package main
import "fmt"
import "math"
func main() {
fmt.Printf("%d\n", 3 + 5)
fmt.Printf("%d\n", 3 - 5)
fmt.Printf("%d\n", 3 * 5)
fmt.Printf("%f\n", math.Pow(3, 5))
fmt.Printf("%d\n", 5 / 3)
fmt.Printf("%f\n", 5.0 / 3)
fmt.Printf("%f\n", 5 / 3.0)
fmt.Printf("%d\n", 5 % 3)
fmt.Printf("%3d\n", 3 * 5)
fmt.Printf("%23.20f\n", 5 / 3.0)
}
package main
import "fmt"
func main() {
var i int = 3 * 5
fmt.Printf("3 * 5 = %d\n", i)
}
package main
import "fmt"
import "math"
func main() {
const a = 0
const b = 1
// 蜿ｰ蠖｢蜑・〒遨榊・
var n int = 2
for j := 1; j <= 10; j++ {
var h float64 = (b - a) / float64(n)
var s float64 = 0
var x float64 = a
for i := 1; i <= n - 1; i++ {
x += h
s += f(x)
}
s = h * ((f(a) + f(b)) / 2 + s)
n *= 2
// 邨先棡繧・ﾏ 縺ｨ豈碑ｼ・
fmt.Printf("%2d : %13.10f, %13.10f\n", j, s, s - math.Pi)
}
}
func f(x float64) float64 {
return (4 / (1 + x * x))
}
package main
import "fmt"
import "math"
func main() {
const a = 0
const b = 1
// 荳ｭ轤ｹ蜑・〒遨榊・
var n int = 2
for j := 1; j <= 10; j++ {
var h float64 = (b - a) / float64(n)
var s float64 = 0
var x float64 = a + (h / 2)
for i := 1; i <= n; i++ {
s += f(x)
x += h
}
s *= h
n *= 2
// 邨先棡繧・ﾏ 縺ｨ豈碑ｼ・
fmt.Printf("%2d : %13.10f, %13.10f\n", j, s, s - math.Pi)
}
}
func f(x float64) float64 {
return (4 / (1 + x * x))
}
package main
import "fmt"
import "math"
func main() {
const a = 0
const b = 1
// Simpson蜑・〒遨榊・
var n int = 2
for j := 1; j <= 5; j++ {
var h float64 = (b - a) / float64(n)
var s2 float64 = 0
var s4 float64 = 0
var x float64 = a + h
for i := 1; i <= n / 2; i++ {
s4 += f(x)
x += h
s2 += f(x)
x += h
}
s2 = (s2 - f(b)) * 2 + f(a) + f(b)
s4 *= 4
var s float64 = (s2 + s4) * h / 3
n *= 2
// 邨先棡繧・ﾏ 縺ｨ豈碑ｼ・
fmt.Printf("%2d : %13.10f, %13.10f\n", j, s, s - math.Pi)
}
}
func f(x float64) float64 {
return (4 / (1 + x * x))
}
package main
import "fmt"
import "math"
func main() {
const a = 0
const b = 1
var t[7][7] float64
// 蜿ｰ蠖｢蜑・〒遨榊・
var n int = 2
for i := 1; i <= 6; i++ {
var h float64 = (b - a) / float64(n)
var s float64 = 0
var x float64 = a
for j := 1; j <= n - 1; j++ {
x += h
s += f(x)
}
// 邨先棡繧剃ｿ晏ｭ・
t[i][1] = h * ((f(a) + f(b)) / 2 + s)
n *= 2
}
// Richardson縺ｮ陬懷､匁ｳ・
n = 4
for j := 2; j <= 6; j++ {
for i := j; i <= 6; i++ {
t[i][j] = t[i][j - 1] + (t[i][j - 1] - t[i - 1][j - 1]) / float64(n - 1)
if i == j {
// 邨先棡繧・ﾏ 縺ｨ豈碑ｼ・
fmt.Printf("%2d : %13.10f, %13.10f\n", j, t[i][j], t[i][j] - math.Pi)
}
}
n *= 4
}
}
func f(x float64) float64 {
return (4 / (1 + x * x))
}
package main
import "fmt"
import "math"
// 繝・・繧ｿ轤ｹ縺ｮ謨ｰ
const N = 7
func main() {
var x [N]float64
var y [N]float64
// 1.5蛻ｻ縺ｿ縺ｧ -4.5・・.5 縺ｾ縺ｧ, ・礼せ縺縺大､繧偵そ繝・ヨ
for i := 0; i < N; i++ {
var d float64 = float64(i) * 1.5 - 4.5
x[i] = d
y[i] = f(d)
}
// 0.5蛻ｻ縺ｿ縺ｧ 荳弱∴繧峨ｌ縺ｦ縺・↑縺・､繧定｣憺俣
for i := 0; i <= 18; i++ {
var d float64 = float64(i) * 0.5 - 4.5
var d1 float64 = f(d)
var d2 float64 = lagrange(d, x[:], y[:])
// 蜈・・髢｢謨ｰ縺ｨ豈碑ｼ・
fmt.Printf("%5.2f\t%8.5f\t%8.5f\t%8.5f\n", d, d1, d2, d1 - d2)
}
}
// 蜈・・髢｢謨ｰ
func f(x float64) float64 {
return x - math.Pow(x,3) / (3 * 2) + math.Pow(x,5) / (5 * 4 * 3 * 2)
}
// Lagrange (繝ｩ繧ｰ繝ｩ繝ｳ繧ｸ繝･) 陬憺俣
func lagrange(d float64, x []float64, y []float64) float64 {
var sum float64 = 0
for i := 0; i < N; i++ {
var prod float64 = y[i]
for j := 0; j < N; j++ {
if (j != i) {
prod *= (d - x[j]) / (x[i] - x[j])
}
}
sum += prod
}
return sum
}
package main
import "fmt"
import "math"
// 繝・・繧ｿ轤ｹ縺ｮ謨ｰ
const N = 7
func main() {
var x [N]float64
var y [N]float64
// 1.5蛻ｻ縺ｿ縺ｧ -4.5・・.5 縺ｾ縺ｧ, ・礼せ縺縺大､繧偵そ繝・ヨ
for i := 0; i < N; i++ {
var d float64 = float64(i) * 1.5 - 4.5
x[i] = d
y[i] = f(d)
}
// 0.5蛻ｻ縺ｿ縺ｧ 荳弱∴繧峨ｌ縺ｦ縺・↑縺・､繧定｣憺俣
