Recently stan has added the integrate_ode method. Unfortunately the only documentation I can find is the stan reference manual (p.191ff). I have a model that would require some driving signal. As I understand the parameter x_r and x_i are supposed to be used for this.
For the sake of a concrete example lets assume I want to implement the example from the documentation with following change:
real[] sho(real t,
real[] y,
real[] theta,
real[] x_r,
int[] x_i) {
real dydt[2];
real input_signal; // Change from here!!!
input_signal <- how_to(t, x_r, x_i);
dydt[1] <- y[2] + input_signal; // Change to here!!!
dydt[2] <- -y[1] - theta[1] * y[2];
return dydt;
}
the input signal is supposed to be a time series that is inputted - let's say I submit input_signal_vector <- sin(t) + rnorm(T, sd=0.1) (which is supposed to be a signal at the time points in ts) and I plan to use for input_signal the closest value in time.
The only way I can imagine is one could concat ts and input_signal_vector in x_r and then a search in this array. But I can not imagine this is the intended use of these parameter. It would also be extremely inefficient.
So if someone could show how such a case is supposed to be solved I would be very grateful.
Related
I want to evaluate a matrix that has a function named alpha. When I take the derivative of alpha, I would like the result to give me an alpha'
Example: if I have sin(alpha) I want to get cos(alpha)alpha' but throughout the matrix.
It is quite unclear what you mean by stating that you have a "function" in Maple, of which you intend to take the derivative.
That could mean some expression depending upon a name such as t, with respect to which you intend on differentiating using Maple's diff command. And such an expression may be assigned to alpha, or it may contain the function call alpha(t).
Or perhaps you wish to treat alpha as an operator name, and differentiate functionally with Maple's D command.
I shall make a guess as to what you meant.
restart;
Typesetting:-Suppress(alpha(t));
Typesetting:-Settings(prime=t):
Typesetting:-Settings(typesetprime=true):
M := Matrix([[ sin(alpha(t)), exp(p*alpha(t)) ]]);
map(diff, M, t);
If that's not the kind of thing that you're after then you should explain your purpose and needs in greater detail.
Your question's title mentions a desire to have something not "evaluate". What did you mean by that? Have you perhaps assigned something to the name f?
Thank you for answering. I found the solution after a lot of guess and checking and reading. Here is my code with my solution.
with(Typesetting) :
Settings(typesetdot = true);
a:= alpha(t)
Rna:= [ cos(alpha), -sin(alpha), 0; sin(alpha), cos(alpha), 0; 0, 0, 1 ]
b := beta(t)
Rab:= [ cos(beta), -sin(beta), 0; sin(beta), cos(beta), 0; 0, 0, 1 ]
Rnab:= Rna . Rab
Rnab:= map(diff, Rnab, t)
Sorry for the multiple answers, I am getting use to the website.
I'm relatively new to Z3 and experimenting with it in python. I've coded a program which returns the order in which different actions is performed, represented with a number. Z3 returns an integer representing the second the action starts.
Now I want to look at the model and see if there is an instance of time where nothing happens. To do this I made a list with only 0's and I want to change the index at the times where each action is being executed, to 1. For instance, if an action start at the 5th second and takes 8 seconds to be executed, the index 5 to 12 would be set to 1. Doing this with all the actions and then look for 0's in the list would hopefully give me the instances where nothing happens.
The problem is: I would like to write something like this for coding the problem
list_for_check = [0]*total_time
m = s.model()
for action in actions:
for index in range(m.evaluate(action.number) , m.evaluate(action.number) + action.time_it_takes):
list_for_check[index] = 1
But I get the error:
'IntNumRef' object cannot be interpreted as an integer
I've understood that Z3 isn't returning normal ints or bools in their models, but writing
if m.evaluate(action.boolean):
works, so I'm assuming the if is overwritten in a way, but this doesn't seem to be the case with range. So my question is: Is there a way to use range with Z3 ints? Or is there another way to do this?
The problem might also be that action.time_it_takes is an integer and adding a Z3int with a "normal" int doesn't work. (Done in the second part of the range).
I've also tried using int(m.evaluate(action.number)), but it doesn't work.
Thanks in advance :)
When you call evaluate it returns an IntNumRef, which is an internal z3 representation of an integer number inside z3. You need to call as_long() method of it to convert it to a Python number. Here's an example:
from z3 import *
s = Solver()
a = Int('a')
s.add(a > 4);
s.add(a < 7);
if s.check() == sat:
m = s.model()
print("a is %s" % m.evaluate(a))
print("Iterating from a to a+5:")
av = m.evaluate(a).as_long()
for index in range(av, av + 5):
print(index)
When I run this, I get:
a is 5
Iterating from a to a+5:
5
6
7
8
9
which is exactly what you're trying to achieve.
The method as_long() is defined here. Note that there are similar conversion functions from bit-vectors and rationals as well. You can search the z3py api using the interface at: https://z3prover.github.io/api/html/namespacez3py.html
I have tried this code:
model var
Real x;
Real y;
Real z;
equation
x=6*time;
when time>=6 then
z=x;
end when;
y=3*z;
end var;
But it will give me y = 3*x(at time = 6) but from time = 6 while i need it from the beginning.
Any direct method for this problem?
Based on folks comments you now know that Modelica is quite strict in its treatment of time behavior. You could argue that it is a more physical representation of time (quantum and other crazy physics aside), as in you can not time-travel in your code.
