UQTk: Uncertainty Quantification Toolkit 3.1.5
Functions
func.h File Reference

Header for implementation of functions of form $y=f(\lambda;x)$. More...

#include "Array1D.h"
#include "Array2D.h"
#include <iostream>
#include <string.h>
#include <stdio.h>
#include <sstream>

Go to the source code of this file.

Functions

Array2D< double > Func_Prop (Array2D< double > &p, Array2D< double > &x, Array2D< double > &fixindnom, void *funcinfo)
 $y=f(\lambda;x)=\lambda x$ for $x\in\mathbf{R}^1$ and $\lambda\in\mathbf{R}^1$
 
Array2D< double > Func_PropQuad (Array2D< double > &p, Array2D< double > &x, Array2D< double > &fixindnom, void *funcinfo)
 $y=f(\lambda;x)=\lambda_1 x+\lambda_2x^2$ for $x\in\mathbf{R}^1$ and $\lambda\in\mathbf{R}^2$
 
Array2D< double > Func_Exp (Array2D< double > &p, Array2D< double > &x, Array2D< double > &fixindnom, void *funcinfo)
 $y=f(\lambda;x)=e^{\lambda_1 +\lambda_2x}$ for $x\in\mathbf{R}^1$ and $\lambda\in\mathbf{R}^2$
 
Array2D< double > Func_ExpQuad (Array2D< double > &p, Array2D< double > &x, Array2D< double > &fixindnom, void *funcinfo)
 $y=f(\lambda;x)=e^{\lambda_1 +\lambda_2x+\lambda_3x^2}$ for $x\in\mathbf{R}^1$ and $\lambda\in\mathbf{R}^3$
 
Array2D< double > Func_Const (Array2D< double > &p, Array2D< double > &x, Array2D< double > &fixindnom, void *funcinfo)
 $y=f(\lambda;x)=\lambda$ for $x\in\mathbf{R}^s$ and $\lambda\in\mathbf{R}^1$
 
Array2D< double > Func_Linear (Array2D< double > &p, Array2D< double > &x, Array2D< double > &fixindnom, void *funcinfo)
 $y=f(\lambda;x)=\lambda_1+\lambda_2x$ for $x\in\mathbf{R}^1$ and $\lambda\in\mathbf{R}^2$
 
Array2D< double > Func_BB (Array2D< double > &p, Array2D< double > &x, Array2D< double > &fixindnom, void *funcinfo)
 $y=f(\lambda;x)$ a black-box function with a script bb.x which takes p.dat and x.dat and returns output in y.dat
 
Array2D< double > Func_HT1 (Array2D< double > &p, Array2D< double > &x, Array2D< double > &fixindnom, void *funcinfo)
 Heat_transfer1: a custom model designed for a tutorial case of a heat conduction problem.
 
Array2D< double > Func_HT2 (Array2D< double > &p, Array2D< double > &x, Array2D< double > &fixindnom, void *funcinfo)
 Heat_transfer2: a custom model designed for a tutorial case of a heat conduction problem.
 
Array2D< double > Func_FracPower (Array2D< double > &p, Array2D< double > &x, Array2D< double > &fixindnom, void *funcinfo)
 $y=f(\lambda;x)=\lambda_1+\lambda_2 x+\lambda_3 x^2+ \lambda_4 (x+1)^{3.5}$ for $x\in\mathbf{R}^1$ and $\lambda\in\mathbf{R}^4$
 
Array2D< double > Func_ExpSketch (Array2D< double > &p, Array2D< double > &x, Array2D< double > &fixindnom, void *funcinfo)
 $y=f(\lambda;x)=\lambda_2 e^{\lambda_1 x} - 2$ for $x\in\mathbf{R}^1$ and $\lambda\in\mathbf{R}^2$
 
Array2D< double > Func_Inputs (Array2D< double > &p, Array2D< double > &x, Array2D< double > &fixindnom, void *funcinfo)
 $y=f(\lambda;x_i)=\lambda_i$ for $i=1,...,d$, $x_i\in\mathbf{R}^1$ and $\lambda\in\mathbf{R}^d$
 
Array2D< double > Func_PCl (Array2D< double > &p, Array2D< double > &x, Array2D< double > &fixindnom, void *funcinfo)
 Legendre PC expansion with $\lambda$'s as coefficients.
 
