{
	"cell_id": 10135449329227921550,
	"cells": [
		{
			"cell_id": 3989415718163890231,
			"cell_origin": "client",
			"cell_type": "latex",
			"cells": [
				{
					"cell_id": 3791214211892782773,
					"cell_origin": "client",
					"cell_type": "latex_view",
					"source": "\\package{cdb.numeric.integrate}{Functions for numeric integration and numeric solutions to differential equations}\n\nA collection of wrappers for some of the numeric functionality of the scipy library in order to accept cadabra Ex objects"
				}
			],
			"hidden": true,
			"source": "\\package{cdb.numeric.integrate}{Functions for numeric integration and numeric solutions to differential equations}\n\nA collection of wrappers for some of the numeric functionality of the scipy library in order to accept cadabra Ex objects"
		},
		{
			"cell_id": 8362589260562156834,
			"cell_origin": "client",
			"cell_type": "input",
			"source": "import numpy\nfrom scipy.integrate import odeint\nfrom cdb.numeric.evaluate import lambdify, _create_sublist"
		},
		{
			"cell_id": 6052509396776782195,
			"cell_origin": "client",
			"cell_type": "latex",
			"cells": [
				{
					"cell_id": 11317838269335231990,
					"cell_origin": "client",
					"cell_type": "latex_view",
					"source": "\\algorithm{integrate_ode(eqns: Ex|Iterable[Ex], variables: Ex|Iterable[Ex], initial_values: List[float], \nendpoint: float, delta: float, constants: Ex|dict) -> List}{Numerically integrate a system of ODEs over a range of values}\n\\begin{description}\n\\item \\verb|eqns| \\\\\n\tList of expressions representing first order derivatives with respect to a common variable. The expression\n\tshould not contain the derivative, so e.g. use $x - \\frac{1}{2}xy$ instead of $\\partial_{t}{x} = x - \\frac{1}{2}xy$.\n\tCan be a comma-separated in an Ex object, or any iterable of Ex objects.\n\\item \\verb|variables| \\\\\n\tList of variables, starting with the derivative variable and then each variable in the order that its derivative appears\n\tin \\verb|eqns|, so $(\\frac{dx}{dt}, \\frac{dy}{dt}, \\frac{dz}{dt})$ would have variables $(t, x, y, z)$\n\\item \\verb|initial_values| \\\\\n\tThe initial values of each variable in \\verb|variables| as a floating point number\n\\item \\verb|endpoint| \\\\\n\tThe value of the derivative variable at which to finish\n\\item \\verb|delta| \\\\\n\tThe amount to increase the derivative variable at each iteration\n\\item \\verb|constants| \\\\\n\tEx or dictionary object with a list of substitutions of constants to be performed before the numeric integration\n\\end{description}"
				}
			],
			"hidden": true,
			"source": "\\algorithm{integrate_ode(eqns: Ex|Iterable[Ex], variables: Ex|Iterable[Ex], initial_values: List[float], \nendpoint: float, delta: float, constants: Ex|dict) -> List}{Numerically integrate a system of ODEs over a range of values}\n\\begin{description}\n\\item \\verb|eqns| \\\\\n\tList of expressions representing first order derivatives with respect to a common variable. The expression\n\tshould not contain the derivative, so e.g. use $x - \\frac{1}{2}xy$ instead of $\\partial_{t}{x} = x - \\frac{1}{2}xy$.\n\tCan be a comma-separated in an Ex object, or any iterable of Ex objects.\n\\item \\verb|variables| \\\\\n\tList of variables, starting with the derivative variable and then each variable in the order that its derivative appears\n\tin \\verb|eqns|, so $(\\frac{dx}{dt}, \\frac{dy}{dt}, \\frac{dz}{dt})$ would have variables $(t, x, y, z)$\n\\item \\verb|initial_values| \\\\\n\tThe initial values of each variable in \\verb|variables| as a floating point number\n\\item \\verb|endpoint| \\\\\n\tThe value of the derivative variable at which to finish\n\\item \\verb|delta| \\\\\n\tThe amount to increase the derivative variable at each iteration\n\\item \\verb|constants| \\\\\n\tEx or dictionary object with a list of substitutions of constants to be performed before the numeric integration\n\\end{description}"
		},
		{
			"cell_id": 17270037226329397630,
			"cell_origin": "client",
