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Peter Aronsson
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double precision function enorm(n,x) | ||
integer n | ||
double precision x(n) | ||
c ********** | ||
c | ||
c function enorm | ||
c | ||
c given an n-vector x, this function calculates the | ||
c euclidean norm of x. | ||
c | ||
c the euclidean norm is computed by accumulating the sum of | ||
c squares in three different sums. the sums of squares for the | ||
c small and large components are scaled so that no overflows | ||
c occur. non-destructive underflows are permitted. underflows | ||
c and overflows do not occur in the computation of the unscaled | ||
c sum of squares for the intermediate components. | ||
c the definitions of small, intermediate and large components | ||
c depend on two constants, rdwarf and rgiant. the main | ||
c restrictions on these constants are that rdwarf**2 not | ||
c underflow and rgiant**2 not overflow. the constants | ||
c given here are suitable for every known computer. | ||
c | ||
c the function statement is | ||
c | ||
c double precision function enorm(n,x) | ||
c | ||
c where | ||
c | ||
c n is a positive integer input variable. | ||
c | ||
c x is an input array of length n. | ||
c | ||
c subprograms called | ||
c | ||
c fortran-supplied ... dabs,dsqrt | ||
c | ||
c argonne national laboratory. minpack project. march 1980. | ||
c burton s. garbow, kenneth e. hillstrom, jorge j. more | ||
c | ||
c ********** | ||
integer i | ||
double precision agiant,floatn,one,rdwarf,rgiant,s1,s2,s3,xabs, | ||
* x1max,x3max,zero | ||
data one,zero,rdwarf,rgiant /1.0d0,0.0d0,3.834d-20,1.304d19/ | ||
s1 = zero | ||
s2 = zero | ||
s3 = zero | ||
x1max = zero | ||
x3max = zero | ||
floatn = n | ||
agiant = rgiant/floatn | ||
do 90 i = 1, n | ||
xabs = dabs(x(i)) | ||
if (xabs .gt. rdwarf .and. xabs .lt. agiant) go to 70 | ||
if (xabs .le. rdwarf) go to 30 | ||
c | ||
c sum for large components. | ||
c | ||
if (xabs .le. x1max) go to 10 | ||
s1 = one + s1*(x1max/xabs)**2 | ||
x1max = xabs | ||
go to 20 | ||
10 continue | ||
s1 = s1 + (xabs/x1max)**2 | ||
20 continue | ||
go to 60 | ||
30 continue | ||
c | ||
c sum for small components. | ||
c | ||
if (xabs .le. x3max) go to 40 | ||
s3 = one + s3*(x3max/xabs)**2 | ||
x3max = xabs | ||
go to 50 | ||
40 continue | ||
if (xabs .ne. zero) s3 = s3 + (xabs/x3max)**2 | ||
50 continue | ||
60 continue | ||
go to 80 | ||
70 continue | ||
c | ||
c sum for intermediate components. | ||
c | ||
s2 = s2 + xabs**2 | ||
80 continue | ||
90 continue | ||
c | ||
c calculation of norm. | ||
c | ||
if (s1 .eq. zero) go to 100 | ||
enorm = x1max*dsqrt(s1+(s2/x1max)/x1max) | ||
go to 130 | ||
100 continue | ||
if (s2 .eq. zero) go to 110 | ||
if (s2 .ge. x3max) | ||
* enorm = dsqrt(s2*(one+(x3max/s2)*(x3max*s3))) | ||
if (s2 .lt. x3max) | ||
* enorm = dsqrt(x3max*((s2/x3max)+(x3max*s3))) | ||
go to 120 | ||
110 continue | ||
enorm = x3max*dsqrt(s3) | ||
120 continue | ||
130 continue | ||
return | ||
c | ||
c last card of function enorm. | ||
c | ||
end |