slantb.f(3)

NAME
slantb.f -

SYNOPSIS

  Functions/Subroutines
REAL function slantb (NORM, UPLO, DIAG, N, K, AB, LDAB, WORK)
SLANTB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular band matrix.

Function/Subroutine Documentation

  REAL function slantb (characterNORM, characterUPLO, characterDIAG, integerN, integerK, real, dimension( ldab, * )AB, integerLDAB, real, dimension( * )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.

Returns:
    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.

Parameters:
    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.

Author:
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Date:
    September 2012

Definition at line 140 of file slantb.f.

Author

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