Previous: slanhs Up: ../lapack-s.html Next: slansp

slansb

 NAME
      SLANSB - return the value of the one norm, or the Frobenius
      norm, or the infinity norm, or the element of largest abso-
      lute value of an n by n symmetric band matrix A, with k
      super-diagonals

 SYNOPSIS
      REAL FUNCTION SLANSB( NORM, UPLO, N, K, AB, LDAB, WORK )

          CHARACTER NORM, UPLO

          INTEGER   K, LDAB, N

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

 PURPOSE
      SLANSB  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
      SLANSB returns the value

         SLANSB = ( 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 SLANSB 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,
              SLANSB is set to zero.

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

      AB      (input) REAL 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) REAL array, dimension (LWORK),
              where LWORK >= N when NORM = 'I' or '1' or 'O'; oth-
              erwise, WORK is not referenced.