Depending on your application there may be ways around your issue. One possibility is to move the time behavior to the initialization. That way you capture the behavior prior to time=0 and start at time=0 with the expected behavior.
For example:
model var
parameter Modelica.SIunits.Time t_zero = 6;
parameter Real x(fixed=false);
Real y;
Real z;
initial equation
x = 6*t_zero; // or some more complicated set of equations/functions
equation
z = x;
y=3*z;
end var;
Recognized this restricts things, potentially too much, but you can have many parameters and have a more complex representation in the initial equation block. You can also call a function x=func() where you have performed integrations, etc. to get the value of x at time=0.
Hope that helps, either now or in the future.
I am relatively new to Modelica (Dymola-environment) and I am getting very desperate/upset that I cannot solve such a simple problem as a random number generation in Modelica and I hope that you can help me out.
The simple function random produces a random number between 0 and 1 with an input seed seedIn[3] and produces the output seed seedOut[3] for the next time step or event. The call
(z,seedOut) = random(seedIn);
works perfectly fine.
The problem is that I cannot find a way in Modelica to compute this assignment over time by using the seedOut[3] as the next seedIn[3], which is very frustrating.
My simple program looks like this:
*model Randomgenerator
Real z;
Integer seedIn[3]( start={1,23,131},fixed=true), seedOut[3];
equation
(z,seedOut) = random(seedIn);
algorithm
seedIn := seedOut;
end Randomgenerator;*
I have tried nearly all possibilities with algorithm assignments, initial conditions and equations but none of them works. I just simply want to use seedOut in the next time step. One problem seems to be that when entering into the algorithm section, neither the initial conditions nor the values from the equation section are used.
Using the 'sample' and 'reinit' functions the code below will calculate a new random number at the frequency specified in 'sample'. Note the way of defining the "start value" of seedIn.
model Randomgenerator
Real seedIn[3] = {1,23,131};
Real z;
Real[3] seedOut;
equation
(z,seedOut) = random(seedIn);
when sample(1,1) then
reinit(seedIn,pre(seedOut));
end when;
end Randomgenerator;
The 'pre' function allows the use of the previous value of the variable. If this was not used, the output 'z' would have returned a constant value. Two things regarding the 'reinint' function, it requires use of 'when' and requires 'Real' variables/expressions hence seedIn and seedOut are now defined as 'Real'.
The simple "random" generator I used was:
function random
input Real[3] seedIn;
output Real z;
output Real[3] seedOut;
algorithm
seedOut[1] :=seedIn[1] + 1;
seedOut[2] :=seedIn[2] + 5;
seedOut[3] :=seedIn[3] + 10;
z :=(0.1*seedIn[1] + 0.2*seedIn[2] + 0.3*seedIn[3])/(0.5*sum(seedIn));
end random;
Surely there are other ways depending on the application to perform this operation. At least this will give you something to start with. Hope it helps.
In Stata, after a regression I know it is possible to call the elements of stored results by name. For example, if I want to manipulate the coefficient on the variable precip, I just type _b[precip]. My question is how do I do the same after the tabstat command? For example, say I want to multiply the coefficient on precip by the sample mean of precip:
reg --variables in regression--
tabstat --variables in regression--
mat X=r(StatTotal)
mat Y=_b[precip]*X[1,precip]
Ah, if only it were that simple. But alas, in the last line X[1, precip] is invalid syntax. Oddly, Stata does recognize display X[1, precip]. And Stata would know what I'm trying to do if instead of precip I used the column number where precip appears in the X vector. If I were just doing this operation once, no problem. But I need to do this operation several times (for several different model specifications) and for several variables which change position in the vector from one model to the next, so I cannot just use the column number.
I am not yet sure I understand exactly what you want to do, but here's my attempt to reproduce what you are doing:
sysuse auto, clear
regress price mpg foreign weight
tabstat mpg foreign weight, save
matrix X = r(StatTotal)
matrix Y = _b[mpg]*X[1, colnumb(X, "mpg") ]
If you need to put this into a cycle, that's doable, too:
matrix bb = e(b)
local explvar : colnames bb
foreach x in `explvar' {
if "`x'" != "_cons" {
matrix Y_`x' = _b[`x'] * X[1, colnumb(X, "`x'")]
}
else {
matrix Y_`x' = _b[`x']
}
}
You'd probably want to put this into a program that you will call after each regression model estimation call, e.g.:
program define reg2mat , prefix( name )
if "`e(cmd)'" != "regress" {
// this will intentionally produce an error
regress
}
tempname bb
matrix `bb' = e(b)
local explvar : colnames `bb'
foreach x in `explvar' {
if "`x'" != "_cons" {
matrix `prefix'_`x' = _b[`x'] * X[1, colnumb(X, "`x'")]
}
else {
matrix `prefix'_`x' = _b[`x']
}
}
end // of reg2mat
At many levels, it is not ideal, as it manipulates with the (global) matrices in Stata memory; most of the time, it is a bad idea, as the programs should only manipulate with objects local to them.
I suspect that what you want to do is addressed, in one way or another, by either omnipowerful margins command, or by an appropriate predict, or by matrix score (which is the low level version of predict). Attributing the effects to a variable only makes sense when your regressors are orthogonal, which only happens in carefully designed and conducted experiments.