// calculates transformation matrix for a single cone of an instrument's profile
func stageMatrix2(radiusIn, radiusOut, radiusCenter, length, radianFrequency float64) [4]complex128 {
xi := complex(radiusIn, 0) // m
xi1 := complex(radiusOut, 0) // m
l := complex(length, 0) // m
w := radianFrequency // rad / s
centerPlaneArea := pi * radiusCenter * radiusCenter // m2
sm := centerPlaneArea
sphericalAreaIn := 4 * pi * radiusIn * radiusIn // m2
si := sphericalAreaIn
rv := math.Sqrt(p * w * sm / (n * pi)) // rad^1/2
r0 := p * c / si // kg/(m4*s) or Pa*s, units of impedance
k := w / c // wavenumber, rad / m
zc := complex(r0, 0) * complex(1+0.369/rv, -0.369/rv) // Pa*s/sqrt(rad)
g := complex(k, 0) * complex(1.045/rv, 1+1.045/rv) // sqrt(rad)/m
gl := g * l // sqrt(rad)
cosh_gl := cmplx.Cosh(gl) // mangled sqrt(rad)
sinh_gl := cmplx.Sinh(gl) // mangled sqrt(rad)
a11 := xi1 / xi * (cosh_gl - sinh_gl/(g*xi1)) // unitless (more mangled sqrt(rad))
a12 := xi / xi1 * zc * sinh_gl // Pa*s + mangle
a21 := 1 / zc * ((xi1/xi-1/(g*g*xi*xi))*sinh_gl + (gl*cosh_gl)/(g*g*xi*xi)) // 1/(Pa*s) + mangle
a22 := xi / xi1 * (cosh_gl + sinh_gl/(g*xi)) // unitless + mangle
return [4]complex128{a11, a12, a21, a22}
}
"strconv"
"sync"
"time"
)
type ComplexFunc func(complex128) complex128
var Funcs []ComplexFunc = []ComplexFunc{
func(z complex128) complex128 { return z*z - 0.61803398875 },
func(z complex128) complex128 { return z*z + complex(0, 1) },
func(z complex128) complex128 { return z*z + complex(-0.835, -0.2321) },
func(z complex128) complex128 { return z*z + complex(0.45, 0.1428) },
func(z complex128) complex128 { return z*z*z + 0.400 },
func(z complex128) complex128 { return cmplx.Exp(z*z*z) - 0.621 },
func(z complex128) complex128 { return (z*z+z)/cmplx.Log(z) + complex(0.268, 0.060) },
func(z complex128) complex128 { return cmplx.Sqrt(cmplx.Sinh(z*z)) + complex(0.065, 0.122) },
}
func RunJulia() {
t := time.Now()
for n, fn := range Funcs {
err := CreatePng("picture-"+strconv.Itoa(n)+".png", fn, 1024)
if err != nil {
log.Fatal(err)
}
}
fmt.Println("Time passed: ", time.Since(t).Seconds())
}
// CreatePng creates a PNG picture file with a Julia image of size n x n.
type ComplexFunc func(complex128) complex128
var Funcs []ComplexFunc = []ComplexFunc{
func(z complex128) complex128 { return z*z - 0.61803398875 },
func(z complex128) complex128 { return z*z + complex(0, 1) },
func(z complex128) complex128 { return z*z + complex(-0.835, -0.2321) },
func(z complex128) complex128 { return z*z + complex(0.45, 0.1428) },
func(z complex128) complex128 { return z*z*z + 0.400 },
func(z complex128) complex128 { return cmplx.Exp(z*z*z) - 0.621 },
func(z complex128) complex128 {
return (z*z+z)/cmplx.Log(z) + complex(0.268,
0.060)
},
func(z complex128) complex128 {
return cmplx.Sqrt(cmplx.Sinh(z*z)) +
complex(0.065, 0.122)
},
}
//This makes the program use all the cores in the processor
func init() {
numcpu := runtime.NumCPU()
runtime.GOMAXPROCS(numcpu) // Try to use all available CPUs.
}
func main() {
wg := new(sync.WaitGroup)
before := time.Now()
for n, fn := range Funcs {
wg.Add(1)
func test1(val, val0 complex128) complex128 {
return cmplx.Sqrt(cmplx.Sinh(val)) + val0
}
