Roots of a function: Difference between revisions

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=={{header|Phix}}==
=={{header|Phix}}==
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<!--<lang Phix>-->
<lang Phix>procedure print_roots(integer f, atom start, atom stop, atom step)
<span style="color: #008080;">procedure</span> <span style="color: #000000;">print_roots</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">f</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">atom</span> <span style="color: #000000;">start</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">stop</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">step</span><span style="color: #0000FF;">)</span>
⚫
-- Print approximate roots of f between x=start and x=stop, using
<span style="color: #000080;font-style:italic;">--
⚫
-- sign changes as an indicator that a root has been encountered.
⚫
-- Print approximate roots of f between x=start and x=stop, using
atom x = start, y = 0
⚫
-- sign changes as an indicator that a root has been encountered.

puts(1,"-----\n")
--</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">x</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">start</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">y</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
while x<=stop do
<span style="color: #7060A8;">puts</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"-----\n"</span><span style="color: #0000FF;">)</span>
atom last_y = y
<span style="color: #008080;">while</span> <span style="color: #000000;">x</span><span style="color: #0000FF;"><=</span><span style="color: #000000;">stop</span> <span style="color: #008080;">do</span>
y = call_func(f,{x})
<span style="color: #004080;">atom</span> <span style="color: #000000;">last_y</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">y</span>
if y=0
<span style="color: #000000;">y</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">f</span><span style="color: #0000FF;">(</span><span style="color: #000000;">x</span><span style="color: #0000FF;">)</span>
or (last_y<0 and y>0)
<span style="color: #008080;">if</span> <span style="color: #000000;">y</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span>
or (last_y>0 and y<0) then
<span style="color: #008080;">or</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">last_y</span><span style="color: #0000FF;"><</span><span style="color: #000000;">0</span> <span style="color: #008080;">and</span> <span style="color: #000000;">y</span><span style="color: #0000FF;">></span><span style="color: #000000;">0</span><span style="color: #0000FF;">)</span>
printf(1,"Root found %s %.10g\n", {iff(y=0?"at":"near"),x})
<span style="color: #008080;">or</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">last_y</span><span style="color: #0000FF;">></span><span style="color: #000000;">0</span> <span style="color: #008080;">and</span> <span style="color: #000000;">y</span><span style="color: #0000FF;"><</span><span style="color: #000000;">0</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
end if
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"Root found %s %.10g\n"</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">{</span><span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #000000;">y</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span><span style="color: #0000FF;">?</span><span style="color: #008000;">"at"</span><span style="color: #0000FF;">:</span><span style="color: #008000;">"near"</span><span style="color: #0000FF;">),</span><span style="color: #000000;">x</span><span style="color: #0000FF;">})</span>
x += step
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
end while
<span style="color: #000000;">x</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">step</span>
end procedure
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>

<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
⚫
-- Smaller steps produce more accurate/precise results in general,
⚫
-- but for many functions we'll never get exact roots, either due
⚫
<span style="color: #000080;font-style:italic;">-- Smaller steps produce more accurate/precise results in general,
⚫
-- to imperfect binary representation or irrational roots.
⚫
-- but for many functions we'll never get exact roots, either due
constant step = 1/256
⚫
-- to imperfect binary representation or irrational roots.</span>

<span style="color: #008080;">constant</span> <span style="color: #000000;">step</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">/</span><span style="color: #000000;">256</span>
function f1(atom x) return x*x*x-3*x*x+2*x end function
function f2(atom x) return x*x-4*x+3 end function
<span style="color: #008080;">function</span> <span style="color: #000000;">f1</span><span style="color: #0000FF;">(</span><span style="color: #004080;">atom</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">return</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">*</span><span style="color: #000000;">x</span><span style="color: #0000FF;">*</span><span style="color: #000000;">x</span><span style="color: #0000FF;">-</span><span style="color: #000000;">3</span><span style="color: #0000FF;">*</span><span style="color: #000000;">x</span><span style="color: #0000FF;">*</span><span style="color: #000000;">x</span><span style="color: #0000FF;">+</span><span style="color: #000000;">2</span><span style="color: #0000FF;">*</span><span style="color: #000000;">x</span> <span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
function f3(atom x) return x-1.5 end function
<span style="color: #008080;">function</span> <span style="color: #000000;">f2</span><span style="color: #0000FF;">(</span><span style="color: #004080;">atom</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">return</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">*</span><span style="color: #000000;">x</span><span style="color: #0000FF;">-</span><span style="color: #000000;">4</span><span style="color: #0000FF;">*</span><span style="color: #000000;">x</span><span style="color: #0000FF;">+</span><span style="color: #000000;">3</span> <span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
function f4(atom x) return x*x-2 end function
<span style="color: #008080;">function</span> <span style="color: #000000;">f3</span><span style="color: #0000FF;">(</span><span style="color: #004080;">atom</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">return</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1.5</span> <span style="color: #008080;">end</span> <span style="color: #008080;">function</span>

<span style="color: #008080;">function</span> <span style="color: #000000;">f4</span><span style="color: #0000FF;">(</span><span style="color: #004080;">atom</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">return</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">*</span><span style="color: #000000;">x</span><span style="color: #0000FF;">-</span><span style="color: #000000;">2</span> <span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
print_roots(routine_id("f1"), -1, 5, step)
print_roots(routine_id("f2"), -1, 5, step)
<span style="color: #000000;">print_roots</span><span style="color: #0000FF;">(</span><span style="color: #000000;">f1</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">5</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">step</span><span style="color: #0000FF;">)</span>
print_roots(routine_id("f3"), 0, 4, step)
<span style="color: #000000;">print_roots</span><span style="color: #0000FF;">(</span><span style="color: #000000;">f2</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">5</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">step</span><span style="color: #0000FF;">)</span>
print_roots(routine_id("f4"), -2, 2, step)</lang>
<span style="color: #000000;">print_roots</span><span style="color: #0000FF;">(</span><span style="color: #000000;">f3</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">4</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">step</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">print_roots</span><span style="color: #0000FF;">(</span><span style="color: #000000;">f4</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">step</span><span style="color: #0000FF;">)</span>
<!--</lang>-->
{{out}}
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