bool ON_Matrix::Multiply( const ON_Matrix& a, const ON_Matrix& b )
{
int i, j, k, mult_count;
double x;
if (a.ColCount() != b.RowCount() )
return false;
if ( a.RowCount() < 1 || a.ColCount() < 1 || b.ColCount() < 1 )
return false;
if ( this == &a ) {
ON_Matrix tmp(a);
return Multiply(tmp,b);
}
if ( this == &b ) {
ON_Matrix tmp(b);
return Multiply(a,tmp);
}
Create( a.RowCount(), b.ColCount() );
mult_count = a.ColCount();
double const*const* am = a.ThisM();
double const*const* bm = b.ThisM();
double** this_m = ThisM();
for ( i = 0; i < m_row_count; i++ ) for ( j = 0; j < m_col_count; j++ ) {
x = 0.0;
for (k = 0; k < mult_count; k++ ) {
x += am[i][k] * bm[k][j];
}
this_m[i][j] = x;
}
return true;
}
void
NurbsTools::pca (const vector_vec3d &data, ON_3dVector &mean, Eigen::Matrix3d &eigenvectors,
Eigen::Vector3d &eigenvalues)
{
if (data.empty ())
{
printf ("[NurbsTools::pca] Error, data is empty\n");
abort ();
}
mean = computeMean (data);
unsigned s = data.size ();
ON_Matrix Q(3, s);
for (unsigned i = 0; i < s; i++) {
Q[0][i] = data[i].x - mean.x;
Q[1][i] = data[i].y - mean.y;
Q[2][i] = data[i].z - mean.z;
}
ON_Matrix Qt = Q;
Qt.Transpose();
ON_Matrix oC;
oC.Multiply(Q,Qt);
Eigen::Matrix3d C(3,3);
for (unsigned i = 0; i < 3; i++) {
for (unsigned j = 0; j < 3; j++) {
C(i,j) = oC[i][j];
}
}
Eigen::SelfAdjointEigenSolver < Eigen::Matrix3d > eigensolver (C);
if (eigensolver.info () != Eigen::Success)
{
printf ("[NurbsTools::pca] Can not find eigenvalues.\n");
abort ();
}
for (int i = 0; i < 3; ++i)
{
eigenvalues (i) = eigensolver.eigenvalues () (2 - i);
if (i == 2)
eigenvectors.col (2) = eigenvectors.col (0).cross (eigenvectors.col (1));
else
eigenvectors.col (i) = eigensolver.eigenvectors ().col (2 - i);
}
}
bool ON_Matrix::Add( const ON_Matrix& a, const ON_Matrix& b )
{
int i, j;
if (a.ColCount() != b.ColCount() )
return false;
if (a.RowCount() != b.RowCount() )
return false;
if ( a.RowCount() < 1 || a.ColCount() < 1 )
return false;
if ( this != &a && this != &b ) {
Create( a.RowCount(), b.ColCount() );
}
double const*const* am = a.ThisM();
double const*const* bm = b.ThisM();
double** this_m = ThisM();
for ( i = 0; i < m_row_count; i++ ) for ( j = 0; j < m_col_count; j++ ) {
this_m[i][j] = am[i][j] + bm[i][j];
}
return true;
}
void ON_TextLog::Print( const ON_Matrix& M, const char* sPreamble, int precision )
{
double x;
char digit[10] = {'0','1','2','3','4','5','6','7','8','9'};
char* sRow;
char* sIJ;
int xi, row_count, column_count, row_index, column_index;
row_count = M.RowCount();
column_count = M.ColCount();
sRow = (char*)alloca( (5*column_count + 2 + 64)*sizeof(*sRow) );
if ( !sPreamble )
sPreamble = "Matrix";
Print("%s (%d rows %d columns)\n",sPreamble,row_count,column_count);
for ( row_index = 0; row_index < row_count; row_index++ ) {
sIJ = sRow;
Print("%5d:",row_index);
if ( precision > 3 ) {
for ( column_index = 0; column_index < column_count; column_index++ ) {
x = M.m[row_index][column_index];
Print( " %8f",x);
}
Print("\n");
}
else {
for ( column_index = 0; column_index < column_count; column_index++ ) {
x = M.m[row_index][column_index];
if ( x == 0.0 ) {
strcpy( sIJ, " 0 " );
sIJ += 4;
}
else {
*sIJ++ = ' ';
*sIJ++ = ( x >0.0 ) ? '+' : '-';
x = fabs( x );
if ( x >= 10.0 ) {
*sIJ++ = '*';
*sIJ++ = ' ';
*sIJ++ = ' ';
}
else if ( x <= ON_SQRT_EPSILON) {
*sIJ++ = '0';
*sIJ++ = ' ';
*sIJ++ = ' ';
}
else if ( x < 0.1) {
*sIJ++ = '~';
*sIJ++ = ' ';
*sIJ++ = ' ';
}
else if ( x < .95 ) {
*sIJ++ = '.';
xi = (int)floor(x*10.0);
if ( xi > 9 )
xi = 9;
else if (xi < 1)
xi = 1;
*sIJ++ = digit[xi];
*sIJ++ = '~';
}
else {
xi = (int)floor(x);
if ( xi < 1 )
xi = 1;
else if (xi > 9)
xi = 9;
*sIJ++ = digit[xi];
if ( x == floor(x) ) {
*sIJ++ = ' ';
*sIJ++ = ' ';
}
else {
*sIJ++ = '.';
*sIJ++ = '~';
}
}
}
}
*sIJ = 0;
Print("%s\n",sRow);
}
}
}