# Approximator Line 1.2.934.b

Approximator Line is an application which allows to synthesize approximation function of one argument.

- LICENSE TYPE:
- Free To Use But Restricted
- USER RATING:
- DEVELOPED BY:
**GLCSoft**- HOMEPAGE:
- glcsoft.com
- CATEGORY:
- ROOT \ Science and Engineering \ Mathematics

Approximator Line is an application which allows to synthesize approximation function of one argument. Both coordinates of known points or mathematical expression can be used as input data.

The application uses evolutionary algorithm which allows to find more optimal results. The enhanced evolutionary algorithm allows to avoid long-time hitting to local maximum.

In few hours the application can evaluate milliards of combinations with using of reasonable number of input data points and on contemporary computer. Approximator Line uses multithreading that can help to utilize maximum computation power.

Approximator Line's primary goal is to search of function, which value, most come nearer to the initial data. The preference is given the smallest functions. The weight of this preference is established in options of synthesis.

Search of function is made by the next way:

The random mathematical variant is under construction. It's fitness to the data is calculated. Further the variant is copied and changes. Fitness of the changed variant is calculated. If it is more, the new variant becomes base. It is simplified.

Key parameter of the found function is fitness of its set goal. Fitness is expressed in percentage. Its value depends on a way of the assignment of fitness of a point (it is established in parameters of synthesis). The program uses two basic such as fitness:

General fitness

Calculates on the general points.

Additional fitness

Calculates on general and additional points. It is used for more exact definition of fitness. It also is used for avoidance of a finding of such functions which correspond to the basic points, but in an interval between them strongly differ.

Additional fitness is used for a finding of the most corresponding functions at smaller amount of computing expenses as it calculates only if the basic fitness more than at the previous variant. Besides each of the mentioned above fitness can be normal or effective.

Normal fitness

Fitness in view of amount of elements of expression.

Effective fitness

Fitness without taking into account amount of elements of expression.

In the list of results normal additional conformity and effective additional conformity is accordingly displayed.

By search of the most suitable variant, or in other words synthesis cancelation constant subexprassions is made also.

Synthesis is based on use of random numbers. Functions making expression, operators variables and numbers get out randomly. The application is optimized on speed. So synthesized function in memory represents a tree of mathematical objects. Values of function are calculates by the most effective way. The mutation also is made above a tree of objects.

· Determine the form of the input data (coordinates or expression).

· Choose points of your graph. Synthesis will be estimated on them.

· Enter coordinates of points (use autonumbering for simplification of input) or expression.

· Determine a range of value of function, amount of the basic points, amount of additional points.

· Open parameters of synthesis and adjust if it is necessary.

· Save the project.

· Press Start of synthesis.

· Pass to results and see on them.

· Leave the application working on long time.

· Periodically check results. When the application will find, in your opinion, suitable function, press Stop and save results.

· libSM.so.6

· libX11.so.6

· libXinerama.so.1

· libXxf86vm.so.1

· libatk-1.0.so.0

· libc.so.6

· libc.so.6(GLIBC_2.0)

· libc.so.6(GLIBC_2.1)

· libc.so.6(GLIBC_2.1.3)

· libc.so.6(GLIBC_2.2)

· libdl.so.2

· libdl.so.2(GLIBC_2.0)

· libdl.so.2(GLIBC_2.1)

· libexpat.so.0

· libgcc_s.so.1

· libgcc_s.so.1(GCC_3.0)

· libgcc_s.so.1(GLIBC_2.0)

· libgdk-x11-2.0.so.0

· libgdk_pixbuf-2.0.so.0

· libglib-2.0.so.0

· libgmodule-2.0.so.0

· libgobject-2.0.so.0

· libgthread-2.0.so.0

· libgtk-x11-2.0.so.0

· libjpeg.so.62

· libm.so.6

· libm.so.6(GLIBC_2.0)

· libpango-1.0.so.0

· libpng12.so.0

· libpthread.so.0

· libpthread.so.0(GLIBC_2.0)

· libpthread.so.0(GLIBC_2.1)

· libpthread.so.0(GLIBC_2.2)

· libpthread.so.0(GLIBC_2.3.2)

· libstdc++.so.6

· libstdc++.so.6(CXXABI_1.3)

· libstdc++.so.6(GLIBCXX_3.4)

· libtiff.so.3 libz.so.1

This license operates up to the end of 2007 year.

