polychaos — A class to manage a Polynomial Chaos expansion.
pc = polychaos_new ( file )
pc = polychaos_new ( srv , ny )
pc = polychaos_new ( pc , nopt , varopt )
polychaos_destroy (pc)
polychaos_setsizetarget ( pc , np )
np = polychaos_getsizetarget ( pc )
polychaos_settarget ( pc , k , j , output )
polychaos_settarget ( pc , k , output )
polychaos_settarget ( pc , output )
output = polychaos_gettarget ( pc , k , j )
output = polychaos_gettarget ( pc , k )
output = polychaos_gettarget ( pc )
polychaos_freememtarget ( pc )
polychaos_readtarget ( pc , file )
polychaos_setdegree ( pc , no )
no = polychaos_getdegree ( pc )
polychaos_setdimoutput ( pc , ny )
ny = polychaos_getdimoutput ( pc )
nx = polychaos_getdiminput ( pc )
p = polychaos_getdimexp ( pc )
polychaos_computeexp ( pc , srv , method )
polychaos_computeexp ( pc , pc2 , invalue , varopt )
polychaos_getmean ( pc , ovar )
polychaos_getmean ( pc )
polychaos_getvariance ( pc , ovar )
polychaos_getvariance ( pc )
polychaos_getindextotal ( pc , ivar , ovar )
polychaos_getindextotal ( pc , ivar )
polychaos_getindextotal ( pc )
polychaos_getindexfirst ( pc , ivar , ovar )
polychaos_getindexfirst ( pc , ivar )
polychaos_getindexfirst ( pc )
polychaos_getcovariance ( pc , ovar1 , ovar2 )
polychaos_getcovariance ( pc )
polychaos_getcorrelation ( pc , ovar1 , ovar2 )
polychaos_getcorrelation ( pc )
polychaos_buildsample ( pc , type , np , order )
polychaos_getsample ( pc , k , ovar )
polychaos_getsample ( pc , k )
polychaos_getsample ( pc )
polychaos_setgroupempty ( pc )
polychaos_setgroupaddvar ( pc , ivar )
polychaos_getgroupinter ( pc , ovar )
polychaos_getgroupinter ( pc )
polychaos_getgroupind ( pc , ovar )
polychaos_getgroupind ( pc )
polychaos_getquantile ( pc , k )
polychaos_getquantile ( pc , alpha , ovar )
polychaos_getquantile ( pc , alpha )
polychaos_getquantwilks ( pc , walpha , wbeta , ovar )
polychaos_getquantwilks ( pc , walpha , wbeta )
polychaos_getinvquantile ( pc , threshold , ovar )
polychaos_getinvquantile ( pc , threshold )
polychaos_realisation ( pc )
polychaos_getlog ( pc )
polychaos_getmultind ( pc )
polychaos_getanovaordco ( pc , threshold , r )
polychaos_getanovaordco ( pc , threshold )
polychaos_getanovaord ( pc )
polychaos_getanova ( pc )
polychaos_getanova ( pc , r )
The polychaos_new function allows to create a new polynomial. The polychaos_destroy function allows to destroy an existing polynomial.
The polychaos_new function returns a token which is a unique identifier for the new polynomial. Indeed, when a new polynomial is created, a counter is updated which corresponds to the returned token. This way, each token is unique and can correspond only to one single polynomial.
The functions polychaos_tokens and polychaos_size allow to manage the polynomials which have already been created. The function polychaos_size returns the number of polynomials, while the polychaos_tokens function returns the list of current polynomials.
Returns a 1-by-n matrix of floating point integers representing the current polychaos tokens, where n is the number of tokens.
Returns a 1-by-1 matrix containing the current number of polychaos tokens currently in use, where n is the number of tokens.
Creates a new PolynomialChaos based on given SetRandomVariable srv and number of output ny.
Create a new polychaos from another polychaos and an array of integers varopt with size nopt (to deal with optimisation with uncertainties)
Creates a new polychaos from a data file.
Destroys the current polynomial.
Set the number of experiments to np.
Returns the number of experiments.
Set the output value for experiment #k and output #j, where 1 ≤ k ≤ np and 1 ≤ j ≤ ny
Set the output for experiment #k to the matrix output, where 1 ≤ k ≤ np, where np is the number of experiments and output is a matrix with size 1 x (ny), where ny is the number of output random variables.
