Index: /issm/trunk-jpl/src/m/classes/adinversion.py =================================================================== --- /issm/trunk-jpl/src/m/classes/adinversion.py (revision 19379) +++ /issm/trunk-jpl/src/m/classes/adinversion.py (revision 19379) @@ -0,0 +1,202 @@ +""" +== == == == == == == == == == == == == == == == == == == +Auto generated python script for ISSM: /home/andrei/issm/trunk-jpl/src/m/classes/adinversion.m +Created on 2015-05-15 via translateToPy.py Ver 1.0 by andrei +== == == == == == == == == == == == == == == == == == == + +Matlab script conversion into python +translateToPy.py Author: Michael Pellegrin +translateToPy.py Date: 09/24/12 +== == == == == == == == == == == == == == == == == == == +""" + +from MatlabFuncs import * + +from EnumDefinitions import * +from numpy import * + +# ADINVERSION class definition + +# + +# Usage: + +# adinversion=adinversion(); + + + +class adinversion: + def __init__(self): + iscontrol = 0 + control_parameters = float('Nan') + control_scaling_factors = float('Nan') + maxsteps = 0 + maxiter = 0 + dxmin = 0 + gttol = 0 + cost_functions = float('Nan') + cost_functions_coefficients = float('Nan') + min_parameters = float('Nan') + max_parameters = float('Nan') + vx_obs = float('Nan') + vy_obs = float('Nan') + vz_obs = float('Nan') + vel_obs = float('Nan') + thickness_obs = float('Nan') + surface_obs = float('Nan') + + def setdefaultparameters(self): + + self.control_parameters=['FrictionCoefficient'] + + +# Scaling factor for each control + self.control_scaling_factors=1 + +# number of iterations + self.maxsteps=20 + self.maxiter=40 + +# several responses can be used: + self.cost_functions=['FrictionCoefficient'] + +# m1qn3 parameters + self.dxmin = 0.1 + self.gttol = 1e-4 + + return self + + def checkconsistency(self, md, solution, analyses): + +# Early return + if not self.iscontrol: + return + + if not IssmConfig('_HAVE_M1QN3_'): + md = checkmessage(md,['M1QN3 has not been installed, ISSM needs to be reconfigured and recompiled with AD']) + + + num_controls=numpy.numel(md.inversion.control_parameters) + num_costfunc=numpy.size(md.inversion.cost_functions,2) + + + md = checkfield(md,'fieldname','inversion.iscontrol','values',[0, 1]) + md = checkfield(md,'fieldname','inversion.control_parameters','cell',1,'values',\ + ['BalancethicknessThickeningRate' 'FrictionCoefficient' 'MaterialsRheologyBbar' 'DamageDbar',\ + 'Vx' 'Vy' 'Thickness' 'BalancethicknessOmega' 'BalancethicknessApparentMassbalance']) + md = checkfield(md,'fieldname','inversion.control_scaling_factors','size',[1, num_controls],'>',0,float('Nan'),1) + md = checkfield(md,'fieldname','inversion.maxsteps','numel',1,'>=',0) + md = checkfield(md,'fieldname','inversion.maxiter','numel',1,'>=',0) + md = checkfield(md,'fieldname','inversion.dxmin','numel',1,'>',0) + md = checkfield(md,'fieldname','inversion.gttol','numel',1,'>',0) + md = checkfield(md,'fieldname','inversion.cost_functions','size',[1, num_costfunc],'values', [i for i in range(101,106)]+[201]+[i for i in range(501,507)]+[i for i in range(601,605)]+[i for i in range(1001, 1011)]) + md = checkfield(md,'fieldname','inversion.cost_functions_coefficients','size',[md.mesh.numberofvertices, num_costfunc],'>=',0) + md = checkfield(md,'fieldname','inversion.min_parameters','size',[md.mesh.numberofvertices, num_controls]) + md = checkfield(md,'fieldname','inversion.max_parameters','size',[md.mesh.numberofvertices, num_controls]) + + + if solution==BalancethicknessSolutionEnum(): + md = checkfield(md,'fieldname','inversion.thickness_obs','size',[md.mesh.numberofvertices, 1],float('Nan'),1) + md = checkfield(md,'fieldname','inversion.surface_obs','size',[md.mesh.numberofvertices, 