C Library Functions - ppvalu (3)
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from |
* a practical guide to splines * by c. de boor
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calls interv
calculates value at x of jderiv-th derivative of pp fct from pp-repr
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i n p u t ******
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break, coef, l, k.....forms the pp-representation of the function | | |
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to be evaluated. specifically, the j-th derivative of | | |
f is
given by
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(d**j)f(x) = coef(j+1,i) + h*(coef(j+2,i) + h*( ... (coef(k-1,i) +
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o
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h*coef(k,i)/(k-j-1))/(k-j-2) ... )/2)/1
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with |
h = x - break(i), and
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i |
= max( 1 , max( j , break(j) .le. x , 1 .le. j .le. l ) ).
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x.....the point at which to evaluate.
jderiv.....integer giving the order of the derivative to be evaluat-
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ed. |
a s s u m e d to be zero or positive.
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o u t p u t ******
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ppvalu.....the value of the (jderiv)-th derivative of | | |
f at x.
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m e t h o d ******
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the interval index | | |
i , appropriate for x , is found through a
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call to |
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interv . the formula above for the jderiv-th derivative
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of |
f is then evaluated (by nested multiplication).
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| Nemo Release 3.1 | ppvalu (3) | June 29, 2025 |
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