// Ditto above, but for doubles
void m3dMatrixMultiply44(M3DMatrix33d product, const M3DMatrix33d a, const M3DMatrix33d b )
{
for (int i = 0; i < 3; i++) {
double ai0=A33(i,0), ai1=A33(i,1), ai2=A33(i,2);
P33(i,0) = ai0 * B33(0,0) + ai1 * B33(1,0) + ai2 * B33(2,0);
P33(i,1) = ai0 * B33(0,1) + ai1 * B33(1,1) + ai2 * B33(2,1);
P33(i,2) = ai0 * B33(0,2) + ai1 * B33(1,2) + ai2 * B33(2,2);
}
}
///////////////////////////////////////////////////////////////////////////////
// Multiply two 3x3 matricies
void m3dMatrixMultiply33(M3DMatrix33f product, const M3DMatrix33f a, const M3DMatrix33f b )
{
for (int i = 0; i < 3; i++) {
float ai0=A33(i,0), ai1=A33(i,1), ai2=A33(i,2);
P33(i,0) = ai0 * B33(0,0) + ai1 * B33(1,0) + ai2 * B33(2,0);
P33(i,1) = ai0 * B33(0,1) + ai1 * B33(1,1) + ai2 * B33(2,1);
P33(i,2) = ai0 * B33(0,2) + ai1 * B33(1,2) + ai2 * B33(2,2);
}
}
int main()
{
std::cout << "============== Test 1 ==============" << std::endl << std::endl;
DoubleInterval A00(2,3);
DoubleInterval A01(0,1);
DoubleInterval A10(1,2);
DoubleInterval A11(2,3);
DoubleInterval B0(0,120);
DoubleInterval B1(60,240);
DoubleMatrix *A = new DoubleMatrix(2,2);
(*A)(0,0) = A00;
(*A)(0,1) = A01;
(*A)(1,0) = A10;
(*A)(1,1) = A11;
std::cout << "A: " << std::endl;
std::cout << *A << std::endl;
DoubleVector *b = new DoubleVector(2, (DoubleInterval)0);
(*b)[0] = B0;
(*b)[1] = B1;
std::cout << "b: " << std::endl;
std::cout << *b << std::endl << std::endl;
DoubleVector *x = new DoubleVector(2, (DoubleInterval)0);
try
{
x = hansen_gaussian_elimination_v1(*A,*b);
if(x != NULL)
{
std::cout << "x = " << std::endl;
std::cout << *x << std::endl << std::endl;
}
}
catch(const std::exception& e)
{
std::cout << e.what() << std::endl << std::endl;
}
catch(std::string& error)
{
std::cout << error << std::endl << std::endl;
}
//Solution should be [[-120,90], [-60,240]]^T
delete A;
delete b;
delete x;
/*std::cout << "============== Test 2 ==============" << std::endl << std::endl;
A = new DoubleMatrix(3,3);
(*A)(0,0) = 2;
(*A)(0,1) = 1;
(*A)(0,2) = -1;
(*A)(1,0) = -3;
(*A)(1,1) = -1;
(*A)(1,2) = 2;
(*A)(2,0) = -2;
(*A)(2,1) = 1;
(*A)(2,2) = 2;
std::cout << "A = " << std::endl;
std::cout << *A << std::endl;
b = new DoubleVector(3, (DoubleInterval)0);
(*b)[0] = 8;
(*b)[1] = -11;
(*b)[2] = -3;
std::cout << "b = " << std::endl;
std::cout << *b << std::endl << std::endl;
x = new DoubleVector(3, (DoubleInterval)0);
try
{
x = hansen_gaussian_elimination_v1(*A,*b);
if(x != NULL)
{
std::cout << "x = " << std::endl;
std::cout << *x << std::endl << std::endl;
}
}
catch(const std::exception& e)
{
std::cout << e.what() << std::endl << std::endl;
}
catch(std::string& error)
{
std::cout << error << std::endl << std::endl;
}
delete A;
delete b;
delete x;
//Solution should be [2, 3, -1]^T
std::cout << "============== Test 3 ==============" << std::endl << std::endl;
A = new DoubleMatrix(2,2);
(*A)(0,0) = 1;
(*A)(0,1) = -2;
(*A)(1,0) = 2;
(*A)(1,1) = -1;
std::cout << "A = " << std::endl;
std::cout << *A << std::endl;
b = new DoubleVector(2, (DoubleInterval)0);
(*b)[0] = 3;
(*b)[1] = 9;
std::cout << "b = " << std::endl;
std::cout << *b << std::endl << std::endl;
x = new DoubleVector(2, (DoubleInterval)0);
try
{
x = hansen_gaussian_elimination_v1(*A,*b);
if(x != NULL)
{
std::cout << "x = " << std::endl;
std::cout << *x << std::endl << std::endl;
}
}
catch(const std::exception& e)
{
std::cout << e.what() << std::endl << std::endl;
}
catch(std::string& error)
{
std::cout << error << std::endl << std::endl;
}
delete A;
delete b;
delete x;
//Solution should be [5, 1]^T
std::cout << "============== Test 4 ==============" << std::endl << std::endl;
A = new DoubleMatrix(3,3);
(*A)(0,0) = 2;
(*A)(0,1) = 3;
(*A)(0,2) = 1;
(*A)(1,0) = 1;
(*A)(1,1) = 1;
(*A)(1,2) = 1;
(*A)(2,0) = 3;
(*A)(2,1) = 4;
(*A)(2,2) = 2;
std::cout << "A = " << std::endl;
std::cout << *A << std::endl;
b = new DoubleVector(3, (DoubleInterval)0);
(*b)[0] = 1;
(*b)[1] = 3;
(*b)[2] = 4;
std::cout << "b = " << std::endl;
std::cout << *b << std::endl << std::endl;
x = new DoubleVector(3, (DoubleInterval)0);
try
{
x = hansen_gaussian_elimination_v1(*A,*b);
if(x != NULL)
{
std::cout << "x = " << std::endl;
std::cout << *x << std::endl << std::endl;
}
}
catch(const std::exception& e)
{
std::cout << e.what() << std::endl << std::endl;
}
catch(std::string& error)
{
std::cout << error << std::endl << std::endl;
}
delete A;
delete b;
delete x;
//There shouldn't be an exact solution as it has free variables
std::cout << "============== Test 5 ==============" << std::endl << std::endl;
