Algorithm Optimisation Championship. - page 37
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You don't say. The complex variable function returns a complex number, so it draws two lines. The complex is in principle not limited to only two parts, it can have an infinite number of parts.
I haven't tried typing by hand).
So, first you gave me one function and then you broke it into parts?
It is not good to do such tricks...))
You claimed earlier that you can graphically plot a function with any number of variables.
I asked - how?
You replied - by plotting functions with one variable on a separate Z-axis layer.
I said - show me.
You replied - ok.
I waited.
You said - the function cannot be inserted.
I tried it myself - it worked.
Did I reproduce the chain of events correctly? You did. You suggested plotting graphs of functions with one variable on separate layers, so you need to break down the overall function into simple terms (I think that's what it's called) and plot two-dimensional graphs (but you tried to plot the overall function graphically for some reason). I did that for you.
What's the problem? I did the work for you. Then what?
A single curve in a graph shows the relationship between the values of two variables.
It is not possible to show in one curved line on a two-dimensional graph the dependence between many variables.
But that's clear to everyone...
You claimed earlier that you can graphically construct a function with any number of variables.
I asked how?
You answered - by plotting functions with one variable on a separate Z-axis layer.
I said - show me.
You replied - ok.
I waited.
You said - the function cannot be inserted.
I tried it myself - it worked.
Did I reproduce the chain of events correctly? You did. You suggested plotting graphs of functions with one variable on separate layers, so you need to break down the overall function into simple terms (I think that's what it's called) and plot the two-dimensional graphs (but you tried to plot the overall function for some reason). I did that for you.
What's the problem? I did the work for you. What is next?
Andrew, I have already expressed my opinion quite clearly from my point of view.
Multidimensional space can be compressed to three dimensions and you can look for maxima of each individual function that builds its own curve expressing the dependence of the value of the object property on another parameter.
I have nothing more to say on the subject...
Andrew, I have already expressed my opinion quite clearly and distinctly, from my point of view.
Multidimensional space can be compressed to three dimensions and look for maxima of each individual function, which builds its curve expressing dependence of value of object property on other parameter.
I have nothing more to say on the subject...
Show how to do this.
You showed me graphs with curved lines. There are several of them.
The function formula of each graph consists of two variables, x and y.
Suppose:
Y is a property of our object (e.g. the temperature of its body).
X is time.
Our function : Y = x1^2, creates a curve on a graph that shows the relationship between the time of day and the temperature of our object. (on the first slide).
Let's say the object has another property, which is density. At a certain temperature it is harder and more compressed, at another it is softer and more airy.
To show the relationship between the temperature of the object and its density, we write another function: Y = x2^3. We plot the curve on the second slide along the Z axis.
Next, we are looking for tops and bottoms of both curves on two flat graphs (slides) located on Z axis one after the other.
That's it.
You showed me graphs with curved lines. There are several of them.
The function formula of each graph consists of two variables, x and y.
Suppose:
Y is a property of our object (e.g. the temperature of its body).
X is time.
Our function : Y = x1^2, creates a curve on a graph that shows the relationship between the time of day and the temperature of our object. (on the first slide).
Let's say the object has another property, which is density. At a certain temperature it is harder and more compressed, at another it is softer and more airy.
To show the relationship between the temperature of the object and its density, we write another function: Y = x2^3. We plot the curve on the second slide along the Z axis.
Then we look for tops and bottoms of both curves on two flat graphs (slides) placed on Z axis one by one.
That's it.
Good. Let's move on.
So, let's go back to the old example.
We have an object - a body. It has a property called temperature.
We built a curve line of its temperature depending on the time of day (external factor) on the space of a two-dimensional graph: Y = x^2; (we will consider one property for now).
Then we found the point in time when the temperature is highest and when it is lowest.
Then, new factors appear that influence the temperature (property) of an object: Light intensity, wind strength, air humidity and atmospheric pressure.
We denote these parameters by q1, q2, q4.
And we add them to the formula: Y = x^2 + q1 + q2 + q3 + q4;
Depending on the time of the day, the values of these parameters (factors influencing the temperature) change, and we substitute their changing values in the formula. As a result we obtain a curve, showing the dependency of body temperature on time of day, taking into account additional factors, which influence it: light intensity, wind strength, air humidity and atmospheric pressure.
The number of factors can be added indefinitely... The main thing is to know their values.
And so, back to the old example.
We have an object - a body. It has a property - temperature.
We built a curve line of its temperature depending on time of day (external factor) on the space of a two-dimensional graph: Y = x^2; (we will consider one property for now).
Then we found the point in time when the temperature is highest and when it is lowest.
Then, new factors appear that influence the temperature (property) of an object: Light intensity, wind strength, air humidity and atmospheric pressure.
We denote these parameters by q1, q2, q4.
And we add them to the formula: Y = x^2 + q1 + q2 + q3 + q4;
Depending on the time of the day, the values of these parameters (factors influencing the temperature) change, and we substitute their changing values in the formula. As a result we get a curve, showing the dependency of body temperature on time of day, taking into account additional factors, which influence it: light intensity, wind strength, air humidity and atmospheric pressure.
The number of factors can be added indefinitely... The main thing is that we know their values.
All this is very interesting. But how does it help to find the optimum of the function that we don't know? At the championship you won't have an opportunity to look inside *.ex5 with FF.
Let's assume you know the optimum values of the factors influencing the temperature of the object:
q1 = 1,
q2 = 2,
q3 = 3,
q4 = 10;
At these values of these factors, the temperature of the object during the day remains in the optimal range, within which the object does not overheat or overcool.
You know these optimum values.
Others do not know these optimum values, but they have the option of going to a function and passing their values of these factors there to see if they will be acceptable to the object. It will not melt down.
In exchange for passing values, the function will return the answer - the temperature of the object. From the logic of the responses you can understand the pattern of influence of different values of various factors on the object's temperature and calculate the optimal range of values for each factor, at which the object will be ok.
The task is to get close to the optimal values of the factors known only to you.
Something like this...