I'm trying to solve a system of differential equations using Mathematica and an error occured:
DSolve::deqx: Supplied equations are not differential equations of the given functions.
Here's my code.
f = 100000;
s = 1;
DSolve[
{
X'[t] == -s*X[t]*w[t] + s*Z[t]*y[t] - 2 s*X[t]^2 - f*Iz[t]*X[t] +
2 f*Ix[t] + 3 f*Ix[t]*Z[t],
Y'[t] == -s*Y[t]*x[t] + s*W[t]*z[t] - f*Iw[t]*Y[t] - 2 s*Y[t]^2 +
2 f*Iy[t] + 3 f*Iy[t]*W[t],
Z'[t] == -s*Z[t]*y[t] + s*X[t]*w[t] - 2 s*Z[t]^2 + 2 f*Iz[t] +
3 f*Iz[t]*X[t] - f*Ix[t]*Z[t],
W'[t] == -s*W[t]*z[t] - 2 s*W[t]^2 + 2 f*Iw[t] + 3 f*Iw[t]*Y[t] +
s*Y[t]*x[t] - f*Iy[t]*W[t],
x'[t] == -s*X[t]*x[t] - s*Y[t]*x[t] + s*emp1[t],
y'[t] == -s*Y[t]*y[t] - s*Z[t]*y[t] + s*emp2[t],
z'[t] == -s*Z[t]*z[t] - s*W[t]*z[t] + s*emp3[t],
w'[t] == -s*W[t]*w[t] - s*X[t]*w[t] + s*emp4[t],
Ix'[t] == s*X[t]^2 - f*Ix[t] - f*Ix[t]*Z[t],
Iy'[t] == s*Y[t]^2 - f*Iy[t] - f*Iy[t]*W[t],
Iz'[t] == s*Z[t]^2 - f*Iz[t] - f*Iz[t]*X[t],
Iw'[t] == s*W[t]^2 - f*Iw[t] - f*Iw[t]*Y[t],
E0'[t] == -f*E0[t]*x[t] + f*E1[t]*y[t] - f*E0[t]*z[t] + f*E1[t]*w[t],
E1'[t] == -E0'[t],
emp1'[t] == 0,
emp2'[t] == 0,
emp3'[t] == 0,
emp4'[t] == 0,
emp1[0] == 100,
emp2[0] == 100,
emp3[0] == 100,
emp4[0] == 100,
X[0] == 1,
Y[0] == 1,
Z[0] == 0,
W[0] == 0,
x[0] == 0,
y[0] == 0,
z[0] == 0,
w[0] == 0,
Ix[0] == 0,
Iy[0] == 0,
Iz[0] == 0,
Iw[0] == 0,
E0[0] == 1,
E1[0] == 0
},
{X[t], Y[t], Z[t], W[t], x[t], y[t], z[t], w[t], Ix[t], Iy[t], Iz[t],
Iw[t], E0[t], E1[t]},
t]
I've tried to clear all the variables before using DSolve,but it didn't work at all.
Could someone help me?Thanks!
emp1[t] through emp4[t] needed to be added to the list of functions in the curly braces on the second to last line.
Related
im new to R and im trying to solve for the minimum number of moves for a knight visit all the moves in a chess board.
I got the python code from:
https://www.geeksforgeeks.org/the-knights-tour-problem-backtracking-1/
and i tried to translate it to r.
But i am always getting the error and I don't know where I went wrong.
This is my code:
chess = rep(-1, times = 64)
board = matrix(data = chess, nrow = 8, ncol = 8, byrow = TRUE)
move_x = c(2, 1, -1, -2, -2, -1, 1, 2)
move_y = c(1, 2, 2, 1, -1, -2, -2, -1)
board[1, 1] = 0
pos = 1
valid_move <- function (x, y, board) {
if (x >= 1 & y >= 1 & x <= 8 & y <= 8 & board[x, y] == -1) {
return (T)
}
return (F)
}
solve <- function (board, curr_x, curr_y, move_x, move_y, pos) {
if (pos == 64) {
return (T)
}
for (i in seq(1:8)) {
new_x = curr_x + move_x[i]
new_y = curr_y + move_y[i]
if (valid_move(new_x, new_y, board)) {
board[new_x, new_y] = pos
if (solve(board, new_x, new_y, move_x, move_y, pos+1)) {
return (TRUE)
}
board[new_x, new_y] = -1
}
}
}
main <- function() {
sims = 10
ctr = 0
number_of_moves = c()
solve(board, 1, 1, move_x, move_y, pos)
print(paste("Minimum number of moves: ", pos))
}
main()
Thanks!