A = new DoubleMatrix(3,3);
(*A)(0,0) = 1;
(*A)(0,1) = 3;
(*A)(0,2) = 1;
(*A)(1,0) = 1;
(*A)(1,1) = 1;
(*A)(1,2) = -1;
(*A)(2,0) = 3;
(*A)(2,1) = 11;
(*A)(2,2) = 5;
std::cout << "A = " << std::endl;
std::cout << *A << std::endl;
b = new DoubleVector(3, (DoubleInterval)0);
(*b)[0] = 9;
(*b)[1] = 1;
(*b)[2] = 35;
std::cout << "b = " << std::endl;
std::cout << *b << std::endl << std::endl;
x = new DoubleVector(3, (DoubleInterval)0);
try
{
x = hansen_gaussian_elimination_v1(*A,*b);
if(x != NULL)
{
std::cout << "x = " << std::endl;
std::cout << *x << std::endl << std::endl;
}
}
catch(const std::exception& e)
{
std::cout << e.what() << std::endl << std::endl;
}
catch(std::string& error)
{
std::cout << error << std::endl << std::endl;
}
delete A;
delete b;
delete x;
//There shouldn't be an exact solution as it has free variables
std::cout << "============== Test 6 ==============" << std::endl << std::endl;
A = new DoubleMatrix(3,2);
(*A)(0,0) = 1;
(*A)(0,1) = 1;
(*A)(1,0) = 2;
(*A)(1,1) = 3;
(*A)(2,0) = 3;
(*A)(2,1) = -2;
std::cout << "A = " << std::endl;
std::cout << *A << std::endl;
b = new DoubleVector(3, (DoubleInterval)0);
(*b)[0] = 0;
(*b)[1] = 0;
(*b)[2] = 0;
std::cout << "b = " << std::endl;
std::cout << *b << std::endl << std::endl;
x = new DoubleVector(2, (DoubleInterval)0);
try
{
x = hansen_gaussian_elimination_v1(*A,*b);
if(x != NULL)
{
std::cout << "x = " << std::endl;
std::cout << *x << std::endl << std::endl;
}
}
catch(const std::exception& e)
{
std::cout << e.what() << std::endl << std::endl;
}
catch(std::string& error)
{
std::cout << error << std::endl << std::endl;
}
delete A;
delete b;
delete x;
//There should be an exact solution as even though the system is overdetermined but
//as the Rank is 2 and the amount of unknowns is 2
std::cout << "============== Test 7 ==============" << std::endl << std::endl;
A = new DoubleMatrix(4,4);
(*A)(0,0) = 1;
(*A)(0,1) = 1;
(*A)(0,2) = 1;
(*A)(0,3) = 1;
(*A)(1,0) = 2;
(*A)(1,1) = 3;
(*A)(1,2) = -1;
(*A)(1,3) = -1;
(*A)(2,0) = 3;
(*A)(2,1) = 2;
(*A)(2,2) = 1;
(*A)(2,3) = 1;
(*A)(3,0) = 3;
(*A)(3,1) = 6;
(*A)(3,2) = -1;
(*A)(3,3) = -1;
std::cout << "A = " << std::endl;
std::cout << *A << std::endl;
b = new DoubleVector(4, (DoubleInterval)0);
(*b)[0] = 0;
(*b)[1] = 2;
(*b)[2] = 5;
(*b)[3] = 4;
std::cout << "b = " << std::endl;
std::cout << *b << std::endl << std::endl;
x = new DoubleVector(4, (DoubleInterval)0);
try
{
x = hansen_gaussian_elimination_v1(*A,*b);
if(x != NULL)
{
std::cout << "x = " << std::endl;
std::cout << *x << std::endl << std::endl;
}
}
catch(const std::exception& e)
{
std::cout << e.what() << std::endl << std::endl;
}
catch(std::string& error)
{
std::cout << error << std::endl << std::endl;
}
delete A;
delete b;
delete x;
//There should be no solutions as the system is inconsistent
std::cout << "============== Test 8 ==============" << std::endl << std::endl;
A = new DoubleMatrix(4,3);
(*A)(0,0) = -1;
(*A)(0,1) = 2;
(*A)(0,2) = -1;
(*A)(1,0) = -2;
(*A)(1,1) = 2;
(*A)(1,2) = 1;
(*A)(2,0) = 3;
(*A)(2,1) = 2;
(*A)(2,2) = 2;
(*A)(3,0) = -3;
(*A)(3,1) = 8;
(*A)(3,2) = 5;
std::cout << "A = " << std::endl;
std::cout << *A << std::endl;
b = new DoubleVector(4, (DoubleInterval)0);
(*b)[0] = 2;
(*b)[1] = 4;
(*b)[2] = 5;
(*b)[3] = 17;
std::cout << "b = " << std::endl;
std::cout << *b << std::endl << std::endl;
x = new DoubleVector(3, (DoubleInterval)0);
try
{
x = hansen_gaussian_elimination_v1(*A,*b);
if(x != NULL)
{
std::cout << "x = " << std::endl;
std::cout << *x << std::endl << std::endl;
}
}
catch(const std::exception& e)
{
std::cout << e.what() << std::endl << std::endl;
}
catch(std::string& error)
{
std::cout << error << std::endl << std::endl;
}
delete A;
delete b;
delete x;
//There should be an exact solution as even though the system is overdetermined but
//as the Rank is 3 and the amount of unknowns is 3
std::cout << "============== Test 9 ==============" << std::endl << std::endl;
A = new DoubleMatrix(3,4);
(*A)(0,0) = 1;
(*A)(0,1) = 3;
(*A)(0,2) = 1;
(*A)(0,3) = 1;
(*A)(1,0) = 2;
(*A)(1,1) = -2;
(*A)(1,2) = 1;
(*A)(1,3) = 2;
(*A)(2,0) = 1;
(*A)(2,1) = -5;
(*A)(2,2) = 0;
(*A)(2,3) = 1;
std::cout << "A = " << std::endl;
std::cout << *A << std::endl;
b = new DoubleVector(3, (DoubleInterval)0);
(*b)[0] = 3;
(*b)[1] = 8;
(*b)[2] = 5;
std::cout << "b = " << std::endl;
std::cout << *b << std::endl << std::endl;
x = new DoubleVector(4, (DoubleInterval)0);
try
{
x = hansen_gaussian_elimination_v1(*A,*b);
if(x != NULL)
{
std::cout << "x = " << std::endl;
