changes to things
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723eb34e40
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307c513a9b
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@ -0,0 +1,13 @@
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class Primes:
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def __init__(self, max):
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self.internal = range(2,max+1)
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def __next__(self):
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i = self.internal.__iter__().__next__()
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self.internal = filter(lambda n : n % i != 0, self.internal)
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return i
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def __iter__(self): return self
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for i in Primes(100):
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print(i)
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@ -0,0 +1,67 @@
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<!DOCTYPE html>
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<meta charset="utf8">
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<canvas id="canvas-but-good" width=768 height=768></canvas>
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<div id="info"></div>
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<script>
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const canv = document.getElementById("canvas-but-good")
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const info = document.getElementById("info")
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const centerX = canv.width / 2
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const centerY = canv.height / 2
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const scale = 0.5
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const G = 0.1
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const vzero = [0, 0]
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const vadd = ([a, b], [c, d]) => [a + c, b + d]
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const vscale = (a, [b, c]) => [a * b, a * c]
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const vsub = (a, b) => vadd(vscale(-1, a), b)
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const vmag = ([a, b]) => Math.hypot(a, b)
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const vnorm = v => vscale(1 / vmag(v), v)
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const vsum = vs => vs.reduce(vadd, vzero)
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const objects = [] /*[
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{ x: [0.5, 0.25], v: vzero, m: 1 },
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{ x: [-0.25, -0.5], v: vzero, m: 0.5 },
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{ x: [0.25, 0.75], v: vzero, m: 2 }
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]*/
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for (let i = 0; i < (1.99 * Math.PI); i += Math.PI / 12) {
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objects.push({ x: [ Math.cos(i), Math.sin(i) ], v: vzero, m: Math.exp(Math.random() - 0.5) })
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}
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const ctx = canv.getContext("2d")
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let previousTimestamp = null
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function step(timestamp) {
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const previousPreviousTimestamp = previousTimestamp
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previousTimestamp = timestamp
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if (!timestamp) {
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return
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}
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const timestep = (timestamp - previousPreviousTimestamp) / 1000
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ctx.fillStyle = "black"
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ctx.fillRect(0, 0, canv.width, canv.height)
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var i = 0
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for (const object of objects) {
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object.x = vadd(object.x, vscale(timestep, object.v))
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const F = vsum(objects.filter(x => x !== object).map(x =>
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vscale(G * (object.m * x.m) * (vmag(vsub(object.x, x.x)) ** -2), vnorm(vsub(object.x, x.x)))
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))
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object.v = vadd(object.v, vscale(timestep, vscale(1 / object.m, F)))
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//console.log(F, object.x, object.v)
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ctx.beginPath()
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const disp = vscale(scale, object.x)
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ctx.arc(centerX + disp[0] * centerX, centerY + disp[1] * centerY, 4 * Math.cbrt(object.m), 0, 2 * Math.PI, false)
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ctx.fillStyle = `hsl(${i * 73}deg, 100%, 60%)`
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ctx.fill()
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i++
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}
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const E_k = objects.map(x => 1/2 * x.m * vmag(x.v) ** 2).reduce((a, b) => a + b)
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// extra division by 2 due to double-counting
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const E_p = objects.map(o1 => objects.filter(o2 => o2 !== o1).map(o2 => -1/2 * o1.m * o2.m * G * (vmag(vsub(o1.x, o2.x)) ** -1)).reduce((a, b) => a + b)).reduce((a, b) => a + b)
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info.innerHTML = `E<sub>k</sub>=${E_k.toFixed(2)}<br>E<sub>p</sub>=${E_p.toFixed(2)}<br>sum=${E_k+E_p}`
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requestAnimationFrame(step)
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}
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requestAnimationFrame(step)
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</script>
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@ -0,0 +1,43 @@
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import time
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import collections
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PIDState = collections.namedtuple("PIDState", ["Kp", "Ki", "Kd", "last_time", "integral", "last_error"])
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def init(Kp, Ki, Kd): return PIDState(Kp, Ki, Kd, None, 0, None)
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def step(state, error, deriv, ts=None):
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ts = ts if ts is not None else time.time()
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integral = state.integral
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if state.last_time:
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tdiff = ts - state.last_time
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integral += 0.5 * (state.last_error + error) * tdiff # approximate actually integrating using a trapzeium
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output = state.Kp * error + state.Ki * integral + state.Kd * deriv
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return PIDState(Kp=state.Kp, Ki=state.Ki, Kd=state.Kd, last_time=ts, integral=integral, last_error=error), output
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if __name__ == "__main__":
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import matplotlib.pyplot as plt, numpy as np
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def extract_series(l, ix): return list(map(lambda x: x[ix], l))
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values = [(10, -10, 0, 0, 0)]
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state = init(10, 4, -0.3)
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setpoint = -5
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max_time = 2
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timestep = 0.05
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times = np.arange(0, max_time, timestep)
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for t in times:
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current_pv = values[-1][0]
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error = setpoint - current_pv
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deriv = (error - (state.last_error or 0)) / timestep
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state, output = step(state, error, deriv, ts=t)
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output = max(min(output, 10), -10)
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print(output, current_pv, error)
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new_pv = current_pv + (output + 1) * 0.05
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values.append((new_pv, error, output, state.integral, deriv))
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#print(values)
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values = values[1:]
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plt.axis([0, max_time, -10, 10])
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plt.plot(times, extract_series(values, 0), label="PV")
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plt.plot(times, extract_series(values, 1), label="error")
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plt.plot(times, extract_series(values, 2), label="output")
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plt.plot(times, extract_series(values, 3), label="integ")
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plt.plot(times, extract_series(values, 4), label="deriv")
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plt.legend()
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plt.show()
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@ -9,6 +9,7 @@
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const centerY = canv.height / 2
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const scale = 0.5
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const G = 0.1
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const stepsPerSecond = 1000
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const vzero = [0, 0]
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const vadd = ([a, b], [c, d]) => [a + c, b + d]
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@ -35,18 +36,27 @@
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if (!timestamp) {
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return
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}
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const timestep = (timestamp - previousPreviousTimestamp) / 1000
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const deltaT = (timestamp - previousPreviousTimestamp) / 1000
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const stepCount = Math.min(Math.ceil(deltaT * stepsPerSecond), 20)
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const timestep = deltaT / stepCount
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console.log(stepCount, deltaT)
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for (let j = 0; j < stepCount; j++) {
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for (const object of objects) {
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object.x = vadd(object.x, vscale(timestep, object.v))
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const F = vsum(objects.filter(x => x !== object).map(x =>
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vscale(G * (object.m * x.m) * (vmag(vsub(object.x, x.x)) ** 2), vnorm(vsub(object.x, x.x)))
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))
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object.v = vadd(object.v, vscale(timestep, vscale(1 / object.m, F)))
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//console.log(F, object.x, object.v)
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}
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}
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ctx.fillStyle = "black"
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ctx.fillRect(0, 0, canv.width, canv.height)
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var i = 0
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for (const object of objects) {
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object.x = vadd(object.x, vscale(timestep, object.v))
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const F = vsum(objects.filter(x => x !== object).map(x =>
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vscale(G * (object.m * x.m) * (vmag(vsub(object.x, x.x)) ** 2), vnorm(vsub(object.x, x.x)))
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))
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object.v = vadd(object.v, vscale(timestep, vscale(1 / object.m, F)))
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//console.log(F, object.x, object.v)
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ctx.beginPath()
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const disp = vscale(scale, object.x)
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