I'm implementing a determinant function in a matrix class, which I'd like to calculate by recursively getting a smaller and smaller minor matrix. The problem lies with the compiler eventually creating a matrix with a dimension of 0, even though I have an if-statement that ensures this doesn't happen in runtime.
I have two questions regarding this:
Here's the header with everything non-related removed. Full source code here: https://github.com/DanielEverland/Artemis/blob/master/ArtemisEngineCore/Engine/Math/Matrices/GenericMatrix.h
The initial matrix is 4x4 matrix of type double.
template<class T, unsigned int rows, unsigned int columns>
class GenericMatrix : BaseMatrix
{
public:
// Returns the determinant of the matrix
// Requires the matrix to be square
T GetDeterminant() const
{
static_assert(rows == columns, "Cannot get determinant of non-square matrix");
T determinant{};
// Seeing as this is always false, a minor matrix is never created, and a zero-sized array should never be created.
if(false)
GetMinor(0, 0).GetDeterminant(); // If I comment-out this line the build succeeds
return determinant;
}
// Returns the minor of this matrix.
// Requires the matrix to be square.
// Will return a matrix[N - 1, N - 1] with a removed row and column.
GenericMatrix<T, rows - 1, columns - 1> GetMinor(unsigned int rowToDelete, unsigned int columnToDelete) const
{
static_assert(rows == columns, "Cannot get minor of non-square matrix");
static_assert(rows >= 2, "Cannot get minor of a matrix that has 2 rows or fewer.");
static_assert(columns >= 2, "Cannot get minor of a matrix that has 2 column or fewer.");
GenericMatrix<T, rows - 1, columns - 1> minor{};
unsigned int rowIndex = 0;
for (unsigned int i = 0; i < minor.GetRows(); i++)
{
if (rowIndex == rowToDelete)
rowIndex++;
unsigned int columnIndex = 0;
for (unsigned int j = 0; j < minor.GetColumns(); j++)
{
if (columnIndex == columnToDelete)
columnIndex++;
minor[i][j] = values[rowIndex][columnIndex];
columnIndex++;
}
rowIndex++;
}
return minor;
}
private:
T values[rows][columns] = { };
};
Here's the build output. As you can tell, a matrix with a dimension of 0 is instantiated
1>------ Build started: Project: UnitTests, Configuration: Debug x64 ------
1>MatrixTests.cpp
1>C:\Users\Daniel\source\repos\Artemis\ArtemisEngineCore\Engine\Math\Matrices\GenericMatrix.h(234,1): error C2087: 'values': missing subscript
1>C:\Users\Daniel\source\repos\Artemis\ArtemisEngineCore\Engine\Math\Matrices\GenericMatrix.h(200): message : see reference to class template instantiation 'ArtemisEngine::Math::Matrices::GenericMatrix<T,0,0>' being compiled
1> with
1> [
1> T=Math::Matrices::T
1> ]
1>C:\Users\Daniel\source\repos\Artemis\ArtemisEngineCore\Engine\Math\Matrices\GenericMatrix.h(194): message : while compiling class template member function 'T ArtemisEngine::Math::Matrices::GenericMatrix<T,1,1>::GetDeterminant(void) const'
1> with
1> [
1> T=Math::Matrices::T
1> ]
1>C:\Users\Daniel\source\repos\Artemis\ArtemisEngineCore\Engine\Math\Matrices\GenericMatrix.h(200): message : see reference to function template instantiation 'T ArtemisEngine::Math::Matrices::GenericMatrix<T,1,1>::GetDeterminant(void) const' being compiled
1> with
1> [
1> T=Math::Matrices::T
1> ]
1>C:\Users\Daniel\source\repos\Artemis\UnitTests\Math\MatrixTests.cpp(375): message : see reference to class template instantiation 'ArtemisEngine::Math::Matrices::GenericMatrix<Math::Matrices::T,1,1>' being compiled
1>C:\Users\Daniel\source\repos\Artemis\UnitTests\Math\MatrixTests.cpp(57): message : see reference to class template instantiation 'ArtemisEngine::Math::Matrices::GenericMatrix<Math::Matrices::T,4,4>' being compiled
1>C:\Users\Daniel\source\repos\Artemis\ArtemisEngineCore\Engine\Math\Matrices\GenericMatrix.h(234,1): warning C4200: nonstandard extension used: zero-sized array in struct/union
1>C:\Users\Daniel\source\repos\Artemis\ArtemisEngineCore\Engine\Math\Matrices\GenericMatrix.h(234,1): message : This member will be ignored by a defaulted constructor or copy/move assignment operator
1>Done building project "UnitTests.vcxproj" -- FAILED.