Array2D< double > Func_PCx (Array2D< double > &p, Array2D< double > &x, Array2D< double > &fixindnom, void *funcinfo)
 Legendre PC expansion with respect to $z=(\lambda,x)$.
 
Array2D< double > Func_PC (Array2D< double > &p, Array2D< double > &x, Array2D< double > &fixindnom, void *funcinfo)
 Legendre PC expansion for each value of $x$.
 
Array2D< double > Func_PCs (Array2D< double > &p, Array2D< double > &x, Array2D< double > &fixindnom, void *funcinfo)
 Legendre PC expansion for each value of $x$.
 
Array2D< double > augment (Array2D< double > &p, Array2D< double > &fixindnom)
 Augments a parameter matrix with 'fixed' columns given indices and nominal values of those.
 

Detailed Description

Header for implementation of functions of form $y=f(\lambda;x)$.

Note
Functions of form $y=f(\lambda;x)$ for $x\in\mathbf{R}^s$ and $\lambda\in\mathbf{R}^d$ at $r$ values of model parameters $\lambda$ and $n$ values of design parameters $x$
Parameters
pModel parameters $\lambda$ as a matrix $r\times d$
xDesign parameters $x$ as a matrix $n\times s$
*funcinfoPotentially function-specific information
Returns
y Output as a matrix $r\times n$

Function Documentation

◆ augment()

Array2D< double > augment ( Array2D< double > & p,
Array2D< double > & fixindnom )

Augments a parameter matrix with 'fixed' columns given indices and nominal values of those.

◆ Func_BB()

Array2D< double > Func_BB ( Array2D< double > & p,
Array2D< double > & x,
Array2D< double > & fixindnom,
void * funcinfo )

$y=f(\lambda;x)$ a black-box function with a script bb.x which takes p.dat and x.dat and returns output in y.dat

◆ Func_Const()

Array2D< double > Func_Const ( Array2D< double > & p,
Array2D< double > & x,
Array2D< double > & fixindnom,
void * funcinfo )

$y=f(\lambda;x)=\lambda$ for $x\in\mathbf{R}^s$ and $\lambda\in\mathbf{R}^1$

◆ Func_Exp()

Array2D< double > Func_Exp ( Array2D< double > & p,
Array2D< double > & x,
Array2D< double > & fixindnom,
void * funcinfo )

$y=f(\lambda;x)=e^{\lambda_1 +\lambda_2x}$ for $x\in\mathbf{R}^1$ and $\lambda\in\mathbf{R}^2$

◆ Func_ExpQuad()

Array2D< double > Func_ExpQuad ( Array2D< double > & p,
Array2D< double > & x,
Array2D< double > & fixindnom,
void * funcinfo )

$y=f(\lambda;x)=e^{\lambda_1 +\lambda_2x+\lambda_3x^2}$ for $x\in\mathbf{R}^1$ and $\lambda\in\mathbf{R}^3$

◆ Func_ExpSketch()

Array2D< double > Func_ExpSketch ( Array2D< double > & p,
Array2D< double > & x,
Array2D< double > & fixindnom,
void * funcinfo )

$y=f(\lambda;x)=\lambda_2 e^{\lambda_1 x} - 2$ for $x\in\mathbf{R}^1$ and $\lambda\in\mathbf{R}^2$

◆ Func_FracPower()

Array2D< double > Func_FracPower ( Array2D< double > & p,
Array2D< double > & x,
Array2D< double > & fixindnom,
void * funcinfo )

$y=f(\lambda;x)=\lambda_1+\lambda_2 x+\lambda_3 x^2+ \lambda_4 (x+1)^{3.5}$ for $x\in\mathbf{R}^1$ and $\lambda\in\mathbf{R}^4$

◆ Func_HT1()

Array2D< double > Func_HT1 ( Array2D< double > & p,
Array2D< double > & x,
Array2D< double > & fixindnom,
void * funcinfo )

Heat_transfer1: a custom model designed for a tutorial case of a heat conduction problem.

$y=f(\lambda;x)=\frac{x d_w}{A_w \lambda}+T_0$ for $x\in\mathbf{R}^1$ and $\lambda\in\mathbf{R}^1$

Note
hardwired parameters: $d_w=0.1, A_w=0.04, T_0=273$

◆ Func_HT2()

Array2D< double > Func_HT2 ( Array2D< double > & p,
Array2D< double > & x,
Array2D< double > & fixindnom,
void * funcinfo )

Heat_transfer2: a custom model designed for a tutorial case of a heat conduction problem.

