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  1. Provenance of code.
  2. Purpose of code.
  3. Specification.
  4. Description of subroutine's operation.
  5. References.
  6. Parameter descriptions.
  7. Error indicators.
  8. Accuracy estimate.
  9. Any additional information.
  10. Example of code
  11. Auxiliary subroutines required.
  12. Keywords.
  13. Download source code.
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Provenance of Source Code

Sree Harsha Lalam, S. Yoshitake, H. Harada, H.K.D.H. Bhadeshia
Phase Transformations Group,
Department of Materials Science and Metallurgy,
University of Cambridge,
Cambridge, U.K.

The neural network program was produced by:

David J. C. MacKay,
Cavendish Laboratory,
University of Cambridge,
Madingley Road,
Cambridge, CB3 0HE, U.K.

Added to MAP: June 1999

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To estimate the lattice parameters of the gamma and gamma-prime phases of nickel base superalloys as a function of the chemical composition and temperature. The inputs to this program consist of the temperature (Centigrade), Ni, Co, Cr, Mo, W, Al, Ti, Nb, Ta, Hf, Rh, V, Fe, Ga, Cu, Au concentrations in atomic percent.

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Language:FORTRAN / C
Product form:Source code / Executable files
Operating System:Solaris 5.5.1 & Windows 95

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MAP_NICKEL_LATTICE lattice parameters of the gamma and gamma-prime phases of nickel base superalloys as a function of the chemical composition and temperature. It makes use of a neural network program called generate44, which was developed by David MacKay and is part of the bigback5 program. The network was trained using a large database of experimental results [1] (some of these data are available on MAP under the Materials Data section as MAP_DATA_LATTMISFIT. The source code for the neural network program can be downloaded from David MacKay's website; the executable files only are available from MAP. Also provided are FORTRAN programs (as source code) for normalising the input data, averaging the results from the neural network program and unnormalising the final output file, along with other files necessary for running the program.

Programs are available which run on a Solaris 5.5.1 unix system and on a PC under Windows 95. Each directory or zip file contains the following files and subdirectories:

A text file containing step-by-step instructions for running the program, including a list of input variables.

A text file containing the minimum and maximum limits of each input and output variable. This file is used to normalise and unnormalise the input and output data.

An input text file containing the input variables used for predictions.

This text file contains the number of rows of data in the file test.dat

This is a unix shell file containing the command steps required to run the module. It can be executed by typing csh gamma.gen or csh gamma_p.gen at the command prompt. These shell files compile and run all the programs necessary for normalising the input data, executing the network for each model, unnormalising the output data and combining the results of each model to produce the final committee result.

gamma.exe / gamma_p.exe
These executable programs for the PC correspond to the unix command files gamma.gen / gamma_p.gen. The source code is given in gamma.c and gamma_p.c which are in subdirectory s.

This executable file reads the information in no_of_rows.dat and creates a file called either spec.gamma or spec.gamma_p, depending on the module.

spec.gamma / spec.gamma_p
A dynamic file, created by spec.ex, which contains information about the module and the number of data items being supplied. It is read by the program generate44.

This a text file which contains the normalised input variables. It is generated by the program normtest.for in subdirectory s.

generate44 / generate55
This is the executable file for the neural network program. generate44 runs on unix systems and generate55 on the PC. It reads the normalised input data file, norm_test.in, and uses the weight files in subdirectory c, to find a value for either the yield strength or ultimate tensile strength. The results are written to the temporary output file _out.

_ot, _out, _res, _sen
These files are created by generate44 and can be deleted.

Gresult / GPresult
Contains the final un-normalised committee results for the predicted lattice parameters.


The source code for program spec.ex.

Program to normalise the data in test.dat and produce the normalised input file norm_test.in. It makes use of information read in from no_of_rows.dat and committee.dat.

This program uses the information in committee.dat and combines the predictions from the individual models, in subdirectory outprdt, to obtain an averaged value (committee prediction). The output (in normalised form) is written to com.dat.

Program to un-normalise the committee results in com.dat and write the output predictions to unnorm_com. This file is then renamed Gresult or GPresult, depending on the module.

A text file containing the number of models to be used to form the committee result and the number of input variables. It is read by gencom.for, normtest.for and treatout.for.


The weights files for the different models.

Files containing information for calculating the size of the error bars for the different models.

Files containing information about the perceived significance value [1] for each model.

Files containing values for the noise, test error and log predictive error [1] for each model.


A normalised output file which was created during the building of the model. It is accessed by generate44 via spec.ys / spec.uts.


out1, out2 etc.
The normalised output files for each model.

The normalised output file containing the committee results. It is generated by gencom.for.


Detailed instructions on the use of the program are given in the README files. Further information about this suite of programs can be obtained from reference 1.

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  1. S. Yoshitake, H. Harada, H.K.D.H. Bhadeshia and D. J. C. MacKay, 1998, ISIJ International, 38 (1998) 495-502.
  2. D.J.C. MacKay, 1997, Mathematical Modelling of Weld Phenomena 3, eds. H Cerjak & H.K.D.H. Bhadeshia, Inst. of Materials, pp 359.
  3. D.J.C MacKay's website at http://wol.ra.phy.cam.ac.uk/mackay/README.html#Source_code
  4. F. Tancret et al., a series of three papers on Design of Nickel Superalloys, 2003

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Input parameters

The input variables for each module are listed in the README file in the corresponding directory. The maximum and minimum values for each variable are given in the file MINMAX.

Output parameters

These programs give the lattice parameters in Angstroms. The output files are called Gresult and GPresult. The format of the output file is:

Prediction    Error	Prediction -  Error	Prediction + Error

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Error Indicators


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A full calculation of the error bars is presented in reference 1.

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Further Comments


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1. Program text

       Complete program.

2. Program data

See sample data file: test.dat.

3. Program results

See sample output file: Gresult or GPresult.

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Auxiliary Routines


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lattice parameters, gamma, gamma-prime, nickel base superalloys

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Download gamma module
Download gamma-prime module

PC Software:
Download both modules

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MAP originated from a joint project of the National Physical Laboratory and the University of Cambridge.

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