September Morn Update
This commit is contained in:
Ingy döt Net
parent
4e2d22a71d
commit
aac6731f2c
6856 changed files with 141342 additions and 21127 deletions
17
Task/Euler-method/Factor/euler-method.factor
Normal file
17
Task/Euler-method/Factor/euler-method.factor
Normal file
|
|
@ -0,0 +1,17 @@
|
|||
USING: formatting fry io kernel locals math math.ranges
|
||||
sequences ;
|
||||
IN: rosetta-code.euler-method
|
||||
|
||||
:: euler ( quot y! a b h -- )
|
||||
a b h <range> [
|
||||
:> t
|
||||
t y "%7.3f %7.3f\n" printf
|
||||
t y quot call h * y + y!
|
||||
] each ; inline
|
||||
|
||||
: cooling ( t y -- x ) nip 20 - -0.07 * ;
|
||||
|
||||
: euler-method-demo ( -- )
|
||||
2 5 10 [ '[ [ cooling ] 100 0 100 _ euler ] call nl ] tri@ ;
|
||||
|
||||
MAIN: euler-method-demo
|
||||
|
|
@ -1,16 +1,14 @@
|
|||
import "futlib/math"
|
||||
|
||||
fun analytic(t0: f64) (time: f64): f64 =
|
||||
let analytic(t0: f64) (time: f64): f64 =
|
||||
20.0 + (t0 - 20.0) * f64.exp(-0.07*time)
|
||||
|
||||
fun cooling(_time: f64) (temperature: f64): f64 =
|
||||
let cooling(_time: f64) (temperature: f64): f64 =
|
||||
-0.07 * (temperature-20.0)
|
||||
|
||||
fun main(t0: f64) (a: f64) (b: f64) (h: f64): []f64 =
|
||||
let steps = i32((b-a)/h)
|
||||
let main(t0: f64) (a: f64) (b: f64) (h: f64): []f64 =
|
||||
let steps = i32.f64 ((b-a)/h)
|
||||
let temps = replicate steps 0.0
|
||||
loop ((t,temps)=(t0,temps)) = for i < steps do
|
||||
let x = a + f64(i) * h
|
||||
let (_,temps) = loop (t,temps)=(t0,temps) for i < steps do
|
||||
let x = a + f64.i32 i * h
|
||||
let temps[i] = f64.abs(t-analytic t0 x)
|
||||
in (t + h * cooling x t,
|
||||
temps)
|
||||
|
|
|
|||
|
|
@ -1,26 +1,25 @@
|
|||
/*REXX pgm solves example of Newton's cooling law via Euler's method (diff. step sizes).*/
|
||||
numeric digits length( e() - 1) /*use the number of decimal digits in E*/
|
||||
e=2.71828182845904523536028747135266249775724709369995957496696762772407663035354759457138
|
||||
numeric digits length(e) - length(.) /*use the number of decimal digits in E*/
|
||||
parse arg Ti Tr cc tt ss /*obtain optional arguments from the CL*/
|
||||
if Ti=='' | Ti=="," then Ti=100 /*given? Default: initial temp in ºC.*/
|
||||
if Tr=='' | Tr=="," then Tr= 20 /* " " room " " " */
|
||||
if cc=='' | cc=="," then cc= 0.07 /* " " cooling constant. */
|
||||
if tt=='' | tt=="," then tt=100 /* " " total time seconds. */
|
||||
if ss ='' | ss ="," then ss=2 5 10 /* " " the step sizes. */
|
||||
if Ti='' | Ti="," then Ti= 100 /*given? Default: initial temp in ºC.*/
|
||||
if Tr='' | Tr="," then Tr= 20 /* " " room " " " */
|
||||
if cc='' | cc="," then cc= 0.07 /* " " cooling constant. */
|
||||
if tt='' | tt="," then tt= 100 /* " " total time seconds. */
|
||||
if ss='' | ss="," then ss= 2 5 10 /* " " the step sizes. */
|
||||
@= '═' /*the character used in title separator*/
|
||||
do sSize=1 for words(ss); say; say; say center('time in' , 11)
|
||||
say center('seconds' , 11, @) center('Euler method', 16, @) ,
|
||||
center('analytic', 18, @) center('difference' , 14, @)
|
||||
$=Ti; inc=word(ss,Ssize) /*the 1st value; obtain the increment.*/
|
||||
do t=0 to Ti by inc /*step through calculations by the inc.*/
|
||||
a=format(Tr + (Ti-Tr)/exp(cc*t),6,9) /*calculate the analytic (exact) value.*/
|
||||
say center(t,11) format($,6,3) 'ºC ' a "ºC" format(abs(a-$)/a*100,6,2) '%'
|
||||
$=$ + inc * cc * (Tr-$) /*calc. next value via Euler's method. */
|
||||
end /*t*/
|
||||
end /*stepSize*/
|
||||
do sSize=1 for words(ss); say; say; say center('time in' , 11)
