Bernstein basis polynomials: Difference between revisions

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   bern (1.00, 1.00, 1.00) --> bern (1.00, 1.00, 1.00, 1.00)
   bern (1.00, 2.00, 6.00) --> bern (1.00, 1.67, 3.33, 6.00)</pre>
+=={{header|Go}}==
+{{trans|Wren}}
+<syntaxhighlight lang="go">package main
+import "fmt"
+func toBern2(a []float64) []float64 {
+    return []float64{a[0], a[0] + a[1]/2, a[0] + a[1] + a[2]}
+}
+// uses de Casteljau's algorithm
+func evalBern2(b []float64, t float64) float64 {
+    s := 1.0 - t
+    b01 := s*b[0] + t*b[1]
+    b12 := s*b[1] + t*b[2]
+    return s*b01 + t*b12
+}
+func toBern3(a []float64) []float64 {
+    b := make([]float64, 4)
+    b[0] = a[0]
+    b[1] = a[0] + a[1]/3
+    b[2] = a[0] + a[1]*2/3 + a[2]/3
+    b[3] = a[0] + a[1] + a[2] + a[3]
+    return b
+}
+// uses de Casteljau's algorithm
+func evalBern3(b []float64, t float64) float64 {
+    s := 1.0 - t
+    b01 := s*b[0] + t*b[1]
+    b12 := s*b[1] + t*b[2]
+    b23 := s*b[2] + t*b[3]
+    b012 := s*b01 + t*b12
+    b123 := s*b12 + t*b23
+    return s*b012 + t*b123
+}
+func bern2to3(q []float64) []float64 {
+    c := make([]float64, 4)
+    c[0] = q[0]
+    c[1] = q[0]/3 + q[1]*2/3
+    c[2] = q[1]*2/3 + q[2]/3
+    c[3] = q[2]
+    return c
+}
+// uses Horner's rule
+func evalMono2(a []float64, t float64) float64 {
+    return a[0] + (t * (a[1] + (t * a[2])))
+}
+// uses Horner's rule
+func evalMono3(a []float64, t float64) float64 {
+    return a[0] + (t * (a[1] + (t * (a[2] + (t * a[3])))))
+}
+func main() {
+    pm := []float64{1, 0, 0}
+    qm := []float64{1, 2, 3}
+    rm := []float64{1, 2, 3, 4}
+    var x, y, m float64
+    fmt.Println("Subprogram(1) examples:")
+    pb2 := toBern2(pm)
+    qb2 := toBern2(qm)
+    fmt.Printf("mono %v --> bern %v\n", pm, pb2)
+    fmt.Printf("mono %v --> bern %v\n", qm, qb2)
+    fmt.Println("\nSubprogram(2) examples:")
+    x = 0.25
+    y = evalBern2(pb2, x)
+    m = evalMono2(pm, x)
+    fmt.Printf("p(%4.2f) = %0.14g (mono %0.14g)\n", x, y, m)
+    x = 7.5
+    y = evalBern2(pb2, x)
+    m = evalMono2(pm, x)
+    fmt.Printf("p(%4.2f) = %0.14g (mono %0.14g)\n", x, y, m)
+    x = 0.25
+    y = evalBern2(qb2, x)
+    m = evalMono2(qm, x)
+    fmt.Printf("q(%4.2f) = %0.14g (mono %0.14g)\n", x, y, m)
+    x = 7.5
+    y = evalBern2(qb2, x)
+    m = evalMono2(qm, x)
+    fmt.Printf("q(%4.2f) = %0.14g (mono %0.14g)\n", x, y, m)
+    fmt.Println("\nSubprogram(3) examples:")
+    pm = append(pm, 0)
+    qm = append(qm, 0)
+    pb3 := toBern3(pm)
+    qb3 := toBern3(qm)
+    rb3 := toBern3(rm)
+    f := "mono $%v --> bern %0.14v\n"
+    fmt.Printf(f, pm, pb3)
+    fmt.Printf(f, qm, qb3)
+    fmt.Printf(f, rm, rb3)
+    fmt.Println("\nSubprogram(4) examples:")
+    x = 0.25
+    y = evalBern3(pb3, x)
+    m = evalMono3(pm, x)
+    fmt.Printf("p(%4.2f) = %0.14g (mono %0.14g)\n", x, y, m)
+    x = 7.5
+    y = evalBern3(pb3, x)
+    m = evalMono3(pm, x)
+    fmt.Printf("p(%4.2f) = %0.14g (mono %0.14g)\n", x, y, m)
+    x = 0.25
+    y = evalBern3(qb3, x)
+    m = evalMono3(qm, x)
+    fmt.Printf("q(%4.2f) = %0.14g (mono %0.14g)\n", x, y, m)
+    x = 7.5
+    y = evalBern3(qb3, x)
+    m = evalMono3(qm, x)
+    fmt.Printf("q(%4.2f) = %0.14g (mono %0.14g)\n", x, y, m)
+    x = 0.25
+    y = evalBern3(rb3, x)
+    m = evalMono3(rm, x)
+    fmt.Printf("r(%4.2f) = %0.14g (mono %0.14g)\n", x, y, m)
+    x = 7.5
+    y = evalBern3(rb3, x)
+    m = evalMono3(rm, x)
+    fmt.Printf("r(%4.2f) = %0.14g (mono %0.14g)\n", x, y, m)
+    fmt.Println("\nSubprogram(5) examples:")
+    pc := bern2to3(pb2)
+    qc := bern2to3(qb2)
+    fmt.Printf("mono %v --> bern %0.14v\n", pb2, pc)
+    fmt.Printf("mono %v --> bern %0.14v\n", qb2, qc)
+}</syntaxhighlight>
+{{out}}
+<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>
 =={{header|jq}}==