Horner's rule for polynomial evaluation: Difference between revisions
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Output: |
Output: |
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<lang>128</lang> |
<lang>128</lang> |
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=={{header|Tcl}}== |
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<lang tcl>package require Tcl 8.5 |
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proc horner {coeffs x} { |
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set y 0 |
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foreach c [lreverse $coeffs] { |
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set y [expr { $y*$x+$c }] |
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} |
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return $y |
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}</lang> |
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Demonstrating: |
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<lang tcl>puts [horner {-19 7 -4 6} 3]</lang> |
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Output: |
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<pre>128</pre> |
Revision as of 09:18, 31 March 2010
A fast scheme for evaluating a polynomial such as:
when
- .
is to arrange the computation as follows:
And compute the result from the innermost brackets outwards as in this pseudocode:
coefficients := [-19, 7, -4, 6] # list coefficients of all x^0..x^n in order x := 3 reversedcoeffs := reverse coefficients accumulator := reversedcoeffs[0] for i in 1 to length(reversedcoffs) do accumulator := ( accumulator * x ) + reversedcoeffs[i] done # accumulator now has the answer
Task Description
- Create a routine that takes a list of coefficients of a polynomial in order of increasing powers of x; together with a value of x to compute its value at, and return the value of the polynomial at that value using Horner's rule.
C.f: Formal power series
Fortran
<lang fortran>program test_horner
implicit none
write (*, '(f5.1)') horner ((/-19.0, 7.0, -4.0, 6.0/), 3.0)
contains
function horner (coeffs, x) result (res)
implicit none real, dimension (:), intent (in) :: coeffs real, intent (in) :: x real :: res integer :: i
res = 0.0 do i = size (coeffs), 1, -1 res = res * x + coeffs (i) end do
end function horner
end program test_horner</lang> Output: <lang>128.0</lang>
Java
<lang java5>import java.util.ArrayList; import java.util.Collections; import java.util.List;
public class Horner {
public static void main(String[] args){ List<Double> coeffs = new ArrayList<Double>(); coeffs.add(-19.0); coeffs.add(7.0); coeffs.add(-4.0); coeffs.add(6.0); System.out.println(polyEval(coeffs, 3)); }
public static double polyEval(List<Double> coefficients, double x) { Collections.reverse(coefficients); Double accumulator = coefficients.get(0); for (int i = 1; i < coefficients.size(); i++) { accumulator = (accumulator * x) + (Double) coefficients.get(i); } return accumulator; }
}</lang> Output:
128.0
Python
<lang python>>>> def horner(coeffs, x): acc = coeffs[-1] for c in reversed(coeffs[:-1]): acc = acc * x + c return acc
>>> horner( (-19, 7, -4, 6), 3) 128</lang>
Functional version
<lang python>>>> try: from functools import reduce except: pass
>>> def horner(coeffs, x): return reduce(lambda acc, c: acc * x + c, reversed(coeffs))
>>> horner( (-19, 7, -4, 6), 3) 128</lang>
Scheme
<lang scheme>(define (horner lst x)
(define (*horner lst x acc) (if (null? lst) acc (*horner (cdr lst) x (+ (* acc x) (car lst))))) (*horner (reverse lst) x 0))
(display (horner (list -19 7 -4 6) 3)) (newline)</lang> Output: <lang>128</lang>
Tcl
<lang tcl>package require Tcl 8.5 proc horner {coeffs x} {
set y 0 foreach c [lreverse $coeffs] { set y [expr { $y*$x+$c }] } return $y
}</lang> Demonstrating: <lang tcl>puts [horner {-19 7 -4 6} 3]</lang> Output:
128