log_value<dcomplex>
TransposeInverseMatrix(const Array2 < complex <doublevar> > & a,
Array2 < complex <doublevar> > & a1,
const int n)
{
Array2 <complex <doublevar> > temp(n,n);
Array1 <int> indx(n);
doublevar d;
// a(i,j) first index i is row index (convention)
// elements of column vectors are stored contiguous in memory in C style arrays
// a(i) refers to a column vector
// calculate the inverse of the transposed matrix because this
// allows to pass a column vector to lubksb() instead of a row
// put the transposed matrix in temp
//cout << "temp " << endl;
for(int i=0;i<n;++i)
{
for(int j=0;j<n;++j)
{
temp(i,j)=a(i,j);
a1(i,j)=complex <doublevar> (0.0,0.0);
}
a1(i,i)=complex <doublevar> (1.0,0.0);
}
//cout << "ludcmp" << endl;
//if the matrix is singular, the determinant is zero.
if(ludcmp(temp,n,indx,d)==0) {
#ifdef SUPERDEBUG
cout << "log_value<dcomplex>TransposeInverseMatrix:zero determinant " << endl;
#endif
return dcomplex(0.0,0.0);
}
//cout << "lubksb" << endl;
for(int j=0;j<n;++j)
{
// get column vector
Array1 <complex <doublevar> > yy;//(a1(j));
yy.refer(a1(j));
lubksb(temp,n,indx,yy);
}
//complex <doublevar> det(d,0);
log_value<dcomplex> det=dcomplex(d,0);
for(int j=0;j<n;++j) {
det *= temp(j,j);
}
return det;
}
// Invert matrix a, but do not change a
// Inverse in a1
void InvertMatrix(const Array2 <doublevar> & a, Array2 <doublevar> & a1, const int n)
{
Array2 <doublevar>& temp(tmp2);
temp.Resize(n,n);
Array1 <int>& indx(itmp1);
indx.Resize(n);
doublevar d;
// a(i,j) first index i is row index (convention)
// elements of column vectors are stored contiguous in memory in C style arrays
// a(i) refers to a column vector
// calculate the inverse of the transposed matrix because this
// allows to pass a column vector to lubksb() instead of a row
// put the transposed matrix in temp
for(int i=0;i<n;++i)
{
for(int j=0;j<n;++j)
{
temp(i,j)=a(j,i);
a1(i,j)=0.0;
}
a1(i,i)=1.0;
}
if(!ludcmp(temp,n,indx,d)) error("singular matrix in inversion");
for(int j=0;j<n;++j)
{
// get column vector
Array1 <doublevar> yy;//(a1(j));
yy.refer(a1(j));
lubksb(temp,n,indx,yy);
}
}
// Calculate the transpose inverse of matrix a
// and return the determinant
log_real_value TransposeInverseMatrix(const Array2 <doublevar> & a, Array2 <doublevar> & a1, const int n)
{
Array2 <doublevar> &temp(tmp2);
temp.Resize(n,n);
Array1 <int>& indx(itmp1);
indx.Resize(n);
doublevar d=1;
log_real_value logdet;
logdet.logval=0; logdet.sign=1;
//for(int i=0; i< n; i++) {
// cout << "matrix ";
// for(int j=0; j< n; j++) cout << a(i,j) << " ";
// cout << endl;
//}
#ifdef USE_LAPACK
//LAPACK routines don't handle n==1 case??
if(n==1) {
a1(0,0)=1.0/a(0,0);
logdet.logval=log(fabs(a(0,0)));
logdet.sign=a(0,0)<0?-1:1;
return logdet;
}
else {
for(int i=0; i < n;++i) {
for(int j=0; j< n; ++j) {
temp(j,i)=a(i,j);
a1(i,j)=0.0;
}
a1(i,i)=1.0;
}
if(dgetrf(n, n, temp.v, n, indx.v)> 0) {
return 0.0;
}
for(int j=0; j< n; ++j) {
dgetrs('N',n,1,temp.v,n,indx.v,a1.v+j*n,n);
}
}
for(int i=0; i< n; i++) {
if(indx(i)!=i+1) logdet.sign*=-1;
logdet.logval+=log(fabs(temp(i,i)));
if(temp(i,i) <0) logdet.sign*=-1;
}
//cout << " det " << det << " logval " << logdet.val() << endl;
//return det;
return logdet;
//#endif
#else
// a(i,j) first index i is row index (convention)
// elements of column vectors are stored contiguous in memory in C style arrays
// a(i) refers to a column vector
// calculate the inverse of the transposed matrix because this
// allows to pass a column vector to lubksb() instead of a row
// put the transposed matrix in temp
//cout << "temp " << endl;
for(int i=0;i<n;++i)
{
for(int j=0;j<n;++j)
{
temp(i,j)=a(i,j);
a1(i,j)=0.0;
}
a1(i,i)=1.0;
}
//cout << "ludcmp" << endl;
//if the matrix is singular, the determinant is zero.
d=1;
if(ludcmp(temp,n,indx,d)==0)
return 0;
//cout << "lubksb" << endl;
for(int j=0;j<n;++j)
{
// get column vector
Array1 <doublevar> yy;//(a1(j));
yy.refer(a1(j));
lubksb(temp,n,indx,yy);
}
//for(int j=0;j<n;++j) {
// d *= temp(j,j);
//}
logdet.logval=0;
logdet.sign=1;
for(int i=0; i< n; i++) {
if(indx(i)!=i) logdet.sign*=-1;
logdet.logval+=log(fabs(temp(i,i)));
if(temp(i,i) <0) logdet.sign*=-1;
}
//cout << " det " << d << " logval " << logdet.val() << endl;
return logdet;
#endif
}