symbolic-math

问题 I am studying Stochastic calculus, and occasionally we need to compute an integral (from -infinity to +infinity) for some complex distribution. In this case, it was with the answer on the right. This is the code I put into Matlab (and I have the symbolic math toolbox), which Matlab simply cannot process: >> syms x t >> f = exp(1+2*x)*(1/((2*pi*t)^0.5))*exp(-(x^2)/(2*t)) >> int(f,-inf,inf) ans = -((2^(1/2)*pi^(1/2)*exp(2*t + 1)*limit(erf((2^(1/2)*((x*1i)/t - 2i))/(2*(-1/t)^(1/2))), x, -Inf)*1i

问题 My project require me to use Matlab to create a symbolic equation with square wave inside. I tried to write it like this but to no avail: syms t; a=square(t); Input arguments must be 'double'. What can i do to solve this problem? Thanks in advance for the helps offered. 回答1: here are a couple of general options using floor and sign functions: f=@(A,T,x0,x) A*sign(sin((2*pi*(x-x0))/T)); f=@(A,T,x0,x) A*(-1).^(floor(2*(x-x0)/T)); So for example using the floor function: syms x sqr=2*floor(x)

问题 My project require me to use Matlab to create a symbolic equation with square wave inside. I tried to write it like this but to no avail: syms t; a=square(t); Input arguments must be 'double'. What can i do to solve this problem? Thanks in advance for the helps offered. 回答1: here are a couple of general options using floor and sign functions: f=@(A,T,x0,x) A*sign(sin((2*pi*(x-x0))/T)); f=@(A,T,x0,x) A*(-1).^(floor(2*(x-x0)/T)); So for example using the floor function: syms x sqr=2*floor(x)

问题 I have the following code: syms t x; e=symfun(x-t,[x,t]); In the problem I want to solve x is a function of t but I only know its value at the given t,so I modeled it here as a variable.I want to differentiate e with respect to time without "losing" x,so that I can then substitute it with x'(t) which is known to me. In another question of mine here,someone suggested that I write the following: e=symfun(exp(t)-t,[t]); and after the differentiation check if I can substitute exp(t) with the

问题 I'm trying to calculate Euler-Lagrange equations for a robotic structure. I'll use q to indicate the vector of the joint variables. In my code, I use syms t; q1 = sym('q1(t)'); q2 = sym('q2(t)'); q = [q1, q2]; to declare that q1 and q2 depend on time t . After I calculate the Lagrangian L (in this case it is a simple link with a rotoidal joint) L = (I1z*diff(q1(t), t)^2)/2 + (L1^2*M1*diff(q1(t), t)^2)/8 The problem is that when I try to differentiate L respect to q using diff(L, q) , I get

问题 I want to modify the behaviour of the vpa function. For that I define my own function called vpa that calls the original vpa function and then does some more stuff. To call the original function from within my modified function I use y = builtin('vpa', varargin{:}); where varargin is a cell array of the function inputs, as usual. The problem is that the above produces a different result than calling the original vpa function. Minimal example, run on Octave 4.2.2: >> vpa([4 5], 20) ans = (sym)

问题 Do symbolic math calculations (especially for solving nonlinear polynomial systems) cause huge performance (calculation speed) disadvantage compared to numeric calculations? Are there any benchmark/data about this? Found a related question: https://scicomp.stackexchange.com/questions/21754/symbolic-computation-vs-numerical-computation Another one: Computational Efficiency of Forward Mode Automatic vs Numeric vs Symbolic Differentiation 回答1: I am the individual who answered the Scicomp

问题 Do symbolic math calculations (especially for solving nonlinear polynomial systems) cause huge performance (calculation speed) disadvantage compared to numeric calculations? Are there any benchmark/data about this? Found a related question: https://scicomp.stackexchange.com/questions/21754/symbolic-computation-vs-numerical-computation Another one: Computational Efficiency of Forward Mode Automatic vs Numeric vs Symbolic Differentiation 回答1: I am the individual who answered the Scicomp

问题 I am building (my first...) MatLab program, it needs to differentiate an equations symbolically and then use this solution many many times (with different numeric inputs). I do not want it to recalculate the symbolic differentiation every time it needs to put in a new set of numeric values. This would probably greatly add to the time taken to run this program (which - given its nature, a numeric optimiser, will probably already be hours). My question is how can I structure my program such

问题 I have this equation in x and y: (x + y)^(1/2) - 6*y*(x + y)^5 - (x + y)^6 + (x - 1)/(2*(x + y)^(1/2)) = 0. Now I call the solver: R_c = @(y)solve((x + y)^(1/2) - 6*y*(x + y)^5 - (x + y)^6 + (x - 1)/(2*(x + y)^(1/2)), x, 'Real', true); which gives me the implicit solutions as a function of y. Now try R_c(.3) to find the explicit solution at y = 0.3. MATLAB's answer is: ans = 0.42846617518653978966562924618638 0.15249587894102346284238111155954 0.12068186494007759990714181154349 However, the