for i := 0; i <= 18; i++ {
var d float64 = float64(i) * 0.5 - 4.5
var d1 float64 = f(d)
var d2 float64 = neville(d, x[:], y[:])
// 蜈・・髢｢謨ｰ縺ｨ豈碑ｼ・
fmt.Printf("%5.2f\t%8.5f\t%8.5f\t%8.5f\n", d, d1, d2, d1 - d2)
}
}
// 蜈・・髢｢謨ｰ
func f(x float64) float64 {
return x - math.Pow(x,3) / (3 * 2) + math.Pow(x,5) / (5 * 4 * 3 * 2)
}
// Neville (繝阪Χ繧｣繝ｫ) 陬憺俣
func neville(d float64, x []float64, y []float64) float64 {
var w[N][N] float64
for i := 0; i < N; i++ {
w[0][i] = y[i]
}
for j := 1; j < N; j++ {
for i := 0; i < N - j; i++ {
w[j][i] = w[j-1][i+1] + (w[j-1][i+1] - w[j-1][i]) * (d - x[i+j]) / (x[i+j] - x[i])
}
}
return w[N-1][0]
}
package main
import "fmt"
import "math"
// 繝・・繧ｿ轤ｹ縺ｮ謨ｰ
const N = 7
func main() {
var x [N]float64
var y [N]float64
// 1.5蛻ｻ縺ｿ縺ｧ -4.5・・.5 縺ｾ縺ｧ, ・礼せ縺縺大､繧偵そ繝・ヨ
for i := 0; i < N; i++ {
var d float64 = float64(i) * 1.5 - 4.5
x[i] = d
y[i] = f(d)
}
// 蟾ｮ蛻・膚縺ｮ陦ｨ繧剃ｽ懊ｋ
var d[N][N] float64
for j := 0; j < N; j++ {
d[0][j] = y[j]
}
for i := 1; i < N; i++ {
for j := 0; j < N - i; j++ {
d[i][j] = (d[i-1][j+1] - d[i-1][j]) / (x[j+i] - x[j])
}
}
// ・朱嚴蟾ｮ蛻・膚
var a [N]float64
for j := 0; j < N; j++ {
a[j] = d[j][0]
}
// 0.5蛻ｻ縺ｿ縺ｧ 荳弱∴繧峨ｌ縺ｦ縺・↑縺・､繧定｣憺俣
for i := 0; i <= 18; i++ {
var d float64 = float64(i) * 0.5 - 4.5
var d1 float64 = f(d)
var d2 float64 = newton(d, x[:], a[:])
// 蜈・・髢｢謨ｰ縺ｨ豈碑ｼ・
fmt.Printf("%5.2f\t%8.5f\t%8.5f\t%8.5f\n", d, d1, d2, d1 - d2)
}
}
// 蜈・・髢｢謨ｰ
func f(x float64) float64 {
return x - math.Pow(x,3) / (3 * 2) + math.Pow(x,5) / (5 * 4 * 3 * 2)
}
// Newton (繝九Η繝ｼ繝医Φ) 陬憺俣
func newton(d float64, x []float64, a []float64) float64 {
var sum float64 = a[0]
for i := 1; i < N; i++ {
var prod float64 = a[i]
for j := 0; j < i; j++ {
prod *= (d - x[j])
}
sum += prod
}
return sum
}
package main
import "fmt"
import "math"
// 繝・・繧ｿ轤ｹ縺ｮ謨ｰ
const N = 7
const Nx2 = 14
func main() {
var x [N]float64
var y [N]float64
var yd [N]float64
// 1.5蛻ｻ縺ｿ縺ｧ -4.5・・.5 縺ｾ縺ｧ, ・礼せ縺縺大､繧偵そ繝・ヨ
for i := 0; i < N; i++ {
var d float64 = float64(i) * 1.5 - 4.5
x[i] = d
y[i] = f(d)
yd[i] = fd(d)
}
// 蟾ｮ蛻・膚縺ｮ陦ｨ繧剃ｽ懊ｋ
var z[Nx2] float64
var d[Nx2][Nx2] float64
for i := 0; i < Nx2; i++ {
j := i / 2
z[i] = x[j]
d[0][i] = y[j]
}
for i := 1; i < Nx2; i++ {
for j := 0; j < Nx2 - i; j++ {
if (i == 1 && j % 2 == 0) {
d[i][j] = yd[j / 2]
} else {
d[i][j] = (d[i-1][j+1] - d[i-1][j]) / (z[j+i] - z[j])
}
}
}
// ・朱嚴蟾ｮ蛻・膚
var a[Nx2] float64
for j := 0; j < Nx2; j++ {
a[j] = d[j][0]
}
// 0.5蛻ｻ縺ｿ縺ｧ 荳弱∴繧峨ｌ縺ｦ縺・↑縺・､繧定｣憺俣
for i := 0; i <= 18; i++ {
var d float64 = float64(i) * 0.5 - 4.5
var d1 float64 = f(d)
var d2 float64 = hermite(d, z[:], a[:])
// 蜈・・髢｢謨ｰ縺ｨ豈碑ｼ・
fmt.Printf("%5.2f\t%8.5f\t%8.5f\t%8.5f\n", d, d1, d2, d1 - d2)
}
}
// 蜈・・髢｢謨ｰ
func f(x float64) float64 {
return x - math.Pow(x,3) / (3 * 2) + math.Pow(x,5) / (5 * 4 * 3 * 2)
}
// 蟆朱未謨ｰ
func fd(x float64) float64 {
return 1 - math.Pow(x,2) / 2 + math.Pow(x,4) / (4 * 3 * 2)
}
// Hermite (繧ｨ繝ｫ繝溘・繝・ 陬憺俣
func hermite(d float64, z []float64, a []float64) float64 {
var sum float64 = a[0]
for i := 1; i < Nx2; i++ {
var prod float64 = a[i]
for j := 0; j < i; j++ {
prod *= (d - z[j])
}
sum += prod
}
return sum
}
package main
import "fmt"
import "math"
// 繝・・繧ｿ轤ｹ縺ｮ謨ｰ
const N = 7
func main() {
var x [N]float64
var y [N]float64
// 1.5蛻ｻ縺ｿ縺ｧ -4.5・・.5 縺ｾ縺ｧ, ・礼せ縺縺大､繧偵そ繝・ヨ
for i := 0; i < N; i++ {
var d float64 = float64(i) * 1.5 - 4.5
x[i] = d
y[i] = f(d)
}
// ・馴・婿遞句ｼ上・菫よ焚縺ｮ陦ｨ繧剃ｽ懊ｋ
var a [N]float64
var b [N]float64
var c [N]float64
var d [N]float64
for i := 1; i < N - 1; i++ {
a[i] = x[i] - x[i-1]
b[i] = 2.0 * (x[i+1] - x[i-1])
c[i] = x[i+1] - x[i]
d[i] = 6.0 * ((y[i+1] - y[i]) / (x[i+1] - x[i]) - (y[i] - y[i-1]) / (x[i] - x[i-1]))