Set the output matrix where output is a matrix with size (np) x (ny), where np is the number of experiments and ny is the number of ouput random variables.
Returns the output value for experiment #k and input random variable #j, where 1 ≤ k ≤ np and 1 ≤ j ≤ nx
returns the output value for experiment #k and input #j, where 1 ≤ k ≤ np where output is a 1 x (nx) matrix with nx the number of input random variables.
Returns the output matrix as a (np) x (nx) matrix, where np is the number of experiments and nx is the number of input random variables.
Free the memory associated with the output of the experiments.
Read the output of the experiments from the file.
Set the degree of the polynomial.
Returns the degree of the polynomial.
Set the number of output random variables to ny.
Returns the number of output random variables.
Returns the number of input random variables.
Returns the dimension of the expansion.
Computes the coefficients of the polynomial chaos expansion where srv is a setrandvar token and method is a string representing the computation algorithm.
The list of possible values for the string method is :
"Integration"
"Regression"
Compute the coefficient of pc based on another polynomial chaos pc2, by setting some input variables which indices are given in varopt to a constant value given in invalue. The polynomial pc2 has n variables while pc has n-nopt variables where nopt < n. The variables invalue and varopt should both be column vectors, with the same number of rows nopt. The invalue variable contains input values of the stochastic variable x, while the variable varopt contains input variable indices.
Returns the mean of the output variable which index is ovar, where 1 ≤ ovar ≤ ny, where ny is the number of output random variables.
Returns the mean of the all output variables, as a 1 x (ny) matrix, where ny is the number of output random variables.
Returns the variance of the output variable which index is ovar, where 1 ≤ ovar ≤ ny.
Returns the variance of the all output variables, as a 1 x (ny) matrix, where ny is the number of output random variables.
Returns the total index for the input variable #ivar and the output variable #ovar, where 1≤ ivar ≤ nx with nx the number of input random variables and 1 ≤ ovar ≤ ny with ny the number of output random variables.
Returns the total index of the input variable #ivar and the output variable #ovar=1, where 1 ≤ ivar ≤ nx with nx the number of input random variables.
Returns all total indices, as a (nx) x (ny) matrix with nx the number of input random variables and ny the number of output random variables.
Returns the first index order of the input variable #ivar and the output variable #ovar, where 1 ≤ ivar ≤ nx and 1 ≤ ovar ≤ ny, with nx the number of input random variables and ny the number of output random variables.
Returns the first index order of the input variable #ivar and the output variable #ovar=1, where 1 ≤ ivar ≤ nx, with nx the number of input random variables.
returns all first index order indices, as a (nx) x (ny) matrix, with nx the number of input random variables and ny the number of output random variables.
returns the covariance of the output random variables #ovar1 and #ovar2, where 1 ≤ ovar1, ovar2 ≤ ny, where ny is the number of output random variables.
Returns the covariance of the all output variables, as a (ny) x (ny) matrix, where ny is the number of output random variables.
returns the correlation of the output random variables #ovar1 and #ovar2, where 1 ≤ ovar1, ovar2 ≤ ny, where ny is the number of output random variables.
Returns the correlation of the all output variables, as a (ny) x (ny) matrix, where ny is the number of output random variables.
Build an internal sampling of given type with size np. If order=0 sample is not ordered else sample is ordered to prepare its using for quantile calculation.
The list of possible values for the input argument "type" is the following.
"MonteCarlo"
"Lhs"
"QmcSobol"
Returns the sample of experiment #k, where 1 ≤ k ≤ np, for output variable #ovar, where 1 ≤ ovar ≤ ny
Returns the sample of experiment #k, where 1 ≤ k ≤ np, as a (1) x ny matrix, where ny is the number of output random variables.
Returns the sampling as a (np) x (ny) matrix, where np is the number of experiments and ny is the number of output random variables.
Setup an empty group of input random variables.
Adds an input variable ivar to the group, with 1 ≤ ivar ≤ nx, where nx is the number of input random variables.
Returns the interaction indice of an output variable ovar, where 1 ≤ ovar ≤ ny, where ny is the number of output random variables.
Returns all interaction indices, as a 1 x (ny) matrix, where ny is the number of output random variables.
