
      !>          Specifies the value to be returned in DLANSB as described
      !>          above.
      !>

  [in]

  UPLO

      !>          UPLO is CHARACTER*1
      !>          Specifies whether the upper or lower triangular part of the
      !>          band matrix A is supplied.
      !>          = 'U':  Upper triangular part is supplied
      !>          = 'L':  Lower triangular part is supplied
      !>

  [in]

  N

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

  [in]

  K

      !>          K is INTEGER
      !>          The number of super-diagonals or sub-diagonals of the
      !>          band matrix A.  K >= 0.
      !>

  [in]

  AB

      !>          AB is DOUBLE PRECISION array, dimension (LDAB,N)
      !>          The upper or lower triangle of the symmetric 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).
      !>

  [in]

  LDAB

      !>          LDAB is INTEGER
      !>          The leading dimension of the array AB.  LDAB >= K+1.
      !>

  [out]

  WORK

      !>          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
      !>          where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
      !>          WORK is not referenced.
      !>

Author
  Univ. of Tennessee
  Univ. of California Berkeley
  Univ. of Colorado Denver
  NAG Ltd.