The problem is that the python code relies on short-circuiting to prevent out-of-bounds errors. & will not short-circuit so you need to use &&.
Here is an example
FALSE && stop()
#> [1] FALSE
FALSE & stop()
#> Error:
Update valid_move to this
valid_move <- function (x, y, board) {
# Changed to && to allow short-circuiting
# if (x >= 1 & y >= 1 & x <= 8 & y <= 8 & board[x, y] == -1) {
if (x >= 1 && y >= 1 && x <= 8 && y <= 8 && board[x, y] == -1) {
return (T)
}
return (F)
}
I have an Angular 7 app with a home page containing a large coloured block (enough to fill the page) at the top with a header and some images. I want to put some lava effect animations into the background similar to this
code in case link is removed:
HTML:
<canvas id="lamp-anim" class="lamp-anim" width="1034" height="613"></canvas>
CSS:
body {
background: #f857a6; /* fallback for old browsers */
background: -webkit-linear-gradient(to top, #ff5858, #f857a6); /* Chrome
10-25, Safari 5.1-6 */
background: linear-gradient(to top, #ff5858, #f857a6); /* W3C, IE 10+/
Edge, Firefox 16+, Chrome 26+, Opera 12+, Safari 7+ */
}
JS:
window.lavaAnimation = function() {
"use strict";
var t, i = {
screen: {
elem: null,
callback: null,
ctx: null,
width: 0,
height: 0,
left: 0,
top: 0,
init: function(t, i, s) {
return this.elem = document.getElementById(t), this.callback = i || null, "CANVAS" == this.elem.tagName && (this.ctx = this.elem.getContext("2d")), window.addEventListener("resize", function() {
this.resize()
}.bind(this), !1), this.elem.onselectstart = function() {
return !1
}, this.elem.ondrag = function() {
return !1
}, s && this.resize(), this
},
resize: function() {
var t = this.elem;
for (this.width = t.offsetWidth, this.height = t.offsetHeight, this.left = 0, this.top = 0; null != t; t = t.offsetParent) this.left += t.offsetLeft, this.top += t.offsetTop;
this.ctx && (this.elem.width = this.width, this.elem.height = this.height), this.callback && this.callback()
}
}
},
s = function(t, i) {
this.x = t, this.y = i, this.magnitude = t * t + i * i, this.computed = 0, this.force = 0
};
s.prototype.add = function(t) {
return new s(this.x + t.x, this.y + t.y)
};
var h = function(t) {
var i = .1,
h = 1.5;
this.vel = new s((Math.random() > .5 ? 1 : -1) * (.2 + .25 * Math.random()), (Math.random() > .5 ? 1 : -1) * (.2 + Math.random())), this.pos = new s(.2 * t.width + Math.random() * t.width * .6, .2 * t.height + Math.random() * t.height * .6), this.size = t.wh / 15 + (Math.random() * (h - i) + i) * (t.wh / 15), this.width = t.width, this.height = t.height
};
h.prototype.move = function() {
this.pos.x >= this.width - this.size ? (this.vel.x > 0 && (this.vel.x = -this.vel.x), this.pos.x = this.width - this.size) : this.pos.x <= this.size && (this.vel.x < 0 && (this.vel.x = -this.vel.x), this.pos.x = this.size), this.pos.y >= this.height - this.size ? (this.vel.y > 0 && (this.vel.y = -this.vel.y), this.pos.y = this.height - this.size) : this.pos.y <= this.size && (this.vel.y < 0 && (this.vel.y = -this.vel.y), this.pos.y = this.size), this.pos = this.pos.add(this.vel)
};
var e = function(t, i, e, n, a) {
this.step = 5, this.width = t, this.height = i, this.wh = Math.min(t, i), this.sx = Math.floor(this.width / this.step), this.sy = Math.floor(this.height / this.step), this.paint = !1, this.metaFill = r(t, i, t, n, a), this.plx = [0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0], this.ply = [0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 1], this.mscases = [0, 3, 0, 3, 1, 3, 0, 3, 2, 2, 0, 2, 1, 1, 0], this.ix = [1, 0, -1, 0, 0, 1, 0, -1, -1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1], this.grid = [], this.balls = [], this.iter = 0, this.sign = 1;
for (var o = 0; o < (this.sx + 2) * (this.sy + 2); o++) this.grid[o] = new s(o % (this.sx + 2) * this.step, Math.floor(o / (this.sx + 2)) * this.step);
