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/**
* Define some basic linear algebra operations.
*/
#ifndef LINEARALGEBRA_H
#define LINEARALGEBRA_H
typedef std::size_t size_t;
typedef std::size_t index_t;
template<class T>
void cholesky(const std::vector<std::vector<T> >& A,
std::vector<std::vector<T> >& L)
{
size_t N = A.size();
for (index_t i = 0; i < N; ++i)
{
for (index_t j = 0; j < N; ++j)
{
if (j <= i)
{
T sum = 0;
for (index_t k = 0; k < j; ++k)
{
sum += L[i][k] * L[j][k];
}
L[i][j] = (i == j) ?
sqrt(A[i][i] - sum) :
(1.0 / L[j][j] * (A[i][j] - sum));
}
else
{
L[i][j] = 0;
}
}
}
}
template<class T>
T spddeterminant(const std::vector<std::vector<T> >& A,
bool isTriangular = false)
{
size_t N = A.size();
T prod = 1;
if (isTriangular)
{
for (index_t i = 0; i < N; ++i)
{
prod *= A[i][i] * A[i][i];
}
return prod;
}
else
{
std::vector<std::vector<T> > L;
L.resize(N);
for (index_t i = 0; i < N; ++i)
{
L[i].resize(N);
}
cholesky(A, L);
for (index_t i = 0; i < N; ++i)
{
prod *= L[i][i] * L[i][i];
}
return prod;
}
}
template<class T>
void multiply(const std::vector<std::vector<T> >& X,
const std::vector<std::vector<T> >& Y,
std::vector<std::vector<T> >& result)
{
size_t rowXN = X.size();
size_t colXN = X[0].size();
size_t rowYN = Y.size();
size_t colYN = Y[0].size();
if (colXN != rowYN)
{
throw std::runtime_error("matrix multiplication: XColNum != YRowNum\n");
}
else
{
for (index_t i = 0; i < rowXN; ++i)
{
for (index_t j = 0; j < colYN; ++j)
{
T sum = 0;
for (index_t k = 0; k < colXN; ++k)
{
sum += X[i][k] * Y[k][j];
}
result[i][j] = sum;
}
}
}
}
template<class T>
void multiplyXTX(const std::vector<std::vector<T> >& X,
std::vector<std::vector<T> >& result)
{
size_t N = X.size();
for (index_t i = 0; i < N; ++i)
{
for (index_t j = 0; j < N; ++j)
{
T sum = 0;
for (index_t k = 0; k < N; ++k)
{
sum += X[k][i] * X[k][j];
}
result[i][j] = sum;
}
}
}
template<class T>
void trianginverse(const std::vector<std::vector<T> >& L,
std::vector<std::vector<T> >& invL)
{
size_t N = L.size();
for (index_t j = 0; j < N; ++j)
{
for (index_t i = 0; i < N; ++i)
{
if (j <= i)
{
T sum = (i == j)? 1 : 0;
for (index_t k = j; k < i; ++k)
{
sum -= L[i][k] * invL[k][j];
}
invL[i][j] = sum / L[i][i];
}
else
{
invL[i][j] = 0;
}
}
}
}
template<class T>
void spdinverse(const std::vector<std::vector<T> >& A,
std::vector<std::vector<T> >& invA,
bool isTriangular = false)
{
size_t N = A.size();
static std::vector<std::vector<T> > invL;
invL.resize(N);
for (index_t i = 0; i < N; ++i)
{
invL[i].resize(N);
}
if (isTriangular)
{
trianginverse(A, invL);
}
else
{
std::vector<std::vector<T> > L;
L.resize(N);
for (index_t i = 0; i < N; ++i)
{
L[i].resize(N);
}
cholesky(A, L);
trianginverse(L, invL);
}
multiplyXTX(invL, invA);
}
template<class T>
T multiplyXTspdAinvX(const std::vector<T>& X,
const std::vector<std::vector<T> >& A,
bool isTriangular = false)
{
size_t N = A.size();
if (N != X.size())
{
throw std::runtime_error("multiplyXTspdAinvX: XNum != ARowNum\n");
}
else
{
std::vector<std::vector<T> > invL;
invL.resize(N);
for (index_t i = 0; i < N; ++i)
{
invL[i].resize(N);
}
if (isTriangular)
{
trianginverse(A, invL);
}
else
{
std::vector<std::vector<T> > L;
L.resize(N);
for (index_t i = 0; i < N; ++i)
{
L[i].resize(N);
}
cholesky(A, L);
trianginverse(L, invL);
}
std::vector<T> tmp(N, 0);
for (index_t i = 0; i < N; ++i)
{
for (index_t j = 0; j < (i+1); ++j)
{
tmp[i] += invL[i][j] * X[j];
}
}
T result = 0;
for (index_t i = 0; i < N; ++i)
{
result += tmp[i] * tmp[i];
}
return result;
}
}
#endif // LINEARALGEBRA_H
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