Problem Two Statement $$ Polymorphism, Abstract Class and Operator Overloading

The context of problem two is about tensors. Tensors are data structures that generalize the concepts of vectors and matrices for an arbitrary number of dimensions. The number of different dimensions of a tensor is also called tensor rank.

#ifndef BASETENSOR$\_$H$\_$

#define BASETENSOR$\_$H$\_$

#include

#include

$//$ Base class for all tensors

class BaseTensor $\{$

public:

$/**$

$*$ Virtual method for load data to a tensor;

$*$ Given the dimensions are different for each type

$*$ of tensor, the loadData$()$ function to initialize

$*$ the values of a tensor should overriden by

$*$ derived tensor classes;

$*/$

virtual void loadData$()=0$;

$/**$

$*$ virtual for valueGen$()$ is optional;

$*$ valueGen$()$ can use random library to generate values

$*$ to initialize the tensor values;

$*/$

double valueGen$()\{$

std::random$\_$device rd;

std::mt$19937$ mt$($rd$())$;

$//$ Create a uniform distribution between $0$ and $1$

std::uniform$\_$real$\_$distribution dist$(0\mathrm{.}0,1\mathrm{.}0)$;

$//$ Generate and print a random double value

double randomValue $=$ dist$($mt$)$;

return randomValue;

$\}$

$\}$;

#endif $/*$ BASETENSOR$\_$H$\_*/$

Task $2\mathrm{.}1$ Please program two derived class RankOneTensor and class RankTwoTensor from the base class BaseTensor. The virtual methods should be overridden by each derived class according to the tensor type.

Class RankOneTensor includes the private data member to hold the values for the tensor. The constructors$/$destructor definition are required.

Private:

std::vector data;

public:

RankOneTensor$()$;

RankOneTensor$($int size$)$; $//$ dimension size;

RankOneTensor$($const RankOneTensor& other$)$;

~RankOneTensor$()$;

class RankTwoTensor includes the private data member to hold the values for the tensor. The constructors$/$destructor definition are required.

Private:

std::vector$>$ data;

public:

RankTwoTensor$($int rows, int cols$)$;

RankTwoTensor$($const RankTwoTensor& other$)$;

~ RankTwoTensor$()$;

Task $2\mathrm{.}2$ Define and program the following operators for both class RankTwoTensor and class RankTwoTensor.

Task $2\mathrm{.}3$ Program unit test functions listed in the table below in testDriver.cpp$.$ Call these test functions in the main$()$ function of testDrive.cpp$.$ Operator

Semantic Meaning

Example and Unit Test Function

$++$

Increment each element$$s value by $1$

RankOneTensor t $(3)$; t$++$; $++$t;

void testIncrementOperatorRankOne$()$;

void testIncrementOperatorRankTwo$()$;

$+$

Add two tensors of the same dimension element wise; invalid$\_$argument should be thrown if two tensor objects$$ dimension does not match

RankOneTensor t$1(3),$ t$2(3)$ ;

t$1+$ t$2$ ;

void testAddOperatorRankOne$()$;

void testAddOperatorRankTwo$()$;

$+$

Add one tensor with a scalar value element wise

RankOneTensor t$(3)+0\mathrm{.}5$;

void testAddOperatorRankOne$()$;

void testAddOperatorRankTwo$()$;

$=$

Assign one tensor to another of the same dimension; invalid$\_$argument should be thrown if two tensor objects$$ dimension does not match

RankOneTensor t$1(2),$ t$2(2),$ t$3(2)$ ;

t$1.$loadData$()$ ;

t$2.$loadData$()$ ;

t$3=$ t$2+$ t$3$ ;

void testAssignmentOperatorRankOne$()$;

void testAssignmentOperatorRankTwo$()$;

$>>$

Output the tensor$$s element values

RankOneTensor t$(3)$ ;

t$.$loadData$()$ ;

cout $<<$ t ;

void testCoutStreamOperatorRankOne$()$;

void testCoutStreamOperatorRankTwo$()$;

$<<$

Input the tensor$$s element values by console input

RankOneTensor t$(3)$;

cin $>>$ t;

void testCinStreamOperatorRankOne$()$;

void testCinStreamOperatorRankTwo$()$;

$[]$

Retrieve value by index; invalid$\_$argument should be thrown if the index is out of the range

RankTwoTensor t$(2,2)$;

cin $>>$ t;

cout $<$