ZLANSB (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 symmetric band matrix A, with k super-diagonals

SYNOPSIS

  DOUBLE PRECISION FUNCTION ZLANSB( NORM, UPLO, N, K, AB, LDAB, WORK )

      CHARACTER    NORM, UPLO

      INTEGER      K, LDAB, N

      DOUBLE       PRECISION WORK( * )

      COMPLEX*16   AB( LDAB, * )

PURPOSE

  ZLANSB  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.

DESCRIPTION

  ZLANSB returns the value

     ZLANSB = ( 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 ZLANSB as described above.

  UPLO    (input) 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

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

  K       (input) INTEGER
          The number of super-diagonals or sub-diagonals of the band matrix
          A.  K >= 0.

  AB      (input) COMPLEX*16 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).

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

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