Bernstein basis polynomials: Difference between revisions
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{{trans|ALGOL 60}} |
{{trans|ALGOL 60}} |
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{{libheader|Wren-fmt}} |
{{libheader|Wren-fmt}} |
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{{libheader|Wren-math}} |
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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. |
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<syntaxhighlight lang="ecmascript">import "./fmt" for Fmt |
<syntaxhighlight lang="ecmascript">import "./fmt" for Fmt |
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import "./math" for Math |
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var toBern2 = Fn.new { |a| [a[0], a[0] + a[1] / 2, a[0] + a[1] + a[2]] } |
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 x |
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var y |
var y |
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var m |
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System.print("Subprogram(1) examples:") |
System.print("Subprogram(1) examples:") |
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var pb2 = toBern2.call(pm) |
var pb2 = toBern2.call(pm) |
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var qb2 = toBern2.call(qm) |
var qb2 = toBern2.call(qm) |
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Fmt.print("mono$n --> bern$n", pm, pb2) |
Fmt.print("mono $n --> bern $n", pm, pb2) |
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Fmt.print("mono$n --> bern$n", qm, qb2) |
Fmt.print("mono $n --> bern $n", qm, qb2) |
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System.print("\nSubprogram(2) examples:") |
System.print("\nSubprogram(2) examples:") |
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x = 0.25 |
x = 0.25 |
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y = evalBern2.call(pb2, x) |
y = evalBern2.call(pb2, x) |
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m = Math.evalPoly(pm[-1..0], x) |
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Fmt.print("p($4.2f) = $j", x, y) |
Fmt.print("p($4.2f) = $j (mono $j)", x, y, m) |
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x = 7.5 |
x = 7.5 |
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y = evalBern2.call(pb2, x) |
y = evalBern2.call(pb2, x) |
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m = Math.evalPoly(pm[-1..0], x) |
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Fmt.print("p($4.2f) = $j", x, y) |
Fmt.print("p($4.2f) = $j (mono $j)", x, y, m) |
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x = 0.25 |
x = 0.25 |
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y = evalBern2.call(qb2, x) |
y = evalBern2.call(qb2, x) |
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m = Math.evalPoly(qm[-1..0], x) |
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Fmt.print("q($4.2f) = $j", x, y) |
Fmt.print("q($4.2f) = $j (mono $j)", x, y, m) |
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x = 7.5 |
x = 7.5 |
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y = evalBern2.call(qb2, x) |
y = evalBern2.call(qb2, x) |
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m = Math.evalPoly(qm[-1..0], x) |
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Fmt.print("q($4.2f) = $j", x, y) |
Fmt.print("q($4.2f) = $j (mono $j)", x, y, m) |
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System.print("\nSubprogram(3) examples:") |
System.print("\nSubprogram(3) examples:") |
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var qb3 = toBern3.call(qm) |
var qb3 = toBern3.call(qm) |
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var rb3 = toBern3.call(rm) |
var rb3 = toBern3.call(rm) |
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Fmt.print("mono$n --> bern$n", pm, pb3) |
Fmt.print("mono $n --> bern $n", pm, pb3) |
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Fmt.print("mono$n --> bern$n", qm, qb3) |
Fmt.print("mono $n --> bern $n", qm, qb3) |
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Fmt.print("mono$n --> bern$n", rm, rb3) |
Fmt.print("mono $n --> bern $n", rm, rb3) |
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System.print("\nSubprogram(4) examples:") |
System.print("\nSubprogram(4) examples:") |
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x = 0.25 |
x = 0.25 |
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y = evalBern3.call(pb3, x) |
y = evalBern3.call(pb3, x) |
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m = Math.evalPoly(pm[-1..0], x) |
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Fmt.print("p($4.2f) = $j", x, y) |
Fmt.print("p($4.2f) = $j (mono $j)", x, y, m) |
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x = 7.5 |
x = 7.5 |
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y = evalBern3.call(pb3, x) |
y = evalBern3.call(pb3, x) |
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m = Math.evalPoly(pm[-1..0], x) |
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Fmt.print("p($4.2f) = $j", x, y) |
Fmt.print("p($4.2f) = $j (mono $j)", x, y, m) |
