logarithmic interpolation

[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?

[Martin Ambuhl]

different wrote:

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>

[David T. Ashley]

"different" <ci**********@gmail.comwrote in message
news:11**********************@l53g2000cwa.googlegr oups.com...

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.

--
David T. Ashley (dt*@e3ft.com)
http://www.e3ft.com (Consulting Home Page)
http://www.dtashley.com (Personal Home Page)
http://gpl.e3ft.com (GPL Publications and Projects)

[user923005]

David T. Ashley wrote:

"different" <ci**********@gmail.comwrote in message
news:11**********************@l53g2000cwa.googlegr oups.com...

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/~desern...og_interpol.ps

--
David T. Ashley (dt*@e3ft.com)
http://www.e3ft.com (Consulting Home Page)
http://www.dtashley.com (Personal Home Page)
http://gpl.e3ft.com (GPL Publications and Projects)

[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.

On 18 Gen, 19:26, Martin Ambuhl <[e-mail]:

different wrote:

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>

[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

[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