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****** |
i n p u t ******
break, coef, l, k.....contains the pp-representation of a certain
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function | | |
f of order k . Specifically,
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d**(k-1)f(x) = coef(k,i) | | |
for break(i).le. x .lt.break(i+1)
lnew.....number of intervals into which the interval (a,b) is to be
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sectioned by the new breakpoint sequence | | |
brknew .
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****** |
o u t p u t ******
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brknew.....array of length | | |
lnew+1 containing the new breakpoint se-
quence
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coefg.....the coefficient part of the pp-repr. | | |
break, coefg, l, 2
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for the monotone p.linear function | | |
g wrto which brknew will
be equidistributed.
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****** |
optional p r i n t e d o u t p u t ******
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coefg.....the pp coeffs of | | |
g are printed out if iprint is set
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.gt. 0 |
in data statement below.
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****** |
m e t h o d ******
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The k-th derivative of the given pp function | | |
f does not exist
(except perhaps as a linear combination of delta functions). Never-
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theless, we construct a p.constant function |
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h with breakpoint se-
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quence |
break which is approximately proportional to abs(d**k(f)).
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Specifically, on | | |
(break(i), break(i+1)),
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abs(jump at break(i) of pc) abs(jump at break(i+1) of pc)
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h = -------------------------- |
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+ ----------------------------
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break(i+1) - break(i-1) | | |
break(i+2) - break(i)
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with |
pc the p.constant (k-1)st derivative of f .
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Then, the p.linear function | | |
g is constructed as
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g(x) |
= integral of h(y)**(1/k) for y from a to x
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and its pp coeffs. stored in | | |
coefg .
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then |
brknew is determined by
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brknew(i) = a + g**(-1)((i-1)*step) , i=1,...,lnew+1
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where |
step = g(b)/lnew and (a,b) = (break(1),break(l+1)) .
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In the event that | | |
pc = d**(k-1)(f) is constant in (a,b) and
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therefore | | |
h = 0 identically, brknew is chosen uniformly spaced.
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