std::cout << *x << std::endl << std::endl;
}
}
catch(const std::exception& e)
{
std::cout << e.what() << std::endl << std::endl;
}
catch(std::string& error)
{
std::cout << error << std::endl << std::endl;
}
delete A;
delete b;
delete x;
//It is an undetermined system, so no exact solution as it has free variables
std::cout << "============== Test 10 ==============" << std::endl << std::endl;
A = new DoubleMatrix(3,4);
(*A)(0,0) = 1;
(*A)(0,1) = 0;
(*A)(0,2) = 0;
(*A)(0,3) = 1;
(*A)(1,0) = 0;
(*A)(1,1) = 1;
(*A)(1,2) = 0;
(*A)(1,3) = 1;
(*A)(2,0) = 0;
(*A)(2,1) = 0;
(*A)(2,2) = 1;
(*A)(2,3) = 1;
std::cout << "A = " << std::endl;
std::cout << *A << std::endl;
b = new DoubleVector(3, (DoubleInterval)0);
(*b)[0] = 1;
(*b)[1] = 1;
(*b)[2] = 1;
std::cout << "b = " << std::endl;
std::cout << *b << std::endl << std::endl;
x = new DoubleVector(4, (DoubleInterval)0);
try
{
x = hansen_gaussian_elimination_v1(*A,*b);
if(x != NULL)
{
std::cout << "x = " << std::endl;
std::cout << *x << std::endl << std::endl;
}
}
catch(const std::exception& e)
{
std::cout << e.what() << std::endl << std::endl;
}
catch(std::string& error)
{
std::cout << error << std::endl << std::endl;
}
delete A;
delete b;
delete x;
std::cout << "============== Test 11 ==============" << std::endl << std::endl;
A = new DoubleMatrix(4,4);
(*A)(0,0) = 1;
(*A)(0,1) = -1;
(*A)(0,2) = 1;
(*A)(0,3) = -1;
(*A)(1,0) = -1;
(*A)(1,1) = 1;
(*A)(1,2) = -1;
(*A)(1,3) = 1;
(*A)(2,0) = 1;
(*A)(2,1) = -1;
(*A)(2,2) = 1;
(*A)(2,3) = -1;
(*A)(3,0) = -1;
(*A)(3,1) = 1;
(*A)(3,2) = -1;
(*A)(3,3) = 1;
std::cout << "A = " << std::endl;
std::cout << *A << std::endl;
b = new DoubleVector(4, (DoubleInterval)0);
(*b)[0] = 0;
(*b)[1] = 0;
(*b)[2] = 0;
(*b)[3] = 0;
std::cout << "b = " << std::endl;
std::cout << *b << std::endl << std::endl;
x = new DoubleVector(4, (DoubleInterval)0);
try
{
x = hansen_gaussian_elimination_v1(*A,*b);
if(x != NULL)
{
std::cout << "x = " << std::endl;
std::cout << *x << std::endl << std::endl;
}
}
catch(const std::exception& e)
{
std::cout << e.what() << std::endl << std::endl;
}
catch(std::string& error)
{
std::cout << error << std::endl << std::endl;
}
delete A;
delete b;
delete x;
//It is an underdetermined system, so no exact solution as it has free variables
//fails here though because no pivoting is done
std::cout << "============== Test 12 ==============" << std::endl << std::endl;
A = new DoubleMatrix(3,3);
(*A)(0,0) = 1;
(*A)(0,1) = 2;
(*A)(0,2) = 3;
(*A)(1,0) = 4;
(*A)(1,1) = 5;
(*A)(1,2) = 6;
(*A)(2,0) = 7;
(*A)(2,1) = 8;
(*A)(2,2) = 9;
std::cout << "A = " << std::endl;
std::cout << *A << std::endl;
b = new DoubleVector(3, (DoubleInterval)0);
(*b)[0] = 0;
(*b)[1] = 0;
(*b)[2] = 0;
std::cout << "b = " << std::endl;
std::cout << *b << std::endl << std::endl;
x = new DoubleVector(3, (DoubleInterval)0);
try
{
x = hansen_gaussian_elimination_v1(*A,*b);
if(x != NULL)
{
std::cout << "x = " << std::endl;
std::cout << *x << std::endl << std::endl;
}
}
catch(const std::exception& e)
{
std::cout << e.what() << std::endl << std::endl;
}
catch(std::string& error)
{
std::cout << error << std::endl << std::endl;
}
delete A;
delete b;
delete x;
//There shouldn't be an exact solution as it has free variables
std::cout << "============== Test 13 ==============" << std::endl << std::endl;
A = new DoubleMatrix(3,3);
(*A)(0,0) = 1;
(*A)(0,1) = -1;
(*A)(0,2) = 2;
(*A)(1,0) = 0;
(*A)(1,1) = 0;
(*A)(1,2) = -1;
(*A)(2,0) = 0;
(*A)(2,1) = 2;
(*A)(2,2) = -1;
std::cout << "A = " << std::endl;
std::cout << *A << std::endl;
b = new DoubleVector(3, (DoubleInterval)0);
(*b)[0] = 8;
(*b)[1] = -11;
(*b)[2] = -3;
std::cout << "b = " << std::endl;
std::cout << *b << std::endl << std::endl;
x = new DoubleVector(3, (DoubleInterval)0);
try
{
x = hansen_gaussian_elimination_v1(*A,*b);
if(x != NULL)
{
std::cout << "x = " << std::endl;
std::cout << *x << std::endl << std::endl;
}
}
catch(const std::exception& e)
{
std::cout << e.what() << std::endl << std::endl;
}
catch(std::string& error)
{
std::cout << error << std::endl << std::endl;
}
delete A;
delete b;
delete x;
//Should gave the same result as test 14 if pivoting has been implemented correctly
std::cout << "============== Test 14 ==============" << std::endl << std::endl;
A = new DoubleMatrix(3,3);
(*A)(0,0) = 1;
(*A)(0,1) = -1;
(*A)(0,2) = 2;
(*A)(1,0) = 0;
(*A)(1,1) = 2;
(*A)(1,2) = -1;
(*A)(2,0) = 0;
(*A)(2,1) = 0;
(*A)(2,2) = -1;
std::cout << "A = " << std::endl;
std::cout << *A << std::endl;
b = new DoubleVector(3, (DoubleInterval)0);
(*b)[0] = 8;
(*b)[1] = -3;
(*b)[2] = -11;