			"cell_type": "input",
			"source": "def integrate_ode(eqns, variables, initial_values, endpoint, step=None, constants=None):\n\t# Collect list of equations and lambdify them\n\tif isinstance(eqns, Ex):\n\t\tif eqns.head() == r\"\\comma\":\n\t\t\tfuncs = [lambdify(eqn.ex(), variables, constants) for eqn in eqns.top().children()]\n\t\telse:\n\t\t\tfuncs = [lambdify(eqns, variables, constants)]\n\telse:\n\t\tfuncs = [lambdify(eqn, variables, constants) for eqn in eqns]\n\t\n\t# Master function\n\tf = lambda xs, t, params: [func(t, *xs) for func in funcs]\n\n\t# Integration range\n\tnpoints = 1000 if step is None else int((1 + endpoint - initial_values[0]) / step)\n\tpoints = numpy.linspace(initial_values[0], endpoint, npoints)\n\n\t# Rebroadcast so that each return list corresponds to a variable\n\tsol = odeint(f, initial_values[1:], points, ((),))\n\treturn [points] + [sol[:,i] for i in range(len(variables)-1)]"
		},
		{
			"cell_id": 12331971389017128553,
			"cell_origin": "client",
			"cell_type": "input",
			"ignore_on_import": true,
			"source": "{t}::Coordinate.\ndx := x-A*x*y.\ndy := -B*y + C*x*y.\n#sols = integrate_ode((dx, dy), $t, x, y$, (0, 1, 1), 10, 0.001, $A->1/2, B->3/4, C->1/4$)\nsols = integrate_ode($@(dx), @(dy)$, $t, x, y$, (0, 1, 1), 10, 0.001, {\"A\": 0.5, \"B\": 3/4, \"C\": 0.25})"
		},
		{
			"cell_id": 10058019511408460871,
			"cell_origin": "client",
			"cell_type": "input",
			"cells": [
				{
					"cell_id": 18371720257697375934,
					"cell_origin": "server",
					"cell_type": "image_png",
					"source": 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"
				}
			],
			"ignore_on_import": true,
			"source": "import matplotlib.pyplot as plt\nfig, axes = plt.subplots(2,1)\naxes[0].plot(sols[0], sols[1])\naxes[0].plot(sols[0], sols[2])\naxes[1].plot(sols[1], sols[2])\nfig;"
		},
		{
			"cell_id": 4262269971924348028,
			"cell_origin": "client",
			"cell_type": "input",
			"cells": [
				{
					"cell_id": 1287486217584996925,
					"cell_origin": "server",
					"cell_type": "latex_view",
					"cells": [
						{
							"cell_id": 6643470899229452613,
							"cell_origin": "server",
							"cell_type": "input_form",
							"source": "Raux"
						}
					],
					"source": "\\begin{dmath*}{}R_{aux}\\end{dmath*}"
				},
				{
					"cell_id": 17755464265255366914,
					"cell_origin": "server",
					"cell_type": "latex_view",
					"cells": [
						{
							"cell_id": 8501208413624250549,
							"cell_origin": "server",
							"cell_type": "input_form",
							"source": "-(4(M)**2 Raux + 2(r)**2 Raux + 2(laux R-3r Raux) M + ((\\omega)**2 (r)**3-laux r) R) (4(M)**2 r-4M (r)**2 + (r)**3)**(-1)"
						}
					],
					"source": "\\begin{dmath*}{}-\\left(4{M}^{2} R_{aux}+2{r}^{2} R_{aux}+2\\left(\\lambda_{aux} R-3r R_{aux}\\right) M+\\left({\\omega}^{2} {r}^{3}-\\lambda_{aux} r\\right) R\\right) {\\left(4{M}^{2} r-4M {r}^{2}+{r}^{3}\\right)}^{-1}\\end{dmath*}"
				}
			],
			"ignore_on_import": true,
			"source": "Raux::LaTeXForm(\"R_{aux}\")\nlaux::LaTeXForm(\"\\lambda_{aux}\")\ndR := Raux;\ndRaux := -(4* M**2* Raux + 2* r**2* Raux + 2*( laux * R - 3* r * Raux ) * M + (\n\t\\omega**2* r**3 - laux * r ) * R ) /(4* M**2* r - 4* M * r**2 + r**3);\nsols = integrate_ode((dR, dRaux), $r, R, Raux$, (0.3, 1, 0.5), 100, 0.01, $M->0.1, \\omega->0.2, k->2, laux->2$)"
		},
		{
			"cell_id": 15414656810465219608,
			"cell_origin": "client",
			"cell_type": "input",
			"cells": [
				{
					"cell_id": 13895594005555715725,
					"cell_origin": "server",
					"cell_type": "image_png",
					"source": 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"
				}
			],
			"source": "fig, axes = plt.subplots(2,1)\naxes[0].plot(sols[0], sols[1])\nfig;"
		},
		{
			"cell_id": 7751065038176589856,
			"cell_origin": "client",
			"cell_type": "input",
			"source": ""
		},
		{
			"cell_id": 14974314265954450945,
			"cell_origin": "client",
			"cell_type": "input",
			"source": ""
		}
	],
	"description": "Cadabra JSON notebook format",
	"version": 1.0
}