Bernstein basis polynomials: Difference between revisions
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Note that the library method, ''Math.evalPoly'', evaluates polynomials of any degree using Horner's rule but requires the coefficients to be presented in highest to lowest degree order.
<syntaxhighlight lang="ecmascript">import "./fmt" for Fmt
import "./math" for Math
var toBern2 = Fn.new { |a| [a[0], a[0] + a[1] / 2, a[0] + a[1] + a[2]] }
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var x
var y
var m
System.print("Subprogram(1) examples:")
var pb2 = toBern2.call(pm)
var qb2 = toBern2.call(qm)
Fmt.print("mono $n --> bern $n", pm, pb2)
Fmt.print("mono $n --> bern $n", qm, qb2)
System.print("\nSubprogram(2) examples:")
x = 0.25
y = evalBern2.call(pb2, x)
m = Math.evalPoly(pm[-1..0], x)
Fmt.print("p($4.2f) = $j (mono $j)", x, y, m)
x = 7.5
y = evalBern2.call(pb2, x)
m = Math.evalPoly(pm[-1..0], x)
Fmt.print("p($4.2f) = $j (mono $j)", x, y, m)
x = 0.25
y = evalBern2.call(qb2, x)
m = Math.evalPoly(qm[-1..0], x)
Fmt.print("q($4.2f) = $j (mono $j)", x, y, m)
x = 7.5
y = evalBern2.call(qb2, x)
m = Math.evalPoly(qm[-1..0], x)
Fmt.print("q($4.2f) = $j (mono $j)", x, y, m)
System.print("\nSubprogram(3) examples:")
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var qb3 = toBern3.call(qm)
var rb3 = toBern3.call(rm)
Fmt.print("mono $n --> bern $n", pm, pb3)
Fmt.print("mono $n --> bern $n", qm, qb3)
Fmt.print("mono $n --> bern $n", rm, rb3)
System.print("\nSubprogram(4) examples:")
x = 0.25
y = evalBern3.call(pb3, x)
m = Math.evalPoly(pm[-1..0], x)
Fmt.print("p($4.2f) = $j (mono $j)", x, y, m)
x = 7.5
y = evalBern3.call(pb3, x)
m = Math.evalPoly(pm[-1..0], x)
Fmt.print("p($4.2f) = $j (mono $j)", x, y, m)
x = 0.25
y = evalBern3.call(qb3, x)
m = Math.evalPoly(qm[-1..0], x)
Fmt.print("q($4.2f) = $j (mono $j)", x, y, m)
x = 7.5
y = evalBern3.call(qb3, x)
m = Math.evalPoly(qm[-1..0], x)
Fmt.print("q($4.2f) = $j (mono $j)", x, y, m)
x = 0.25
y = evalBern3.call(rb3, x)
m = Math.evalPoly(rm[-1..0], x)
Fmt.print("r($4.2f) = $j (mono $j)", x, y, m)
x = 7.5
y = evalBern3.call(rb3, x)
m = Math.evalPoly(rm[-1..0], x)
Fmt.print("r($4.2f) = $j (mono $j)", x, y, m)
System.print("\nSubprogram(5) examples:")
var pc = bern2to3.call(pb2)
var qc = bern2to3.call(qb2)
Fmt.print("mono $n --> bern $n", pb2, pc)
Fmt.print("mono $n --> bern $n", qb2, qc)</syntaxhighlight>
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<pre>
Subprogram(1) examples:
mono [1, 0, 0] --> bern [1, 1, 1]
mono [1, 2, 3] --> bern [1, 2, 6]
Subprogram(2) examples:
p(0.25) = 1 (mono 1)
p(7.50) = 1 (mono 1)
q(0.25) = 1.6875 (mono 1.6875)
q(7.50) = 184.75 (mono 184.75)
Subprogram(3) examples:
mono [1, 0, 0, 0] --> bern [1, 1, 1, 1]
mono [1, 2, 3, 0] --> bern [1, 1.6666666666667, 3.3333333333333, 6]
mono [1, 2, 3, 4] --> bern [1, 1.6666666666667, 3.3333333333333, 10]
Subprogram(4) examples:
p(0.25) = 1 (mono 1)
p(7.50) = 1 (mono 1)
q(0.25) = 1.6875 (mono 1.6875)
q(7.50) = 184.75 (mono 184.75)
r(0.25) = 1.75 (mono 1.75)
r(7.50) = 1872.25 (mono 1872.25)
Subprogram(5) examples:
mono [1, 1, 1] --> bern [1, 1, 1, 1]
mono [1, 2, 6] --> bern [1, 1.6666666666667, 3.3333333333333, 6]
</pre>
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