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x = 0.25 |
x = 0.25 |
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y = evalBern3.call(qb3, x) |
y = evalBern3.call(qb3, x) |
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m = Math.evalPoly(qm[-1..0], x) |
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Fmt.print("q($4.2f) = $j", x, y) |
Fmt.print("q($4.2f) = $j (mono $j)", x, y, m) |
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x = 7.5 |
x = 7.5 |
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y = evalBern3.call(qb3, x) |
y = evalBern3.call(qb3, x) |
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m = Math.evalPoly(qm[-1..0], x) |
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Fmt.print("q($4.2f) = $j", x, y) |
Fmt.print("q($4.2f) = $j (mono $j)", x, y, m) |
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x = 0.25 |
x = 0.25 |
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y = evalBern3.call(rb3, x) |
y = evalBern3.call(rb3, x) |
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m = Math.evalPoly(rm[-1..0], x) |
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Fmt.print("r($4.2f) = $j", x, y) |
Fmt.print("r($4.2f) = $j (mono $j)", x, y, m) |
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x = 7.5 |
x = 7.5 |
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y = evalBern3.call(rb3, x) |
y = evalBern3.call(rb3, x) |
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m = Math.evalPoly(rm[-1..0], x) |
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Fmt.print("r($4.2f) = $j", x, y) |
Fmt.print("r($4.2f) = $j (mono $j)", x, y, m) |
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System.print("\nSubprogram(5) examples:") |
System.print("\nSubprogram(5) examples:") |
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var pc = bern2to3.call(pb2) |
var pc = bern2to3.call(pb2) |
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var qc = bern2to3.call(qb2) |
var qc = bern2to3.call(qb2) |
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Fmt.print("mono$n --> bern$n", pb2, pc) |
Fmt.print("mono $n --> bern $n", pb2, pc) |
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Fmt.print("mono$n --> bern$n", qb2, qc)</syntaxhighlight> |
Fmt.print("mono $n --> bern $n", qb2, qc)</syntaxhighlight> |
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{{out}} |
{{out}} |
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<pre> |
<pre> |
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Subprogram(1) examples: |
Subprogram(1) examples: |
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mono[1, 0, 0] --> bern[1, 1, 1] |
mono [1, 0, 0] --> bern [1, 1, 1] |
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mono[1, 2, 3] --> bern[1, 2, 6] |
mono [1, 2, 3] --> bern [1, 2, 6] |
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Subprogram(2) examples: |
Subprogram(2) examples: |
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p(0.25) = 1 |
p(0.25) = 1 (mono 1) |
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p(7.50) = 1 |
p(7.50) = 1 (mono 1) |
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q(0.25) = 1.6875 |
q(0.25) = 1.6875 (mono 1.6875) |
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q(7.50) = 184.75 |
q(7.50) = 184.75 (mono 184.75) |
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Subprogram(3) examples: |
Subprogram(3) examples: |
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mono[1, 0, 0, 0] --> bern[1, 1, 1, 1] |
mono [1, 0, 0, 0] --> bern [1, 1, 1, 1] |
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mono[1, 2, 3, 0] --> bern[1, 1.6666666666667, 3.3333333333333, 6] |
mono [1, 2, 3, 0] --> bern [1, 1.6666666666667, 3.3333333333333, 6] |
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mono[1, 2, 3, 4] --> bern[1, 1.6666666666667, 3.3333333333333, 10] |
mono [1, 2, 3, 4] --> bern [1, 1.6666666666667, 3.3333333333333, 10] |
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Subprogram(4) examples: |
Subprogram(4) examples: |
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p(0.25) = 1 |
p(0.25) = 1 (mono 1) |
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p(7.50) = 1 |
p(7.50) = 1 (mono 1) |
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q(0.25) = 1.6875 |
q(0.25) = 1.6875 (mono 1.6875) |
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q(7.50) = 184.75 |
q(7.50) = 184.75 (mono 184.75) |
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r(0.25) = 1.75 |
r(0.25) = 1.75 (mono 1.75) |
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r(7.50) = 1872.25 |
r(7.50) = 1872.25 (mono 1872.25) |
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Subprogram(5) examples: |
Subprogram(5) examples: |
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mono[1, 1, 1] --> bern[1, 1, 1, 1] |
mono [1, 1, 1] --> bern [1, 1, 1, 1] |
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mono[1, 2, 6] --> bern[1, 1.6666666666667, 3.3333333333333, 6] |
mono [1, 2, 6] --> bern [1, 1.6666666666667, 3.3333333333333, 6] |
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</pre> |
</pre> |
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