std::cout << "b = " << std::endl;
std::cout << *b << std::endl << std::endl;
x = new DoubleVector(3, (DoubleInterval)0);
try
{
x = hansen_gaussian_elimination_v1(*A,*b);
if(x != NULL)
{
std::cout << "x = " << std::endl;
std::cout << *x << std::endl << std::endl;
}
}
catch(const std::exception& e)
{
std::cout << e.what() << std::endl << std::endl;
}
catch(std::string& error)
{
std::cout << error << std::endl << std::endl;
}
delete A;
delete b;
delete x;
//Same system of equations as test 13*/
std::cout << "============== Test 15 ==============" << std::endl << std::endl;
A = new DoubleMatrix(2,2);
(*A)(0,0) = A10;
(*A)(0,1) = A11;
(*A)(1,0) = A00;
(*A)(1,1) = A01;
std::cout << "A = " << std::endl;
std::cout << *A << std::endl;
b = new DoubleVector(2, (DoubleInterval)0);
(*b)[0] = B1;
(*b)[1] = B0;
std::cout << "b = " << std::endl;
std::cout << *b << std::endl << std::endl;
x = new DoubleVector(2, (DoubleInterval)0);
try
{
x = hansen_gaussian_elimination_v1(*A,*b);
if(x != NULL)
{
std::cout << "x = " << std::endl;
std::cout << *x << std::endl << std::endl;
}
}
catch(const std::exception& e)
{
std::cout << e.what() << std::endl << std::endl;
}
catch(std::string& error)
{
std::cout << error << std::endl << std::endl;
}
delete A;
delete b;
delete x;
std::cout << "============== Test 16 ==============" << std::endl << std::endl;
A = new DoubleMatrix(2,2);
A00.assign(3,4);
A01.assign(1,2);
A10.assign(0,1);
A11.assign(7,8);
(*A)(0,0) = A00;
(*A)(0,1) = A01;
(*A)(1,0) = A10;
(*A)(1,1) = A11;
std::cout << "A = " << std::endl;
std::cout << *A << std::endl;
b = new DoubleVector(2, (DoubleInterval)0);
B0.assign(2,4);
B1.assign(-1,1);
(*b)[0] = B0;
(*b)[1] = B1;
std::cout << "b = " << std::endl;
std::cout << *b << std::endl << std::endl;
x = new DoubleVector(2, (DoubleInterval)0);
try
{
x = hansen_gaussian_elimination_v1(*A,*b);
if(x != NULL)
{
std::cout << "x = " << std::endl;
std::cout << *x << std::endl << std::endl;
}
}
catch(const std::exception& e)
{
std::cout << e.what() << std::endl << std::endl;
}
catch(std::string& error)
{
std::cout << error << std::endl << std::endl;
}
delete A;
delete b;
delete x;
std::cout << "============== Test 17 ==============" << std::endl << std::endl;
A = new DoubleMatrix(2,2);
A00.assign(2,4);
A01.assign(8,10);
A10.assign(2,4);
A11.assign(4,6);
(*A)(0,0) = -A00;
(*A)(0,1) = A01;
(*A)(1,0) = A10;
(*A)(1,1) = A11;
std::cout << "A = " << std::endl;
std::cout << *A << std::endl;
b = new DoubleVector(2, (DoubleInterval)0);
B0.assign(4,6);
B1.assign(8,10);
(*b)[0] = -B0;
(*b)[1] = -B1;
std::cout << "b = " << std::endl;
std::cout << *b << std::endl << std::endl;
x = new DoubleVector(2, (DoubleInterval)0);
try
{
x = hansen_gaussian_elimination_v1(*A,*b);
if(x != NULL)
{
std::cout << "x = " << std::endl;
std::cout << *x << std::endl << std::endl;
}
}
catch(const std::exception& e)
{
std::cout << e.what() << std::endl << std::endl;
}
catch(std::string& error)
{
std::cout << error << std::endl << std::endl;
}
delete A;
delete b;
delete x;
std::cout << "============== Test 18 ==============" << std::endl << std::endl;
A = new DoubleMatrix(4,4);
A00.assign(4,6);
A01.assign(-6,-4);
A10.assign(9,11);
A11.assign(-11,-9);
DoubleInterval A33(-1,1);
(*A)(0,0) = A00;
(*A)(0,1) = A33;
(*A)(0,2) = A33;
(*A)(0,3) = A33;
(*A)(1,0) = A33;
(*A)(1,1) = A01;
(*A)(1,2) = A33;
(*A)(1,3) = A33;
(*A)(2,0) = A33;
(*A)(2,1) = A33;
(*A)(2,2) = A10;
(*A)(2,3) = A33;
(*A)(3,0) = A33;
(*A)(3,1) = A33;
(*A)(3,2) = A33;
(*A)(3,3) = A11;
std::cout << "A = " << std::endl;
std::cout << *A << std::endl;
b = new DoubleVector(4, (DoubleInterval)0);
B0.assign(-2,4);
B1.assign(1,8);
DoubleInterval B2(-4,10);
DoubleInterval B3(2,12);
(*b)[0] = B0;
(*b)[1] = B1;
(*b)[2] = B2;
(*b)[3] = B3;
std::cout << "b = " << std::endl;
std::cout << *b << std::endl << std::endl;
x = new DoubleVector(4, (DoubleInterval)0);
try
{
x = hansen_gaussian_elimination_v1(*A,*b);
if(x != NULL)
{
std::cout << "x = " << std::endl;
std::cout << *x << std::endl << std::endl;
}
}
catch(const std::exception& e)
{
std::cout << e.what() << std::endl << std::endl;
}
catch(std::string& error)
{
std::cout << error << std::endl << std::endl;
}
delete A;
delete b;
delete x;
std::cout << "============== Test 19 ==============" << std::endl << std::endl;
A = new DoubleMatrix(3,3);
A00.assign(3.7, 4.3);
A01.assign(-1.5, -0.5);
A10.assign(3.7, 4.3);
(*A)(0,0) = A00;
(*A)(0,1) = A01;
(*A)(0,2) = (DoubleInterval)0;
(*A)(1,0) = A01;
(*A)(1,1) = A10;
(*A)(1,2) = A01;
(*A)(2,0) = (DoubleInterval)0;
(*A)(2,1) = A01;