}
// ・馴・婿遞句ｼ上ｒ隗｣縺・(繝茨ｼ阪・繧ｹ豕・
var g [N]float64
var s [N]float64
g[1] = b[1]
s[1] = d[1]
for i := 2; i < N - 1; i++ {
g[i] = b[i] - a[i] * c[i-1] / g[i-1]
s[i] = d[i] - a[i] * s[i-1] / g[i-1]
}
var z [N]float64
z[0] = 0
z[N-1] = 0
z[N-2] = s[N-2] / g[N-2]
for i := N - 3; i >= 1; i-- {
z[i] = (s[i] - c[i] * z[i+1]) / g[i]
}
// 0.5蛻ｻ縺ｿ縺ｧ 荳弱∴繧峨ｌ縺ｦ縺・↑縺・､繧定｣憺俣
for i := 0; i <= 18; i++ {
var d1 float64 = float64(i) * 0.5 - 4.5
var d2 float64 = f(d1)
var d3 float64 = spline(d1, x[:], y[:], z[:])
// 蜈・・髢｢謨ｰ縺ｨ豈碑ｼ・
fmt.Printf("%5.2f\t%8.5f\t%8.5f\t%8.5f\n", d1, d2, d3, d2 - d3)
}
}
// 蜈・・髢｢謨ｰ
func f(x float64) float64 {
return x - math.Pow(x,3) / (3 * 2) + math.Pow(x,5) / (5 * 4 * 3 * 2)
}
// Spline (繧ｹ繝励Λ繧､繝ｳ) 陬憺俣
func spline(d float64, x []float64, y []float64, z []float64) float64 {
// 陬憺俣髢｢謨ｰ蛟､縺後←縺ｮ蛹ｺ髢薙↓縺ゅｋ縺・
k := -1
for i := 1; i < N; i++ {
if d <= x[i] {
k = i - 1
break
}
}
if k < 0 {
k = N - 1
}
var d1 float64 = x[k+1] - d
var d2 float64 = d - x[k]
var d3 float64 = x[k+1] - x[k]
return (z[k] * math.Pow(d1,3) + z[k+1] * math.Pow(d2,3)) / (6.0 * d3) +
(y[k] / d3 - z[k] * d3 / 6.0) * d1 +
(y[k+1] / d3 - z[k+1] * d3 / 6.0) * d2
}
package main
import "fmt"
import "math"
// 驥榊鴨蜉騾溷ｺｦ
const g float64 = -9.8
// 遨ｺ豌玲慣謚嶺ｿよ焚
const k float64 = -0.01
// 譎る俣髢馴囈(遘・
const h float64 = 0.01
func main() {
// 隗貞ｺｦ
var degree float64 = 45
var radian float64 = degree * math.Pi / 180.0
// 蛻晞・250 km/h -> 遘帝溘↓螟画鋤
var v float64 = 250 * 1000 / 3600
// 豌ｴ蟷ｳ譁ｹ蜷代・騾溷ｺｦ
var vx[2] float64
vx[0] = v * math.Cos(radian)
// 驩帷峩譁ｹ蜷代・騾溷ｺｦ
var vy[2] float64
vy[0] = v * math.Sin(radian)
// 邨碁℃遘呈焚
var t float64 = 0.0
// 菴咲ｽｮ
var x float64 = 0.0
var y float64 = 0.0
// Euler豕・
for i := 1; y >= 0.0; i++ {
// 邨碁℃遘呈焚
t = float64(i) * h
// 菴咲ｽｮ
x += h * vx[0]
y += h * vy[0]
fmt.Printf("%4.2f\t%8.5f\t%9.5f\t%9.5f\t%8.5f\n", t, vx[0], vy[0], x, y)
// 騾溷ｺｦ
vx[1] = vx[0] + h * fx(vx[0], vy[0])
vy[1] = vy[0] + h * fy(vx[0], vy[0])
vx[0] = vx[1]
vy[0] = vy[1]
}
}
// 遨ｺ豌玲慣謚励↓繧医ｋ豌ｴ蟷ｳ譁ｹ蜷代・貂幃溷・
func fx(vx float64, vy float64) float64 {
return k * math.Sqrt(vx * vx + vy * vy) * vx
}
// 驥榊鴨縺ｨ遨ｺ豌玲慣謚励↓繧医ｋ驩帷峩譁ｹ蜷代・貂幃溷・
func fy(vx float64, vy float64) float64 {
return g + (k * math.Sqrt(vx * vx + vy * vy) * vy)
}
package main
import "fmt"
import "math"
// 驥榊鴨蜉騾溷ｺｦ
const g float64 = -9.8
// 遨ｺ豌玲慣謚嶺ｿよ焚
const k float64 = -0.01
// 譎る俣髢馴囈(遘・
const h float64 = 0.01
func main() {
// 隗貞ｺｦ
var degree float64 = 45
var radian float64 = degree * math.Pi / 180.0
// 蛻晞・250 km/h -> 遘帝溘↓螟画鋤
var v float64 = 250 * 1000 / 3600
// 豌ｴ蟷ｳ譁ｹ蜷代・騾溷ｺｦ
var vx[3] float64
vx[0] = v * math.Cos(radian)
// 驩帷峩譁ｹ蜷代・騾溷ｺｦ
var vy[3] float64
vy[0] = v * math.Sin(radian)
// 邨碁℃遘呈焚
var t float64 = 0.0
// 菴咲ｽｮ
var x[3] float64
x[0] = 0.0
var y[3] float64
y[0] = 0.0
// Heun豕・
for i := 1; y[0] >= 0.0; i++ {
// 邨碁℃遘呈焚
t = float64(i) * h
// 菴咲ｽｮ繝ｻ騾溷ｺｦ
x[1] = x[0] + h * vx[0]
y[1] = y[0] + h * vy[0]
vx[1] = vx[0] + h * fx(vx[0], vy[0])
vy[1] = vy[0] + h * fy(vx[0], vy[0])
x[2] = x[0] + h * ( vx[0] + vx[1] ) / 2
y[2] = y[0] + h * ( vy[0] + vy[1] ) / 2
vx[2] = vx[0] + h * (fx(vx[0], vy[0]) + fx(vx[1], vy[1])) / 2
vy[2] = vy[0] + h * (fy(vx[0], vy[0]) + fy(vx[1], vy[1])) / 2
x[0] = x[2]
y[0] = y[2]
vx[0] = vx[2]
vy[0] = vy[2]
fmt.Printf("%4.2f\t%8.5f\t%9.5f\t%9.5f\t%9.5f\n", t, vx[0], vy[0], x[0], y[0])
}
}
// 遨ｺ豌玲慣謚励↓繧医ｋ豌ｴ蟷ｳ譁ｹ蜷代・貂幃溷・
func fx(vx float64, vy float64) float64 {
return k * math.Sqrt(vx * vx + vy * vy) * vx
}
// 驥榊鴨縺ｨ遨ｺ豌玲慣謚励↓繧医ｋ驩帷峩譁ｹ蜷代・貂幃溷・
func fy(vx float64, vy float64) float64 {
return g + (k * math.Sqrt(vx * vx + vy * vy) * vy)
}
package main
import "fmt"
import "math"
// 驥榊鴨蜉騾溷ｺｦ