for (var l = 0; e > l; l++) this.balls[l] = new h(this)
};
e.prototype.computeForce = function(t, i, s) {
var h, e = s || t + i * (this.sx + 2);
if (0 === t || 0 === i || t === this.sx || i === this.sy) h = .6 * this.sign;
else {
h = 0;
for (var r, n = this.grid[e], a = 0; r = this.balls[a++];) h += r.size * r.size / (-2 * n.x * r.pos.x - 2 * n.y * r.pos.y + r.pos.magnitude + n.magnitude);
h *= this.sign
}
return this.grid[e].force = h, h
}, e.prototype.marchingSquares = function(t) {
var i = t[0],
s = t[1],
h = t[2],
e = i + s * (this.sx + 2);
if (this.grid[e].computed === this.iter) return !1;
for (var r, n = 0, a = 0; 4 > a; a++) {
var l = i + this.ix[a + 12] + (s + this.ix[a + 16]) * (this.sx + 2),
d = this.grid[l].force;
(d > 0 && this.sign < 0 || 0 > d && this.sign > 0 || !d) && (d = this.computeForce(i + this.ix[a + 12], s + this.ix[a + 16], l)), Math.abs(d) > 1 && (n += Math.pow(2, a))
}
if (15 === n) return [i, s - 1, !1];
5 === n ? r = 2 === h ? 3 : 1 : 10 === n ? r = 3 === h ? 0 : 2 : (r = this.mscases[n], this.grid[e].computed = this.iter);
var p = this.step / (Math.abs(Math.abs(this.grid[i + this.plx[4 * r + 2] + (s + this.ply[4 * r + 2]) * (this.sx + 2)].force) - 1) / Math.abs(Math.abs(this.grid[i + this.plx[4 * r + 3] + (s + this.ply[4 * r + 3]) * (this.sx + 2)].force) - 1) + 1);
return o.lineTo(this.grid[i + this.plx[4 * r] + (s + this.ply[4 * r]) * (this.sx + 2)].x + this.ix[r] * p, this.grid[i + this.plx[4 * r + 1] + (s + this.ply[4 * r + 1]) * (this.sx + 2)].y + this.ix[r + 4] * p), this.paint = !0, [i + this.ix[r + 4], s + this.ix[r + 8], r]
}, e.prototype.renderMetaballs = function() {
for (var t, i = 0; t = this.balls[i++];) t.move();
for (this.iter++, this.sign = -this.sign, this.paint = !1, o.fillStyle = this.metaFill, o.beginPath(), i = 0; t = this.balls[i++];) {
var s = [Math.round(t.pos.x / this.step), Math.round(t.pos.y / this.step), !1];
do s = this.marchingSquares(s); while (s);
this.paint && (o.fill(), o.closePath(), o.beginPath(), this.paint = !1)
}
};
var r = function(t, i, s, h, e) {
var r = o.createRadialGradient(t / 1, i / 1, 0, t / 1, i / 1, s);
return r.addColorStop(0, h), r.addColorStop(1, e), r
};
if (document.getElementById("lamp-anim")) {
var n = function() {
requestAnimationFrame(n), o.clearRect(0, 0, a.width, a.height), t.renderMetaballs()
},
a = i.screen.init("lamp-anim", null, !0),
o = a.ctx;
a.resize(), t = new e(a.width, a.height, 6, "#3494E6", "#EC6EAD")
}
return {
run: n
}
}();
if (document.getElementById('lamp-anim')) {
lavaAnimation.run();
}
setTimeout(function() {
$('.js-works-d-list').addClass('is-loaded');
}, 150);
Is it possible to convert/do this in angular animations? Are they flexible enough to do this sort of (what id call advanced) animation?
I think the question of 'can I convert this to Angular' is a bit off because Angular runs on Typescript, which is a language built from javascript. So, yes you can do all this in Angular or rather using Typescript within an Angular app.
We're always here to help once you get some code written in an Angular app! But in general, we are here to help you were you get stuck in code and help you solve the problem. It's a bit more challenging to say 'yes it will work' without seeing how you implement it in your project and can't really guide or help you until we see how your angular components are written.
Short answer: Yeah, I think it can work. But it also depends how you implement this code into your Angular app.
I'm trying to calculate determinants with any order using Lua. I can calculate determinants for order less than 4, but not for greater equals than 4 ones.
I have a 4x4 matrix and its determinant with the program is 0, but the real solution is 56.