(*A)(2,2) = A10;
std::cout << "A = " << std::endl;
std::cout << *A << std::endl;
b = new DoubleVector(3, (DoubleInterval)0);
B0.assign(-14,14);
B1.assign(-9,9);
B2.assign(-3,3);
(*b)[0] = B0;
(*b)[1] = B1;
(*b)[2] = B2;
std::cout << "b = " << std::endl;
std::cout << *b << std::endl << std::endl;
x = new DoubleVector(3, (DoubleInterval)0);
try
{
x = hansen_gaussian_elimination_v1(*A,*b);
if(x != NULL)
{
std::cout << "x = " << std::endl;
std::cout << *x << std::endl << std::endl;
}
}
catch(const std::exception& e)
{
std::cout << e.what() << std::endl << std::endl;
}
catch(std::string& error)
{
std::cout << error << std::endl << std::endl;
}
delete A;
delete b;
delete x;
std::cout << "============== Test 20 ==============" << std::endl << std::endl;
A = new DoubleMatrix(3,3);
A00.assign(3.7, 4.3);
A01.assign(-1.5, -0.5);
A10.assign(3.7, 4.3);
(*A)(0,0) = A00;
(*A)(0,1) = A01;
(*A)(0,2) = (DoubleInterval)0;
(*A)(1,0) = A01;
(*A)(1,1) = A10;
(*A)(1,2) = A01;
(*A)(2,0) = (DoubleInterval)0;
(*A)(2,1) = A01;
(*A)(2,2) = A10;
std::cout << "A = " << std::endl;
std::cout << *A << std::endl;
b = new DoubleVector(3, (DoubleInterval)0);
B0.assign(-14,0);
B1.assign(-9,0);
B2.assign(-3,0);
(*b)[0] = B0;
(*b)[1] = B1;
(*b)[2] = B2;
std::cout << "b = " << std::endl;
std::cout << *b << std::endl << std::endl;
x = new DoubleVector(3, (DoubleInterval)0);
try
{
x = hansen_gaussian_elimination_v1(*A,*b);
if(x != NULL)
{
std::cout << "x = " << std::endl;
std::cout << *x << std::endl << std::endl;
}
}
catch(const std::exception& e)
{
std::cout << e.what() << std::endl << std::endl;
}
catch(std::string& error)
{
std::cout << error << std::endl << std::endl;
}
delete A;
delete b;
delete x;
std::cout << "============== Test 21 ==============" << std::endl << std::endl;
A = new DoubleMatrix(3,3);
A00.assign(3.7, 4.3);
A01.assign(-1.5, -0.5);
A10.assign(3.7, 4.3);
(*A)(0,0) = A00;
(*A)(0,1) = A01;
(*A)(0,2) = (DoubleInterval)0;
(*A)(1,0) = A01;
(*A)(1,1) = A10;
(*A)(1,2) = A01;
(*A)(2,0) = (DoubleInterval)0;
(*A)(2,1) = A01;
(*A)(2,2) = A10;
std::cout << "A = " << std::endl;
std::cout << *A << std::endl;
b = new DoubleVector(3, (DoubleInterval)0);
B0.assign(0,14);
B1.assign(0,9);
B2.assign(0,3);
(*b)[0] = B0;
(*b)[1] = B1;
(*b)[2] = B2;
std::cout << "b = " << std::endl;
std::cout << *b << std::endl << std::endl;
x = new DoubleVector(3, (DoubleInterval)0);
try
{
x = hansen_gaussian_elimination_v1(*A,*b);
if(x != NULL)
{
std::cout << "x = " << std::endl;
std::cout << *x << std::endl << std::endl;
}
}
catch(const std::exception& e)
{
std::cout << e.what() << std::endl << std::endl;
}
catch(std::string& error)
{
std::cout << error << std::endl << std::endl;
}
delete A;
delete b;
delete x;
std::cout << "============== Test 22 ==============" << std::endl << std::endl;
A = new DoubleMatrix(3,3);
A00.assign(3.7, 4.3);
A01.assign(-1.5, -0.5);
A10.assign(3.7, 4.3);
(*A)(0,0) = A00;
(*A)(0,1) = A01;
(*A)(0,2) = (DoubleInterval)0;
(*A)(1,0) = A01;
(*A)(1,1) = A10;
(*A)(1,2) = A01;
(*A)(2,0) = (DoubleInterval)0;
(*A)(2,1) = A01;
(*A)(2,2) = A10;
std::cout << "A = " << std::endl;
std::cout << *A << std::endl;
b = new DoubleVector(3, (DoubleInterval)0);
B0.assign(2,14);
B1.assign(-9,-3);
B2.assign(-3,1);
(*b)[0] = B0;
(*b)[1] = B1;
(*b)[2] = B2;
std::cout << "b = " << std::endl;
std::cout << *b << std::endl << std::endl;
x = new DoubleVector(3, (DoubleInterval)0);
try
{
x = hansen_gaussian_elimination_v1(*A,*b);
if(x != NULL)
{
std::cout << "x = " << std::endl;
std::cout << *x << std::endl << std::endl;
}
}
catch(const std::exception& e)
{
std::cout << e.what() << std::endl << std::endl;
}
catch(std::string& error)
{
std::cout << error << std::endl << std::endl;
}
delete A;
delete b;
delete x;
std::cout << "============== Test 23 ==============" << std::endl << std::endl;
A = new DoubleMatrix(2,2);
A00.assign(2,3);
A01.assign(-1,1);
A10.assign(0,5);
A11.assign(3,4);
(*A)(0,0) = A00;
(*A)(0,1) = A01;
(*A)(1,0) = A10;
(*A)(1,1) = A11;
std::cout << "A = " << std::endl;
std::cout << *A << std::endl;
b = new DoubleVector(2, (DoubleInterval)0);
B0.assign(2,14);
B1.assign(3,9);
(*b)[0] = B0;
(*b)[1] = B1;
std::cout << "b = " << std::endl;
std::cout << *b << std::endl << std::endl;
x = new DoubleVector(2, (DoubleInterval)0);
try
{
x = hansen_gaussian_elimination_v1(*A,*b);
if(x != NULL)
{
std::cout << "x = " << std::endl;
std::cout << *x << std::endl << std::endl;
}
}
catch(const std::exception& e)
{
std::cout << e.what() << std::endl << std::endl;
}
catch(std::string& error)
{
