DLANSP(3)      LAPACK routine of NEC Numeric Library Collection      DLANSP(3)



NAME
       DLANSP

SYNOPSIS
       DOUBLE PRECISION FUNCTION DLANSP (NORM, UPLO, N, AP, WORK)



PURPOSE
            DLANSP  returns the value of the one norm,  or the Frobenius norm, or
            the  infinity norm,  or the  element of  largest absolute value  of a
            real symmetric matrix A,  supplied in packed form.


       Returns:
           DLANSP

               DLANSP = ( 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.




ARGUMENTS
           NORM      (input)
                     NORM is CHARACTER*1
                     Specifies the value to be returned in DLANSP as described
                     above.

           UPLO      (input)
                     UPLO is CHARACTER*1
                     Specifies whether the upper or lower triangular part of the
                     symmetric matrix A is supplied.
                     = 'U':  Upper triangular part of A is supplied
                     = 'L':  Lower triangular part of A is supplied

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

           AP        (input)
                     AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
                     The upper or lower triangle of the symmetric matrix A, packed
                     columnwise in a linear array.  The j-th column of A is stored
                     in the array AP as follows:
                     if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
                     if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.

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



LAPACK routine                  31 October 2017                      DLANSP(3)