I don't know if the problem is in getSubmatrix method or is in detMat method, because I don't have any error message from the console.
I've ported the methods from my own java code, where it works fine.
Here's all my code:
function numMat(n, A)
local S = {}
for i = 1, #A, 1 do
local T = {}
S[i] = T
for j =1, #A[1], 1 do
T[j] = n * A[i][j]
end
end
return S
end
function sumMat(A, B)
local C = {}
for i = 1, #A do
local D = {}
C[i] = D
for j = 1, #A[1] do
D[j] = A[i][j] + B[i][j]
end
end
return C
end
function subMat(A, B)
return sumMat(A, numMat(-1, B))
end
function printMatrix(A)
for i, v in ipairs(A) do
for j, w in ipairs(v) do
print(w)
end
end
end
function escalarProduct(u, v)
local w = 0
for i = 1, #u do
w = w + u[i] * v[i]
end
return w
end
function prodMat(A, B)
local C = {}
for i = 1, #A do
C[i] = {}
for j = 1, #B[1] do
local num = A[i][1] * B[1][j]
for k = 2, #A[1] do
num = num + A[i][k] * B[k][j]
end
C[i][j] = num
end
end
return C
end
function powMat(A, power)
local B = {}
local C = {}
C = A
for i = 1, power - 1 do
B = prodMat(C, A)
C = B
end
return B
end
function trasposeMat(A)
local B = {}
for i = 1, #A do
local C = {}
B[i] = C
for j = 1, #A[1] do
C[j] = A[j][i]
end
end
return B
end
function productDiag(m)
local prod = 1
for i = 1, #m do
for j = 1, #m do
if i == j then prod = prod * m[i][i] end
end
end
return prod
end
function isDiagonal(A)
for i = 1, #A do
for j = 1, #A do
if i ~= j and A[i][j] ~= 0 then return false end
end
end
return true
end
function isTriangSup(m)
for i = 1, #m do
for j = 1, i do
if m[i][j] == 0 then return true end
end
end
return false
end
function isTriangInf(m)
return isTriangSup(trasposeMat(m))
end
function isTriang(m)
if(isTriangSup(m)) then return true
else
return false
end
end
function getSubmatrix(A, rows, cols, col)
local submatrix = {}
local k = 1
for j = 1, cols do
--local D = {}
--submatrix[j] = D
if j == col then
break
end
for i = 2, rows do
submatrix[i-1][k] = A[i][j]
--D[k] = A[i][j]
end
k = k + 1
end
return submatrix
end
function det2Mat(A)
assert(#A == 2 and #A == #A[1], 'Error: The matrix must be squared, order 2.')
return A[1][1] * A[2][2] - A[1][2] * A[2][1]
end
function det3Mat(A)
assert(#A == 3 and #A == #A[1], 'Error: The matrix must be squared, order 3.')
s1 = A[1][1] * A[2][2] * A[3][3] + A[2][1] * A[3][2] * A[1][3] + A[1][2] * A[2][3] * A[3][1]
s2 = A[1][3] * A[2][2] * A[3][1] + A[1][2] * A[2][1] * A[3][3] + A[2][3] * A[3][2] * A[1][1]
return s1 - s2
end
function detMat(A)
local submatrix = {}
local det
local sign = 1
local rows = #A
local cols = #A[1]
assert(rows == cols, 'Error: The matrix must be squared.')
if rows == 1 then
return A[1][1]
end
if rows == 2 then
return det2Mat(A)
end
if rows == 3 then
return det3Mat(A)
end
if isDiagonal(A) or isTriang(A) then return productDiag(A) end
if rows > 3 then
for column = 1, cols do
submatrix = getSubmatrix(A, rows, cols, column)
det = det + sign * A[1][column] * detMat(submatrix)
sign = -sign
end
end
return det
end
A = {{1, 3}, {5, 6}}
B = {{2, 4}, {3, 1}}
C = {{2, 3, 4}, {-5, 4, 7}, {7, 1, 0}}
D = {{2, 0, 0, 0}, {0, 4, 0, 0}, {0, 0, 7, 0}, {0, 0, 0, 6}}
E = {{2, 3, 4, -3}, {-5, 4, 7, -2}, {7, 1, 0, 5}, {3, 4, 5, 6}}
--printMatrix(numMat(-1, A))
--printMatrix(sumMat(A, B))
--printMatrix(subMat(A, B))
--print(escalarProduct({1, 3}, {5, 6}))
--printMatrix(prodMat(A, B))
--printMatrix(trasposeMat(A))
--printMatrix(powMat(A, 2))
--printMatrix(powMat(A, 3))
print(detMat(A))
print(detMat(B))
print(detMat(C))
print(detMat(D))
print(detMat(E)) --The solution must be 56
And the console solution is:
-9
-10
1
336
0
The error is when I want to find out the determinant of the matrix E.