|
||||
say center('seconds' , 11, @) center('Euler method', 16, @) ,
|
||||
center('analytic', 18, @) center('difference' , 14, @)
|
||||
$=Ti; inc= word(ss, sSize) /*the 1st value; obtain the increment.*/
|
||||
do t=0 to Ti by inc /*step through calculations by the inc.*/
|
||||
a= format(Tr + (Ti-Tr)/exp(cc*t),6,10) /*calculate the analytic (exact) value.*/
|
||||
say center(t,11) format($,6,3) 'ºC ' a "ºC" format(abs(a-$)/a*100,6,2) '%'
|
||||
$= $ + inc * cc * (Tr-$) /*calc. next value via Euler's method. */
|
||||
end /*t*/
|
||||
end /*sSize*/
|
||||
exit /*stick a fork in it, we're all done. */
|
||||
/*──────────────────────────────────────────────────────────────────────────────────────*/
|
||||
e: return 2.718281828459045235360287471352662497757247093699959574966967627724076630353548
|
||||
/*──────────────────────────────────────────────────────────────────────────────────────*/
|
||||
exp: procedure; parse arg x; ix=x%1; if abs(x-ix)>.5 then ix=ix+sign(x); x=x-ix; z=1
|
||||
_=1; w=1; do j=1; _=_*x/j; z=(z+_)/1; if z==w then leave; w=z; end /*j*/
|
||||
if z\==0 then z=e()**ix * z; return z
|
||||
exp: procedure expose e; arg x; ix= x%1; if abs(x-ix)>.5 then ix=ix+sign(x); x= x-ix; z=1
|
||||
_=1; w=1; do j=1; _= _*x/j; z= (z+_)/1; if z==w then leave; w=z
|
||||
end /*j*/; if z\==0 then z= e**ix * z; return z
|
||||
|
|
|
|||
34
Task/Euler-method/Rust/euler-method.rust
Normal file
34
Task/Euler-method/Rust/euler-method.rust
Normal file
|
|
@ -0,0 +1,34 @@
|
|||
fn header() {
|
||||
print!(" Time: ");
|
||||
for t in (0..100).step_by(10) {
|
||||
print!(" {:7}", t);
|
||||
}
|
||||
println!();
|
||||
}
|
||||
|
||||
fn analytic() {
|
||||
print!("Analytic: ");
|
||||
for t in (0..=100).step_by(10) {
|
||||
print!(" {:7.3}", 20.0 + 80.0 * (-0.07 * f64::from(t)).exp());
|
||||
}
|
||||
println!();
|
||||
}
|
||||
|
||||
fn euler<F: Fn(f64) -> f64>(f: F, mut y: f64, step: usize, end: usize) {
|
||||
print!(" Step {:2}: ", step);
|
||||
for t in (0..=end).step_by(step) {
|
||||
if t % 10 == 0 {
|
||||
print!(" {:7.3}", y);
|
||||
}
|
||||
y += step as f64 * f(y);
|
||||
}
|
||||
println!();
|
||||
}
|
||||
|
||||
fn main() {
|
||||
header();
|
||||
analytic();
|
||||
for &i in &[2, 5, 10] {
|
||||
euler(|temp| -0.07 * (temp - 20.0), 100.0, i, 100);
|
||||
}
|
||||
}
|
||||
36
Task/Euler-method/VBA/euler-method.vba
Normal file
36
Task/Euler-method/VBA/euler-method.vba
Normal file
|
|
@ -0,0 +1,36 @@
|
|||
Private Sub ivp_euler(f As String, y As Double, step As Integer, end_t As Integer)
|
||||
Dim t As Integer
|
||||
Debug.Print " Step "; step; ": ",
|
||||
Do While t <= end_t
|
||||
If t Mod 10 = 0 Then Debug.Print Format(y, "0.000"),
|
||||
y = y + step * Application.Run(f, y)
|
||||
t = t + step
|
||||
Loop
|
||||
Debug.Print
|
||||
End Sub
|
||||
|
||||
Sub analytic()
|
||||
Debug.Print " Time: ",
|
||||
For t = 0 To 100 Step 10
|
||||
Debug.Print " "; t,
|
||||
Next t
|
||||
Debug.Print
|
||||
Debug.Print "Analytic: ",
|
||||
For t = 0 To 100 Step 10
|
||||
Debug.Print Format(20 + 80 * Exp(-0.07 * t), "0.000"),
|
||||
Next t
|
||||
Debug.Print
|
||||
End Sub
|
||||
|
||||
Private Function cooling(temp As Double) As Double
|
||||
cooling = -0.07 * (temp - 20)
|
||||
End Function
|
||||
|
||||
Public Sub euler_method()
|
||||
Dim r_cooling As String
|
||||
r_cooling = "cooling"
|
||||
analytic
|
||||
ivp_euler r_cooling, 100, 2, 100
|
||||
ivp_euler r_cooling, 100, 5, 100
|
||||
ivp_euler r_cooling, 100, 10, 100
|
||||
End Sub
|
||||
Loading…
Add table
Add a link
Reference in a new issue