SLANTR  returns the value of the one norm,  or the Frobenius norm, or


 the  infinity norm,  or the  element of  largest absolute value  of a


 trapezoidal or triangular matrix A.

SLANTR

    SLANTR = ( 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 SLANTR as described


          above.

UPLO

          UPLO is CHARACTER*1


          Specifies whether the matrix A is upper or lower trapezoidal.


          = 'U':  Upper trapezoidal


          = 'L':  Lower trapezoidal


          Note that A is triangular instead of trapezoidal if M = N.

DIAG

          DIAG is CHARACTER*1


          Specifies whether or not the matrix A has unit diagonal.


          = 'N':  Non-unit diagonal


          = 'U':  Unit diagonal

M

          M is INTEGER


          The number of rows of the matrix A.  M >= 0, and if


          UPLO = 'U', M <= N.  When M = 0, SLANTR is set to zero.

N

          N is INTEGER


          The number of columns of the matrix A.  N >= 0, and if


          UPLO = 'L', N <= M.  When N = 0, SLANTR is set to zero.

A

          A is REAL array, dimension (LDA,N)


          The trapezoidal matrix A (A is triangular if M = N).


          If UPLO = 'U', the leading m by n upper trapezoidal part of


          the array A contains the upper trapezoidal matrix, and the


          strictly lower triangular part of A is not referenced.


          If UPLO = 'L', the leading m by n lower trapezoidal part of


          the array A contains the lower trapezoidal matrix, and the


          strictly upper triangular part of A is not referenced.  Note


          that when DIAG = 'U', the diagonal elements of A are not


          referenced and are assumed to be one.

LDA

          LDA is INTEGER


          The leading dimension of the array A.  LDA >= max(M,1).

WORK

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


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


          referenced.

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NAG Ltd.

September 2012