========== Build: 0 succeeded, 1 failed, 2 up-to-date, 0 skipped ==========
Build time 00:00:00.726
Build ended at 27/01/2020 12.56.52
As already pointed out in the comments, you have to stop the recursion by defining the specialization GenericMatrix . The if(false)
is evaluated at runtime (as already pointed out in the comments the c++17 feature if consexpr
can be used here as well, however the following answer is not based on that feature since the question is not labelled c++17). This directly answers your first question. See the following example:
GenericMatrix<double,3,3> mat;
auto det = mat.GetDeterminant();
mat.GetDeterminant()
internally calls GetMinor
that returns GenericMatrix<double,2,2>
. Now the returned GenericMatrix<double,2,2>
-object itself calls GetDeterminant
and everything starts from the beginning, since if(false)
does not stop the compile time recursion. Therefore, you must provide a sepcialization template<class T> GenericMatrix<T,1,1>
whose GetDeterminant
does not call GetMinor
Regarding the second question,here's a simplified example:
#include <iostream>
template<class T, unsigned int rows, unsigned int columns>
class GenericMatrix
{
public:
// Returns the determinant of the matrix
// Requires the matrix to be square
T GetDeterminant() const
{
T determinant = 0.;
std::cout << "call GenericMatrix<T," << rows <<","
<< columns <<">::GetDeterminant" << std::endl;
auto det_minor = this->GetMinor(0, 0).GetDeterminant();
// do semething with det_minor
return determinant;
}
private:
// Returns the minor of this matrix.
// Requires the matrix to be square.
// Will return a matrix[N - 1, N - 1] with a removed row and column.
GenericMatrix<T, rows - 1, columns - 1>
GetMinor(unsigned int rowToDelete, unsigned int columnToDelete) const
{
GenericMatrix<T, rows - 1, columns - 1> minor{};
std::cout << "call GenericMatrix<T,"
<< rows <<","<< columns <<">::GetMinor with return type "
<< "GenericMatrix<T," << rows-1 <<","
<< columns-1 <<">::GetDeterminant"
<< std::endl;
return minor;
}
T values[rows][columns] = { };
};
template<class T>
class GenericMatrix<T,1,1>
{
public:
// Returns the determinant of the matrix
T GetDeterminant() const
{
T determinant = 0.;
std::cout << "call GenericMatrix<T,1,1>::GetDeterminant" << std::endl;
return determinant;
}
private:
T value = { };
};
int main()
{
GenericMatrix<double,4,4> mat;
std::cout << mat.GetDeterminant() << std::endl;
return 0;
}
Here is the compiled code which outputs
call GenericMatrix<T,4,4>::GetDeterminant
call GenericMatrix<T,4,4>::GetMinor with return type GenericMatrix<T,3,3>::GetDeterminant
call GenericMatrix<T,3,3>::GetDeterminant
call GenericMatrix<T,3,3>::GetMinor with return type GenericMatrix<T,2,2>::GetDeterminant
call GenericMatrix<T,2,2>::GetDeterminant
call GenericMatrix<T,2,2>::GetMinor with return type GenericMatrix<T,1,1>::GetDeterminant
call GenericMatrix<T,1,1>::GetDeterminant
0
The technical post webpages of this site follow the CC BY-SA 4.0 protocol. If you need to reprint, please indicate the site URL or the original address.Any question please contact:yoyou2525@163.com.