const g float64 = -9.8
// 遨ｺ豌玲慣謚嶺ｿよ焚
const k float64 = -0.01
// 譎る俣髢馴囈(遘・
const h float64 = 0.01
func main() {
// 隗貞ｺｦ
var degree float64 = 45
var radian float64 = degree * math.Pi / 180.0
// 蛻晞・250 km/h -> 遘帝溘↓螟画鋤
var v float64 = 250 * 1000 / 3600
// 豌ｴ蟷ｳ譁ｹ蜷代・騾溷ｺｦ
var vx[2] float64
vx[0] = v * math.Cos(radian)
// 驩帷峩譁ｹ蜷代・騾溷ｺｦ
var vy[2] float64
vy[0] = v * math.Sin(radian)
// 邨碁℃遘呈焚
var t float64 = 0.0
// 菴咲ｽｮ
var x[2] float64
x[0] = 0.0
var y[2] float64
y[0] = 0.0
// 荳ｭ轤ｹ豕・
for i := 1; y[0] >= 0.0; i++ {
// 邨碁℃遘呈焚
t = float64(i) * h
// 菴咲ｽｮ繝ｻ騾溷ｺｦ
vx[1] = h * fx(vx[0], vy[0])
vy[1] = h * fy(vx[0], vy[0])
var wx float64 = vx[0] + vx[1] / 2
var wy float64 = vy[0] + vy[1] / 2
vx[0] = vx[0] + h * fx(wx, wy)
vy[0] = vy[0] + h * fy(wx, wy)
x[0] = x[0] + h * wx
y[0] = y[0] + h * wy
fmt.Printf("%4.2f\t%8.5f\t%9.5f\t%9.5f\t%9.5f\n", t, vx[0], vy[0], x[0], y[0])
}
}
// 遨ｺ豌玲慣謚励↓繧医ｋ豌ｴ蟷ｳ譁ｹ蜷代・貂幃溷・
func fx(vx float64, vy float64) float64 {
return k * math.Sqrt(vx * vx + vy * vy) * vx
}
// 驥榊鴨縺ｨ遨ｺ豌玲慣謚励↓繧医ｋ驩帷峩譁ｹ蜷代・貂幃溷・
func fy(vx float64, vy float64) float64 {
return g + (k * math.Sqrt(vx * vx + vy * vy) * vy)
}
package main
import "fmt"
import "math"
// 驥榊鴨蜉騾溷ｺｦ
const g float64 = -9.8
// 遨ｺ豌玲慣謚嶺ｿよ焚
const k float64 = -0.01
// 譎る俣髢馴囈(遘・
const h float64 = 0.01
func main() {
// 隗貞ｺｦ
var degree float64 = 45
var radian float64 = degree * math.Pi / 180.0
// 蛻晞・250 km/h -> 遘帝溘↓螟画鋤
var v float64 = 250 * 1000 / 3600
// 豌ｴ蟷ｳ譁ｹ蜷代・騾溷ｺｦ
var vx[5] float64
vx[0] = v * math.Cos(radian)
// 驩帷峩譁ｹ蜷代・騾溷ｺｦ
var vy[5] float64
vy[0] = v * math.Sin(radian)
// 邨碁℃遘呈焚
var t float64 = 0.0
// 菴咲ｽｮ
var x[5] float64
x[0] = 0.0
var y[5] float64
y[0] = 0.0
// Runge-Kutta豕・
for i := 1; y[0] >= 0.0; i++ {
// 邨碁℃遘呈焚
t = float64(i) * h
// 菴咲ｽｮ繝ｻ騾溷ｺｦ
x[1] = h * vx[0]
y[1] = h * vy[0]
vx[1] = h * fx(vx[0], vy[0])
vy[1] = h * fy(vx[0], vy[0])
var wx float64 = vx[0] + vx[1] / 2
var wy float64 = vy[0] + vy[1] / 2
x[2] = h * wx
y[2] = h * wy
vx[2] = h * fx(wx, wy)
vy[2] = h * fy(wx, wy)
wx = vx[0] + vx[2] / 2
wy = vy[0] + vy[2] / 2
x[3] = h * wx
y[3] = h * wy
vx[3] = h * fx(wx, wy)
vy[3] = h * fy(wx, wy)
wx = vx[0] + vx[3]
wy = vy[0] + vy[3]
x[4] = h * wx
y[4] = h * wy
vx[4] = h * fx(wx, wy)
vy[4] = h * fy(wx, wy)
x[0] += ( x[1] + x[2] * 2 + x[3] * 2 + x[4]) / 6
y[0] += ( y[1] + y[2] * 2 + y[3] * 2 + y[4]) / 6
vx[0] += (vx[1] + vx[2] * 2 + vx[3] * 2 + vx[4]) / 6
vy[0] += (vy[1] + vy[2] * 2 + vy[3] * 2 + vy[4]) / 6
fmt.Printf("%4.2f\t%8.5f\t%9.5f\t%9.5f\t%9.5f\n", t, vx[0], vy[0], x[0], y[0])
}
}
// 遨ｺ豌玲慣謚励↓繧医ｋ豌ｴ蟷ｳ譁ｹ蜷代・貂幃溷・
func fx(vx float64, vy float64) float64 {
return k * math.Sqrt(vx * vx + vy * vy) * vx
}
// 驥榊鴨縺ｨ遨ｺ豌玲慣謚励↓繧医ｋ驩帷峩譁ｹ蜷代・貂幃溷・
func fy(vx float64, vy float64) float64 {
return g + (k * math.Sqrt(vx * vx + vy * vy) * vy)
}
package main
import "fmt"
import "math"
// 驥榊鴨蜉騾溷ｺｦ
const g float64 = -9.8
// 遨ｺ豌玲慣謚嶺ｿよ焚
const k float64 = -0.01
// 譎る俣髢馴囈(遘・
const h float64 = 0.01
func main() {
// 隗貞ｺｦ
var degree float64 = 45
var radian float64 = degree * math.Pi / 180.0
// 蛻晞・250 km/h -> 遘帝溘↓螟画鋤
var v float64 = 250 * 1000 / 3600
// 豌ｴ蟷ｳ譁ｹ蜷代・騾溷ｺｦ
var vx[5] float64
vx[0] = v * math.Cos(radian)
// 驩帷峩譁ｹ蜷代・騾溷ｺｦ
var vy[5] float64
vy[0] = v * math.Sin(radian)
// 邨碁℃遘呈焚
var t float64 = 0.0
// 菴咲ｽｮ
var x[5] float64
x[0] = 0.0
var y[5] float64
y[0] = 0.0
// Runge-Kutta-Gill豕・
for i := 1; y[0] >= 0.0; i++ {
// 邨碁℃遘呈焚
t = float64(i) * h
// 菴咲ｽｮ繝ｻ騾溷ｺｦ
x[1] = h * vx[0]
y[1] = h * vy[0]
vx[1] = h * fx(vx[0], vy[0])
vy[1] = h * fy(vx[0], vy[0])
var wx float64 = vx[0] + vx[1] / 2
var wy float64 = vy[0] + vy[1] / 2
x[2] = h * wx
y[2] = h * wy
vx[2] = h * fx(wx, wy)
vy[2] = h * fy(wx, wy)
