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****** |
i n p u t ******
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t |
the knot array, of length left+k (at least)
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k |
the order of the b-splines to be evaluated
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x |
the point at which these values are sought
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left |
an integer indicating the left endpoint of the interval of
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interest. the | | |
k b-splines whose support contains the interval
(t(left), t(left+1))
are to be considered.
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a s s u m p t i o n | | |
- - - it is assumed that
t(left) .lt. t(left+1)
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division by zero will result otherwise (in | | |
b s p l v b ).
also, the output is as advertised only if
t(left) .le. x .le. t(left+1) .
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nderiv |
an integer indicating that values of b-splines and their
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derivatives up to but not including the | | |
nderiv-th are asked
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for. ( nderiv | | |
is replaced internally by the integer m h i g h
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in |
(1,k) closest to it.)
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****** |
w o r k a r e a ******
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a |
an array of order (k,k), to contain b-coeff.s of the derivat-
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ives of a certain order of the | | |
k b-splines of interest.
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****** |
o u t p u t ******
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dbiatx |
an array of order (k,nderiv). its entry (i,m) contains
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value of | | |
(m-1)st derivative of (left-k+i)-th b-spline of
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order |
k for knot sequence t , i=1,...,k, m=1,...,nderiv.
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****** |
m e t h o d ******
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values at | | |
x of all the relevant b-splines of order k,k-1,...,
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k+1-nderiv | | |
are generated via bsplvb and stored temporarily in
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dbiatx . | | |
then, the b-coeffs of the required derivatives of the b-
splines of interest are generated by differencing, each from the pre-
ceding one of lower order, and combined with the values of b-splines
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of corresponding order in | | |
dbiatx to produce the desired values .
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