I have a code that is failing to work because of curly bracket issues
o1 = read.table('/Users/manshi/Desktop/PSYC57H3/PSYC57_Homework3/Object1.csv', header=TRUE, sep=",")
PredictedValue = vector(mode = 'numeric', length = 100)
PredictionError = vector(mode = 'numeric', length = 100)
PredictedValue[1] = 0
AlAccepts = vector(mode = 'logical', length = 100)
for (trial in 1:100){
ifelse (AlAccepts[trial] == FALSE, 0, 1) {
PredictionError[trial] = o1$Reward[trial] - PredictedValue[trial]
PredictedValue[trial + 1] = PredictedValue[trial] + .3*PredictionError[trial]
} ifelse (AlAccepts[trial] == TRUE, 0, 1) {
PredictedValue[trial + 1] = PredictedValue[trial]
}
}
The error message that I am getting is:
> for (trial in 1:100){
+ ifelse (AlAccepts[trial] == FALSE, 0, 1) {
Error: unexpected '{' in:
"for (trial in 1:100){
ifelse (AlAccepts[trial] == FALSE, 0, 1) {"
> PredictionError[trial] = o1$Reward[trial] - PredictedValue[trial]
> PredictedValue[trial + 1] = PredictedValue[trial] + .3*PredictionError[trial]
> } ifelse (AlAccepts[trial] == TRUE, 0, 1) {
Error: unexpected '}' in " }"
> PredictedValue[trial + 1] = PredictedValue[trial]
> }
Error: unexpected '}' in " }"
> }
Error: unexpected '}' in "}"
>
What am I doing wrong?
ifelse (AlAccepts[trial] == FALSE, 0, 1) is a function and results in a return value, in this case 0 or 1. Further conditioned excecution is not done so the following brackets show a syntax error. Using else if(){} should work as you intended:
for (trial in 1:100){
if (AlAccepts[trial] == FALSE) {
PredictionError[trial] = o1$Reward[trial] - PredictedValue[trial]
PredictedValue[trial + 1] = PredictedValue[trial] + .3*PredictionError[trial]
} else if(AlAccepts[trial] == TRUE) {
PredictedValue[trial + 1] = PredictedValue[trial]
}
}
I am trying to solve a differential equation numerically but I need to vary y0 for my plot and view result for constant x. I can solve my equation normally as I expected:but I can't get result when I try for my real purpose as you can see
`\[Sigma] = 1;
n = 23.04;
Rop = y[x];
R = 0.5;
sz = R/(Rop + R);
F = -n*\[Sigma]*y[x]*(1 - 2*sz);
s = NDSolve[{y'[x] == F, y[0] == 0.8}, y, {x, 0, 0.07}]
Plot[Evaluate[y[x] /. s], {x, 0, 0.07}, PlotRange -> All,]`
`[Sigma] = 1;
n = 23.04;
Rop = y[x];
R = 0.5;
sz = R/(Rop + R);
F = -n*\[Sigma]*y[x]*(1 - 2*sz);
y0 = 0.8;
\!\(\*
ButtonBox["Array",
BaseStyle->"Link",
ButtonData->"paclet:ref/Array"]\)[s, 140]
i = 1;
For[i < 140,
s = NDSolve[{y'[x] == F, y[0] == y0}, y, {x, 0, 0.07}]
Plot[Evaluate[y[] /. s], x = 0.07, {y0, 0.8, 2.2}] // print
y0 == y0 + i*0.01];`
A variety of typos or misunderstandings
\[Sigma] = 1;
n = 23.04;
Rop = y[x];
R = 0.5;
sz = R/(Rop + R);
F = -n*\[Sigma]*y[x]*(1 - 2*sz);
y0 = 0.8;
For[i = 1, i < 140, i++,
s = NDSolve[{y'[x] == F, y[0] == y0}, y, {x, 0, 0.07}];
Plot[Evaluate[y[x] /. s], {x, 0, 0.07}] // Print;
y0 = y0 + i*0.01
];
Go through that and compare it a character at a time against your original.
After you have figured out why each of the changes were made then you can try to decide whether to put your Button back in that or not.