wx = vx[0] + vx[1] * ((math.Sqrt(2.0) - 1) / 2) + vx[2] * (1 - 1 / math.Sqrt(2.0))
wy = vy[0] + vy[1] * ((math.Sqrt(2.0) - 1) / 2) + vy[2] * (1 - 1 / math.Sqrt(2.0))
x[3] = h * wx
y[3] = h * wy
vx[3] = h * fx(wx, wy)
vy[3] = h * fy(wx, wy)
wx = vx[0] - vx[2] / math.Sqrt(2.0) + vx[3] * (1 + 1 / math.Sqrt(2.0))
wy = vy[0] - vy[2] / math.Sqrt(2.0) + vy[3] * (1 + 1 / math.Sqrt(2.0))
x[4] = h * wx
y[4] = h * wy
vx[4] = h * fx(wx, wy)
vy[4] = h * fy(wx, wy)
x[0] += ( x[1] + x[2] * (2 - math.Sqrt(2.0)) + x[3] * (2 + math.Sqrt(2.0)) + x[4]) / 6
y[0] += ( y[1] + y[2] * (2 - math.Sqrt(2.0)) + y[3] * (2 + math.Sqrt(2.0)) + y[4]) / 6
vx[0] += (vx[1] + vx[2] * (2 - math.Sqrt(2.0)) + vx[3] * (2 + math.Sqrt(2.0)) + vx[4]) / 6
vy[0] += (vy[1] + vy[2] * (2 - math.Sqrt(2.0)) + vy[3] * (2 + math.Sqrt(2.0)) + vy[4]) / 6
fmt.Printf("%4.2f\t%8.5f\t%9.5f\t%9.5f\t%9.5f\n", t, vx[0], vy[0], x[0], y[0])
}
}
// 遨ｺ豌玲慣謚励↓繧医ｋ豌ｴ蟷ｳ譁ｹ蜷代・貂幃溷・
func fx(vx float64, vy float64) float64 {
return k * math.Sqrt(vx * vx + vy * vy) * vx
}
// 驥榊鴨縺ｨ遨ｺ豌玲慣謚励↓繧医ｋ驩帷峩譁ｹ蜷代・貂幃溷・
func fy(vx float64, vy float64) float64 {
return g + (k * math.Sqrt(vx * vx + vy * vy) * vy)
}
package main
import "fmt"
import "math"
func main() {
var a float64 = 1
var b float64 = 2
fmt.Printf("%12.10f\n", bisection(a, b))
}
func bisection(a float64, b float64) float64 {
var c float64
for {
// 蛹ｺ髢・(a, b) 縺ｮ荳ｭ轤ｹ c = (a + b) / 2
c = (a + b) / 2
fmt.Printf("%12.10f\t%13.10f\n", c, c - math.Sqrt(2))
var fc float64 = f(c)
if math.Fabs(fc) < 0.0000000001 {
break
}
if fc < 0 {
// f(c) < 0 縺ｧ縺ゅｌ縺ｰ, 隗｣縺ｯ蛹ｺ髢・(c, b) 縺ｮ荳ｭ縺ｫ蟄伜惠
a = c
} else {
// f(c) > 0 縺ｧ縺ゅｌ縺ｰ, 隗｣縺ｯ蛹ｺ髢・(a, c) 縺ｮ荳ｭ縺ｫ蟄伜惠
b = c
}
}
return c
}
func f(x float64) float64 {
return x * x - 2
}
package main
import "fmt"
import "math"
func main() {
var a float64 = 1
var b float64 = 2
fmt.Printf("%12.10f\n", falseposition(a, b))
}
func falseposition(a float64, b float64) float64 {
var c float64
for {
// 轤ｹ (a,f(a)) 縺ｨ 轤ｹ (b,f(b)) 繧堤ｵ舌・逶ｴ邱壹→ x霆ｸ縺ｮ莠､轤ｹ
c = (a * f(b) - b * f(a)) / (f(b) - f(a))
fmt.Printf("%12.10f\t%13.10f\n", c, c - math.Sqrt(2))
var fc float64 = f(c)
if math.Fabs(fc) < 0.0000000001 {
break
}
if fc < 0 {
// f(c) < 0 縺ｧ縺ゅｌ縺ｰ, 隗｣縺ｯ蛹ｺ髢・(c, b) 縺ｮ荳ｭ縺ｫ蟄伜惠
a = c
} else {
// f(c) > 0 縺ｧ縺ゅｌ縺ｰ, 隗｣縺ｯ蛹ｺ髢・(a, c) 縺ｮ荳ｭ縺ｫ蟄伜惠
b = c
}
}
return c
}
func f(x float64) float64 {
return x * x - 2
}
package main
import "fmt"
import "math"
func main() {
var x float64 = 1
fmt.Printf("%12.10f\n", iterative(x))
}
func iterative(x0 float64) float64 {
var x1 float64
for {
x1 = g(x0)
fmt.Printf("%12.10f\t%13.10f\n", x1, x1 - math.Sqrt(2))
if math.Fabs(x1 - x0) < 0.0000000001 {
break
}
x0 = x1
}
return x1
}
func g(x float64) float64 {
return (x / 2) + (1 / x)
}
package main
import "fmt"
import "math"
func main() {
var x float64 = 2
fmt.Printf("%12.10f\n", newton(x))
}
func newton(x0 float64) float64 {
var x1 float64
for {
x1 = x0 - (f0(x0) / f1(x0))
fmt.Printf("%12.10f\t%13.10f\n", x1, x1 - math.Sqrt(2))
if math.Fabs(x1 - x0) < 0.0000000001 {
break
}
x0 = x1
}
return x1
}
func f0(x float64) float64 {
return x * x - 2
}
func f1(x float64) float64 {
return 2 * x
}
package main
import "fmt"
import "math"
func main() {
var x float64 = 2
fmt.Printf("%12.10f\n", bailey(x))
}
func bailey(x0 float64) float64 {
var x1 float64
for {
x1 = x0 - (f0(x0) / (f1(x0) - (f0(x0) * f2(x0) / (2 * f1(x0)))))
fmt.Printf("%12.10f\t%13.10f\n", x1, x1 - math.Sqrt(2))
if math.Fabs(x1 - x0) < 0.0000000001 {
break
}
x0 = x1
}
return x1
}
func f0(x float64) float64 {
return x * x - 2
}
func f1(x float64) float64 {
return 2 * x
}
func f2(x float64) float64 {
return 2
}