1], float('Nan'),1) + elif solution==BalancethicknessSoftSolutionEnum(): + md = checkfield(md,'fieldname','inversion.thickness_obs','size',[md.mesh.numberofvertices, 1],float('Nan'),1) + else: + md = checkfield(md,'fieldname','inversion.vx_obs','size',[md.mesh.numberofvertices, 1],float('Nan'),1) + if not numpy.strcmp(domaintype(md.mesh),'2Dvertical'): + md = checkfield(md,'fieldname','inversion.vy_obs','size',[md.mesh.numberofvertices, 1],float('Nan'),1) + return md + + def __repr__(self): + string = ' adinversion parameters:' + string ="%s\n\%s"%(string, fielddisplay(self,'iscontrol','is inversion activated?')) + string ="%s\n\%s"%(string, fielddisplay(self,'control_parameters','ex: [''FrictionCoefficient''], or [''MaterialsRheologyBbar'']')) + string ="%s\n\%s"%(string, fielddisplay(self,'control_scaling_factors','order of magnitude of each control (useful for multi-parameter optimization)')) + string ="%s\n\%s"%(string, fielddisplay(self,'maxsteps','maximum number of iterations (gradient computation)')) + string ="%s\n\%s"%(string, fielddisplay(self,'maxiter','maximum number of Function evaluation (forward run)')) + string ="%s\n\%s"%(string, fielddisplay(self,'dxmin','convergence criterion: two points less than dxmin from eachother (sup-norm) are considered identical')) + string ="%s\n\%s"%(string, fielddisplay(self,'gttol','convergence criterion: ||g(X)||/||g(X0)|| (g(X0): gradient at initial guess X0)')) + string ="%s\n\%s"%(string, fielddisplay(self,'cost_functions','indicate the type of response for each optimization step')) + string ="%s\n\%s"%(string, fielddisplay(self,'cost_functions_coefficients','cost_functions_coefficients applied to the misfit of each vertex and for each control_parameter')) + string ="%s\n\%s"%(string, fielddisplay(self,'min_parameters','absolute minimum acceptable value of the inversed parameter on each vertex')) + string ="%s\n\%s"%(string, fielddisplay(self,'max_parameters','absolute maximum acceptable value of the inversed parameter on each vertex')) + string ="%s\n\%s"%(string, fielddisplay(self,'vx_obs','observed velocity x component [m/yr]')) + string ="%s\n\%s"%(string, fielddisplay(self,'vy_obs','observed velocity y component [m/yr]')) + string ="%s\n\%s"%(string, fielddisplay(self,'vel_obs','observed velocity magnitude [m/yr]')) + string ="%s\n\%s"%(string, fielddisplay(self,'thickness_obs','observed thickness [m]')) + string ="%s\n\%s"%(string, fielddisplay(self,'surface_obs','observed surface elevation [m]')) + string ="%s\n%s"%(string,'Available cost functions:'); + string ="%s\n%s"%(string,' 101: SurfaceAbsVelMisfit'); + string ="%s\n%s"%(string,' 102: SurfaceRelVelMisfit'); + string ="%s\n%s"%(string,' 103: SurfaceLogVelMisfit'); + string ="%s\n%s"%(string,' 104: SurfaceLogVxVyMisfit'); + string ="%s\n%s"%(string,' 105: SurfaceAverageVelMisfit'); + string ="%s\n%s"%(string,' 201: ThicknessAbsMisfit'); + string ="%s\n%s"%(string,' 501: DragCoefficientAbsGradient'); + string ="%s\n%s"%(string,' 502: RheologyBbarAbsGradient'); + string ="%s\n%s"%(string,' 503: ThicknessAbsGradient'); + + return string + + def marshall(self): + + yts=365.0*24.0*3600.0; + + WriteData(fid,'object',self,'class','inversion','fieldname','iscontrol','format','Boolean'); + WriteData(fid,'enum',InversionTypeEnum(),'data',4,'format','Integer'); + if not self.iscontrol: + return + WriteData(fid,'object',self,'class','inversion','fieldname','control_scaling_factors','format','DoubleMat','mattype',3); + WriteData(fid,'object',self,'class','inversion','fieldname','maxsteps','format','Integer'); + WriteData(fid,'object',self,'class','inversion','fieldname','maxiter','format','Integer'); + WriteData(fid,'object',self,'class','inversion','fieldname','dxmin','format','Double'); + WriteData(fid,'object',self,'class','inversion','fieldname','gttol','format','Double'); + WriteData(fid,'object',self,'class','inversion','fieldname','cost_functions_coefficients','format','DoubleMat','mattype',1); + WriteData(fid,'object',self,'class','inversion','fieldname','min_parameters','format','DoubleMat','mattype',3); + WriteData(fid,'object',self,'class','inversion','fieldname','max_parameters','format','DoubleMat','mattype',3); + WriteData(fid,'object',self,'class','inversion','fieldname','vx_obs','format','DoubleMat','mattype',1,'scale',1./yts); + WriteData(fid,'object',self,'class','inversion','fieldname','vy_obs','format','DoubleMat','mattype',1,'scale',1./yts); + WriteData(fid,'object',self,'class','inversion','fieldname','vz_obs','format','DoubleMat','mattype',1,'scale',1./yts); + if(numel(self.thickness_obs)==md.mesh.numberofelements): + mattype=2; + else: + mattype=1; + + WriteData(fid,'object',self,'class','inversion','fieldname','thickness_obs','format','DoubleMat','mattype',mattype); + WriteData(fid,'object',self,'class','inversion','fieldname','surface_obs','format','DoubleMat','mattype',mattype); + + #process control parameters + num_control_parameters = numpy.numel(self.control_parameters); + data = numpy.array([StringToEnum(self.control_parameter[0]) for control_parameter in self.control_parameters]).reshape(1,-1) + + WriteData(fid,'data',data,'enum',InversionControlParametersEnum(),'format','DoubleMat','mattype',3); + WriteData(fid,'data',num_control_parameters,'enum',InversionNumControlParametersEnum(),'format','Integer'); + + #process cost functions + num_cost_functions=numpy.size(self.cost_functions,2); + data=copy.deepcopy(self.cost_functions) + data[numpy.nonzero(self.cost_functions==101)] =SurfaceAbsVelMisfitEnum(); + data[numpy.nonzero(self.cost_functions==102)]=SurfaceRelVelMisfitEnum(); + data[numpy.nonzero(self.cost_functions==103)]=SurfaceLogVelMisfitEnum(); + data[numpy.nonzero(self.cost_functions==104)]=SurfaceLogVxVyMisfitEnum(); + data[numpy.nonzero(self.cost_functions==105)]=SurfaceAverageVelMisfitEnum(); + data[numpy.nonzero(self.cost_functions==201)]=ThicknessAbsMisfitEnum(); + data[numpy.nonzero(self.cost_functions==501)]=DragCoefficientAbsGradientEnum(); + data[numpy.nonzero(self.cost_functions==502)]=RheologyBbarAbsGradientEnum(); + data[numpy.nonzero(self.cost_functions==503)]=ThicknessAbsGradientEnum(); + data[numpy.nonzero(self.cost_functions==504)]=ThicknessAlongGradientEnum(); + data[numpy.nonzero(self.cost_functions==505)]=ThicknessAcrossGradientEnum(); + data[numpy.nonzero(self.cost_functions==506)]=BalancethicknessMisfitEnum(); + data[numpy.nonzero(self.cost_functions==601)]=SurfaceAbsMisfitEnum(); + data[numpy.nonzero(self.cost_functions==1001)]=Outputdefinition1Enum(); + data[numpy.nonzero(self.cost_functions==1002)]=Outputdefinition2Enum(); + data[numpy.nonzero(self.cost_functions==1003)]=Outputdefinition3Enum(); + data[numpy.nonzero(self.cost_functions==1004)]=Outputdefinition4Enum(); + data[numpy.nonzero(self.cost_functions==1005)]=Outputdefinition5Enum(); + data[numpy.nonzero(self.cost_functions==1006)]=Outputdefinition6Enum(); + data[numpy.nonzero(self.cost_functions==1007)]=Outputdefinition7Enum(); + data[numpy.nonzero(self.cost_functions==1008)]=Outputdefinition8Enum(); + data[numpy.nonzero(self.cost_functions==1009)]=Outputdefinition8Enum(); + data[numpy.nonzero(self.cost_functions==1010)]=Outputdefinition10Enum(); + WriteData(fid,'data',data,'enum',InversionCostFunctionsEnum(),'format','DoubleMat','mattype',3); + WriteData(fid,'data',num_cost_functions,'enum',InversionNumCostFunctionsEnum(),'format','Integer'); + Index: /issm/trunk-jpl/src/m/classes/taoinversion.py =================================================================== --- /issm/trunk-jpl/src/m/classes/taoinversion.py (revision 19379) +++ /issm/trunk-jpl/src/m/classes/taoinversion.py (revision 19379) @@ -0,0 +1,200 @@ +import numpy +from project3d import project3d +from WriteData import WriteData +from checkfield import checkfield +from fielddisplay import fielddisplay +from IssmConfig import IssmConfig +from EnumDefinitions import * +from marshallcostfunctions import marshallcostfunctions + + +class taoinversion: + def __init__(self): + iscontrol = 0 + incomplete_adjoint = 0 + control_parameters = float('NaN') + maxsteps = 0 + maxiter = 0 + fatol = 0 + frtol = 0 + gatol = 0 + grtol = 0 + gttol = 0 + algorithm = '' + cost_functions = float('NaN') + cost_functions_coefficients = float('NaN') + min_parameters = float('NaN') + max_parameters = float('NaN') + vx_obs = float('NaN') + vy_obs = float('NaN') + vz_obs = float('NaN') + vel_obs = float('NaN') + thickness_obs = float('NaN') + surface_obs = float('NaN') + + def __repr__(self): + string = ' taoinversion parameters:' + string = "%s\n\%s"%(string, fieldstring(self,'iscontrol','is inversion activated?')) + string="%s\n%s"%(string,fieldstring(self,'mantle_viscosity','mantle viscosity constraints (NaN means no constraint) (Pa s)')) + string="%s\n%s"%(string,fieldstring(self,'lithosphere_thickness','lithosphere thickness constraints (NaN means no constraint) (m)')) + string="%s\n%s"%(string,fieldstring(self,'cross_section_shape',"1: square-edged, 2: elliptical-edged surface")) + string="%s\n%s"%(string,fieldstring(self,'incomplete_adjoint','1: linear viscosity, 0: non-linear viscosity')) + string="%s\n%s"%(string,fieldstring(self,'control_parameters','ex: {''FrictionCoefficient''}, or {''MaterialsRheologyBbar''}')) + string="%s\n%s"%(string,fieldstring(self,'maxsteps','maximum number of iterations (gradient computation)')) + string="%s\n%s"%(string,fieldstring(self,'maxiter','maximum number of Function evaluation (forward run)')) + string="%s\n%s"%(string,fieldstring(self,'fatol','convergence criterion: f(X)-f(X*) (X: current iteration, X*: "true" solution, f: cost function)')) + string="%s\n%s"%(string,fieldstring(self,'frtol','convergence criterion: |f(X)-f(X*)|/|f(X*)|')) + string="%s\n%s"%(string,fieldstring(self,'gatol','convergence criterion: ||g(X)|| (g: gradient of the cost function)')) + string="%s\n%s"%(string,fieldstring(self,'grtol','convergence criterion: ||g(X)||/|f(X)|')) + string="%s\n%s"%(string,fieldstring(self,'gttol','convergence criterion: ||g(X)||/||g(X0)|| (g(X0): gradient at initial guess X0)')) + string="%s\n%s"%(string,fieldstring(self,'algorithm','minimization algorithm: ''tao_blmvm'', ''tao_cg'', ''tao_lmvm''')) + string="%s\n%s"%(string,fieldstring(self,'cost_functions','indicate the type of response for each optimization step')) + string="%s\n%s"%(string,fieldstring(self,'cost_functions_coefficients','cost_functions_coefficients applied to the misfit of each vertex and for each control_parameter')) + string="%s\n%s"%(string,fieldstring(self,'min_parameters','absolute minimum acceptable value of the inversed parameter on each vertex')) + string="%s\n%s"%(string,fieldstring(self,'max_parameters','absolute maximum acceptable value of the inversed parameter on each vertex')) + string="%s\n%s"%(string,fieldstring(self,'vx_obs','observed velocity x component [m/yr]')) + string="%s\n%s"%(string,fieldstring(self,'vy_obs','observed velocity y component [m/yr]')) + string="%s\n%s"%(string,fieldstring(self,'vel_obs','observed velocity magnitude [m/yr]')) + string="%s\n%s"%(string,fieldstring(self,'thickness_obs','observed