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.

SLANTB

    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 consistent matrix norm.

NORM

          NORM is CHARACTER*1


          Specifies the value to be returned in SLANTB as described


          above.

UPLO

          UPLO is CHARACTER*1


          Specifies whether the matrix A is upper or lower triangular.


          = 'U':  Upper triangular


          = 'L':  Lower triangular

DIAG

          DIAG is CHARACTER*1


          Specifies whether or not the matrix A is unit triangular.


          = 'N':  Non-unit triangular


          = 'U':  Unit triangular

N

          N is INTEGER


          The order of the matrix A.  N >= 0.  When N = 0, SLANTB is


          set to zero.

K

          K is 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

          AB is 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

          LDAB is INTEGER


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

WORK

          WORK is REAL array, dimension (MAX(1,LWORK)),


          where LWORK >= N when NORM = 'I'; otherwise, WORK is not


          referenced.

Univ. of Tennessee

Univ. of California Berkeley

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NAG Ltd.

September 2012