std::cout << error << std::endl << std::endl;
}
delete A;
delete b;
delete x;
return 0;
}
int main()
{
std::cout << "============== Test 1 ==============" << std::endl << std::endl;
DoubleInterval A00(2,3);
DoubleInterval A01(0,1);
DoubleInterval A10(1,2);
DoubleInterval A11(2,3);
DoubleInterval B0(0,120);
DoubleInterval B1(60,240);
DoubleMatrix *A = new DoubleMatrix(2,2);
(*A)(0,0) = A00;
(*A)(0,1) = A01;
(*A)(1,0) = A10;
(*A)(1,1) = A11;
std::cout << "A: " << std::endl;
std::cout << *A << std::endl;
DoubleVector *b = new DoubleVector(2, (DoubleInterval)0);
(*b)[0] = B0;
(*b)[1] = B1;
std::cout << "b: " << std::endl;
std::cout << *b << std::endl << std::endl;
try
{
get_exact_system(*A,*b);
}
catch(const std::exception& e)
{
std::cout << e.what() << std::endl << std::endl;
}
catch(std::string& error)
{
std::cout << error << std::endl << std::endl;
}
delete A;
delete b;
std::cout << "============== Test 2 ==============" << std::endl << std::endl;
A00.assign(-1,3);
A = new DoubleMatrix(2,2);
(*A)(0,0) = A00;
(*A)(0,1) = A01;
(*A)(1,0) = A10;
(*A)(1,1) = A11;
std::cout << "A: " << std::endl;
std::cout << *A << std::endl;
b = new DoubleVector(2, (DoubleInterval)0);
(*b)[0] = B0;
(*b)[1] = B1;
std::cout << "b: " << std::endl;
std::cout << *b << std::endl << std::endl;
try
{
get_exact_system(*A,*b);
}
catch(const std::exception& e)
{
std::cout << e.what() << std::endl << std::endl;
}
catch(std::string& error)
{
std::cout << error << std::endl << std::endl;
}
delete A;
delete b;
std::cout << "============== Test 3 ==============" << std::endl << std::endl;
A00.assign(2,3);
A01.assign(-5,6);
A = new DoubleMatrix(2,2);
(*A)(0,0) = A00;
(*A)(0,1) = A01;
(*A)(1,0) = A10;
(*A)(1,1) = A11;
std::cout << "A: " << std::endl;
std::cout << *A << std::endl;
b = new DoubleVector(2, (DoubleInterval)0);
B0.assign(1,3);
B1.assign(3,4);
(*b)[0] = B0;
(*b)[1] = B1;
std::cout << "b: " << std::endl;
std::cout << *b << std::endl << std::endl;
try
{
get_exact_system(*A,*b);
}
catch(const std::exception& e)
{
std::cout << e.what() << std::endl << std::endl;
}
catch(std::string& error)
{
std::cout << error << std::endl << std::endl;
}
delete A;
delete b;
std::cout << "============== Test 4 ==============" << std::endl << std::endl;
A00.assign(-2,1);
A01.assign(1,5);
A = new DoubleMatrix(2,2);
(*A)(0,0) = A00;
(*A)(0,1) = A01;
(*A)(1,0) = A10;
(*A)(1,1) = A11;
std::cout << "A: " << std::endl;
std::cout << *A << std::endl;
b = new DoubleVector(2, (DoubleInterval)0);
B0.assign(1,3);
B1.assign(3,4);
(*b)[0] = B0;
(*b)[1] = B1;
std::cout << "b: " << std::endl;
std::cout << *b << std::endl << std::endl;
try
{
get_exact_system(*A,*b);
}
catch(const std::exception& e)
{
std::cout << e.what() << std::endl << std::endl;
}
catch(std::string& error)
{
std::cout << error << std::endl << std::endl;
}
delete A;
delete b;
std::cout << "============== Test 5 ==============" << std::endl << std::endl;
A00.assign(2,3);
A01.assign(3,4);
DoubleInterval A02(1,2);
DoubleInterval A12(0,1);
DoubleInterval A21(6,8);
DoubleInterval A22(4,5);
B0.assign(0,120);
B1.assign(310,440);
DoubleInterval B2(50,120);
A = new DoubleMatrix(3,3);
(*A)(0,0) = A00;
(*A)(0,1) = A01;
(*A)(0,2) = A02;
(*A)(1,0) = A00;
(*A)(1,1) = A00;
(*A)(1,2) = A12;
(*A)(2,0) = A00;
(*A)(2,1) = A21;
(*A)(2,2) = A22;
std::cout << "A: " << std::endl;
std::cout << *A << std::endl;
b = new DoubleVector(3, (DoubleInterval)0);
(*b)[0] = B0;
(*b)[1] = B1;
(*b)[2] = B2;
std::cout << "b: " << std::endl;
std::cout << *b << std::endl << std::endl;
try
{
get_exact_system(*A,*b);
}
catch(const std::exception& e)
{
std::cout << e.what() << std::endl << std::endl;
}
catch(std::string& error)
{
std::cout << error << std::endl << std::endl;
}
delete A;
delete b;
/*std::cout << "============== Test 6 ==============" << std::endl << std::endl;
A00.assign(2,3);
A = new DoubleMatrix(1,1);
(*A)(0,0) = A00;
std::cout << "A: " << std::endl;
std::cout << *A << std::endl;
B0.assign(4,5);
b = new DoubleVector(1, (DoubleInterval)0);
(*b)[0] = B0;
std::cout << "b: " << std::endl;
std::cout << *b << std::endl << std::endl;
try
{
get_exact_system(*A,*b, argc, argv);
}
catch(const std::exception& e)
{
std::cout << e.what() << std::endl << std::endl;
}
catch(std::string& error)
{
std::cout << error << std::endl << std::endl;
}
delete A;
delete b;
std::cout << "============== Test 7 ==============" << std::endl << std::endl;
A00.assign(1,2);
A = new DoubleMatrix(1,1);
(*A)(0,0) = A00;
std::cout << "A: " << std::endl;
std::cout << *A << std::endl;
B0.assign(-5,10);
b = new DoubleVector(1, (DoubleInterval)0);