thickness [m]')) + string="%s\n%s"%(string,fieldstring(self,'surface_obs','observed surface elevation [m]')) + string="%s\n%s"%(string,'Available cost functions:') + string="%s\n%s"%(string, ' 101: SurfaceAbsVelMisfit') + string="%s\n%s"%(string, ' 102: SurfaceRelVelMisfit') + string="%s\n%s"%(string, ' 103: SurfaceLogVelMisfit') + string="%s\n%s"%(string, ' 104: SurfaceLogVxVyMisfit') + string="%s\n%s"%(string, ' 105: SurfaceAverageVelMisfit') + string="%s\n%s"%(string, ' 201: ThicknessAbsMisfit') + string="%s\n%s"%(string, ' 501: DragCoefficientAbsGradient') + string="%s\n%s"%(string, ' 502: RheologyBbarAbsGradient') + string="%s\n%s"%(string, ' 503: ThicknessAbsGradient') + return string + def setdefaultparameters(self): + + #default is incomplete adjoint for now + self.incomplete_adjoint=1 + + #parameter to be inferred by control methods (only + #drag and B are supported yet) + self.control_parameters=['FrictionCoefficient'] + + #number of iterations and steps + self.maxsteps=20; + self.maxiter =30; + + #default tolerances + self.fatol = 0; + self.frtol = 0; + self.gatol = 0; + self.grtol = 0; + self.gttol = 1e-4; + + #minimization algorithm + PETSCMAJOR = IssmConfig('_PETSC_MAJOR_') + PETSCMINOR = IssmConfig('_PETSC_MINOR_') + if(PETSCMAJOR>3 or (PETSCMAJOR==3 and PETSCMINOR>=5)): + self.algorithm = 'blmvm'; + else: + self.algorithm = 'tao_blmvm'; + + #several responses can be used: + self.cost_functions=101; + + return self + + def extrude(self,md): + self.vx_obs=project3d(md,'vector',self.vx_obs,'type','node') + self.vy_obs=project3d(md,'vector',self.vy_obs,'type','node') + self.vel_obs=project3d(md,'vector',self.vel_obs,'type','node') + self.thickness_obs=project3d(md,'vector',self.thickness_obs,'type','node') + + if numel(self.cost_functions_coefficients) > 1: + self.cost_functions_coefficients=project3d(md,'vector',self.cost_functions_coefficients,'type','node') + + if numel(self.min_parameters) > 1: + self.min_parameters=project3d(md,'vector',self.min_parameters,'type','node') + + if numel(self.max_parameters)>1: + self.max_parameters=project3d(md,'vector',self.max_parameters,'type','node') + + return self + + def checkconsistency(self,md,solution,analyses): + if not self.control: + return md + if not IssmConfig('_HAVE_TAO_'): + md = checkmessage(md,['TAO has not been installed, ISSM needs to be reconfigured and recompiled with TAO']) + + + num_controls= numpy.numel(md.inversion.control_parameters) + num_costfunc= numpy.size(md.inversion.cost_functions,2) + + md = checkfield(md,'fieldname','inversion.iscontrol','values',[0, 1]) + md = checkfield(md,'fieldname','inversion.incomplete_adjoint','values',[0, 1]) + md = checkfield(md,'fieldname','inversion.control_parameters','cell',1,'values',supportedcontrols()) + md = checkfield(md,'fieldname','inversion.maxsteps','numel',1,'>=',0) + md = checkfield(md,'fieldname','inversion.maxiter','numel',1,'>=',0) + md = checkfield(md,'fieldname','inversion.fatol','numel',1,'>=',0) + md = checkfield(md,'fieldname','inversion.frtol','numel',1,'>=',0) + md = checkfield(md,'fieldname','inversion.gatol','numel',1,'>=',0) + md = checkfield(md,'fieldname','inversion.grtol','numel',1,'>=',0) + md = checkfield(md,'fieldname','inversion.gttol','numel',1,'>=',0) + + + PETSCMAJOR = IssmConfig('_PETSC_MAJOR_') + PETSCMINOR = IssmConfig('_PETSC_MINOR_') + if(PETSCMAJOR>3 or (PETSCMAJOR==3 and PETSCMINOR>=5)): + md = checkfield(md,'fieldname','inversion.algorithm','values',{'blmvm','cg','lmvm'}) + else: + md = checkfield(md,'fieldname','inversion.algorithm','values',{'tao_blmvm','tao_cg','tao_lmvm'}) + + + md = checkfield(md,'fieldname','inversion.cost_functions','size',[1, num_costfunc],'values',supportedcostfunctions()) + md = checkfield(md,'fieldname','inversion.cost_functions_coefficients','size',[md.mesh.numberofvertices, num_costfunc],'>=',0) + md = checkfield(md,'fieldname','inversion.min_parameters','size',[md.mesh.numberofvertices, num_controls]) + md = checkfield(md,'fieldname','inversion.max_parameters','size',[md.mesh.numberofvertices, num_controls]) + + + if solution==BalancethicknessSolutionEnum(): + md = checkfield(md,'fieldname','inversion.thickness_obs','size',[md.mesh.numberofvertices, 1],'NaN',1) + elif solution==BalancethicknessSoftSolutionEnum(): + md = checkfield(md,'fieldname','inversion.thickness_obs','size',[md.mesh.numberofvertices, 1],'NaN',1) + else: + md = checkfield(md,'fieldname','inversion.vx_obs','size',[md.mesh.numberofvertices, 1],'NaN',1) + md = checkfield(md,'fieldname','inversion.vy_obs','size',[md.mesh.numberofvertices, 1],'NaN',1) + + def marshall(self, md, fid): + + yts=365.0*24.0*3600.0; + WriteData(fid,'object',self,'class','inversion','fieldname','iscontrol','format','Boolean') + WriteData(fid,'enum',InversionTypeEnum(),'data',1,'format','Integer') + if not self.iscontrol: + return + WriteData(fid,'object',self,'class','inversion','fieldname','incomplete_adjoint','format','Boolean') + WriteData(fid,'object',self,'class','inversion','fieldname','maxsteps','format','Integer') + WriteData(fid,'object',self,'class','inversion','fieldname','maxiter','format','Integer') + WriteData(fid,'object',self,'class','inversion','fieldname','fatol','format','Double') + WriteData(fid,'object',self,'class','inversion','fieldname','frtol','format','Double') + WriteData(fid,'object',self,'class','inversion','fieldname','gatol','format','Double') + WriteData(fid,'object',self,'class','inversion','fieldname','grtol','format','Double') + WriteData(fid,'object',self,'class','inversion','fieldname','gttol','format','Double') + WriteData(fid,'object',self,'class','inversion','fieldname','algorithm','format','String') + WriteData(fid,'object',self,'class','inversion','fieldname','cost_functions_coefficients','format','DoubleMat','mattype',1) + WriteData(fid,'object',self,'class','inversion','fieldname','min_parameters','format','DoubleMat','mattype',3) + WriteData(fid,'object',self,'class','inversion','fieldname','max_parameters','format','DoubleMat','mattype',3) + WriteData(fid,'object',self,'class','inversion','fieldname','vx_obs','format','DoubleMat','mattype',1,'scale',1./yts) + WriteData(fid,'object',self,'class','inversion','fieldname','vy_obs','format','DoubleMat','mattype',1,'scale',1./yts) + WriteData(fid,'object',self,'class','inversion','fieldname','vz_obs','format','DoubleMat','mattype',1,'scale',1./yts) + WriteData(fid,'object',self,'class','inversion','fieldname','thickness_obs','format','DoubleMat','mattype',1) + WriteData(fid,'object',self,'class','inversion','fieldname','surface_obs','format','DoubleMat','mattype',1) + + #process control parameters + num_control_parameters = numpy.numel(self.control_parameters) + data = numpy.array([StringToEnum(self.control_parameter[0]) for control_parameter in self.control_parameters]).reshape(1,-1) + WriteData(fid,'data',data,'enum',InversionControlParametersEnum(),'format','DoubleMat','mattype',3) + WriteData(fid,'data',num_control_parameters,'enum',InversionNumControlParametersEnum(),'format','Integer') + + #process cost functions + num_cost_functions = numpy.size(self.cost_functions,2) + data= marshallcostfunctions(self.cost_functions) + WriteData(fid,'data',data,'enum',InversionCostFunctionsEnum(),'format','DoubleMat','mattype',3) + WriteData(fid,'data',num_cost_functions,'enum',InversionNumCostFunctionsEnum(),'format','Integer')