package main
import "fmt"
import "math"
func main() {
var x0 float64 = 1
var x1 float64 = 2
fmt.Printf("%12.10f\n", secant(x0, x1))
}
func secant(x0 float64, x1 float64) float64 {
var x2 float64
for {
x2 = x1 - f(x1) * (x1 - x0) / (f(x1) - f(x0))
fmt.Printf("%12.10f\t%13.10f\n", x2, x2 - math.Sqrt(2))
if math.Fabs(x2 - x1) < 0.0000000001 {
break
}
x0 = x1
x1 = x2
}
return x2
}
func f(x float64) float64 {
return x * x - 2
}
package main
import "fmt"
import "math"
const N = 4
func main() {
var a [N][N]float64 = [N][N]float64{{9,2,1,1},{2,8,-2,1},{-1,-2,7,-2},{1,-1,-2,6}}
var b = []float64{20,16,8,17}
var c = []float64{0,0,0,0}
jacobi(a,b,c)
fmt.Println("X")
for i := 0; i < N; i++ {
fmt.Printf("%14.10f\t", c[i])
}
fmt.Println("")
}
func jacobi(a[N][N]float64, b[]float64, x0[]float64) {
for {
var x1 = []float64{0,0,0,0}
var finish = true
for i := 0; i < N; i++ {
x1[i] = b[i]
for j := 0; j < N; j++ {
if (j != i) {
x1[i] -= a[i][j] * x0[j]
}
}
x1[i] /= a[i][i]
if (math.Abs(x1[i] - x0[i]) > 0.0000000001) {
finish = false
}
}
for i := 0; i < N; i++ {
x0[i] = x1[i]
fmt.Printf("%14.10f\t", x1[i])
}
fmt.Println("")
if (finish) {
return
}
}
}
package main
import "fmt"
import "math"
const N = 4
func main() {
var a [N][N]float64 = [N][N]float64{{9,2,1,1},{2,8,-2,1},{-1,-2,7,-2},{1,-1,-2,6}}
var b = []float64{20,16,8,17}
var c = []float64{0,0,0,0}
gauss(a,b,c)
fmt.Println("X")
for i := 0; i < N; i++ {
fmt.Printf("%14.10f\t", c[i])
}
fmt.Println("")
}
func gauss(a[N][N]float64, b[]float64, x0[]float64) {
for {
var x1 float64
var finish = true
for i := 0; i < N; i++ {
x1 = b[i]
for j := 0; j < N; j++ {
if (j != i) {
x1 -= a[i][j] * x0[j]
}
}
x1 /= a[i][i]
if (math.Abs(x1 - x0[i]) > 0.0000000001) {
finish = false
}
x0[i] = x1
}
for i := 0; i < N; i++ {
fmt.Printf("%14.10f\t", x0[i])
}
fmt.Println("")
if (finish) {
return
}
}
}
package main
import "fmt"
import "math"
const N = 4
func main() {
var a [N][N]float64 = [N][N]float64{{-1,-2,7,-2},{1,-1,-2,6},{9,2,1,1},{2,8,-2,1}}
var b []float64 = []float64{8,17,20,16}
pivoting(&a,b)
fmt.Println("pivoting")
disp_progress(a,b)
forward_elimination(&a,b)
fmt.Println("forward_elimination")
disp_progress(a,b)
backward_substitution(&a,b)
fmt.Println("X")
for i := 0; i < N; i++ {
fmt.Printf("%14.10f\t", b[i])
}
fmt.Println("")
}
func forward_elimination(a *[N][N]float64, b []float64) {
for pivot := 0; pivot < N - 1; pivot++ {
for row := pivot + 1; row < N; row++ {
var s = a[row][pivot] / a[pivot][pivot]
for col := pivot; col < N; col++ {
a[row][col] -= a[pivot][col] * s
}
b[row] -= b[pivot] * s
}
}
}
func backward_substitution(a *[N][N]float64, b []float64) {
for row := N - 1; row >= 0; row-- {
for col := N - 1; col > row; col-- {
b[row] -= a[row][col] * b[col]
}
b[row] /= a[row][row]
}
}
func pivoting(a *[N][N]float64, b []float64) {
for pivot := 0; pivot < N; pivot++ {
var max_row = pivot
var max_val float64 = 0.0
for row := pivot; row < N; row++ {
if math.Abs(a[row][pivot]) > max_val {
max_val = math.Abs(a[row][pivot])
max_row = row
}
}
if (max_row != pivot) {
var tmp float64 = 0.0
for col := 0; col < N; col++ {
tmp = a[max_row][col]
a[max_row][col] = a[pivot][col]
a[pivot][col] = tmp
}
tmp = b[max_row]
b[max_row] = b[pivot]
b[pivot] = tmp
}
}
}
func disp_progress(a[N][N]float64, b[]float64) {
for i := 0; i < N; i++ {
for j := 0; j < N; j++ {
fmt.Printf("%14.10f\t", a[i][j])
}
fmt.Printf("%14.10f\t\n", b[i])
}
fmt.Println()
}
package main
import "fmt"
import "math"
const N = 4
func main() {
var a [N][N]float64 = [N][N]float64{{-1,-2,7,-2},{1,-1,-2,6},{9,2,1,1},{2,8,-2,1}}
