To define a set of points we write something like this:
point(x1,y1; x2,y2; x3,y3; ...)
To get the linear interpolation we type
f(x=a) [ENTER/COMPUTE] and the calculator gives x=a and y=b as solutions
or
f(y=b) [ENTER/COMPUTE] and the calculator gives x=a and y=b as solutions.
Example:
point(3,6; 4,8) [COMPUTE]
and
f(x=3.1) [COMPUTE]
The prog calculte the function Y=bX+c based on (3,6) and (4,8)
and then calculate Y1=b*3.1+c and it should give the result
X=3.1
Y=Y1
Do you want to say something about this ?
Have you any other idea ?
Thanks
it is called the "slope-intercept" form
it is usually written as
Y = mX + b
or
f(X) = mX + b
where m is the slope of the graphed line
and b is the intercept (or Y intercept, the value of Y where the graphed line crosses the origin)
you can solve for m and b with any 2 points via simultaneus equations
Dave,
Quote
"Undefined"
how about interpolate/extrapolate
i.e., when they enter a linear equation, it waits for them to enter an X or Y to plot the point
...then add a BSL function with interpolate/extrapolate
This was your idea or suggestion.
Now the problem is how to integrate it in calculaXX.
To do a linear interpolation, the
first thing to do
is to define a set of points (x,y). How ?
My suggestion is to create a function
(a) point(x1,y1; x2,y2; ...;xn,yn)
In this way we put that set of points in one table in the memory.
After this the problem is how to interpolate ?
My suggestion is to create 2 functions
f(x=number) or f(y=number)
In this way, in calculaXX, when we type an input like
f(x=3.1) calculaXX use the table defined by function (a), and execute
a linear interpolation to get the result y and show the result
x=number y=result
Did you understand ?
What about this ?
first, a linear equation may be described using only 2 points
(X1, Y1)
(X2, Y2)
if they define a 3rd point and it is not on the same line, then it is not a linear equation
probably the easiest way to solve for "m" (slope) and "b" (intercept) is to solve for "m", first:
m = (Y2 - Y1) / (X2 - X1) = (Y1 - Y2) / (X1 - X2)
the slope is often described as "the rise over the run"
be careful not to execute divide-by-zero :P
if X1 = X2, it is a line, straight up and down
then, it is easy to solve for "b"
b = Y1 - m * X1 = Y2 - m * X2
once you have "m" and "b", they can enter any X value and get a Y, or enter any Y value and get an X
that handles both interpolation and extrapolation
Dave,
1. I think you agree with me about the functions
point(x1,y1; x2,y2; ...;xn,yn), f(x=number) and f(y=number)
to execute interpolation using calculaXX;
2. I think you dont know exactly what is a linear interpolation.
To use a linear interpolation we dont need to have a set
of points that follow a linear equation y=mx+b.
We can define any set of points, not 2 points (X1, Y1) and (X2, Y2).
That set of points can follow a complex function y=f(x), it
is not important if we want to get an approximation, in this
case, using one linear equation y=mx+b. Obviously that approximation
may be good or bad. This is linear interpolation.
3. Suppose we have the function f(x)=x^2+1. The points (0,1), (1,3), (2,5)
follow that function.
We can use a linear interpolation to estimate the value of f(0.1)
In this case we use the points (0,1), (1,3) to get the linear equation
y=mx+b and we calculate y=m*0.1+b and at the end we say y is an estimate
of f(0.1).[Obviously we calculate m and b from (0,1), (1,3)]
Obviously it is not a good idea to use that y=mx+b to get an estimate
of f(3)! The better idea is to use (1,3), (2,5) i think.
Any doubt ?
you are right, of course
you may use linear interpolation for any function
results may vary :P
the farther apart the 2 points are, the less likely you are to get good results (depends on the function, of course)
what i was thinking about was a simple linear function
the reason i brought it up was - my calculator can do it :bg
you can enter 2 points and either a Y or X value, and it will give you the X or Y
it will also do average, median, standard deviation - all that stuff
it would be nice if i could plug a function in and get the slope at a given X or Y :P
Dave,
Quote
the reason i brought it up was - my calculator can do it
you can enter 2 points and either a Y or X value, and it will give you the X or Y
Thanks for your idea.
I will try to implement it in the next calcula36.
We define up to 10 points, minimum 2 using
point(x1,y1; x2,y2; ...; x9,y9; x10,y10)
for some more ideas....
http://www.softpedia.com/progScreenshots/SuperCalc-Screenshot-40384.html