This license entitles to free-of-charge using, copying, distribution of the "Approximator Line" Beta versions. You are using this program on your own risk. The author does not carry any responsibility for results of work of the program. The author does not carry any responsibility for any damages or the damage, called by the given program or results of its work.

The application uses evolutionary algorithm which allows to find more optimal results. The enhanced evolutionary algorithm allows to avoid long-time hitting to local maximum.

In few hours the application can evaluate milliards of combinations with using of reasonable number of input data points and on contemporary computer. Approximator Line uses multithreading that can help to utilize maximum computation power.

Approximator Line's primary goal is to search of function, which value, most come nearer to the initial data. The preference is given the smallest functions. The weight of this preference is established in options of synthesis.

Search of function is made by the next way:

The random mathematical variant is under construction. It's fitness to the data is calculated. Further the variant is copied and changes. Fitness of the changed variant is calculated. If it is more, the new variant becomes base. It is simplified.

Key parameter of the found function is fitness of its set goal. Fitness is expressed in percentage. Its value depends on a way of the assignment of fitness of a point (it is established in parameters of synthesis). The program uses two basic such as fitness:

General fitness

Calculates on the general points.

Additional fitness

Calculates on general and additional points. It is used for more exact definition of fitness. It also is used for avoidance of a finding of such functions which correspond to the basic points, but in an interval between them strongly differ.

Additional fitness is used for a finding of the most corresponding functions at smaller amount of computing expenses as it calculates only if the basic fitness more than at the previous variant. Besides each of the mentioned above fitness can be normal or effective.

Normal fitness

Fitness in view of amount of elements of expression.

Effective fitness

Fitness without taking into account amount of elements of expression.

In the list of results normal additional conformity and effective additional conformity is accordingly displayed.

By search of the most suitable variant, or in other words synthesis cancelation constant subexprassions is made also.

Synthesis is based on use of random numbers. Functions making expression, operators variables and numbers get out randomly. The application is optimized on speed. So synthesized function in memory represents a tree of mathematical objects. Values of function are calculates by the most effective way. The mutation also is made above a tree of objects.

**Usage:**· Determine the form of the input data (coordinates or expression).

· Choose points of your graph. Synthesis will be estimated on them.

· Enter coordinates of points (use autonumbering for simplification of input) or expression.

· Determine a range of value of function, amount of the basic points, amount of additional points.

· Open parameters of synthesis and adjust if it is necessary.

· Save the project.

· Press Start of synthesis.

· Pass to results and see on them.

· Leave the application working on long time.

· Periodically check results. When the application will find, in your opinion, suitable function, press Stop and save results.

**Requirements:**· libSM.so.6

· libX11.so.6

· libXinerama.so.1

· libXxf86vm.so.1

· libatk-1.0.so.0

· libc.so.6

· libc.so.6(GLIBC_2.0)

· libc.so.6(GLIBC_2.1)

· libc.so.6(GLIBC_2.1.3)

· libc.so.6(GLIBC_2.2)

· libdl.so.2

· libdl.so.2(GLIBC_2.0)

· libdl.so.2(GLIBC_2.1)

· libexpat.so.0

· libgcc_s.so.1

· libgcc_s.so.1(GCC_3.0)

· libgcc_s.so.1(GLIBC_2.0)

· libgdk-x11-2.0.so.0

· libgdk_pixbuf-2.0.so.0

· libglib-2.0.so.0

· libgmodule-2.0.so.0

· libgobject-2.0.so.0

· libgthread-2.0.so.0

· libgtk-x11-2.0.so.0

· libjpeg.so.62

· libm.so.6

· libm.so.6(GLIBC_2.0)

· libpango-1.0.so.0

· libpng12.so.0

· libpthread.so.0

· libpthread.so.0(GLIBC_2.0)

· libpthread.so.0(GLIBC_2.1)

· libpthread.so.0(GLIBC_2.2)

· libpthread.so.0(GLIBC_2.3.2)

· libstdc++.so.6

· libstdc++.so.6(CXXABI_1.3)

· libstdc++.so.6(GLIBCXX_3.4)

· libtiff.so.3 libz.so.1

**Limitations:**This license operates up to the end of 2007 year.

This license entitles to free-of-charge using, copying, distribution of the "Approximator Line" Beta versions. You are using this program on your own risk. The author does not carry any responsibility for results of work of the program. The author does not carry any responsibility for any damages or the damage, called by the given program or results of its work.

Last updated on April 27th, 2007

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