Returns the sensitivity indice of an output variable ovar, where 1 ≤ ovar ≤ ny, where ny is the number of output random variables.
Returns all sensitivity indices, as a 1 x (ny) matrix, where ny is the number of output random variables.
Generates the source code to compute the polynomial chaos into the file filename. The generated function name is funname.
Saves the polynomial chaos into file.
Compute the output as a 1-by-ny matrix of doubles,
depending on the input as a 1-by-nx matrix of doubles.
Evaluates the value of the chaos polynomial (uses it as a meta-model).
Returns the quantile of order alpha for output random variable #ovar, where 1 ≤ ovar ≤ ny, where ny is the number of output random variables.
Returns the quantiles of order alpha for all output variables, as a (1) x ny matrix, where ny is the number of output random variables.
Returns the Wilks quantile of order alpha with confidence beta for output variable #ovar, where 1 ≤ ovar ≤ ny
Returns the Wilks quantiles of order alpha with confidence beta for all output variables, as a (1) x ny matrix, where ny is the number of output random variables.
Returns the probability of having an output variable ovar over a given threshold, where 1 ≤ ovar ≤ ny with ny the number of output random variables.
returns the probability of having an output variable over a given threshold, as a 1 x (ny) matrix with ny the number of output random variables.
A realisation of the polynomial chaos viewed as a random variable. The scalar value is obtained via value=polychaos_getoutput(pc,ovar) where 1 ≤ ovar ≤ ny or as a vector with value=polychaos_getoutput(pc)
Prints out a log of current polynomial.
Prints the multiple indices.
Prints out the anova ordered coefficients until the fraction of the variance is less of threshold for the output of rank ovar with 1 ≤ ovar ≤ ny
Prints out the anova ordered coefficients until the fraction of the variance is less of threshold for the first output.
Prints out the anova ordered coefficients.
Prints out the anova for the first output.
Prints out the anova for the output of rank ovar with 1 ≤ ovar ≤ ny
function y = Exemple (x)
y(1) = x(1) * x(2);
endfunction
// 1. Two stochastic (normalized) variables
vx1 = randvar_new("Normale");
vx2 = randvar_new("Uniforme");
// 2. A collection of stoch. variables.
srvx = setrandvar_new();
setrandvar_addrandvar ( srvx,vx1);
setrandvar_addrandvar ( srvx,vx2);
// 3. Two uncertain parameters
vu1 = randvar_new("Normale",1.0,0.5);
vu2 = randvar_new("Uniforme",1.0,2.5);
// 4. A collection of uncertain parameters
srvu = setrandvar_new();
setrandvar_addrandvar ( srvu,vu1);
setrandvar_addrandvar ( srvu,vu2);
// 5. Create the Design Of Experiments
degre = 2;
setrandvar_buildsample(srvx,"Quadrature",degre);
setrandvar_buildsample( srvu , srvx );
// 6. Create the polynomial
ny = 1;
pc = polychaos_new ( srvx , ny );
np = setrandvar_getsize(srvx);
polychaos_setsizetarget(pc,np);
// 7. Perform the DOE
for k=1:np
inputdata = setrandvar_getsample(srvu,k);
outputdata = Exemple(inputdata);
polychaos_settarget(pc,k,outputdata);
end
// 8. Compute the coefficients of the polynomial expansion
polychaos_setdegree(pc,degre);
polychaos_computeexp(pc,srvx,"Integration");
// 9. Get the sensitivity indices
average = polychaos_getmean(pc);
var = polychaos_getvariance(pc);
mprintf("Mean = %f\n",average);
mprintf("Variance = %f\n",var);
mprintf("First order sensitivity indices\n");
mprintf(" Variable X1 = %f\n",polychaos_getindexfirst(pc,1));
mprintf(" Variable X2 = %f\n",polychaos_getindexfirst(pc,2));
mprintf("Total sensitivity indices\n");
mprintf(" Variable X1 = %f\n",polychaos_getindextotal(pc,1));
mprintf(" Variable X2 = %f\n",polychaos_getindextotal(pc,2));
// Clean-up
polychaos_destroy(pc);
randvar_destroy(vu1);
randvar_destroy(vu2);
randvar_destroy(vx1);
randvar_destroy(vx2);
setrandvar_destroy(srvu);
setrandvar_destroy(srvx);