var b []float64 = []float64{8,17,20,16}
pivoting(&a,b)
fmt.Println("pivoting")
disp_progress(a,b)
forward_elimination(&a,b)
fmt.Println("forward_elimination")
disp_progress(a,b)
backward_substitution(&a,b)
fmt.Println("X")
for i := 0; i < N; i++ {
fmt.Printf("%14.10f\t", b[i])
}
fmt.Println("")
}
func forward_elimination(a *[N][N]float64, b []float64) {
for pivot := 0; pivot < N; pivot++ {
var s = a[pivot][pivot]
for col := 0; col < N; col++ {
a[pivot][col] /= s
}
b[pivot] /= s
}
fmt.Println("forward_elimination")
disp_progress(*a,b)
for pivot := 0; pivot < N; pivot++ {
for row := 0; row < N; row++ {
if (row == pivot) {
continue
}
var s = a[row][pivot] / a[pivot][pivot]
for col := pivot; col < N; col++ {
a[row][col] -= a[pivot][col] * s
}
b[row] -= b[pivot] * s
}
}
}
func backward_substitution(a *[N][N]float64, b []float64) {
for pivot := 0; pivot < N; pivot++ {
b[pivot] /= a[pivot][pivot]
}
}
func pivoting(a *[N][N]float64, b []float64) {
for pivot := 0; pivot < N; pivot++ {
var max_row = pivot
var max_val float64 = 0.0
for row := pivot; row < N; row++ {
if math.Abs(a[row][pivot]) > max_val {
max_val = math.Abs(a[row][pivot])
max_row = row
}
}
if (max_row != pivot) {
var tmp float64 = 0.0
for col := 0; col < N; col++ {
tmp = a[max_row][col]
a[max_row][col] = a[pivot][col]
a[pivot][col] = tmp
}
tmp = b[max_row]
b[max_row] = b[pivot]
b[pivot] = tmp
}
}
}
func disp_progress(a[N][N]float64, b[]float64) {
for i := 0; i < N; i++ {
for j := 0; j < N; j++ {
fmt.Printf("%14.10f\t", a[i][j])
}
fmt.Printf("%14.10f\t\n", b[i])
}
fmt.Println()
}
package main
import "fmt"
import "math"
const N = 4
func main() {
var a [N][N]float64 = [N][N]float64{{-1,-2,7,-2},{1,-1,-2,6},{9,2,1,1},{2,8,-2,1}}
var b []float64 = []float64{8,17,20,16}
pivoting(&a,b)
fmt.Println("pivoting")
disp_progress(a,b)
// LU
var x []float64 = []float64{0,0,0,0}
decomp(&a,b,x)
fmt.Println("X")
for i := 0; i < N; i++ {
fmt.Printf("%14.10f\t", x[i])
}
fmt.Println()
}
// LU
func decomp(a *[N][N]float64, b []float64, x []float64) {
//
forward_elimination(a,b)
//
fmt.Println("L")
for i := 0; i < N; i++ {
for j := 0; j < N; j++ {
if (i > j) {
fmt.Printf("%14.10f\t", a[i][j])
} else if (i == j) {
fmt.Printf("%14.10f\t", 1.0)
} else {
fmt.Printf("%14.10f\t", 0.0)
}
}
fmt.Println()
}
fmt.Println()
//
fmt.Println("U")
for i := 0; i < N; i++ {
for j := 0; j < N; j++ {
if (i <= j) {
fmt.Printf("%14.10f\t", a[i][j])
} else {
fmt.Printf("%14.10f\t", 0.0)
}
}
fmt.Println()
}
fmt.Println()
// Ly=b
var y []float64 = []float64{0,0,0,0}
for row := 0; row < N; row++ {
for col := 0; col < row; col++ {
b[row] -= a[row][col] * y[col]
}
y[row] = b[row]
}
// y
fmt.Println("Y")
for i := 0; i < N; i++ {
fmt.Printf("%14.10f\t", y[i])
}
fmt.Println("\n")
// Ux=y
for row := N - 1; row >= 0; row-- {
for col := N - 1; col > row; col-- {
y[row] -= a[row][col] * x[col]
}
x[row] = y[row] / a[row][row]
}
}
//
func forward_elimination(a *[N][N]float64, b []float64) {
for pivot := 0; pivot < N - 1; pivot++ {
for row := pivot + 1; row < N; row++ {
var s = a[row][pivot] / a[pivot][pivot]
for col := pivot; col < N; col++ {
a[row][col] -= a[pivot][col] * s //
}
a[row][pivot] = s //
// b[row] -= b[pivot] * s //
}
}
}
func pivoting(a *[N][N]float64, b []float64) {
for pivot := 0; pivot < N; pivot++ {
var max_row = pivot
var max_val float64 = 0.0
for row := pivot; row < N; row++ {
if math.Abs(a[row][pivot]) > max_val {
max_val = math.Abs(a[row][pivot])
max_row = row
}
}
if (max_row != pivot) {
var tmp float64 = 0.0
for col := 0; col < N; col++ {
tmp = a[max_row][col]
a[max_row][col] = a[pivot][col]
a[pivot][col] = tmp