$y=f(\lambda;x)=\frac{x Q}{A_w \lambda_1}+\lambda_2$ for $x\in\mathbf{R}^1$ and $\lambda\in\mathbf{R}^2$

Note
hardwired parameters: $A_w=0.04, Q=20.0$

◆ Func_Inputs()

Array2D< double > Func_Inputs ( Array2D< double > & p,
Array2D< double > & x,
Array2D< double > & fixindnom,
void * funcinfo )

$y=f(\lambda;x_i)=\lambda_i$ for $i=1,...,d$, $x_i\in\mathbf{R}^1$ and $\lambda\in\mathbf{R}^d$

◆ Func_Linear()

Array2D< double > Func_Linear ( Array2D< double > & p,
Array2D< double > & x,
Array2D< double > & fixindnom,
void * funcinfo )

$y=f(\lambda;x)=\lambda_1+\lambda_2x$ for $x\in\mathbf{R}^1$ and $\lambda\in\mathbf{R}^2$

◆ Func_PC()

Array2D< double > Func_PC ( Array2D< double > & p,
Array2D< double > & x,
Array2D< double > & fixindnom,
void * funcinfo )

Legendre PC expansion for each value of $x$.

$y=f(\lambda;x^{(i)})=\sum_{\alpha\in{\cal S}} c_{\alpha,i} \Psi_\alpha(\lambda)$ for $x\in\mathbf{R}^s$ and $\lambda\in\mathbf{R}^d$

Note
hardwired parameters: common multiindex set for all PCs ${\cal S}$ is given in a file mindexp.dat, coefficients $c_{\alpha,i}$ are given in a file pccf_all.dat

◆ Func_PCl()

Array2D< double > Func_PCl ( Array2D< double > & p,
Array2D< double > & x,
Array2D< double > & fixindnom,
void * funcinfo )

Legendre PC expansion with $\lambda$'s as coefficients.

$y=f(\lambda;x)=\sum_{\alpha\in{\cal S}} \lambda_\alpha \Psi_\alpha(x)$ for $x\in\mathbf{R}^s$ and $\lambda\in\mathbf{R}^{|{\cal S}|}$

Note
hardwired parameter: multiindex set ${\cal S}$ is given in a file mindexx.dat

◆ Func_PCs()

Array2D< double > Func_PCs ( Array2D< double > & p,
Array2D< double > & x,
Array2D< double > & fixindnom,
void * funcinfo )

Legendre PC expansion for each value of $x$.

$y=f(\lambda;x^{(i)})=\sum_{\alpha\in{\cal S}_i} c_{\alpha,i} \Psi_\alpha(\lambda)$ for $x\in\mathbf{R}^s$ and $\lambda\in\mathbf{R}^d$

Note
hardwired parameters: multiindex sets for all PCs ${\cal S}$ are given in files mindexp.i.dat, coefficients $c_{\alpha,i}$ are given in files pccfp.i.dat

◆ Func_PCx()

Array2D< double > Func_PCx ( Array2D< double > & p,
Array2D< double > & x,
Array2D< double > & fixindnom,
void * funcinfo )

Legendre PC expansion with respect to $z=(\lambda,x)$.

$y=f(\lambda;x)=\sum_{\alpha\in{\cal S}} c_\alpha \Psi_\alpha(\lambda,x)$ for $x\in\mathbf{R}^s$ and $\lambda\in\mathbf{R}^d$

Note
hardwired parameters: multiindex set ${\cal S}$ is given in a file mindexpx.dat, coefficients $c_\alpha$ given in a file pccfpx.dat

◆ Func_Prop()

Array2D< double > Func_Prop ( Array2D< double > & p,
Array2D< double > & x,
Array2D< double > & fixindnom,
void * funcinfo )

$y=f(\lambda;x)=\lambda x$ for $x\in\mathbf{R}^1$ and $\lambda\in\mathbf{R}^1$

◆ Func_PropQuad()

Array2D< double > Func_PropQuad ( Array2D< double > & p,
Array2D< double > & x,
Array2D< double > & fixindnom,
void * funcinfo )

$y=f(\lambda;x)=\lambda_1 x+\lambda_2x^2$ for $x\in\mathbf{R}^1$ and $\lambda\in\mathbf{R}^2$

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