(*b)[0] = B0;
std::cout << "b: " << std::endl;
std::cout << *b << std::endl << std::endl;
try
{
get_exact_system(*A,*b, argc, argv);
}
catch(const std::exception& e)
{
std::cout << e.what() << std::endl << std::endl;
}
catch(std::string& error)
{
std::cout << error << std::endl << std::endl;
}*/
std::cout << "============== Test 15 ==============" << std::endl << std::endl;
A = new DoubleMatrix(2,2);
(*A)(0,0) = A10;
(*A)(0,1) = A11;
(*A)(1,0) = A00;
(*A)(1,1) = A01;
std::cout << "A = " << std::endl;
std::cout << *A << std::endl;
b = new DoubleVector(2, (DoubleInterval)0);
(*b)[0] = B1;
(*b)[1] = B0;
std::cout << "b = " << std::endl;
std::cout << *b << std::endl << std::endl;
try
{
get_exact_system(*A,*b);
}
catch(const std::exception& e)
{
std::cout << e.what() << std::endl << std::endl;
}
catch(std::string& error)
{
std::cout << error << std::endl << std::endl;
}
delete A;
delete b;
std::cout << "============== Test 16 ==============" << std::endl << std::endl;
A = new DoubleMatrix(2,2);
A00.assign(3,4);
A01.assign(1,2);
A10.assign(0,1);
A11.assign(7,8);
(*A)(0,0) = A00;
(*A)(0,1) = A01;
(*A)(1,0) = A10;
(*A)(1,1) = A11;
std::cout << "A = " << std::endl;
std::cout << *A << std::endl;
b = new DoubleVector(2, (DoubleInterval)0);
B0.assign(2,4);
B1.assign(-1,1);
(*b)[0] = B0;
(*b)[1] = B1;
std::cout << "b = " << std::endl;
std::cout << *b << std::endl << std::endl;
try
{
get_exact_system(*A,*b);
}
catch(const std::exception& e)
{
std::cout << e.what() << std::endl << std::endl;
}
catch(std::string& error)
{
std::cout << error << std::endl << std::endl;
}
delete A;
delete b;
std::cout << "============== Test 17 ==============" << std::endl << std::endl;
A = new DoubleMatrix(2,2);
A00.assign(2,4);
A01.assign(8,10);
A10.assign(2,4);
A11.assign(4,6);
(*A)(0,0) = -A00;
(*A)(0,1) = A01;
(*A)(1,0) = A10;
(*A)(1,1) = A11;
std::cout << "A = " << std::endl;
std::cout << *A << std::endl;
b = new DoubleVector(2, (DoubleInterval)0);
B0.assign(4,6);
B1.assign(8,10);
(*b)[0] = -B0;
(*b)[1] = -B1;
std::cout << "b = " << std::endl;
std::cout << *b << std::endl << std::endl;
try
{
get_exact_system(*A,*b);
}
catch(const std::exception& e)
{
std::cout << e.what() << std::endl << std::endl;
}
catch(std::string& error)
{
std::cout << error << std::endl << std::endl;
}
delete A;
delete b;
std::cout << "============== Test 18 ==============" << std::endl << std::endl;
A = new DoubleMatrix(4,4);
A00.assign(4,6);
A01.assign(-6,-4);
A10.assign(9,11);
A11.assign(-11,-9);
DoubleInterval A33(-1,1);
(*A)(0,0) = A00;
(*A)(0,1) = A33;
(*A)(0,2) = A33;
(*A)(0,3) = A33;
(*A)(1,0) = A33;
(*A)(1,1) = A01;
(*A)(1,2) = A33;
(*A)(1,3) = A33;
(*A)(2,0) = A33;
(*A)(2,1) = A33;
(*A)(2,2) = A10;
(*A)(2,3) = A33;
(*A)(3,0) = A33;
(*A)(3,1) = A33;
(*A)(3,2) = A33;
(*A)(3,3) = A11;
std::cout << "A = " << std::endl;
std::cout << *A << std::endl;
b = new DoubleVector(4, (DoubleInterval)0);
B0.assign(-2,4);
B1.assign(1,8);
B2.assign(-4,10);
DoubleInterval B3(2,12);
(*b)[0] = B0;
(*b)[1] = B1;
(*b)[2] = B2;
(*b)[3] = B3;
std::cout << "b = " << std::endl;
std::cout << *b << std::endl << std::endl;
try
{
get_exact_system(*A,*b);
}
catch(const std::exception& e)
{
std::cout << e.what() << std::endl << std::endl;
}
catch(std::string& error)
{
std::cout << error << std::endl << std::endl;
}
delete A;
delete b;
std::cout << "============== Test 19 ==============" << std::endl << std::endl;
A = new DoubleMatrix(3,3);
A00.assign(3.7, 4.3);
A01.assign(-1.5, -0.5);
A10.assign(3.7, 4.3);
(*A)(0,0) = A00;
(*A)(0,1) = A01;
(*A)(0,2) = (DoubleInterval)0;
(*A)(1,0) = A01;
(*A)(1,1) = A10;
(*A)(1,2) = A01;
(*A)(2,0) = (DoubleInterval)0;
(*A)(2,1) = A01;
(*A)(2,2) = A10;
std::cout << "A = " << std::endl;
std::cout << *A << std::endl;
b = new DoubleVector(3, (DoubleInterval)0);
B0.assign(-14,14);
B1.assign(-9,9);
B2.assign(-3,3);
(*b)[0] = B0;
(*b)[1] = B1;
(*b)[2] = B2;
std::cout << "b = " << std::endl;
std::cout << *b << std::endl << std::endl;
try
{
get_exact_system(*A,*b);
}
catch(const std::exception& e)
{
std::cout << e.what() << std::endl << std::endl;
}
catch(std::string& error)
{
std::cout << error << std::endl << std::endl;
}
delete A;
delete b;
std::cout << "============== Test 20 ==============" << std::endl << std::endl;
A = new DoubleMatrix(3,3);
A00.assign(3.7, 4.3);
A01.assign(-1.5, -0.5);
A10.assign(3.7, 4.3);
(*A)(0,0) = A00;
(*A)(0,1) = A01;
(*A)(0,2) = (DoubleInterval)0;
(*A)(1,0) = A01;
(*A)(1,1) = A10;
(*A)(1,2) = A01;
(*A)(2,0) = (DoubleInterval)0;
(*A)(2,1) = A01;
