logarithmic interpolation

D

different

Hi, I have a program which reads a file containing integers in [0,10].
The program reads the value of a variable every 2 seconds, then maps it
to another interval, say [20,22000], obtaining a new value.
I already have a function which updates the variable, gradually
changing from the old one to the new one during the 2 seconds, which
uses a linear function.
Know I need to make the value of the variable change between old and
new in a "logarithmic way", that is the values between old and new must
follow a logarithmic scale.
How can I do that?
 
M

Martin Ambuhl

different said:
Hi, I have a program which reads a file containing integers in [0,10].
The program reads the value of a variable every 2 seconds, then maps it
to another interval, say [20,22000], obtaining a new value.
I already have a function which updates the variable, gradually
changing from the old one to the new one during the 2 seconds, which
uses a linear function.
Know I need to make the value of the variable change between old and
new in a "logarithmic way", that is the values between old and new must
follow a logarithmic scale.
How can I do that?

This is not a question about C but about elementary arithmetic. I will
offer an explanation but it is al; off-topic in comp.lang.c and should
not be replied to.

<ot>
You are looking for a function that maps a linear variable x onto an
exponential variable y.
y = A*exp(bx)
using a for log(A), this is the same as
log(y) = a + bx
We have a form with two unknowns and we have two data points:
log(20) = a + 0*b
log(22000) = a + 10b
so we know immediately that
a = log(20)
or A = 20
and that
b = (log(22000) - log(20)) / 10
or
b = log(1100) / 10
so the mapping is
log(y) = log(20) + x * log(1100)/10

y = 20 * pow(1100, x/10);

</ot>
 
D

David T. Ashley

different said:
Hi, I have a program which reads a file containing integers in [0,10].
The program reads the value of a variable every 2 seconds, then maps it
to another interval, say [20,22000], obtaining a new value.
I already have a function which updates the variable, gradually
changing from the old one to the new one during the 2 seconds, which
uses a linear function.
Know I need to make the value of the variable change between old and
new in a "logarithmic way", that is the values between old and new must
follow a logarithmic scale.
How can I do that?

sci.math and related groups have a large pool of bored mathematicians and
students who will gladly address such topics.
 
U

user923005

David said:
different said:
Hi, I have a program which reads a file containing integers in [0,10].
The program reads the value of a variable every 2 seconds, then maps it
to another interval, say [20,22000], obtaining a new value.
I already have a function which updates the variable, gradually
changing from the old one to the new one during the 2 seconds, which
uses a linear function.
Know I need to make the value of the variable change between old and
new in a "logarithmic way", that is the values between old and new must
follow a logarithmic scale.
How can I do that?

sci.math and related groups have a large pool of bored mathematicians and
students who will gladly address such topics.

They might even point him to this:
http://www.mpip-mainz.mpg.de/~deserno/science_notes/log_interpol/log_interpol.ps
 
D

different

Sorry, I know that it was OT, but I always tried sci.math and another
forum about algorithms, but they did not give me an answer in one week.
Thank you for the reply.

different said:
Hi, I have a program which reads a file containing integers in [0,10].
The program reads the value of a variable every 2 seconds, then maps it
to another interval, say [20,22000], obtaining a new value.
I already have a function which updates the variable, gradually
changing from the old one to the new one during the 2 seconds, which
uses a linear function.
Know I need to make the value of the variable change between old and
new in a "logarithmic way", that is the values between old and new must
follow a logarithmic scale.
How can I do that?This is not a question about C but about elementary arithmetic. I will
offer an explanation but it is al; off-topic in comp.lang.c and should
not be replied to.

<ot>
You are looking for a function that maps a linear variable x onto an
exponential variable y.
y = A*exp(bx)
using a for log(A), this is the same as
log(y) = a + bx
We have a form with two unknowns and we have two data points:
log(20) = a + 0*b
log(22000) = a + 10b
so we know immediately that
a = log(20)
or A = 20
and that
b = (log(22000) - log(20)) / 10
or
b = log(1100) / 10
so the mapping is
log(y) = log(20) + x * log(1100)/10

y = 20 * pow(1100, x/10);

</ot>
 
Z

Zbigniew Karno

different napisal(a):
Hi, I have a program which reads a file containing integers in [0,10].
The program reads the value of a variable every 2 seconds, then maps it
to another interval, say [20,22000], obtaining a new value.
I already have a function which updates the variable, gradually
changing from the old one to the new one during the 2 seconds, which
uses a linear function.
Know I need to make the value of the variable change between old and
new in a "logarithmic way", that is the values between old and new must
follow a logarithmic scale.
How can I do that?

Instead of the function log(x), rather you have
to use the following one: log(x - 1), for x >= 0.

Then the interpolation formula for x in [x_1,x_2]
with ratio f = a/(a+b), looks as follows:

(log(x_2 -1) - log(x - 1)) / (log(x - 1) - log(x_1 - 1)) = (1/f) - 1

After a simple calculation one can get

x = (x_1 - 1)^{f - 1} * (x_2 - 1)^{f} + 1 ,

what you expect.

Best Regards,
Z. Karno
 
Z

Zbigniew Karno

Zbigniew Karno napisal(a):
different napisal(a):
Hi, I have a program which reads a file containing integers in [0,10].
The program reads the value of a variable every 2 seconds, then maps it
to another interval, say [20,22000], obtaining a new value.
I already have a function which updates the variable, gradually
changing from the old one to the new one during the 2 seconds, which
uses a linear function.
Know I need to make the value of the variable change between old and
new in a "logarithmic way", that is the values between old and new must
follow a logarithmic scale.
How can I do that?

Instead of the function log(x), rather you have
to use the following one: log(x - 1), for x >= 0.

Then the interpolation formula for x in [x_1,x_2]
with ratio f = a/(a+b), looks as follows:

(log(x_2 -1) - log(x - 1)) / (log(x - 1) - log(x_1 - 1)) = (1/f) - 1

After a simple calculation one can get

x = (x_1 - 1)^{f - 1} * (x_2 - 1)^{f} + 1 ,

what you expect.

Best Regards,
Z. Karno

Incorrect.
The sign - should be replaced by +.

So, the following function has to be used:
log(x + 1), for x >= 0.
In this case, the interpolation formula looks as
follows:
(log(x_2 +1) - log(x + 1)) / (log(x + 1) - log(x_1 + 1)) = (1/f) -
1.
Thus
x = (x_1 + 1)^{f -1} * (x_2 + 1)^{f} - 1 .

Regards,
Z. Karno
 

Ask a Question

Want to reply to this thread or ask your own question?

You'll need to choose a username for the site, which only take a couple of moments. After that, you can post your question and our members will help you out.

Ask a Question

Members online

No members online now.

Forum statistics

Threads
473,744
Messages
2,569,482
Members
44,901
Latest member
Noble71S45

Latest Threads

Top