}
tmp = b[max_row]
b[max_row] = b[pivot]
b[pivot] = tmp
}
}
}
func disp_progress(a[N][N]float64, b[]float64) {
for i := 0; i < N; i++ {
for j := 0; j < N; j++ {
fmt.Printf("%14.10f\t", a[i][j])
}
fmt.Printf("%14.10f\t\n", b[i])
}
fmt.Println()
}
package main
import "fmt"
import "math"
const N = 4
func main() {
var a [N][N]float64 = [N][N]float64{{5,2,3,4},{2,10,6,7},{3,6,15,9},{4,7,9,20}}
var b []float64 = []float64{34,68,96,125}
fmt.Println("A")
disp_progress(a)
// LU
var x []float64 = []float64{0,0,0,0}
decomp(&a,b,x)
fmt.Println("X")
for i := 0; i < N; i++ {
fmt.Printf("%14.10f\t", x[i])
}
fmt.Println()
}
// LU
func decomp(a *[N][N]float64, b []float64, x []float64) {
//
forward_elimination(a,b)
//
fmt.Println("L")
for i := 0; i < N; i++ {
for j := 0; j < N; j++ {
if (j <= i) {
fmt.Printf("%14.10f\t", a[i][j])
} else {
fmt.Printf("%14.10f\t", a[j][i])
}
}
fmt.Println()
}
fmt.Println()
//
// Ly=b
var y []float64 = []float64{0,0,0,0}
for row := 0; row < N; row++ {
for col := 0; col < row; col++ {
b[row] -= a[row][col] * y[col]
}
y[row] = b[row] / a[row][row]
}
// y
fmt.Println("Y")
for i := 0; i < N; i++ {
fmt.Printf("%14.10f\t", y[i])
}
fmt.Println("\n")
// Ux=y
for row := N - 1; row >= 0; row-- {
for col := N - 1; col > row; col-- {
y[row] -= a[col][row] * x[col]
}
x[row] = y[row] / a[row][row]
}
}
//
func forward_elimination(a *[N][N]float64, b []float64) {
for pivot := 0; pivot < N; pivot++ {
var s = 0.0
for col := 0; col < pivot; col++ {
s += a[pivot][col] * a[pivot][col]
}
a[pivot][pivot] = math.Sqrt(a[pivot][pivot] - s)
for row := pivot + 1; row < N; row++ {
s = a[row][pivot] / a[pivot][pivot]
s = 0
for col := 0; col < pivot; col++ {
s += a[row][col] * a[pivot][col]
}
a[row][pivot] = (a[row][pivot] - s) / a[pivot][pivot]
}
}
}
func disp_progress(a[N][N]float64) {
for i := 0; i < N; i++ {
for j := 0; j < N; j++ {
fmt.Printf("%14.10f\t", a[i][j])
}
fmt.Println()
}
}
package main
import "fmt"
const N = 4
func main() {
var a [N][N]float64 = [N][N]float64{{5,2,3,4},{2,10,6,7},{3,6,15,9},{4,7,9,20}}
var b []float64 = []float64{34,68,96,125}
fmt.Println("A")
disp_progress(a)
// LU
var x []float64 = []float64{0,0,0,0}
decomp(&a,b,x)
fmt.Println("X")
for i := 0; i < N; i++ {
fmt.Printf("%14.10f\t", x[i])
}
fmt.Println()
}
// LU
func decomp(a *[N][N]float64, b []float64, x []float64) {
//
forward_elimination(a,b)
//
fmt.Println("L")
for i := 0; i < N; i++ {
for j := 0; j < N; j++ {
if (j <= i) {
fmt.Printf("%14.10f\t", a[i][j])
} else {
fmt.Printf("%14.10f\t", a[j][i])
}
}
fmt.Println()
}
fmt.Println()
//
// Ly=b
var y []float64 = []float64{0,0,0,0}
for row := 0; row < N; row++ {
for col := 0; col < row; col++ {
b[row] -= a[row][col] * y[col]
}
y[row] = b[row]
}
// y
fmt.Println("Y")
for i := 0; i < N; i++ {
fmt.Printf("%14.10f\t", y[i])
}
fmt.Println("\n")
// Ux=y
for row := N - 1; row >= 0; row-- {
for col := N - 1; col > row; col-- {
y[row] -= a[col][row] * a[row][row] * x[col]
}
x[row] = y[row] / a[row][row]
}
}
//
func forward_elimination(a *[N][N]float64, b []float64) {
for pivot := 0; pivot < N; pivot++ {
var s = 0.0
// pivot < k
for col := 0; col < pivot; col++ {
s = a[pivot][col]
for k := 0; k < col; k++ {
s -= a[pivot][k] * a[col][k] * a[k][k]
}
a[pivot][col] = s / a[col][col]
}
// pivot == k
s = a[pivot][pivot]
for k := 0; k < pivot; k++ {
s -= a[pivot][k] * a[pivot][k] * a[k][k]
}
a[pivot][pivot] = s
}
}
func disp_progress(a[N][N]float64) {
for i := 0; i < N; i++ {
for j := 0; j < N; j++ {
fmt.Printf("%14.10f\t", a[i][j])
}
fmt.Println()
}
}
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