(*A)(2,2) = A10;
std::cout << "A = " << std::endl;
std::cout << *A << std::endl;
b = new DoubleVector(3, (DoubleInterval)0);
B0.assign(-14,0);
B1.assign(-9,0);
B2.assign(-3,0);
(*b)[0] = B0;
(*b)[1] = B1;
(*b)[2] = B2;
std::cout << "b = " << std::endl;
std::cout << *b << std::endl << std::endl;
try
{
get_exact_system(*A,*b);
}
catch(const std::exception& e)
{
std::cout << e.what() << std::endl << std::endl;
}
catch(std::string& error)
{
std::cout << error << std::endl << std::endl;
}
delete A;
delete b;
std::cout << "============== Test 21 ==============" << std::endl << std::endl;
A = new DoubleMatrix(3,3);
A00.assign(3.7, 4.3);
A01.assign(-1.5, -0.5);
A10.assign(3.7, 4.3);
(*A)(0,0) = A00;
(*A)(0,1) = A01;
(*A)(0,2) = (DoubleInterval)0;
(*A)(1,0) = A01;
(*A)(1,1) = A10;
(*A)(1,2) = A01;
(*A)(2,0) = (DoubleInterval)0;
(*A)(2,1) = A01;
(*A)(2,2) = A10;
std::cout << "A = " << std::endl;
std::cout << *A << std::endl;
b = new DoubleVector(3, (DoubleInterval)0);
B0.assign(0,14);
B1.assign(0,9);
B2.assign(0,3);
(*b)[0] = B0;
(*b)[1] = B1;
(*b)[2] = B2;
std::cout << "b = " << std::endl;
std::cout << *b << std::endl << std::endl;
try
{
get_exact_system(*A,*b);
}
catch(const std::exception& e)
{
std::cout << e.what() << std::endl << std::endl;
}
catch(std::string& error)
{
std::cout << error << std::endl << std::endl;
}
delete A;
delete b;
std::cout << "============== Test 22 ==============" << std::endl << std::endl;
A = new DoubleMatrix(3,3);
A00.assign(3.7, 4.3);
A01.assign(-1.5, -0.5);
A10.assign(3.7, 4.3);
(*A)(0,0) = A00;
(*A)(0,1) = A01;
(*A)(0,2) = (DoubleInterval)0;
(*A)(1,0) = A01;
(*A)(1,1) = A10;
(*A)(1,2) = A01;
(*A)(2,0) = (DoubleInterval)0;
(*A)(2,1) = A01;
(*A)(2,2) = A10;
std::cout << "A = " << std::endl;
std::cout << *A << std::endl;
b = new DoubleVector(3, (DoubleInterval)0);
B0.assign(2,14);
B1.assign(-9,-3);
B2.assign(-3,1);
(*b)[0] = B0;
(*b)[1] = B1;
(*b)[2] = B2;
std::cout << "b = " << std::endl;
std::cout << *b << std::endl << std::endl;
try
{
get_exact_system(*A,*b);
}
catch(const std::exception& e)
{
std::cout << e.what() << std::endl << std::endl;
}
catch(std::string& error)
{
std::cout << error << std::endl << std::endl;
}
delete A;
delete b;
std::cout << "============== Test 23 ==============" << std::endl << std::endl;
A = new DoubleMatrix(3,3);
A00.assign(2,3);
A01.assign(4,5);
A02.assign(1,2);
A10.assign(-6,-5);
A11.assign(-3,-2);
A12.assign(3,4);
DoubleInterval A20(-4,0);
A21.assign(-5,-4);
(*A)(0,0) = A00;
(*A)(0,1) = A01;
(*A)(0,2) = A02;
(*A)(1,0) = A10;
(*A)(1,1) = A11;
(*A)(1,2) = A12;
(*A)(2,0) = A20;
(*A)(2,1) = A21;
(*A)(2,2) = A00;
std::cout << "A = " << std::endl;
std::cout << *A << std::endl;
b = new DoubleVector(3, (DoubleInterval)0);
B0.assign(2,14);
B1.assign(9,300);
B2.assign(3,100);
(*b)[0] = B0;
(*b)[1] = B1;
(*b)[2] = B2;
std::cout << "b = " << std::endl;
std::cout << *b << std::endl << std::endl;
try
{
get_exact_system(*A,*b);
}
catch(const std::exception& e)
{
std::cout << e.what() << std::endl << std::endl;
}
catch(std::string& error)
{
std::cout << error << std::endl << std::endl;
}
delete A;
delete b;
std::cout << "============== Test 24 ==============" << std::endl << std::endl;
A = new DoubleMatrix(2,2);
A00.assign(2,3);
A01.assign(-1,1);
A10.assign(0,5);
A11.assign(3,4);
(*A)(0,0) = A00;
(*A)(0,1) = A01;
(*A)(1,0) = A10;
(*A)(1,1) = A11;
std::cout << "A = " << std::endl;
std::cout << *A << std::endl;
b = new DoubleVector(2, (DoubleInterval)0);
B0.assign(2,14);
B1.assign(3,9);
(*b)[0] = B0;
(*b)[1] = B1;
std::cout << "b = " << std::endl;
std::cout << *b << std::endl << std::endl;
try
{
get_exact_system(*A,*b);
}
catch(const std::exception& e)
{
std::cout << e.what() << std::endl << std::endl;
}
catch(std::string& error)
{
std::cout << error << std::endl << std::endl;
}
delete A;
delete b;
std::cout << "============== Test 25 ==============" << std::endl << std::endl;
A = new DoubleMatrix(2,2);
A00.assign(1,1000);
A01.assign(1,1000);
A10.assign(-1000,1);
A11.assign(1,1000);
(*A)(0,0) = A00;
(*A)(0,1) = A01;
(*A)(1,0) = A10;
(*A)(1,1) = A11;
std::cout << "A = " << std::endl;
std::cout << *A << std::endl;
b = new DoubleVector(2, (DoubleInterval)0);
B0.assign(1,2);
B1.assign(3,4);
(*b)[0] = B0;
(*b)[1] = B1;
std::cout << "b = " << std::endl;
std::cout << *b << std::endl << std::endl;
try
{
get_exact_system(*A,*b);
}
catch(const std::exception& e)
{
std::cout << e.what() << std::endl << std::endl;
}
catch(std::string& error)
{
std::cout << error << std::endl << std::endl;
}
delete A;
delete b;
return 0;
}